linear_algebra.charpoly.to_matrix | Mathlib porting status

Changes since the initial port

The following section lists changes to this file in mathlib3 and mathlib4 that occured after the initial port. Most recent changes are shown first. Hovering over a commit will show all commits associated with the same mathlib3 commit.

Changes in mathlib3

baab5d30

(last sync)

Changes in mathlib3port

mathlib3

mathlib3port

a87d2257

bump to nightly-2023-09-24-06

mathlib commit https://github.com/leanprover-community/mathlib/commit/ce64cd319bb6b3e82f31c2d38e79080d377be451

5655435f

Diff

@@ -3,8 +3,8 @@ Copyright (c) 2021 Riccardo Brasca. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Riccardo Brasca
 -/
-import Mathbin.LinearAlgebra.Charpoly.Basic
-import Mathbin.LinearAlgebra.Matrix.Basis
+import LinearAlgebra.Charpoly.Basic
+import LinearAlgebra.Matrix.Basis
 
 #align_import linear_algebra.charpoly.to_matrix from "leanprover-community/mathlib"@"a87d22575d946e1e156fc1edd1e1269600a8a282"

a87d2257

bump to nightly-2023-07-20-09

mathlib commit https://github.com/leanprover-community/mathlib/commit/8ea5598db6caeddde6cb734aa179cc2408dbd345

9c56d0dd

Diff

@@ -2,15 +2,12 @@
 Copyright (c) 2021 Riccardo Brasca. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Riccardo Brasca
-
-! This file was ported from Lean 3 source module linear_algebra.charpoly.to_matrix
-! leanprover-community/mathlib commit a87d22575d946e1e156fc1edd1e1269600a8a282
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.LinearAlgebra.Charpoly.Basic
 import Mathbin.LinearAlgebra.Matrix.Basis
 
+#align_import linear_algebra.charpoly.to_matrix from "leanprover-community/mathlib"@"a87d22575d946e1e156fc1edd1e1269600a8a282"
+
 /-!
 
 # Characteristic polynomial

a87d2257

bump to nightly-2023-06-13-21

mathlib commit https://github.com/leanprover-community/mathlib/commit/9fb8964792b4237dac6200193a0d533f1b3f7423

829520ac

Diff

@@ -42,6 +42,7 @@ namespace LinearMap
 
 section Basic
 
+#print LinearMap.charpoly_toMatrix /-
 /-- `charpoly f` is the characteristic polynomial of the matrix of `f` in any basis. -/
 @[simp]
 theorem charpoly_toMatrix {ι : Type w} [Fintype ι] (b : Basis ι R M) :
@@ -91,6 +92,7 @@ theorem charpoly_toMatrix {ι : Type w} [Fintype ι] (b : Basis ι R M) :
     _ = (scalar ι' X - C.map_matrix A').det := by rw [← det_mul, hPQ, det_one, one_mul]
     _ = f.charpoly := rfl
 #align linear_map.charpoly_to_matrix LinearMap.charpoly_toMatrix
+-/
 
 end Basic

a87d2257

bump to nightly-2023-06-09-07

mathlib commit https://github.com/leanprover-community/mathlib/commit/7e5137f579de09a059a5ce98f364a04e221aabf0

16afdc39

Diff

@@ -90,7 +90,6 @@ theorem charpoly_toMatrix {ι : Type w} [Fintype ι] (b : Basis ι R M) :
       by ring
     _ = (scalar ι' X - C.map_matrix A').det := by rw [← det_mul, hPQ, det_one, one_mul]
     _ = f.charpoly := rfl
-    
 #align linear_map.charpoly_to_matrix LinearMap.charpoly_toMatrix
 
 end Basic

a87d2257

bump to nightly-2023-05-28-18

mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb

8d353152

Diff

@@ -32,7 +32,7 @@ variable {R : Type u} {M : Type v} [CommRing R] [Nontrivial R]
 
 variable [AddCommGroup M] [Module R M] [Module.Free R M] [Module.Finite R M] (f : M →ₗ[R] M)
 
-open Classical Matrix
+open scoped Classical Matrix
 
 noncomputable section

a87d2257

bump to nightly-2023-05-28-06

mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb

ba5d8b97

Diff

@@ -42,9 +42,6 @@ namespace LinearMap
 
 section Basic
 
-/- warning: linear_map.charpoly_to_matrix -> LinearMap.charpoly_toMatrix is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align linear_map.charpoly_to_matrix LinearMap.charpoly_toMatrixₓ'. -/
 /-- `charpoly f` is the characteristic polynomial of the matrix of `f` in any basis. -/
 @[simp]
 theorem charpoly_toMatrix {ι : Type w} [Fintype ι] (b : Basis ι R M) :

a87d2257

bump to nightly-2023-05-28-03

mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb

6c6011cf

Diff

@@ -43,10 +43,7 @@ namespace LinearMap
 section Basic
 
 /- warning: linear_map.charpoly_to_matrix -> LinearMap.charpoly_toMatrix is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : CommRing.{u1} R] [_inst_2 : Nontrivial.{u1} R] [_inst_3 : AddCommGroup.{u2} M] [_inst_4 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3)] [_inst_5 : Module.Free.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4] [_inst_6 : Module.Finite.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4] (f : LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) {ι : Type.{u3}} [_inst_7 : Fintype.{u3} ι] (b : Basis.{u3, u1, u2} ι R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4), Eq.{succ u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Matrix.charpoly.{u1, u3} R _inst_1 ι (fun (a : ι) (b : ι) => Classical.propDecidable (Eq.{succ u3} ι a b)) _inst_7 (coeFn.{max (succ u2) (succ (max u3 u1)), max (succ u2) (succ (max u3 u1))} (LinearEquiv.{u1, u1, u2, max u3 u1} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (LinearMap.toMatrix._proof_1.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.toMatrix._proof_2.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Matrix.{u3, u3, u1} ι ι R) (LinearMap.addCommMonoid.{u1, u1, u2, u2} R R M M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Matrix.addCommMonoid.{u1, u3, u3} ι ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u2} R R R M M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_4 (LinearMap.toMatrix._proof_3.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)) (Matrix.module.{u1, u3, u3, u1} ι ι R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (_x : LinearEquiv.{u1, u1, u2, max u3 u1} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (LinearMap.toMatrix._proof_1.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.toMatrix._proof_2.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Matrix.{u3, u3, u1} ι ι R) (LinearMap.addCommMonoid.{u1, u1, u2, u2} R R M M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Matrix.addCommMonoid.{u1, u3, u3} ι ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u2} R R R M M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_4 (LinearMap.toMatrix._proof_3.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)) (Matrix.module.{u1, u3, u3, u1} ι ι R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) => (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) -> (Matrix.{u3, u3, u1} ι ι R)) (LinearEquiv.hasCoeToFun.{u1, u1, u2, max u3 u1} R R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Matrix.{u3, u3, u1} ι ι R) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u2} R R M M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Matrix.addCommMonoid.{u1, u3, u3} ι ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u2} R R R M M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_4 (LinearMap.toMatrix._proof_3.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)) (Matrix.module.{u1, u3, u3, u1} ι ι R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (LinearMap.toMatrix._proof_1.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.toMatrix._proof_2.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.toMatrix.{u1, u3, u3, u2, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) ι ι _inst_7 _inst_7 (fun (a : ι) (b : ι) => Classical.propDecidable (Eq.{succ u3} ι a b)) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4 b b) f)) (LinearMap.charpoly.{u1, u2} R M _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 f)
-but is expected to have type
-  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : CommRing.{u1} R] [_inst_2 : Nontrivial.{u1} R] [_inst_3 : AddCommGroup.{u2} M] [_inst_4 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3)] [_inst_5 : Module.Free.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4] [_inst_6 : Module.Finite.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4] (f : LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) {ι : Type.{u3}} [_inst_7 : Fintype.{u3} ι] (b : Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4), Eq.{succ u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Matrix.charpoly.{u1, u3} R _inst_1 ι (fun (a : ι) (b : ι) => Classical.propDecidable (Eq.{succ u3} ι a b)) _inst_7 (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), succ u2, max (succ u1) (succ u3)} (LinearEquiv.{u1, u1, u2, max u1 u3} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Matrix.{u3, u3, u1} ι ι R) (LinearMap.addCommMonoid.{u1, u1, u2, u2} R R M M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Matrix.addCommMonoid.{u1, u3, u3} ι ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u2} R R R M M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_4 (smulCommClass_self.{u1, u2} R M (CommSemiring.toCommMonoid.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (MulActionWithZero.toMulAction.{u1, u2} R M (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3))) (Module.toMulActionWithZero.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))) (Matrix.module.{u1, u3, u3, u1} ι ι R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (fun (_x : LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) => Matrix.{u3, u3, u1} ι ι R) _x) (SMulHomClass.toFunLike.{max (max u1 u2) u3, u1, u2, max u1 u3} (LinearEquiv.{u1, u1, u2, max u1 u3} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Matrix.{u3, u3, u1} ι ι R) (LinearMap.addCommMonoid.{u1, u1, u2, u2} R R M M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Matrix.addCommMonoid.{u1, u3, u3} ι ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u2} R R R M M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_4 (smulCommClass_self.{u1, u2} R M (CommSemiring.toCommMonoid.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (MulActionWithZero.toMulAction.{u1, u2} R M (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3))) (Module.toMulActionWithZero.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))) (Matrix.module.{u1, u3, u3, u1} ι ι R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Matrix.{u3, u3, u1} ι ι R) (SMulZeroClass.toSMul.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (AddMonoid.toZero.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (AddCommMonoid.toAddMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (LinearMap.addCommMonoid.{u1, u1, u2, u2} R R M M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (DistribSMul.toSMulZeroClass.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (AddMonoid.toAddZeroClass.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (AddCommMonoid.toAddMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (LinearMap.addCommMonoid.{u1, u1, u2, u2} R R M M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (DistribMulAction.toDistribSMul.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (LinearMap.addCommMonoid.{u1, u1, u2, u2} R R M M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Module.toDistribMulAction.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u2} R R M M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u2} R R R M M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_4 (smulCommClass_self.{u1, u2} R M (CommSemiring.toCommMonoid.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (MulActionWithZero.toMulAction.{u1, u2} R M (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3))) (Module.toMulActionWithZero.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))))))) (SMulZeroClass.toSMul.{u1, max u1 u3} R (Matrix.{u3, u3, u1} ι ι R) (AddMonoid.toZero.{max u1 u3} (Matrix.{u3, u3, u1} ι ι R) (AddCommMonoid.toAddMonoid.{max u1 u3} (Matrix.{u3, u3, u1} ι ι R) (Matrix.addCommMonoid.{u1, u3, u3} ι ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (DistribSMul.toSMulZeroClass.{u1, max u1 u3} R (Matrix.{u3, u3, u1} ι ι R) (AddMonoid.toAddZeroClass.{max u1 u3} (Matrix.{u3, u3, u1} ι ι R) (AddCommMonoid.toAddMonoid.{max u1 u3} (Matrix.{u3, u3, u1} ι ι R) (Matrix.addCommMonoid.{u1, u3, u3} ι ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (DistribMulAction.toDistribSMul.{u1, max u1 u3} R (Matrix.{u3, u3, u1} ι ι R) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{max u1 u3} (Matrix.{u3, u3, u1} ι ι R) (Matrix.addCommMonoid.{u1, u3, u3} ι ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (Module.toDistribMulAction.{u1, max u1 u3} R (Matrix.{u3, u3, u1} ι ι R) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Matrix.addCommMonoid.{u1, u3, u3} ι ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Matrix.module.{u1, u3, u3, u1} ι ι R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u1 u2) u3, u1, u2, max u1 u3} (LinearEquiv.{u1, u1, u2, max u1 u3} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Matrix.{u3, u3, u1} ι ι R) (LinearMap.addCommMonoid.{u1, u1, u2, u2} R R M M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Matrix.addCommMonoid.{u1, u3, u3} ι ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u2} R R R M M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_4 (smulCommClass_self.{u1, u2} R M (CommSemiring.toCommMonoid.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (MulActionWithZero.toMulAction.{u1, u2} R M (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3))) (Module.toMulActionWithZero.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))) (Matrix.module.{u1, u3, u3, u1} ι ι R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Matrix.{u3, u3, u1} ι ι R) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (LinearMap.addCommMonoid.{u1, u1, u2, u2} R R M M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (AddCommMonoid.toAddMonoid.{max u1 u3} (Matrix.{u3, u3, u1} ι ι R) (Matrix.addCommMonoid.{u1, u3, u3} ι ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (Module.toDistribMulAction.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u2} R R M M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u2} R R R M M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_4 (smulCommClass_self.{u1, u2} R M (CommSemiring.toCommMonoid.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (MulActionWithZero.toMulAction.{u1, u2} R M (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3))) (Module.toMulActionWithZero.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4))))) (Module.toDistribMulAction.{u1, max u1 u3} R (Matrix.{u3, u3, u1} ι ι R) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Matrix.addCommMonoid.{u1, u3, u3} ι ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Matrix.module.{u1, u3, u3, u1} ι ι R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (SemilinearMapClass.distribMulActionHomClass.{u1, u2, max u1 u3, max (max u1 u2) u3} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Matrix.{u3, u3, u1} ι ι R) (LinearEquiv.{u1, u1, u2, max u1 u3} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Matrix.{u3, u3, u1} ι ι R) (LinearMap.addCommMonoid.{u1, u1, u2, u2} R R M M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Matrix.addCommMonoid.{u1, u3, u3} ι ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u2} R R R M M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_4 (smulCommClass_self.{u1, u2} R M (CommSemiring.toCommMonoid.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (MulActionWithZero.toMulAction.{u1, u2} R M (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3))) (Module.toMulActionWithZero.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))) (Matrix.module.{u1, u3, u3, u1} ι ι R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u2} R R M M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Matrix.addCommMonoid.{u1, u3, u3} ι ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u2} R R R M M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_4 (smulCommClass_self.{u1, u2} R M (CommSemiring.toCommMonoid.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (MulActionWithZero.toMulAction.{u1, u2} R M (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3))) (Module.toMulActionWithZero.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))) (Matrix.module.{u1, u3, u3, u1} ι ι R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (SemilinearEquivClass.instSemilinearMapClass.{u1, u1, u2, max u1 u3, max (max u1 u2) u3} R R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Matrix.{u3, u3, u1} ι ι R) (LinearEquiv.{u1, u1, u2, max u1 u3} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Matrix.{u3, u3, u1} ι ι R) (LinearMap.addCommMonoid.{u1, u1, u2, u2} R R M M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Matrix.addCommMonoid.{u1, u3, u3} ι ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u2} R R R M M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_4 (smulCommClass_self.{u1, u2} R M (CommSemiring.toCommMonoid.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (MulActionWithZero.toMulAction.{u1, u2} R M (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3))) (Module.toMulActionWithZero.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))) (Matrix.module.{u1, u3, u3, u1} ι ι R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u2} R R M M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Matrix.addCommMonoid.{u1, u3, u3} ι ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u2} R R R M M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_4 (smulCommClass_self.{u1, u2} R M (CommSemiring.toCommMonoid.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (MulActionWithZero.toMulAction.{u1, u2} R M (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3))) (Module.toMulActionWithZero.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))) (Matrix.module.{u1, u3, u3, u1} ι ι R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u1, u1, u2, max u1 u3} R R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Matrix.{u3, u3, u1} ι ι R) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u2} R R M M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Matrix.addCommMonoid.{u1, u3, u3} ι ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u2} R R R M M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_4 (smulCommClass_self.{u1, u2} R M (CommSemiring.toCommMonoid.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (MulActionWithZero.toMulAction.{u1, u2} R M (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3))) (Module.toMulActionWithZero.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))) (Matrix.module.{u1, u3, u3, u1} ι ι R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (LinearMap.toMatrix.{u1, u3, u3, u2, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) ι ι _inst_7 _inst_7 (fun (a : ι) (b : ι) => Classical.propDecidable (Eq.{succ u3} ι a b)) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4 b b) f)) (LinearMap.charpoly.{u1, u2} R M _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 f)
+<too large>
 Case conversion may be inaccurate. Consider using '#align linear_map.charpoly_to_matrix LinearMap.charpoly_toMatrixₓ'. -/
 /-- `charpoly f` is the characteristic polynomial of the matrix of `f` in any basis. -/
 @[simp]

a87d2257

bump to nightly-2023-05-26-03

mathlib commit https://github.com/leanprover-community/mathlib/commit/e1a18cad9cd462973d760af7de36b05776b8811c

d59ee359

Diff

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Riccardo Brasca
 
 ! This file was ported from Lean 3 source module linear_algebra.charpoly.to_matrix
-! leanprover-community/mathlib commit baab5d3091555838751562e6caad33c844bea15e
+! leanprover-community/mathlib commit a87d22575d946e1e156fc1edd1e1269600a8a282
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -15,6 +15,9 @@ import Mathbin.LinearAlgebra.Matrix.Basis
 
 # Characteristic polynomial
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 ## Main result
 
 * `linear_map.charpoly_to_matrix f` : `charpoly f` is the characteristic polynomial of the matrix

baab5d30

bump to nightly-2023-05-24-12

mathlib commit https://github.com/leanprover-community/mathlib/commit/8d33f09cd7089ecf074b4791907588245aec5d1b

2a3e3db2

Diff

@@ -39,6 +39,12 @@ namespace LinearMap
 
 section Basic
 
+/- warning: linear_map.charpoly_to_matrix -> LinearMap.charpoly_toMatrix is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : CommRing.{u1} R] [_inst_2 : Nontrivial.{u1} R] [_inst_3 : AddCommGroup.{u2} M] [_inst_4 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3)] [_inst_5 : Module.Free.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4] [_inst_6 : Module.Finite.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4] (f : LinearMap.{u1, u1, u2, u2} R R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) {ι : Type.{u3}} [_inst_7 : Fintype.{u3} ι] (b : Basis.{u3, u1, u2} ι R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4), Eq.{succ u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Matrix.charpoly.{u1, u3} R _inst_1 ι (fun (a : ι) (b : ι) => Classical.propDecidable (Eq.{succ u3} ι a b)) _inst_7 (coeFn.{max (succ u2) (succ (max u3 u1)), max (succ u2) (succ (max u3 u1))} (LinearEquiv.{u1, u1, u2, max u3 u1} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (LinearMap.toMatrix._proof_1.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.toMatrix._proof_2.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Matrix.{u3, u3, u1} ι ι R) (LinearMap.addCommMonoid.{u1, u1, u2, u2} R R M M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Matrix.addCommMonoid.{u1, u3, u3} ι ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u2} R R R M M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_4 (LinearMap.toMatrix._proof_3.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)) (Matrix.module.{u1, u3, u3, u1} ι ι R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (_x : LinearEquiv.{u1, u1, u2, max u3 u1} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (LinearMap.toMatrix._proof_1.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.toMatrix._proof_2.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Matrix.{u3, u3, u1} ι ι R) (LinearMap.addCommMonoid.{u1, u1, u2, u2} R R M M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Matrix.addCommMonoid.{u1, u3, u3} ι ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u2} R R R M M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_4 (LinearMap.toMatrix._proof_3.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)) (Matrix.module.{u1, u3, u3, u1} ι ι R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) => (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) -> (Matrix.{u3, u3, u1} ι ι R)) (LinearEquiv.hasCoeToFun.{u1, u1, u2, max u3 u1} R R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Matrix.{u3, u3, u1} ι ι R) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u2} R R M M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Matrix.addCommMonoid.{u1, u3, u3} ι ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (LinearMap.module.{u1, u1, u1, u2, u2} R R R M M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_4 (LinearMap.toMatrix._proof_3.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)) (Matrix.module.{u1, u3, u3, u1} ι ι R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (LinearMap.toMatrix._proof_1.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.toMatrix._proof_2.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.toMatrix.{u1, u3, u3, u2, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) ι ι _inst_7 _inst_7 (fun (a : ι) (b : ι) => Classical.propDecidable (Eq.{succ u3} ι a b)) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4 b b) f)) (LinearMap.charpoly.{u1, u2} R M _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 f)
+but is expected to have type
+  forall {R : Type.{u1}} {M : Type.{u2}} [_inst_1 : CommRing.{u1} R] [_inst_2 : Nontrivial.{u1} R] [_inst_3 : AddCommGroup.{u2} M] [_inst_4 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3)] [_inst_5 : Module.Free.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4] [_inst_6 : Module.Finite.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4] (f : LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) {ι : Type.{u3}} [_inst_7 : Fintype.{u3} ι] (b : Basis.{u3, u1, u2} ι R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4), Eq.{succ u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Matrix.charpoly.{u1, u3} R _inst_1 ι (fun (a : ι) (b : ι) => Classical.propDecidable (Eq.{succ u3} ι a b)) _inst_7 (FunLike.coe.{max (max (succ u1) (succ u2)) (succ u3), succ u2, max (succ u1) (succ u3)} (LinearEquiv.{u1, u1, u2, max u1 u3} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Matrix.{u3, u3, u1} ι ι R) (LinearMap.addCommMonoid.{u1, u1, u2, u2} R R M M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Matrix.addCommMonoid.{u1, u3, u3} ι ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u2} R R R M M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_4 (smulCommClass_self.{u1, u2} R M (CommSemiring.toCommMonoid.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (MulActionWithZero.toMulAction.{u1, u2} R M (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3))) (Module.toMulActionWithZero.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))) (Matrix.module.{u1, u3, u3, u1} ι ι R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (fun (_x : LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) => Matrix.{u3, u3, u1} ι ι R) _x) (SMulHomClass.toFunLike.{max (max u1 u2) u3, u1, u2, max u1 u3} (LinearEquiv.{u1, u1, u2, max u1 u3} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Matrix.{u3, u3, u1} ι ι R) (LinearMap.addCommMonoid.{u1, u1, u2, u2} R R M M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Matrix.addCommMonoid.{u1, u3, u3} ι ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u2} R R R M M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_4 (smulCommClass_self.{u1, u2} R M (CommSemiring.toCommMonoid.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (MulActionWithZero.toMulAction.{u1, u2} R M (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3))) (Module.toMulActionWithZero.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))) (Matrix.module.{u1, u3, u3, u1} ι ι R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Matrix.{u3, u3, u1} ι ι R) (SMulZeroClass.toSMul.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (AddMonoid.toZero.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (AddCommMonoid.toAddMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (LinearMap.addCommMonoid.{u1, u1, u2, u2} R R M M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (DistribSMul.toSMulZeroClass.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (AddMonoid.toAddZeroClass.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (AddCommMonoid.toAddMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (LinearMap.addCommMonoid.{u1, u1, u2, u2} R R M M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (DistribMulAction.toDistribSMul.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (LinearMap.addCommMonoid.{u1, u1, u2, u2} R R M M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Module.toDistribMulAction.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u2} R R M M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u2} R R R M M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_4 (smulCommClass_self.{u1, u2} R M (CommSemiring.toCommMonoid.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (MulActionWithZero.toMulAction.{u1, u2} R M (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3))) (Module.toMulActionWithZero.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))))))) (SMulZeroClass.toSMul.{u1, max u1 u3} R (Matrix.{u3, u3, u1} ι ι R) (AddMonoid.toZero.{max u1 u3} (Matrix.{u3, u3, u1} ι ι R) (AddCommMonoid.toAddMonoid.{max u1 u3} (Matrix.{u3, u3, u1} ι ι R) (Matrix.addCommMonoid.{u1, u3, u3} ι ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (DistribSMul.toSMulZeroClass.{u1, max u1 u3} R (Matrix.{u3, u3, u1} ι ι R) (AddMonoid.toAddZeroClass.{max u1 u3} (Matrix.{u3, u3, u1} ι ι R) (AddCommMonoid.toAddMonoid.{max u1 u3} (Matrix.{u3, u3, u1} ι ι R) (Matrix.addCommMonoid.{u1, u3, u3} ι ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (DistribMulAction.toDistribSMul.{u1, max u1 u3} R (Matrix.{u3, u3, u1} ι ι R) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{max u1 u3} (Matrix.{u3, u3, u1} ι ι R) (Matrix.addCommMonoid.{u1, u3, u3} ι ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (Module.toDistribMulAction.{u1, max u1 u3} R (Matrix.{u3, u3, u1} ι ι R) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Matrix.addCommMonoid.{u1, u3, u3} ι ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Matrix.module.{u1, u3, u3, u1} ι ι R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (DistribMulActionHomClass.toSMulHomClass.{max (max u1 u2) u3, u1, u2, max u1 u3} (LinearEquiv.{u1, u1, u2, max u1 u3} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Matrix.{u3, u3, u1} ι ι R) (LinearMap.addCommMonoid.{u1, u1, u2, u2} R R M M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Matrix.addCommMonoid.{u1, u3, u3} ι ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u2} R R R M M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_4 (smulCommClass_self.{u1, u2} R M (CommSemiring.toCommMonoid.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (MulActionWithZero.toMulAction.{u1, u2} R M (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3))) (Module.toMulActionWithZero.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))) (Matrix.module.{u1, u3, u3, u1} ι ι R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Matrix.{u3, u3, u1} ι ι R) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{u2} (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (LinearMap.addCommMonoid.{u1, u1, u2, u2} R R M M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (AddCommMonoid.toAddMonoid.{max u1 u3} (Matrix.{u3, u3, u1} ι ι R) (Matrix.addCommMonoid.{u1, u3, u3} ι ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))) (Module.toDistribMulAction.{u1, u2} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u2} R R M M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u2} R R R M M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_4 (smulCommClass_self.{u1, u2} R M (CommSemiring.toCommMonoid.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (MulActionWithZero.toMulAction.{u1, u2} R M (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3))) (Module.toMulActionWithZero.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4))))) (Module.toDistribMulAction.{u1, max u1 u3} R (Matrix.{u3, u3, u1} ι ι R) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Matrix.addCommMonoid.{u1, u3, u3} ι ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Matrix.module.{u1, u3, u3, u1} ι ι R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (SemilinearMapClass.distribMulActionHomClass.{u1, u2, max u1 u3, max (max u1 u2) u3} R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Matrix.{u3, u3, u1} ι ι R) (LinearEquiv.{u1, u1, u2, max u1 u3} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Matrix.{u3, u3, u1} ι ι R) (LinearMap.addCommMonoid.{u1, u1, u2, u2} R R M M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Matrix.addCommMonoid.{u1, u3, u3} ι ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u2} R R R M M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_4 (smulCommClass_self.{u1, u2} R M (CommSemiring.toCommMonoid.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (MulActionWithZero.toMulAction.{u1, u2} R M (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3))) (Module.toMulActionWithZero.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))) (Matrix.module.{u1, u3, u3, u1} ι ι R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u2} R R M M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Matrix.addCommMonoid.{u1, u3, u3} ι ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u2} R R R M M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_4 (smulCommClass_self.{u1, u2} R M (CommSemiring.toCommMonoid.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (MulActionWithZero.toMulAction.{u1, u2} R M (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3))) (Module.toMulActionWithZero.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))) (Matrix.module.{u1, u3, u3, u1} ι ι R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (SemilinearEquivClass.instSemilinearMapClass.{u1, u1, u2, max u1 u3, max (max u1 u2) u3} R R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Matrix.{u3, u3, u1} ι ι R) (LinearEquiv.{u1, u1, u2, max u1 u3} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Matrix.{u3, u3, u1} ι ι R) (LinearMap.addCommMonoid.{u1, u1, u2, u2} R R M M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Matrix.addCommMonoid.{u1, u3, u3} ι ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u2} R R R M M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_4 (smulCommClass_self.{u1, u2} R M (CommSemiring.toCommMonoid.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (MulActionWithZero.toMulAction.{u1, u2} R M (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3))) (Module.toMulActionWithZero.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))) (Matrix.module.{u1, u3, u3, u1} ι ι R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u2} R R M M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Matrix.addCommMonoid.{u1, u3, u3} ι ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u2} R R R M M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_4 (smulCommClass_self.{u1, u2} R M (CommSemiring.toCommMonoid.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (MulActionWithZero.toMulAction.{u1, u2} R M (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3))) (Module.toMulActionWithZero.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))) (Matrix.module.{u1, u3, u3, u1} ι ι R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u1, u1, u2, max u1 u3} R R (LinearMap.{u1, u1, u2, u2} R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4) (Matrix.{u3, u3, u1} ι ι R) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (LinearMap.addCommMonoid.{u1, u1, u2, u2} R R M M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Matrix.addCommMonoid.{u1, u3, u3} ι ι R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (LinearMap.instModuleLinearMapAddCommMonoid.{u1, u1, u1, u2, u2} R R R M M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_4 (smulCommClass_self.{u1, u2} R M (CommSemiring.toCommMonoid.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (MulActionWithZero.toMulAction.{u1, u2} R M (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3))) (Module.toMulActionWithZero.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4)))) (Matrix.module.{u1, u3, u3, u1} ι ι R R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (RingHomInvPair.ids.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))))) (LinearMap.toMatrix.{u1, u3, u3, u2, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) ι ι _inst_7 _inst_7 (fun (a : ι) (b : ι) => Classical.propDecidable (Eq.{succ u3} ι a b)) M M (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M _inst_3) _inst_4 _inst_4 b b) f)) (LinearMap.charpoly.{u1, u2} R M _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 f)
+Case conversion may be inaccurate. Consider using '#align linear_map.charpoly_to_matrix LinearMap.charpoly_toMatrixₓ'. -/
 /-- `charpoly f` is the characteristic polynomial of the matrix of `f` in any basis. -/
 @[simp]
 theorem charpoly_toMatrix {ι : Type w} [Fintype ι] (b : Basis ι R M) :

baab5d30

bump to nightly-2023-02-21-16

mathlib commit https://github.com/leanprover-community/mathlib/commit/bd9851ca476957ea4549eb19b40e7b5ade9428cc

1107b979

Changes in mathlib4

mathlib3

mathlib4

baab5d30

chore(LinearAlgebra/Charpoly/ToMatrix): characteristic polynomials of isomorphic endomorphisms are equal (#12359)

b94f96cf

Diff

@@ -15,7 +15,7 @@ import Mathlib.LinearAlgebra.Matrix.Basis
 ## Main result
 
 * `LinearMap.charpoly_toMatrix f` : `charpoly f` is the characteristic polynomial of the matrix
-of `f` in any basis.
+  of `f` in any basis.
 
 -/
 
@@ -24,6 +24,8 @@ universe u v w
 
 variable {R M M₁ M₂ : Type*} [CommRing R] [Nontrivial R]
 variable [AddCommGroup M] [Module R M] [Module.Free R M] [Module.Finite R M]
+variable [AddCommGroup M₁] [Module R M₁] [Module.Finite R M₁] [Module.Free R M₁]
+variable [AddCommGroup M₂] [Module R M₂] [Module.Finite R M₂] [Module.Free R M₂]
 variable (f : M →ₗ[R] M)
 
 open Matrix
@@ -34,10 +36,8 @@ open Module.Free Polynomial Matrix
 
 namespace LinearMap
 
-section Basic
-
+/- These attribute tweaks save ~ 2000 heartbeats in `LinearMap.charpoly_toMatrix`. -/
 attribute [-instance] instCoeOut
-
 attribute [local instance 2000] RingHomClass.toNonUnitalRingHomClass
 attribute [local instance 2000] NonUnitalRingHomClass.toMulHomClass
 
@@ -85,9 +85,7 @@ theorem charpoly_toMatrix {ι : Type w} [DecidableEq ι] [Fintype ι] (b : Basis
     _ = f.charpoly := rfl
 #align linear_map.charpoly_to_matrix LinearMap.charpoly_toMatrix
 
-lemma charpoly_prodMap [AddCommGroup M₁] [AddCommGroup M₂] [Module R M₁] [Module R M₂]
-    [Module.Finite R M₁] [Module.Finite R M₂] [Module.Free R M₁] [Module.Free R M₂]
-    (f₁ : M₁ →ₗ[R] M₁) (f₂ : M₂ →ₗ[R] M₂) :
+lemma charpoly_prodMap (f₁ : M₁ →ₗ[R] M₁) (f₂ : M₂ →ₗ[R] M₂) :
     (f₁.prodMap f₂).charpoly = f₁.charpoly * f₂.charpoly := by
   let b₁ := chooseBasis R M₁
   let b₂ := chooseBasis R M₂
@@ -95,6 +93,13 @@ lemma charpoly_prodMap [AddCommGroup M₁] [AddCommGroup M₂] [Module R M₁] [
   rw [← charpoly_toMatrix f₁ b₁, ← charpoly_toMatrix f₂ b₂, ← charpoly_toMatrix (f₁.prodMap f₂) b,
     toMatrix_prodMap b₁ b₂ f₁ f₂, Matrix.charpoly_fromBlocks_zero₁₂]
 
-end Basic
-
 end LinearMap
+
+@[simp]
+lemma LinearEquiv.charpoly_conj (e : M₁ ≃ₗ[R] M₂) (φ : Module.End R M₁) :
+    (e.conj φ).charpoly = φ.charpoly := by
+  let b := chooseBasis R M₁
+  rw [← LinearMap.charpoly_toMatrix φ b, ← LinearMap.charpoly_toMatrix (e.conj φ) (b.map e)]
+  congr 1
+  ext i j : 1
+  simp [Matrix.charmatrix, LinearMap.toMatrix, Matrix.diagonal, LinearEquiv.conj_apply]

baab5d30

chore: prepare Lean version bump with explicit simp (#10999)

Co-authored-by: Scott Morrison <scott.morrison@gmail.com>

38bce757

Diff

@@ -67,7 +67,7 @@ theorem charpoly_toMatrix {ι : Type w} [DecidableEq ι] [Fintype ι] (b : Basis
       rw [basis_toMatrix_mul_linearMap_toMatrix_mul_basis_toMatrix]
     _ = det (scalar ι' X - C.mapMatrix (φ₁ P * φ₂ A' * φ₃ Q)) := by
       rw [reindexLinearEquiv_mul, reindexLinearEquiv_mul]
-    _ = det (scalar ι' X - C.mapMatrix (φ₁ P) * C.mapMatrix A' * C.mapMatrix (φ₃ Q)) := by simp
+    _ = det (scalar ι' X - C.mapMatrix (φ₁ P) * C.mapMatrix A' * C.mapMatrix (φ₃ Q)) := by simp [φ₂]
     _ = det (scalar ι' X * C.mapMatrix (φ₁ P) * C.mapMatrix (φ₃ Q) -
           C.mapMatrix (φ₁ P) * C.mapMatrix A' * C.mapMatrix (φ₃ Q)) := by
       rw [Matrix.mul_assoc ((scalar ι') X), hPQ, Matrix.mul_one]

baab5d30

feat(LinearAlgebra/Charpoly): the characteristic polynomial of a direct sum (#10663)

... is the product of the characteristic polynomials.

a4fac96e

Diff

@@ -22,9 +22,9 @@ of `f` in any basis.
 
 universe u v w
 
-variable {R : Type u} {M : Type v} [CommRing R] [Nontrivial R]
-
-variable [AddCommGroup M] [Module R M] [Module.Free R M] [Module.Finite R M] (f : M →ₗ[R] M)
+variable {R M M₁ M₂ : Type*} [CommRing R] [Nontrivial R]
+variable [AddCommGroup M] [Module R M] [Module.Free R M] [Module.Finite R M]
+variable (f : M →ₗ[R] M)
 
 open Matrix
 
@@ -85,6 +85,16 @@ theorem charpoly_toMatrix {ι : Type w} [DecidableEq ι] [Fintype ι] (b : Basis
     _ = f.charpoly := rfl
 #align linear_map.charpoly_to_matrix LinearMap.charpoly_toMatrix
 
+lemma charpoly_prodMap [AddCommGroup M₁] [AddCommGroup M₂] [Module R M₁] [Module R M₂]
+    [Module.Finite R M₁] [Module.Finite R M₂] [Module.Free R M₁] [Module.Free R M₂]
+    (f₁ : M₁ →ₗ[R] M₁) (f₂ : M₂ →ₗ[R] M₂) :
+    (f₁.prodMap f₂).charpoly = f₁.charpoly * f₂.charpoly := by
+  let b₁ := chooseBasis R M₁
+  let b₂ := chooseBasis R M₂
+  let b := b₁.prod b₂
+  rw [← charpoly_toMatrix f₁ b₁, ← charpoly_toMatrix f₂ b₂, ← charpoly_toMatrix (f₁.prodMap f₂) b,
+    toMatrix_prodMap b₁ b₂ f₁ f₂, Matrix.charpoly_fromBlocks_zero₁₂]
+
 end Basic
 
 end LinearMap

baab5d30

refactor(Data/FunLike): use unbundled inheritance from FunLike (#8386)

The FunLike hierarchy is very big and gets scanned through each time we need a coercion (via the CoeFun instance). It looks like unbundled inheritance suits Lean 4 better here. The only class that still extends FunLike is EquivLike, since that has a custom coe_injective' field that is easier to implement. All other classes should take FunLike or EquivLike as a parameter.

Zulip thread

Important changes

Previously, morphism classes would be Type-valued and extend FunLike:

/-- `MyHomClass F A B` states that `F` is a type of `MyClass.op`-preserving morphisms.
You should extend this class when you extend `MyHom`. -/
class MyHomClass (F : Type*) (A B : outParam <| Type*) [MyClass A] [MyClass B]
  extends FunLike F A B :=
(map_op : ∀ (f : F) (x y : A), f (MyClass.op x y) = MyClass.op (f x) (f y))

After this PR, they should be Prop-valued and take FunLike as a parameter:

/-- `MyHomClass F A B` states that `F` is a type of `MyClass.op`-preserving morphisms.
You should extend this class when you extend `MyHom`. -/
class MyHomClass (F : Type*) (A B : outParam <| Type*) [MyClass A] [MyClass B]
  [FunLike F A B] : Prop :=
(map_op : ∀ (f : F) (x y : A), f (MyClass.op x y) = MyClass.op (f x) (f y))

(Note that A B stay marked as outParam even though they are not purely required to be so due to the FunLike parameter already filling them in. This is required to see through type synonyms, which is important in the category theory library. Also, I think keeping them as outParam is slightly faster.)

Similarly, MyEquivClass should take EquivLike as a parameter.

As a result, every mention of [MyHomClass F A B] should become [FunLike F A B] [MyHomClass F A B].

Remaining issues

Slower (failing) search

While overall this gives some great speedups, there are some cases that are noticeably slower. In particular, a failing application of a lemma such as map_mul is more expensive. This is due to suboptimal processing of arguments. For example:

variable [FunLike F M N] [Mul M] [Mul N] (f : F) (x : M) (y : M)

theorem map_mul [MulHomClass F M N] : f (x * y) = f x * f y

example [AddHomClass F A B] : f (x * y) = f x * f y := map_mul f _ _

Before this PR, applying map_mul f gives the goals [Mul ?M] [Mul ?N] [MulHomClass F ?M ?N]. Since M and N are out_params, [MulHomClass F ?M ?N] is synthesized first, supplies values for ?M and ?N and then the Mul M and Mul N instances can be found.

After this PR, the goals become [FunLike F ?M ?N] [Mul ?M] [Mul ?N] [MulHomClass F ?M ?N]. Now [FunLike F ?M ?N] is synthesized first, supplies values for ?M and ?N and then the Mul M and Mul N instances can be found, before trying MulHomClass F M N which fails. Since the Mul hierarchy is very big, this can be slow to fail, especially when there is no such Mul instance.

A long-term but harder to achieve solution would be to specify the order in which instance goals get solved. For example, we'd like to change the arguments to map_mul to look like [FunLike F M N] [Mul M] [Mul N] [highPriority <| MulHomClass F M N] because MulHomClass fails or succeeds much faster than the others.

As a consequence, the simpNF linter is much slower since by design it tries and fails to apply many map_ lemmas. The same issue occurs a few times in existing calls to simp [map_mul], where map_mul is tried "too soon" and fails. Thanks to the speedup of leanprover/lean4#2478 the impact is very limited, only in files that already were close to the timeout.

`simp` not firing sometimes

This affects map_smulₛₗ and related definitions. For simp lemmas Lean apparently uses a slightly different mechanism to find instances, so that rw can find every argument to map_smulₛₗ successfully but simp can't: leanprover/lean4#3701.

Missing instances due to unification failing

Especially in the category theory library, we might sometimes have a type A which is also accessible as a synonym (Bundled A hA).1. Instance synthesis doesn't always work if we have f : A →* B but x * y : (Bundled A hA).1 or vice versa. This seems to be mostly fixed by keeping A B as outParams in MulHomClass F A B. (Presumably because Lean will do a definitional check A =?= (Bundled A hA).1 instead of using the syntax in the discrimination tree.)

Workaround for issues

The timeouts can be worked around for now by specifying which map_mul we mean, either as map_mul f for some explicit f, or as e.g. MonoidHomClass.map_mul.

map_smulₛₗ not firing as simp lemma can be worked around by going back to the pre-FunLike situation and making LinearMap.map_smulₛₗ a simp lemma instead of the generic map_smulₛₗ. Writing simp [map_smulₛₗ _] also works.

Co-authored-by: Matthew Ballard <matt@mrb.email> Co-authored-by: Scott Morrison <scott.morrison@gmail.com> Co-authored-by: Scott Morrison <scott@tqft.net> Co-authored-by: Anne Baanen <Vierkantor@users.noreply.github.com>

c6a73d4f

Diff

@@ -39,7 +39,7 @@ section Basic
 attribute [-instance] instCoeOut
 
 attribute [local instance 2000] RingHomClass.toNonUnitalRingHomClass
-attribute [local instance 2000] NonUnitalRingHomClass.toMulHomClass MulHomClass.toDFunLike
+attribute [local instance 2000] NonUnitalRingHomClass.toMulHomClass
 
 /-- `charpoly f` is the characteristic polynomial of the matrix of `f` in any basis. -/
 @[simp]

baab5d30

chore(*): rename FunLike to DFunLike (#9785)

This prepares for the introduction of a non-dependent synonym of FunLike, which helps a lot with keeping #8386 readable.

This is entirely search-and-replace in 680197f combined with manual fixes in 4145626, e900597 and b8428f8. The commands that generated this change:

sed -i 's/\bFunLike\b/DFunLike/g' {Archive,Counterexamples,Mathlib,test}/**/*.lean
sed -i 's/\btoFunLike\b/toDFunLike/g' {Archive,Counterexamples,Mathlib,test}/**/*.lean
sed -i 's/import Mathlib.Data.DFunLike/import Mathlib.Data.FunLike/g' {Archive,Counterexamples,Mathlib,test}/**/*.lean
sed -i 's/\bHom_FunLike\b/Hom_DFunLike/g' {Archive,Counterexamples,Mathlib,test}/**/*.lean     
sed -i 's/\binstFunLike\b/instDFunLike/g' {Archive,Counterexamples,Mathlib,test}/**/*.lean
sed -i 's/\bfunLike\b/instDFunLike/g' {Archive,Counterexamples,Mathlib,test}/**/*.lean
sed -i 's/\btoo many metavariables to apply `fun_like.has_coe_to_fun`/too many metavariables to apply `DFunLike.hasCoeToFun`/g' {Archive,Counterexamples,Mathlib,test}/**/*.lean

Co-authored-by: Anne Baanen <Vierkantor@users.noreply.github.com>

82656743

Diff

@@ -39,7 +39,7 @@ section Basic
 attribute [-instance] instCoeOut
 
 attribute [local instance 2000] RingHomClass.toNonUnitalRingHomClass
-attribute [local instance 2000] NonUnitalRingHomClass.toMulHomClass MulHomClass.toFunLike
+attribute [local instance 2000] NonUnitalRingHomClass.toMulHomClass MulHomClass.toDFunLike
 
 /-- `charpoly f` is the characteristic polynomial of the matrix of `f` in any basis. -/
 @[simp]

baab5d30

chore: Reorganize results about rank and finrank. (#9349)

The files Mathlib.LinearAlgebra.FreeModule.Rank, Mathlib.LinearAlgebra.FreeModule.Finite.Rank, Mathlib.LinearAlgebra.Dimension and Mathlib.LinearAlgebra.Finrank were reorganized into a folder Mathlib.LinearAlgebra.Dimension, containing the following files

Basic.lean: Contains the definition of Module.rank.
Finrank.lean: Contains the definition of FiniteDimensional.finrank.
StrongRankCondition.lean: Contains results about rank and finrank over rings satisfying strong rank condition
Free.lean: Contains results about rank and finrank of free modules
Finite.lean: Contains conditions or consequences for rank to be finite or zero
Constructions.lean: Contains the calculation of the rank of various constructions.
DivisionRing.lean: Contains results about rank and finrank of spaces over division rings.
LinearMap.lean: Contains results about LinearMap.rank

API changes: IsNoetherian.rank_lt_aleph0 and FiniteDimensional.rank_lt_aleph0 are replaced with rank_lt_aleph0. Module.Free.finite_basis was renamed to Module.Finite.finite_basis. FiniteDimensional.finrank_eq_rank was renamed to finrank_eq_rank. rank_eq_cardinal_basis and rank_eq_cardinal_basis' were removed in favour of Basis.mk_eq_mk and Basis.mk_eq_mk''.

Co-authored-by: Andrew Yang <36414270+erdOne@users.noreply.github.com>

0b41ea95

Diff

@@ -36,6 +36,11 @@ namespace LinearMap
 
 section Basic
 
+attribute [-instance] instCoeOut
+
+attribute [local instance 2000] RingHomClass.toNonUnitalRingHomClass
+attribute [local instance 2000] NonUnitalRingHomClass.toMulHomClass MulHomClass.toFunLike
+
 /-- `charpoly f` is the characteristic polynomial of the matrix of `f` in any basis. -/
 @[simp]
 theorem charpoly_toMatrix {ι : Type w} [DecidableEq ι] [Fintype ι] (b : Basis ι R M) :

baab5d30

refactor(Data/Matrix/Basic): use a defeq for scalar that matches its docstring (#8115)

This changes the defeq from scalar a = a • 1 to scalar a = diagonal fun _ => a, which has the nice bonus of making algebraMap_eq_diagonal true by rfl.

As a result, we need a new smul_one_eq_diagonal lemma to rewrite diagonal fun _ => a back into a • 1, along with some variants for convenience.

In the long term we could generalize this to non-unital rings, now that it needs no 1.

4b30f25b

Diff

@@ -36,7 +36,6 @@ namespace LinearMap
 
 section Basic
 
-set_option maxHeartbeats 250000 in
 /-- `charpoly f` is the characteristic polynomial of the matrix of `f` in any basis. -/
 @[simp]
 theorem charpoly_toMatrix {ι : Type w} [DecidableEq ι] [Fintype ι] (b : Basis ι R M) :
@@ -68,7 +67,8 @@ theorem charpoly_toMatrix {ι : Type w} [DecidableEq ι] [Fintype ι] (b : Basis
           C.mapMatrix (φ₁ P) * C.mapMatrix A' * C.mapMatrix (φ₃ Q)) := by
       rw [Matrix.mul_assoc ((scalar ι') X), hPQ, Matrix.mul_one]
     _ = det (C.mapMatrix (φ₁ P) * scalar ι' X * C.mapMatrix (φ₃ Q) -
-          C.mapMatrix (φ₁ P) * C.mapMatrix A' * C.mapMatrix (φ₃ Q)) := by simp
+          C.mapMatrix (φ₁ P) * C.mapMatrix A' * C.mapMatrix (φ₃ Q)) := by
+      rw [scalar_commute _ commute_X]
     _ = det (C.mapMatrix (φ₁ P) * (scalar ι' X - C.mapMatrix A') * C.mapMatrix (φ₃ Q)) := by
       rw [← Matrix.sub_mul, ← Matrix.mul_sub]
     _ = det (C.mapMatrix (φ₁ P)) * det (scalar ι' X - C.mapMatrix A') * det (C.mapMatrix (φ₃ Q)) :=

baab5d30

refactor(Data/Matrix): Eliminate ⬝ notation in favor of HMul (#6487)

The main difficulty here is that * has a slightly difference precedence to ⬝. notably around smul and neg.

The other annoyance is that ↑U ⬝ A ⬝ ↑U⁻¹ : Matrix m m 𝔸 now has to be written U.val * A * (U⁻¹).val in order to typecheck.

A downside of this change to consider: if you have a goal of A * (B * C) = (A * B) * C, mul_assoc now gives the illusion of matching, when in fact Matrix.mul_assoc is needed. Previously the distinct symbol made it easy to avoid this mistake.

On the flipside, there is now no need to rewrite by Matrix.mul_eq_mul all the time (indeed, the lemma is now removed).

38c07226

Diff

@@ -52,24 +52,24 @@ theorem charpoly_toMatrix {ι : Type w} [DecidableEq ι] [Fintype ι] (b : Basis
   let φ₃ := reindexLinearEquiv R R (Equiv.refl ι') e
   let P := b.toMatrix b'
   let Q := b'.toMatrix b
-  have hPQ : C.mapMatrix (φ₁ P) ⬝ C.mapMatrix (φ₃ Q) = 1 := by
+  have hPQ : C.mapMatrix (φ₁ P) * C.mapMatrix (φ₃ Q) = 1 := by
     rw [RingHom.mapMatrix_apply, RingHom.mapMatrix_apply, ← Matrix.map_mul,
       reindexLinearEquiv_mul R R, Basis.toMatrix_mul_toMatrix_flip,
       reindexLinearEquiv_one, ← RingHom.mapMatrix_apply, RingHom.map_one]
   calc
     A.charpoly = (reindex e e A).charpoly := (charpoly_reindex _ _).symm
     _ = det (scalar ι' X - C.mapMatrix (φ A)) := rfl
-    _ = det (scalar ι' X - C.mapMatrix (φ (P ⬝ A' ⬝ Q))) := by
+    _ = det (scalar ι' X - C.mapMatrix (φ (P * A' * Q))) := by
       rw [basis_toMatrix_mul_linearMap_toMatrix_mul_basis_toMatrix]
-    _ = det (scalar ι' X - C.mapMatrix (φ₁ P ⬝ φ₂ A' ⬝ φ₃ Q)) := by
+    _ = det (scalar ι' X - C.mapMatrix (φ₁ P * φ₂ A' * φ₃ Q)) := by
       rw [reindexLinearEquiv_mul, reindexLinearEquiv_mul]
-    _ = det (scalar ι' X - C.mapMatrix (φ₁ P) ⬝ C.mapMatrix A' ⬝ C.mapMatrix (φ₃ Q)) := by simp
-    _ = det (scalar ι' X ⬝ C.mapMatrix (φ₁ P) ⬝ C.mapMatrix (φ₃ Q) -
-          C.mapMatrix (φ₁ P) ⬝ C.mapMatrix A' ⬝ C.mapMatrix (φ₃ Q)) := by
+    _ = det (scalar ι' X - C.mapMatrix (φ₁ P) * C.mapMatrix A' * C.mapMatrix (φ₃ Q)) := by simp
+    _ = det (scalar ι' X * C.mapMatrix (φ₁ P) * C.mapMatrix (φ₃ Q) -
+          C.mapMatrix (φ₁ P) * C.mapMatrix A' * C.mapMatrix (φ₃ Q)) := by
       rw [Matrix.mul_assoc ((scalar ι') X), hPQ, Matrix.mul_one]
-    _ = det (C.mapMatrix (φ₁ P) ⬝ scalar ι' X ⬝ C.mapMatrix (φ₃ Q) -
-          C.mapMatrix (φ₁ P) ⬝ C.mapMatrix A' ⬝ C.mapMatrix (φ₃ Q)) := by simp
-    _ = det (C.mapMatrix (φ₁ P) ⬝ (scalar ι' X - C.mapMatrix A') ⬝ C.mapMatrix (φ₃ Q)) := by
+    _ = det (C.mapMatrix (φ₁ P) * scalar ι' X * C.mapMatrix (φ₃ Q) -
+          C.mapMatrix (φ₁ P) * C.mapMatrix A' * C.mapMatrix (φ₃ Q)) := by simp
+    _ = det (C.mapMatrix (φ₁ P) * (scalar ι' X - C.mapMatrix A') * C.mapMatrix (φ₃ Q)) := by
       rw [← Matrix.sub_mul, ← Matrix.mul_sub]
     _ = det (C.mapMatrix (φ₁ P)) * det (scalar ι' X - C.mapMatrix A') * det (C.mapMatrix (φ₃ Q)) :=
       by rw [det_mul, det_mul]

baab5d30

feat: presheaf of modules over a presheaf of rings (#4670)

This is extracted from the draft PR https://github.com/leanprover-community/mathlib4/pull/4116 which tries to compare this definition with the definition in terms of a presheaf in RingMod.

Co-authored-by: Oliver Nash <github@olivernash.org> Co-authored-by: Christopher Hoskin <christopher.hoskin@gmail.com> Co-authored-by: Ruben Van de Velde <65514131+Ruben-VandeVelde@users.noreply.github.com> Co-authored-by: Anatole Dedecker <anatolededecker@gmail.com> Co-authored-by: Matthew Robert Ballard <k.buzzard@imperial.ac.uk> Co-authored-by: Peter Nelson <71660771+apnelson1@users.noreply.github.com> Co-authored-by: Eric Wieser <wieser.eric@gmail.com> Co-authored-by: Rémy Degenne <remydegenne@gmail.com> Co-authored-by: Thomas Browning <tb65536@uw.edu> Co-authored-by: Scott Morrison <scott.morrison@gmail.com> Co-authored-by: Matthew Robert Ballard <matt@mrb.email> Co-authored-by: Joël Riou <joel.riou@universite-paris-saclay.fr> Co-authored-by: Yury G. Kudryashov <urkud@urkud.name> Co-authored-by: Arend Mellendijk <arend.mellendijk@gmail.com> Co-authored-by: Markus Himmel <markus@himmel-villmar.de> Co-authored-by: Christopher Hoskin <christopher.hoskin@overleaf.com> Co-authored-by: Bulhwi Cha <chabulhwi@semmalgil.com> Co-authored-by: Floris van Doorn <fpvdoorn@gmail.com> Co-authored-by: negiizhao <egresf@gmail.com> Co-authored-by: Alex J Best <alex.j.best@gmail.com> Co-authored-by: Jeremy Tan Jie Rui <reddeloostw@gmail.com> Co-authored-by: Kyle Miller <kmill31415@gmail.com> Co-authored-by: Chris Hughes <chrishughes24@gmail.com> Co-authored-by: Jz Pan <acme_pjz@hotmail.com>

f2c3294f

Diff

@@ -36,6 +36,7 @@ namespace LinearMap
 
 section Basic
 
+set_option maxHeartbeats 250000 in
 /-- `charpoly f` is the characteristic polynomial of the matrix of `f` in any basis. -/
 @[simp]
 theorem charpoly_toMatrix {ι : Type w} [DecidableEq ι] [Fintype ι] (b : Basis ι R M) :

baab5d30

chore(LinearAlgebra): remove open Classical (#6320)

This uncovers a few situations where a lemma was stated with the wrong decidability assumption. The corrected lemmas are strictly more syntactically-general.

This is exhaustive in the LinearAlgebra folder.

Where removal is impractical, this switches to open Classical in to make the intent clear.

73993336

Diff

@@ -26,7 +26,7 @@ variable {R : Type u} {M : Type v} [CommRing R] [Nontrivial R]
 
 variable [AddCommGroup M] [Module R M] [Module.Free R M] [Module.Finite R M] (f : M →ₗ[R] M)
 
-open Classical Matrix
+open Matrix
 
 noncomputable section
 
@@ -38,7 +38,7 @@ section Basic
 
 /-- `charpoly f` is the characteristic polynomial of the matrix of `f` in any basis. -/
 @[simp]
-theorem charpoly_toMatrix {ι : Type w} [Fintype ι] (b : Basis ι R M) :
+theorem charpoly_toMatrix {ι : Type w} [DecidableEq ι] [Fintype ι] (b : Basis ι R M) :
     (toMatrix b b f).charpoly = f.charpoly := by
   let A := toMatrix b b f
   let b' := chooseBasis R M

baab5d30

chore: script to replace headers with #align_import statements (#5979)

depends on: #5966

Co-authored-by: Eric Wieser <wieser.eric@gmail.com> Co-authored-by: Scott Morrison <scott.morrison@gmail.com>

89aa3a3b

Diff

@@ -2,15 +2,12 @@
 Copyright (c) 2021 Riccardo Brasca. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Riccardo Brasca
-
-! This file was ported from Lean 3 source module linear_algebra.charpoly.to_matrix
-! leanprover-community/mathlib commit baab5d3091555838751562e6caad33c844bea15e
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.LinearAlgebra.Charpoly.Basic
 import Mathlib.LinearAlgebra.Matrix.Basis
 
+#align_import linear_algebra.charpoly.to_matrix from "leanprover-community/mathlib"@"baab5d3091555838751562e6caad33c844bea15e"
+
 /-!
 
 # Characteristic polynomial

baab5d30

feat: port LinearAlgebra.Charpoly.ToMatrix (#4295)

468469a4

`linear_algebra.charpoly.to_matrix` ⟷ `Mathlib.LinearAlgebra.Charpoly.ToMatrix`

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Important changes

Remaining issues

Slower (failing) search

`simp` not firing sometimes

Missing instances due to unification failing

Workaround for issues

Dependencies 10 + 633

linear_algebra.charpoly.to_matrix ⟷ Mathlib.LinearAlgebra.Charpoly.ToMatrix

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Important changes

Remaining issues

Slower (failing) search

simp not firing sometimes

Missing instances due to unification failing

Workaround for issues

Dependencies 10 + 633

`linear_algebra.charpoly.to_matrix` ⟷ `Mathlib.LinearAlgebra.Charpoly.ToMatrix`

`simp` not firing sometimes