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cdec422 | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 | 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
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