| import Mathlib | |
| namespace OAI | |
| namespace MatrixAllFields | |
| open scoped BigOperators Topology Polynomial | |
| namespace MatrixMultiplication.PermutationMatching | |
| variable {C : Type*} {P X Y : C → Type*} | |
| structure CompleteWordPair (P X Y : C → Type*) where | |
| left : ∀ c, P c → X c | |
| right : ∀ c, P c → Y c | |
| abbrev HalfClassPermutations (P : C → Type*) := | |
| (∀ c, Equiv.Perm (P c)) × (∀ c, Equiv.Perm (P c)) | |
| instance completeWordPairMulAction : | |
| MulAction (HalfClassPermutations P) (CompleteWordPair P X Y) where | |
| smul g w := | |
| { left := fun c i => w.left c ((g.1 c).symm i) | |
| right := fun c i => w.right c ((g.2 c).symm i) } | |
| one_smul w := by cases w; rfl | |
| mul_smul g h w := rfl | |
| @[simp] theorem smul_completeWordPair_left (g : HalfClassPermutations P) | |
| (w : CompleteWordPair P X Y) (c : C) (i : P c) : | |
| (g • w).left c i = w.left c ((g.1 c).symm i) := rfl | |
| @[simp] theorem smul_completeWordPair_right (g : HalfClassPermutations P) | |
| (w : CompleteWordPair P X Y) (c : C) (i : P c) : | |
| (g • w).right c i = w.right c ((g.2 c).symm i) := rfl | |
| end MatrixMultiplication.PermutationMatching | |
| end MatrixAllFields | |
| end OAI | |