| import Mathlib | |
| import OAI.LinearAlgebra.MatrixFields.Construction.InitialState | |
| namespace OAI | |
| namespace MatrixAllFields | |
| open scoped BigOperators Topology Polynomial | |
| noncomputable section | |
| namespace MatrixMultiplication.AllFieldFiniteFamily | |
| open MatrixMultiplication.Foundation | |
| variable {F : Type*} [Field F] | |
| private theorem matrixCoefficients_decidable (A B C : Type) | |
| (dA eA : DecidableEq A) (dB eB : DecidableEq B) (dC eC : DecidableEq C) : | |
| @Tensor.matrixCoefficients F _ A B C dA dB dC = | |
| @Tensor.matrixCoefficients F _ A B C eA eB eC := by | |
| have hA : dA = eA := Subsingleton.elim _ _ | |
| have hB : dB = eB := Subsingleton.elim _ _ | |
| have hC : dC = eC := Subsingleton.elim _ _ | |
| cases hA | |
| cases hB | |
| cases hC | |
| rfl | |
| namespace LocalMap | |
| def redecideMatrix {X Y Z A B C : Type} | |
| [Fintype X] [Fintype Y] [Fintype Z] | |
| {source : Tensor F X Y Z} | |
| {dA : DecidableEq A} {dB : DecidableEq B} {dC : DecidableEq C} | |
| (map : LocalMap source (@Tensor.matrixCoefficients F _ A B C dA dB dC)) | |
| (eA : DecidableEq A) (eB : DecidableEq B) (eC : DecidableEq C) : | |
| LocalMap source (@Tensor.matrixCoefficients F _ A B C eA eB eC) where | |
| x := map.x | |
| y := map.y | |
| z := map.z | |
| coefficient := map.coefficient.trans | |
| (matrixCoefficients_decidable A B C dA eA dB eB dC eC) | |
| end LocalMap | |
| end MatrixMultiplication.AllFieldFiniteFamily | |
| end | |
| end MatrixAllFields | |
| end OAI | |