linear_algebra.matrix.charpoly.basic | 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

70fd9563

(last sync)

Changes in mathlib3port

mathlib3

mathlib3port

4280f5f3

bump to nightly-2024-03-17-08

mathlib commit https://github.com/leanprover-community/mathlib/commit/65a1391a0106c9204fe45bc73a039f056558cb83

22f01ce4

Diff

@@ -139,18 +139,18 @@ theorem Matrix.aeval_self_charpoly (M : Matrix n n R) : aeval M M.charpoly = 0 :
     (adjugate_mul _).symm
   -- Using the algebra isomorphism `matrix n n R[X] ≃ₐ[R] polynomial (matrix n n R)`,
   -- we have the same identity in `polynomial (matrix n n R)`.
-  apply_fun matPolyEquiv at h 
-  simp only [mat_poly_equiv.map_mul, Matrix.matPolyEquiv_charmatrix] at h 
+  apply_fun matPolyEquiv at h
+  simp only [mat_poly_equiv.map_mul, Matrix.matPolyEquiv_charmatrix] at h
   -- Because the coefficient ring `matrix n n R` is non-commutative,
   -- evaluation at `M` is not multiplicative.
   -- However, any polynomial which is a product of the form $N * (t I - M)$
   -- is sent to zero, because the evaluation function puts the polynomial variable
   -- to the right of any coefficients, so everything telescopes.
-  apply_fun fun p => p.eval M at h 
-  rw [eval_mul_X_sub_C] at h 
+  apply_fun fun p => p.eval M at h
+  rw [eval_mul_X_sub_C] at h
   -- Now $χ_M (t) I$, when thought of as a polynomial of matrices
   -- and evaluated at some `N` is exactly $χ_M (N)$.
-  rw [matPolyEquiv_smul_one, eval_map] at h 
+  rw [matPolyEquiv_smul_one, eval_map] at h
   -- Thus we have $χ_M(M) = 0$, which is the desired result.
   exact h
 #align matrix.aeval_self_charpoly Matrix.aeval_self_charpoly

4280f5f3

bump to nightly-2024-02-17-08

mathlib commit https://github.com/leanprover-community/mathlib/commit/65a1391a0106c9204fe45bc73a039f056558cb83

42bef5c2

Diff

@@ -45,69 +45,70 @@ variable {n : Type w} [DecidableEq n] [Fintype n]
 
 open Finset
 
-#print charmatrix /-
+#print Matrix.charmatrix /-
 /-- The "characteristic matrix" of `M : matrix n n R` is the matrix of polynomials $t I - M$.
 The determinant of this matrix is the characteristic polynomial.
 -/
-def charmatrix (M : Matrix n n R) : Matrix n n R[X] :=
+def Matrix.charmatrix (M : Matrix n n R) : Matrix n n R[X] :=
   Matrix.scalar n (X : R[X]) - (C : R →+* R[X]).mapMatrix M
-#align charmatrix charmatrix
+#align charmatrix Matrix.charmatrix
 -/
 
-#print charmatrix_apply /-
-theorem charmatrix_apply (M : Matrix n n R) (i j : n) :
-    charmatrix M i j = X * (1 : Matrix n n R[X]) i j - C (M i j) :=
+#print Matrix.charmatrix_apply /-
+theorem Matrix.charmatrix_apply (M : Matrix n n R) (i j : n) :
+    Matrix.charmatrix M i j = X * (1 : Matrix n n R[X]) i j - C (M i j) :=
   rfl
-#align charmatrix_apply charmatrix_apply
+#align charmatrix_apply Matrix.charmatrix_apply
 -/
 
-#print charmatrix_apply_eq /-
+#print Matrix.charmatrix_apply_eq /-
 @[simp]
-theorem charmatrix_apply_eq (M : Matrix n n R) (i : n) :
-    charmatrix M i i = (X : R[X]) - C (M i i) := by
-  simp only [charmatrix, sub_left_inj, Pi.sub_apply, scalar_apply_eq, RingHom.mapMatrix_apply,
-    map_apply, DMatrix.sub_apply]
-#align charmatrix_apply_eq charmatrix_apply_eq
+theorem Matrix.charmatrix_apply_eq (M : Matrix n n R) (i : n) :
+    Matrix.charmatrix M i i = (X : R[X]) - C (M i i) := by
+  simp only [Matrix.charmatrix, sub_left_inj, Pi.sub_apply, scalar_apply_eq,
+    RingHom.mapMatrix_apply, map_apply, DMatrix.sub_apply]
+#align charmatrix_apply_eq Matrix.charmatrix_apply_eq
 -/
 
-#print charmatrix_apply_ne /-
+#print Matrix.charmatrix_apply_ne /-
 @[simp]
-theorem charmatrix_apply_ne (M : Matrix n n R) (i j : n) (h : i ≠ j) :
-    charmatrix M i j = -C (M i j) := by
-  simp only [charmatrix, Pi.sub_apply, scalar_apply_ne _ _ _ h, zero_sub, RingHom.mapMatrix_apply,
-    map_apply, DMatrix.sub_apply]
-#align charmatrix_apply_ne charmatrix_apply_ne
+theorem Matrix.charmatrix_apply_ne (M : Matrix n n R) (i j : n) (h : i ≠ j) :
+    Matrix.charmatrix M i j = -C (M i j) := by
+  simp only [Matrix.charmatrix, Pi.sub_apply, scalar_apply_ne _ _ _ h, zero_sub,
+    RingHom.mapMatrix_apply, map_apply, DMatrix.sub_apply]
+#align charmatrix_apply_ne Matrix.charmatrix_apply_ne
 -/
 
-#print matPolyEquiv_charmatrix /-
-theorem matPolyEquiv_charmatrix (M : Matrix n n R) : matPolyEquiv (charmatrix M) = X - C M :=
+#print Matrix.matPolyEquiv_charmatrix /-
+theorem Matrix.matPolyEquiv_charmatrix (M : Matrix n n R) :
+    matPolyEquiv (Matrix.charmatrix M) = X - C M :=
   by
   ext k i j
   simp only [matPolyEquiv_coeff_apply, coeff_sub, Pi.sub_apply]
   by_cases h : i = j
-  · subst h; rw [charmatrix_apply_eq, coeff_sub]
+  · subst h; rw [Matrix.charmatrix_apply_eq, coeff_sub]
     simp only [coeff_X, coeff_C]
     split_ifs <;> simp
-  · rw [charmatrix_apply_ne _ _ _ h, coeff_X, coeff_neg, coeff_C, coeff_C]
+  · rw [Matrix.charmatrix_apply_ne _ _ _ h, coeff_X, coeff_neg, coeff_C, coeff_C]
     split_ifs <;> simp [h]
-#align mat_poly_equiv_charmatrix matPolyEquiv_charmatrix
+#align mat_poly_equiv_charmatrix Matrix.matPolyEquiv_charmatrix
 -/
 
-#print charmatrix_reindex /-
-theorem charmatrix_reindex {m : Type v} [DecidableEq m] [Fintype m] (e : n ≃ m) (M : Matrix n n R) :
-    charmatrix (reindex e e M) = reindex e e (charmatrix M) :=
+#print Matrix.charmatrix_reindex /-
+theorem Matrix.charmatrix_reindex {m : Type v} [DecidableEq m] [Fintype m] (e : n ≃ m)
+    (M : Matrix n n R) : Matrix.charmatrix (reindex e e M) = reindex e e (Matrix.charmatrix M) :=
   by
   ext i j x
   by_cases h : i = j
   all_goals simp [h]
-#align charmatrix_reindex charmatrix_reindex
+#align charmatrix_reindex Matrix.charmatrix_reindex
 -/
 
 #print Matrix.charpoly /-
 /-- The characteristic polynomial of a matrix `M` is given by $\det (t I - M)$.
 -/
 def Matrix.charpoly (M : Matrix n n R) : R[X] :=
-  (charmatrix M).det
+  (Matrix.charmatrix M).det
 #align matrix.charpoly Matrix.charpoly
 -/
 
@@ -116,7 +117,7 @@ theorem Matrix.charpoly_reindex {m : Type v} [DecidableEq m] [Fintype m] (e : n
     (M : Matrix n n R) : (reindex e e M).charpoly = M.charpoly :=
   by
   unfold Matrix.charpoly
-  rw [charmatrix_reindex, Matrix.det_reindex_self]
+  rw [Matrix.charmatrix_reindex, Matrix.det_reindex_self]
 #align matrix.charpoly_reindex Matrix.charpoly_reindex
 -/
 
@@ -133,12 +134,13 @@ theorem Matrix.aeval_self_charpoly (M : Matrix n n R) : aeval M M.charpoly = 0 :
   by
   -- We begin with the fact $χ_M(t) I = adjugate (t I - M) * (t I - M)$,
   -- as an identity in `matrix n n R[X]`.
-  have h : M.charpoly • (1 : Matrix n n R[X]) = adjugate (charmatrix M) * charmatrix M :=
+  have h :
+    M.charpoly • (1 : Matrix n n R[X]) = adjugate (Matrix.charmatrix M) * Matrix.charmatrix M :=
     (adjugate_mul _).symm
   -- Using the algebra isomorphism `matrix n n R[X] ≃ₐ[R] polynomial (matrix n n R)`,
   -- we have the same identity in `polynomial (matrix n n R)`.
   apply_fun matPolyEquiv at h 
-  simp only [mat_poly_equiv.map_mul, matPolyEquiv_charmatrix] at h 
+  simp only [mat_poly_equiv.map_mul, Matrix.matPolyEquiv_charmatrix] at h 
   -- Because the coefficient ring `matrix n n R` is non-commutative,
   -- evaluation at `M` is not multiplicative.
   -- However, any polynomial which is a product of the form $N * (t I - M)$

4280f5f3

bump to nightly-2023-09-24-06

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

5655435f

Diff

@@ -3,10 +3,10 @@ Copyright (c) 2020 Scott Morrison. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Scott Morrison
 -/
-import Mathbin.LinearAlgebra.Matrix.Adjugate
-import Mathbin.RingTheory.PolynomialAlgebra
-import Mathbin.Tactic.ApplyFun
-import Mathbin.Tactic.Squeeze
+import LinearAlgebra.Matrix.Adjugate
+import RingTheory.PolynomialAlgebra
+import Tactic.ApplyFun
+import Tactic.Squeeze
 
 #align_import linear_algebra.matrix.charpoly.basic from "leanprover-community/mathlib"@"4280f5f32e16755ec7985ce11e189b6cd6ff6735"

4280f5f3

bump to nightly-2023-07-20-09

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

9c56d0dd

Diff

@@ -2,17 +2,14 @@
 Copyright (c) 2020 Scott Morrison. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Scott Morrison
-
-! This file was ported from Lean 3 source module linear_algebra.matrix.charpoly.basic
-! leanprover-community/mathlib commit 4280f5f32e16755ec7985ce11e189b6cd6ff6735
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.LinearAlgebra.Matrix.Adjugate
 import Mathbin.RingTheory.PolynomialAlgebra
 import Mathbin.Tactic.ApplyFun
 import Mathbin.Tactic.Squeeze
 
+#align_import linear_algebra.matrix.charpoly.basic from "leanprover-community/mathlib"@"4280f5f32e16755ec7985ce11e189b6cd6ff6735"
+
 /-!
 # Characteristic polynomials and the Cayley-Hamilton theorem

4280f5f3

bump to nightly-2023-06-20-01

mathlib commit https://github.com/leanprover-community/mathlib/commit/2a0ce625dbb0ffbc7d1316597de0b25c1ec75303

9b351f8c

Diff

@@ -85,7 +85,7 @@ theorem charmatrix_apply_ne (M : Matrix n n R) (i j : n) (h : i ≠ j) :
 #print matPolyEquiv_charmatrix /-
 theorem matPolyEquiv_charmatrix (M : Matrix n n R) : matPolyEquiv (charmatrix M) = X - C M :=
   by
-  ext (k i j)
+  ext k i j
   simp only [matPolyEquiv_coeff_apply, coeff_sub, Pi.sub_apply]
   by_cases h : i = j
   · subst h; rw [charmatrix_apply_eq, coeff_sub]
@@ -100,7 +100,7 @@ theorem matPolyEquiv_charmatrix (M : Matrix n n R) : matPolyEquiv (charmatrix M)
 theorem charmatrix_reindex {m : Type v} [DecidableEq m] [Fintype m] (e : n ≃ m) (M : Matrix n n R) :
     charmatrix (reindex e e M) = reindex e e (charmatrix M) :=
   by
-  ext (i j x)
+  ext i j x
   by_cases h : i = j
   all_goals simp [h]
 #align charmatrix_reindex charmatrix_reindex

4280f5f3

bump to nightly-2023-06-13-21

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

829520ac

Diff

@@ -57,25 +57,32 @@ def charmatrix (M : Matrix n n R) : Matrix n n R[X] :=
 #align charmatrix charmatrix
 -/
 
+#print charmatrix_apply /-
 theorem charmatrix_apply (M : Matrix n n R) (i j : n) :
     charmatrix M i j = X * (1 : Matrix n n R[X]) i j - C (M i j) :=
   rfl
 #align charmatrix_apply charmatrix_apply
+-/
 
+#print charmatrix_apply_eq /-
 @[simp]
 theorem charmatrix_apply_eq (M : Matrix n n R) (i : n) :
     charmatrix M i i = (X : R[X]) - C (M i i) := by
   simp only [charmatrix, sub_left_inj, Pi.sub_apply, scalar_apply_eq, RingHom.mapMatrix_apply,
     map_apply, DMatrix.sub_apply]
 #align charmatrix_apply_eq charmatrix_apply_eq
+-/
 
+#print charmatrix_apply_ne /-
 @[simp]
 theorem charmatrix_apply_ne (M : Matrix n n R) (i j : n) (h : i ≠ j) :
     charmatrix M i j = -C (M i j) := by
   simp only [charmatrix, Pi.sub_apply, scalar_apply_ne _ _ _ h, zero_sub, RingHom.mapMatrix_apply,
     map_apply, DMatrix.sub_apply]
 #align charmatrix_apply_ne charmatrix_apply_ne
+-/
 
+#print matPolyEquiv_charmatrix /-
 theorem matPolyEquiv_charmatrix (M : Matrix n n R) : matPolyEquiv (charmatrix M) = X - C M :=
   by
   ext (k i j)
@@ -87,6 +94,7 @@ theorem matPolyEquiv_charmatrix (M : Matrix n n R) : matPolyEquiv (charmatrix M)
   · rw [charmatrix_apply_ne _ _ _ h, coeff_X, coeff_neg, coeff_C, coeff_C]
     split_ifs <;> simp [h]
 #align mat_poly_equiv_charmatrix matPolyEquiv_charmatrix
+-/
 
 #print charmatrix_reindex /-
 theorem charmatrix_reindex {m : Type v} [DecidableEq m] [Fintype m] (e : n ≃ m) (M : Matrix n n R) :
@@ -115,6 +123,7 @@ theorem Matrix.charpoly_reindex {m : Type v} [DecidableEq m] [Fintype m] (e : n
 #align matrix.charpoly_reindex Matrix.charpoly_reindex
 -/
 
+#print Matrix.aeval_self_charpoly /-
 -- This proof follows http://drorbn.net/AcademicPensieve/2015-12/CayleyHamilton.pdf
 /-- The **Cayley-Hamilton Theorem**, that the characteristic polynomial of a matrix,
 applied to the matrix itself, is zero.
@@ -146,4 +155,5 @@ theorem Matrix.aeval_self_charpoly (M : Matrix n n R) : aeval M M.charpoly = 0 :
   -- Thus we have $χ_M(M) = 0$, which is the desired result.
   exact h
 #align matrix.aeval_self_charpoly Matrix.aeval_self_charpoly
+-/

4280f5f3

bump to nightly-2023-06-04-18

mathlib commit https://github.com/leanprover-community/mathlib/commit/5f25c089cb34db4db112556f23c50d12da81b297

3fb4268b

Diff

@@ -131,14 +131,14 @@ theorem Matrix.aeval_self_charpoly (M : Matrix n n R) : aeval M M.charpoly = 0 :
     (adjugate_mul _).symm
   -- Using the algebra isomorphism `matrix n n R[X] ≃ₐ[R] polynomial (matrix n n R)`,
   -- we have the same identity in `polynomial (matrix n n R)`.
-  apply_fun matPolyEquiv  at h 
+  apply_fun matPolyEquiv at h 
   simp only [mat_poly_equiv.map_mul, matPolyEquiv_charmatrix] at h 
   -- Because the coefficient ring `matrix n n R` is non-commutative,
   -- evaluation at `M` is not multiplicative.
   -- However, any polynomial which is a product of the form $N * (t I - M)$
   -- is sent to zero, because the evaluation function puts the polynomial variable
   -- to the right of any coefficients, so everything telescopes.
-  apply_fun fun p => p.eval M  at h 
+  apply_fun fun p => p.eval M at h 
   rw [eval_mul_X_sub_C] at h 
   -- Now $χ_M (t) I$, when thought of as a polynomial of matrices
   -- and evaluated at some `N` is exactly $χ_M (N)$.

4280f5f3

bump to nightly-2023-06-01-16

mathlib commit https://github.com/leanprover-community/mathlib/commit/cca40788df1b8755d5baf17ab2f27dacc2e17acb

b9c87c70

Diff

@@ -131,18 +131,18 @@ theorem Matrix.aeval_self_charpoly (M : Matrix n n R) : aeval M M.charpoly = 0 :
     (adjugate_mul _).symm
   -- Using the algebra isomorphism `matrix n n R[X] ≃ₐ[R] polynomial (matrix n n R)`,
   -- we have the same identity in `polynomial (matrix n n R)`.
-  apply_fun matPolyEquiv  at h
-  simp only [mat_poly_equiv.map_mul, matPolyEquiv_charmatrix] at h
+  apply_fun matPolyEquiv  at h 
+  simp only [mat_poly_equiv.map_mul, matPolyEquiv_charmatrix] at h 
   -- Because the coefficient ring `matrix n n R` is non-commutative,
   -- evaluation at `M` is not multiplicative.
   -- However, any polynomial which is a product of the form $N * (t I - M)$
   -- is sent to zero, because the evaluation function puts the polynomial variable
   -- to the right of any coefficients, so everything telescopes.
-  apply_fun fun p => p.eval M  at h
-  rw [eval_mul_X_sub_C] at h
+  apply_fun fun p => p.eval M  at h 
+  rw [eval_mul_X_sub_C] at h 
   -- Now $χ_M (t) I$, when thought of as a polynomial of matrices
   -- and evaluated at some `N` is exactly $χ_M (N)$.
-  rw [matPolyEquiv_smul_one, eval_map] at h
+  rw [matPolyEquiv_smul_one, eval_map] at h 
   -- Thus we have $χ_M(M) = 0$, which is the desired result.
   exact h
 #align matrix.aeval_self_charpoly Matrix.aeval_self_charpoly

4280f5f3

bump to nightly-2023-06-01-04

mathlib commit https://github.com/leanprover-community/mathlib/commit/cca40788df1b8755d5baf17ab2f27dacc2e17acb

4d9eaa85

Diff

@@ -115,7 +115,6 @@ theorem Matrix.charpoly_reindex {m : Type v} [DecidableEq m] [Fintype m] (e : n
 #align matrix.charpoly_reindex Matrix.charpoly_reindex
 -/
 
-#print Matrix.aeval_self_charpoly /-
 -- This proof follows http://drorbn.net/AcademicPensieve/2015-12/CayleyHamilton.pdf
 /-- The **Cayley-Hamilton Theorem**, that the characteristic polynomial of a matrix,
 applied to the matrix itself, is zero.
@@ -147,5 +146,4 @@ theorem Matrix.aeval_self_charpoly (M : Matrix n n R) : aeval M M.charpoly = 0 :
   -- Thus we have $χ_M(M) = 0$, which is the desired result.
   exact h
 #align matrix.aeval_self_charpoly Matrix.aeval_self_charpoly
--/

4280f5f3

bump to nightly-2023-05-28-18

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

8d353152

Diff

@@ -40,7 +40,7 @@ universe u v w
 
 open Polynomial Matrix
 
-open BigOperators Polynomial
+open scoped BigOperators Polynomial
 
 variable {R : Type u} [CommRing R]

4280f5f3

bump to nightly-2023-05-28-06

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

ba5d8b97

Diff

@@ -57,20 +57,11 @@ def charmatrix (M : Matrix n n R) : Matrix n n R[X] :=
 #align charmatrix charmatrix
 -/
 
-/- warning: charmatrix_apply -> charmatrix_apply is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align charmatrix_apply charmatrix_applyₓ'. -/
 theorem charmatrix_apply (M : Matrix n n R) (i j : n) :
     charmatrix M i j = X * (1 : Matrix n n R[X]) i j - C (M i j) :=
   rfl
 #align charmatrix_apply charmatrix_apply
 
-/- warning: charmatrix_apply_eq -> charmatrix_apply_eq is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {n : Type.{u2}} [_inst_2 : DecidableEq.{succ u2} n] [_inst_3 : Fintype.{u2} n] (M : Matrix.{u2, u2, u1} n n R) (i : n), Eq.{succ u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (charmatrix.{u1, u2} R _inst_1 n (fun (a : n) (b : n) => _inst_2 a b) _inst_3 M i i) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (instHSub.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.X.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (fun (_x : RingHom.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) => R -> (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)))) (RingHom.hasCoeToFun.{u1, u1} R (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))))) (Polynomial.C.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1))) (M i i)))
-but is expected to have type
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-Case conversion may be inaccurate. Consider using '#align charmatrix_apply_eq charmatrix_apply_eqₓ'. -/
 @[simp]
 theorem charmatrix_apply_eq (M : Matrix n n R) (i : n) :
     charmatrix M i i = (X : R[X]) - C (M i i) := by
@@ -78,12 +69,6 @@ theorem charmatrix_apply_eq (M : Matrix n n R) (i : n) :
     map_apply, DMatrix.sub_apply]
 #align charmatrix_apply_eq charmatrix_apply_eq
 
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 @[simp]
 theorem charmatrix_apply_ne (M : Matrix n n R) (i j : n) (h : i ≠ j) :
     charmatrix M i j = -C (M i j) := by
@@ -91,9 +76,6 @@ theorem charmatrix_apply_ne (M : Matrix n n R) (i j : n) (h : i ≠ j) :
     map_apply, DMatrix.sub_apply]
 #align charmatrix_apply_ne charmatrix_apply_ne
 
-/- warning: mat_poly_equiv_charmatrix -> matPolyEquiv_charmatrix is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align mat_poly_equiv_charmatrix matPolyEquiv_charmatrixₓ'. -/
 theorem matPolyEquiv_charmatrix (M : Matrix n n R) : matPolyEquiv (charmatrix M) = X - C M :=
   by
   ext (k i j)

4280f5f3

bump to nightly-2023-05-28-04

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

6797a637

Diff

@@ -99,8 +99,7 @@ theorem matPolyEquiv_charmatrix (M : Matrix n n R) : matPolyEquiv (charmatrix M)
   ext (k i j)
   simp only [matPolyEquiv_coeff_apply, coeff_sub, Pi.sub_apply]
   by_cases h : i = j
-  · subst h
-    rw [charmatrix_apply_eq, coeff_sub]
+  · subst h; rw [charmatrix_apply_eq, coeff_sub]
     simp only [coeff_X, coeff_C]
     split_ifs <;> simp
   · rw [charmatrix_apply_ne _ _ _ h, coeff_X, coeff_neg, coeff_C, coeff_C]

4280f5f3

bump to nightly-2023-05-28-03

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

6c6011cf

Diff

@@ -58,10 +58,7 @@ def charmatrix (M : Matrix n n R) : Matrix n n R[X] :=
 -/
 
 /- warning: charmatrix_apply -> charmatrix_apply is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align charmatrix_apply charmatrix_applyₓ'. -/
 theorem charmatrix_apply (M : Matrix n n R) (i j : n) :
     charmatrix M i j = X * (1 : Matrix n n R[X]) i j - C (M i j) :=
@@ -95,10 +92,7 @@ theorem charmatrix_apply_ne (M : Matrix n n R) (i j : n) (h : i ≠ j) :
 #align charmatrix_apply_ne charmatrix_apply_ne
 
 /- warning: mat_poly_equiv_charmatrix -> matPolyEquiv_charmatrix is a dubious translation:
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_inst_3 (fun (a : n) (b : n) => _inst_2 a b))))))) (DistribSMul.toSMulZeroClass.{u1, max u1 u2} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddMonoid.toAddZeroClass.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))))))) (DistribMulAction.toDistribSMul.{u1, max u1 u2} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) _inst_3 (fun (a : n) (b : n) => _inst_2 a b)))))) (Module.toDistribMulAction.{u1, max u1 u2} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))))) (Algebra.toModule.{u1, max u1 u2} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) _inst_3 (fun (a : n) (b : n) => _inst_2 a b)) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) _inst_3 (fun (a : n) (b : n) => _inst_2 a b) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))))) (SMulZeroClass.toSMul.{u1, max u1 u2} R (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (AddMonoid.toZero.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (AddCommMonoid.toAddMonoid.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (Semiring.toNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b)))))))) (DistribSMul.toSMulZeroClass.{u1, max u1 u2} R (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (AddMonoid.toAddZeroClass.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (AddCommMonoid.toAddMonoid.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (Semiring.toNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b)))))))) (DistribMulAction.toDistribSMul.{u1, max u1 u2} R (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (Semiring.toNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))))))) (Module.toDistribMulAction.{u1, max u1 u2} R (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (Semiring.toNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b)))))) (Algebra.toModule.{u1, max u1 u2} R (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (Polynomial.algebraOfAlgebra.{u1, max u2 u1} R (Matrix.{u2, u2, u1} n n R) (CommRing.toCommSemiring.{u1} R _inst_1) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b)) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R R _inst_3 (fun (a : n) (b : n) => _inst_2 a b) (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))))) (DistribMulActionHomClass.toSMulHomClass.{max u1 u2, u1, max u1 u2, max u1 u2} (AlgEquiv.{u1, max u1 u2, max u1 u2} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (CommRing.toCommSemiring.{u1} R _inst_1) (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) _inst_3 (fun (a : n) (b : n) => _inst_2 a b)) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) _inst_3 (fun (a : n) (b : n) => _inst_2 a b) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, max u2 u1} R (Matrix.{u2, u2, u1} n n R) (CommRing.toCommSemiring.{u1} R _inst_1) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b)) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R R _inst_3 (fun (a : n) (b : n) => _inst_2 a b) (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) _inst_3 (fun (a : n) (b : n) => _inst_2 a b)))))) (AddCommMonoid.toAddMonoid.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (Semiring.toNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))))))) (Module.toDistribMulAction.{u1, max u1 u2} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))))) (Algebra.toModule.{u1, max u1 u2} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) _inst_3 (fun (a : n) (b : n) => _inst_2 a b)) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) _inst_3 (fun (a : n) (b : n) => _inst_2 a b) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Module.toDistribMulAction.{u1, max u1 u2} R (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (Semiring.toNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b)))))) (Algebra.toModule.{u1, max u1 u2} R (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (Polynomial.algebraOfAlgebra.{u1, max u2 u1} R (Matrix.{u2, u2, u1} n n R) (CommRing.toCommSemiring.{u1} R _inst_1) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b)) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R R _inst_3 (fun (a : n) (b : n) => _inst_2 a b) (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u1 u2, u1, max u1 u2, max u1 u2} (AlgEquiv.{u1, max u1 u2, max u1 u2} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (CommRing.toCommSemiring.{u1} R _inst_1) (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) _inst_3 (fun (a : n) (b : n) => _inst_2 a b)) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) _inst_3 (fun (a : n) (b : n) => _inst_2 a b) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, max u2 u1} R (Matrix.{u2, u2, u1} n n R) (CommRing.toCommSemiring.{u1} R _inst_1) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b)) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R R _inst_3 (fun (a : n) (b : n) => _inst_2 a b) (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) _inst_3 (fun (a : n) (b : n) => _inst_2 a b)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (Semiring.toNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))))) (Module.toDistribMulAction.{u1, max u1 u2} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))))) (Algebra.toModule.{u1, max u1 u2} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) _inst_3 (fun (a : n) (b : n) => _inst_2 a b)) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) _inst_3 (fun (a : n) (b : n) => _inst_2 a b) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Module.toDistribMulAction.{u1, max u1 u2} R (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (Semiring.toNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b)))))) (Algebra.toModule.{u1, max u1 u2} R (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (Polynomial.algebraOfAlgebra.{u1, max u2 u1} R (Matrix.{u2, u2, u1} n n R) (CommRing.toCommSemiring.{u1} R _inst_1) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b)) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R R _inst_3 (fun (a : n) (b : n) => _inst_2 a b) (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u1, max u1 u2, max u1 u2, max u1 u2} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Polynomial.{max 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(CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, max u2 u1} R (Matrix.{u2, u2, u1} n n R) (CommRing.toCommSemiring.{u1} R _inst_1) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b)) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R R _inst_3 (fun (a : n) (b : n) => _inst_2 a b) (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AlgEquiv.{u1, max u1 u2, max u1 u2} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Polynomial.{max u1 u2} (Matrix.{u2, 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_inst_3 (fun (a : n) (b : n) => _inst_2 a b))))) (Matrix.{u2, u2, u1} n n R) (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (NonUnitalNonAssocSemiring.toMul.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Semiring.toNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))))) (NonUnitalNonAssocSemiring.toMul.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (Semiring.toNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (Polynomial.semiring.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b)))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, max u1 u2, max u1 u2} (RingHom.{max u1 u2, max u1 u2} (Matrix.{u2, u2, u1} n n R) (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (Semiring.toNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (Semiring.toNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (Polynomial.semiring.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))))) (Matrix.{u2, u2, u1} n n R) (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Semiring.toNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (Semiring.toNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (Polynomial.semiring.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, max u1 u2, max u1 u2} (RingHom.{max u1 u2, max u1 u2} (Matrix.{u2, u2, u1} n n R) (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (Semiring.toNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (Semiring.toNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (Polynomial.semiring.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))))) (Matrix.{u2, u2, u1} n n R) (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (Semiring.toNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (Semiring.toNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (Polynomial.semiring.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b)))) (RingHom.instRingHomClassRingHom.{max u1 u2, max u1 u2} (Matrix.{u2, u2, u1} n n R) (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (Semiring.toNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (Semiring.toNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (Polynomial.semiring.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b)))))))) (Polynomial.C.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) M))
+<too large>
 Case conversion may be inaccurate. Consider using '#align mat_poly_equiv_charmatrix matPolyEquiv_charmatrixₓ'. -/
 theorem matPolyEquiv_charmatrix (M : Matrix n n R) : matPolyEquiv (charmatrix M) = X - C M :=
   by

4280f5f3

bump to nightly-2023-05-24-06

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

fbc7b476

Diff

@@ -98,7 +98,7 @@ theorem charmatrix_apply_ne (M : Matrix n n R) (i j : n) (h : i ≠ j) :
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {n : Type.{u2}} [_inst_2 : DecidableEq.{succ u2} n] [_inst_3 : Fintype.{u2} n] (M : Matrix.{u2, u2, u1} n n R), Eq.{succ (max u2 u1)} (Polynomial.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (coeFn.{succ (max u2 u1), succ (max u2 u1)} (AlgEquiv.{u1, max u2 u1, max u2 u1} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Polynomial.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (CommRing.toCommSemiring.{u1} R _inst_1) (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) _inst_3 (fun (a : n) (b : n) => _inst_2 a b)) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (Matrix.algebra.{u1, u2, u1} n R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) _inst_3 (fun (a : n) (b : n) => _inst_2 a b) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, max u2 u1} R (Matrix.{u2, u2, u1} n n R) (CommRing.toCommSemiring.{u1} R _inst_1) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b)) (Matrix.algebra.{u1, u2, u1} n R R _inst_3 (fun (a : n) (b : n) => _inst_2 a b) (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (_x : AlgEquiv.{u1, max u2 u1, max u2 u1} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Polynomial.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (CommRing.toCommSemiring.{u1} R _inst_1) (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R 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(Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b)) (Matrix.algebra.{u1, u2, u1} n R R _inst_3 (fun (a : n) (b : n) => _inst_2 a b) (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) => (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) -> (Polynomial.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b)))) (AlgEquiv.hasCoeToFun.{u1, max u2 u1, max u2 u1} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Polynomial.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (CommRing.toCommSemiring.{u1} R _inst_1) (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) _inst_3 (fun (a : n) (b : n) => _inst_2 a b)) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (Matrix.algebra.{u1, u2, u1} n R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) _inst_3 (fun (a : n) (b : n) => _inst_2 a b) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, max u2 u1} R (Matrix.{u2, u2, u1} n n R) (CommRing.toCommSemiring.{u1} R _inst_1) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b)) (Matrix.algebra.{u1, u2, u1} n R R _inst_3 (fun (a : n) (b : n) => _inst_2 a b) (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (matPolyEquiv.{u2, u1} R (CommRing.toCommSemiring.{u1} R _inst_1) n (fun (a : n) (b : n) => _inst_2 a b) _inst_3) (charmatrix.{u1, u2} R _inst_1 n (fun (a : n) (b : n) => _inst_2 a b) _inst_3 M)) (HSub.hSub.{max u2 u1, max u2 u1, max u2 u1} (Polynomial.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (Polynomial.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (Polynomial.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (instHSub.{max u2 u1} (Polynomial.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (Polynomial.sub.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.ring.{u1, u2} n R _inst_3 (fun (a : n) (b : n) => _inst_2 a b) (CommRing.toRing.{u1} R _inst_1)))) (Polynomial.X.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (coeFn.{succ (max u2 u1), succ (max u2 u1)} (RingHom.{max u2 u1, max u2 u1} (Matrix.{u2, u2, u1} n n R) (Polynomial.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (Semiring.toNonAssocSemiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (Semiring.toNonAssocSemiring.{max u2 u1} (Polynomial.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))))) (fun (_x : RingHom.{max u2 u1, max u2 u1} (Matrix.{u2, u2, u1} n n R) (Polynomial.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (Semiring.toNonAssocSemiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (Semiring.toNonAssocSemiring.{max u2 u1} (Polynomial.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))))) => (Matrix.{u2, u2, u1} n n R) -> (Polynomial.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b)))) (RingHom.hasCoeToFun.{max u2 u1, max u2 u1} (Matrix.{u2, u2, u1} n n R) (Polynomial.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (Semiring.toNonAssocSemiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (Semiring.toNonAssocSemiring.{max u2 u1} (Polynomial.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))))) (Polynomial.C.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) M))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {n : Type.{u2}} [_inst_2 : DecidableEq.{succ u2} n] [_inst_3 : Fintype.{u2} n] (M : Matrix.{u2, u2, u1} n n R), Eq.{max (succ u1) (succ u2)} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) => Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (charmatrix.{u1, u2} R _inst_1 n (fun (a : n) (b : n) => _inst_2 a b) _inst_3 M)) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), max (succ u1) (succ u2)} (AlgEquiv.{u1, max u1 u2, max u1 u2} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (CommRing.toCommSemiring.{u1} R _inst_1) (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) _inst_3 (fun (a : n) (b : n) => _inst_2 a b)) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) _inst_3 (fun (a : n) (b : n) => _inst_2 a b) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, max u2 u1} R (Matrix.{u2, u2, u1} n n R) (CommRing.toCommSemiring.{u1} R _inst_1) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b)) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R R _inst_3 (fun (a : n) (b : n) => _inst_2 a b) (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (fun (_x : Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) => Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) _x) (SMulHomClass.toFunLike.{max u1 u2, u1, max u1 u2, max u1 u2} (AlgEquiv.{u1, max u1 u2, max u1 u2} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (CommRing.toCommSemiring.{u1} R _inst_1) (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) _inst_3 (fun (a : n) (b : n) => _inst_2 a b)) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) _inst_3 (fun (a : n) (b : n) => _inst_2 a b) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, max u2 u1} R (Matrix.{u2, u2, u1} n n R) (CommRing.toCommSemiring.{u1} R _inst_1) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b)) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R R _inst_3 (fun (a : n) (b : n) => _inst_2 a b) (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (SMulZeroClass.toSMul.{u1, max u1 u2} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddMonoid.toZero.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))))))) (DistribSMul.toSMulZeroClass.{u1, max u1 u2} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddMonoid.toAddZeroClass.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))))))) (DistribMulAction.toDistribSMul.{u1, max u1 u2} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) _inst_3 (fun (a : n) (b : n) => _inst_2 a b)))))) (Module.toDistribMulAction.{u1, max u1 u2} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))))) (Algebra.toModule.{u1, max u1 u2} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) _inst_3 (fun (a : n) (b : n) => _inst_2 a b)) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) _inst_3 (fun (a : n) (b : n) => _inst_2 a b) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))))) (SMulZeroClass.toSMul.{u1, max u1 u2} R (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (AddMonoid.toZero.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (AddCommMonoid.toAddMonoid.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (Semiring.toNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b)))))))) (DistribSMul.toSMulZeroClass.{u1, max u1 u2} R (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (AddMonoid.toAddZeroClass.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (AddCommMonoid.toAddMonoid.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (Semiring.toNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b)))))))) (DistribMulAction.toDistribSMul.{u1, max u1 u2} R (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (Semiring.toNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))))))) (Module.toDistribMulAction.{u1, max u1 u2} R (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (Semiring.toNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b)))))) (Algebra.toModule.{u1, max u1 u2} R (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (Polynomial.algebraOfAlgebra.{u1, max u2 u1} R (Matrix.{u2, u2, u1} n n R) (CommRing.toCommSemiring.{u1} R _inst_1) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b)) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R R _inst_3 (fun (a : n) (b : n) => _inst_2 a b) (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))))) (DistribMulActionHomClass.toSMulHomClass.{max u1 u2, u1, max u1 u2, max u1 u2} (AlgEquiv.{u1, max u1 u2, max u1 u2} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (CommRing.toCommSemiring.{u1} R _inst_1) (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) _inst_3 (fun (a : n) (b : n) => _inst_2 a b)) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) _inst_3 (fun (a : n) (b : n) => _inst_2 a b) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, max u2 u1} R (Matrix.{u2, u2, u1} n n R) (CommRing.toCommSemiring.{u1} R _inst_1) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b)) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R R _inst_3 (fun (a : n) (b : n) => _inst_2 a b) (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) _inst_3 (fun (a : n) (b : n) => _inst_2 a b)))))) (AddCommMonoid.toAddMonoid.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (Semiring.toNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))))))) (Module.toDistribMulAction.{u1, max u1 u2} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))))) (Algebra.toModule.{u1, max u1 u2} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) _inst_3 (fun (a : n) (b : n) => _inst_2 a b)) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) _inst_3 (fun (a : n) (b : n) => _inst_2 a b) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Module.toDistribMulAction.{u1, max u1 u2} R (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (Semiring.toNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b)))))) (Algebra.toModule.{u1, max u1 u2} R (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (Polynomial.algebraOfAlgebra.{u1, max u2 u1} R (Matrix.{u2, u2, u1} n n R) (CommRing.toCommSemiring.{u1} R _inst_1) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b)) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R R _inst_3 (fun (a : n) (b : n) => _inst_2 a b) (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u1 u2, u1, max u1 u2, max u1 u2} (AlgEquiv.{u1, max u1 u2, max u1 u2} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (CommRing.toCommSemiring.{u1} R _inst_1) (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) _inst_3 (fun (a : n) (b : n) => _inst_2 a b)) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) _inst_3 (fun (a : n) (b : n) => _inst_2 a b) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, max u2 u1} R (Matrix.{u2, u2, u1} n n R) (CommRing.toCommSemiring.{u1} R _inst_1) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b)) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R R _inst_3 (fun (a : n) (b : n) => _inst_2 a b) (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) _inst_3 (fun (a : n) (b : n) => _inst_2 a b)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (Semiring.toNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))))) (Module.toDistribMulAction.{u1, max u1 u2} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))))) (Algebra.toModule.{u1, max u1 u2} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) _inst_3 (fun (a : n) (b : n) => _inst_2 a b)) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) _inst_3 (fun (a : n) (b : n) => _inst_2 a b) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Module.toDistribMulAction.{u1, max u1 u2} R (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (Semiring.toNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b)))))) (Algebra.toModule.{u1, max u1 u2} R (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (Polynomial.algebraOfAlgebra.{u1, max u2 u1} R (Matrix.{u2, u2, u1} n n R) (CommRing.toCommSemiring.{u1} R _inst_1) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b)) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R R _inst_3 (fun (a : n) (b : n) => _inst_2 a b) (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u1, max u1 u2, max u1 u2, max u1 u2} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (CommRing.toCommSemiring.{u1} R _inst_1) (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) _inst_3 (fun (a : n) (b : n) => _inst_2 a b)) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) _inst_3 (fun (a : n) (b : n) => _inst_2 a b) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, max u2 u1} R (Matrix.{u2, u2, u1} n n R) (CommRing.toCommSemiring.{u1} R _inst_1) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b)) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R R _inst_3 (fun (a : n) (b : n) => _inst_2 a b) (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AlgEquiv.{u1, max u1 u2, max u1 u2} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (CommRing.toCommSemiring.{u1} R _inst_1) (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) _inst_3 (fun (a : n) (b : n) => _inst_2 a b)) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) _inst_3 (fun (a : n) (b : n) => _inst_2 a b) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R 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(Semiring.toNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (Semiring.toNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (Polynomial.semiring.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, max u1 u2, max u1 u2} (RingHom.{max u1 u2, max u1 u2} (Matrix.{u2, u2, u1} n n R) (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (Semiring.toNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (Semiring.toNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (Polynomial.semiring.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))))) (Matrix.{u2, u2, u1} n n R) (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (Semiring.toNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (Semiring.toNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (Polynomial.semiring.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b)))) (RingHom.instRingHomClassRingHom.{max u1 u2, max u1 u2} (Matrix.{u2, u2, u1} n n R) (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (Semiring.toNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (Semiring.toNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (Polynomial.semiring.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b)))))))) (Polynomial.C.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) M))
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {n : Type.{u2}} [_inst_2 : DecidableEq.{succ u2} n] [_inst_3 : Fintype.{u2} n] (M : Matrix.{u2, u2, u1} n n R), Eq.{max (succ u1) (succ u2)} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) => Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (charmatrix.{u1, u2} R _inst_1 n (fun (a : n) (b : n) => _inst_2 a b) _inst_3 M)) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), max (succ u1) (succ u2)} (AlgEquiv.{u1, max u1 u2, max u1 u2} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (CommRing.toCommSemiring.{u1} R _inst_1) (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) _inst_3 (fun (a : n) (b : n) => _inst_2 a b)) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) _inst_3 (fun (a : n) (b : n) => _inst_2 a b) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, max u2 u1} R (Matrix.{u2, u2, u1} n n R) (CommRing.toCommSemiring.{u1} R _inst_1) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b)) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R R _inst_3 (fun (a : n) (b : n) => _inst_2 a b) (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (fun (_x : Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) => Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) _x) (SMulHomClass.toFunLike.{max u1 u2, u1, max u1 u2, max u1 u2} (AlgEquiv.{u1, max u1 u2, max u1 u2} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (CommRing.toCommSemiring.{u1} R _inst_1) (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) _inst_3 (fun (a : n) (b : n) => _inst_2 a b)) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) _inst_3 (fun (a : n) (b : n) => _inst_2 a b) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, max u2 u1} R (Matrix.{u2, u2, u1} n n R) (CommRing.toCommSemiring.{u1} R _inst_1) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b)) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R R _inst_3 (fun (a : n) (b : n) => _inst_2 a b) (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (SMulZeroClass.toSMul.{u1, max u1 u2} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddMonoid.toZero.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))))))) (DistribSMul.toSMulZeroClass.{u1, max u1 u2} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddMonoid.toAddZeroClass.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))))))) (DistribMulAction.toDistribSMul.{u1, max u1 u2} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) _inst_3 (fun (a : n) (b : n) => _inst_2 a b)))))) (Module.toDistribMulAction.{u1, max u1 u2} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))))) (Algebra.toModule.{u1, max u1 u2} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) _inst_3 (fun (a : n) (b : n) => _inst_2 a b)) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) _inst_3 (fun (a : n) (b : n) => _inst_2 a b) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))))) (SMulZeroClass.toSMul.{u1, max u1 u2} R (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (AddMonoid.toZero.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (AddCommMonoid.toAddMonoid.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (Semiring.toNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b)))))))) (DistribSMul.toSMulZeroClass.{u1, max u1 u2} R (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (AddMonoid.toAddZeroClass.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (AddCommMonoid.toAddMonoid.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (Semiring.toNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b)))))))) (DistribMulAction.toDistribSMul.{u1, max u1 u2} R (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (Semiring.toNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))))))) (Module.toDistribMulAction.{u1, max u1 u2} R (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (Semiring.toNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b)))))) (Algebra.toModule.{u1, max u1 u2} R (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (Polynomial.algebraOfAlgebra.{u1, max u2 u1} R (Matrix.{u2, u2, u1} n n R) (CommRing.toCommSemiring.{u1} R _inst_1) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b)) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R R _inst_3 (fun (a : n) (b : n) => _inst_2 a b) (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))))) (DistribMulActionHomClass.toSMulHomClass.{max u1 u2, u1, max u1 u2, max u1 u2} (AlgEquiv.{u1, max u1 u2, max u1 u2} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (CommRing.toCommSemiring.{u1} R _inst_1) (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) _inst_3 (fun (a : n) (b : n) => _inst_2 a b)) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) _inst_3 (fun (a : n) (b : n) => _inst_2 a b) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, max u2 u1} R (Matrix.{u2, u2, u1} n n R) (CommRing.toCommSemiring.{u1} R _inst_1) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b)) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R R _inst_3 (fun (a : n) (b : n) => _inst_2 a b) (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) _inst_3 (fun (a : n) (b : n) => _inst_2 a b)))))) (AddCommMonoid.toAddMonoid.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (Semiring.toNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))))))) (Module.toDistribMulAction.{u1, max u1 u2} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))))) (Algebra.toModule.{u1, max u1 u2} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) _inst_3 (fun (a : n) (b : n) => _inst_2 a b)) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) _inst_3 (fun (a : n) (b : n) => _inst_2 a b) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Module.toDistribMulAction.{u1, max u1 u2} R (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (Semiring.toNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b)))))) (Algebra.toModule.{u1, max u1 u2} R (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (Polynomial.algebraOfAlgebra.{u1, max u2 u1} R (Matrix.{u2, u2, u1} n n R) (CommRing.toCommSemiring.{u1} R _inst_1) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b)) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R R _inst_3 (fun (a : n) (b : n) => _inst_2 a b) (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u1 u2, u1, max u1 u2, max u1 u2} (AlgEquiv.{u1, max u1 u2, max u1 u2} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (CommRing.toCommSemiring.{u1} R _inst_1) (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) _inst_3 (fun (a : n) (b : n) => _inst_2 a b)) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) _inst_3 (fun (a : n) (b : n) => _inst_2 a b) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, max u2 u1} R (Matrix.{u2, u2, u1} n n R) (CommRing.toCommSemiring.{u1} R _inst_1) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b)) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R R _inst_3 (fun (a : n) (b : n) => _inst_2 a b) (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) _inst_3 (fun (a : n) (b : n) => _inst_2 a b)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (Semiring.toNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))))) (Module.toDistribMulAction.{u1, max u1 u2} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))))) (Algebra.toModule.{u1, max u1 u2} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) _inst_3 (fun (a : n) (b : n) => _inst_2 a b)) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) _inst_3 (fun (a : n) (b : n) => _inst_2 a b) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Module.toDistribMulAction.{u1, max u1 u2} R (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (Semiring.toNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b)))))) (Algebra.toModule.{u1, max u1 u2} R (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (Polynomial.algebraOfAlgebra.{u1, max u2 u1} R (Matrix.{u2, u2, u1} n n R) (CommRing.toCommSemiring.{u1} R _inst_1) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b)) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R R _inst_3 (fun (a : n) (b : n) => _inst_2 a b) (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u1, max u1 u2, max u1 u2, max u1 u2} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (CommRing.toCommSemiring.{u1} R _inst_1) (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) _inst_3 (fun (a : n) (b : n) => _inst_2 a b)) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) _inst_3 (fun (a : n) (b : n) => _inst_2 a b) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, max u2 u1} R (Matrix.{u2, u2, u1} n n R) (CommRing.toCommSemiring.{u1} R _inst_1) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b)) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R R _inst_3 (fun (a : n) (b : n) => _inst_2 a b) (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AlgEquiv.{u1, max u1 u2, max u1 u2} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (CommRing.toCommSemiring.{u1} R _inst_1) (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) _inst_3 (fun (a : n) (b : n) => _inst_2 a b)) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) _inst_3 (fun (a : n) (b : n) => _inst_2 a b) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, max u2 u1} R (Matrix.{u2, u2, u1} n n R) (CommRing.toCommSemiring.{u1} R _inst_1) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b)) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R R _inst_3 (fun (a : n) (b : n) => _inst_2 a b) (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (AlgEquivClass.toAlgHomClass.{max u1 u2, u1, max u1 u2, max u1 u2} (AlgEquiv.{u1, max u1 u2, max u1 u2} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R 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u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (Semiring.toNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (Semiring.toNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (Polynomial.semiring.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b)))) (RingHom.instRingHomClassRingHom.{max u1 u2, max u1 u2} (Matrix.{u2, u2, u1} n n R) (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (Semiring.toNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (Semiring.toNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (Polynomial.semiring.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b)))))))) (Polynomial.C.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) M))
 Case conversion may be inaccurate. Consider using '#align mat_poly_equiv_charmatrix matPolyEquiv_charmatrixₓ'. -/
 theorem matPolyEquiv_charmatrix (M : Matrix n n R) : matPolyEquiv (charmatrix M) = X - C M :=
   by

4280f5f3

bump to nightly-2023-05-23-03

mathlib commit https://github.com/leanprover-community/mathlib/commit/75e7fca56381d056096ce5d05e938f63a6567828

ed98987c

Diff

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Scott Morrison
 
 ! This file was ported from Lean 3 source module linear_algebra.matrix.charpoly.basic
-! leanprover-community/mathlib commit 70fd9563a21e7b963887c9360bd29b2393e6225a
+! leanprover-community/mathlib commit 4280f5f32e16755ec7985ce11e189b6cd6ff6735
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -16,6 +16,9 @@ import Mathbin.Tactic.Squeeze
 /-!
 # Characteristic polynomials and the Cayley-Hamilton theorem
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 We define characteristic polynomials of matrices and
 prove the Cayley–Hamilton theorem over arbitrary commutative rings.

70fd9563

bump to nightly-2023-05-21-14

mathlib commit https://github.com/leanprover-community/mathlib/commit/33c67ae661dd8988516ff7f247b0be3018cdd952

876ce566

Diff

@@ -45,18 +45,32 @@ variable {n : Type w} [DecidableEq n] [Fintype n]
 
 open Finset
 
+#print charmatrix /-
 /-- The "characteristic matrix" of `M : matrix n n R` is the matrix of polynomials $t I - M$.
 The determinant of this matrix is the characteristic polynomial.
 -/
 def charmatrix (M : Matrix n n R) : Matrix n n R[X] :=
   Matrix.scalar n (X : R[X]) - (C : R →+* R[X]).mapMatrix M
 #align charmatrix charmatrix
+-/
 
+/- warning: charmatrix_apply -> charmatrix_apply is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align charmatrix_apply charmatrix_applyₓ'. -/
 theorem charmatrix_apply (M : Matrix n n R) (i j : n) :
     charmatrix M i j = X * (1 : Matrix n n R[X]) i j - C (M i j) :=
   rfl
 #align charmatrix_apply charmatrix_apply
 
+/- warning: charmatrix_apply_eq -> charmatrix_apply_eq is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {n : Type.{u2}} [_inst_2 : DecidableEq.{succ u2} n] [_inst_3 : Fintype.{u2} n] (M : Matrix.{u2, u2, u1} n n R) (i : n), Eq.{succ u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (charmatrix.{u1, u2} R _inst_1 n (fun (a : n) (b : n) => _inst_2 a b) _inst_3 M i i) (HSub.hSub.{u1, u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (M i i)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (instHSub.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.sub.{u1} R (CommRing.toRing.{u1} R _inst_1))) (Polynomial.X.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) 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+Case conversion may be inaccurate. Consider using '#align charmatrix_apply_eq charmatrix_apply_eqₓ'. -/
 @[simp]
 theorem charmatrix_apply_eq (M : Matrix n n R) (i : n) :
     charmatrix M i i = (X : R[X]) - C (M i i) := by
@@ -64,6 +78,12 @@ theorem charmatrix_apply_eq (M : Matrix n n R) (i : n) :
     map_apply, DMatrix.sub_apply]
 #align charmatrix_apply_eq charmatrix_apply_eq
 
+/- warning: charmatrix_apply_ne -> charmatrix_apply_ne is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align charmatrix_apply_ne charmatrix_apply_neₓ'. -/
 @[simp]
 theorem charmatrix_apply_ne (M : Matrix n n R) (i j : n) (h : i ≠ j) :
     charmatrix M i j = -C (M i j) := by
@@ -71,6 +91,12 @@ theorem charmatrix_apply_ne (M : Matrix n n R) (i j : n) (h : i ≠ j) :
     map_apply, DMatrix.sub_apply]
 #align charmatrix_apply_ne charmatrix_apply_ne
 
+/- warning: mat_poly_equiv_charmatrix -> matPolyEquiv_charmatrix is a dubious translation:
+lean 3 declaration is
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(Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b)) (Matrix.algebra.{u1, u2, u1} n R R _inst_3 (fun (a : n) (b : n) => _inst_2 a b) (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (fun (_x : AlgEquiv.{u1, max u2 u1, max u2 u1} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Polynomial.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (CommRing.toCommSemiring.{u1} R _inst_1) (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) _inst_3 (fun (a : n) (b : n) => _inst_2 a b)) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (Matrix.algebra.{u1, u2, u1} n R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) _inst_3 (fun (a : n) (b : n) => _inst_2 a b) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, max u2 u1} R (Matrix.{u2, u2, u1} n n R) (CommRing.toCommSemiring.{u1} R _inst_1) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b)) (Matrix.algebra.{u1, u2, u1} n R R _inst_3 (fun (a : n) (b : n) => _inst_2 a b) (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) => (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) -> (Polynomial.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b)))) (AlgEquiv.hasCoeToFun.{u1, max u2 u1, max u2 u1} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Polynomial.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (CommRing.toCommSemiring.{u1} R _inst_1) (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) _inst_3 (fun (a : n) (b : n) => _inst_2 a b)) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (Matrix.algebra.{u1, u2, u1} n R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) _inst_3 (fun (a : n) (b : n) => _inst_2 a b) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, max u2 u1} R (Matrix.{u2, u2, u1} n n R) (CommRing.toCommSemiring.{u1} R _inst_1) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b)) (Matrix.algebra.{u1, u2, u1} n R R _inst_3 (fun (a : n) (b : n) => _inst_2 a b) (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) (matPolyEquiv.{u2, u1} R (CommRing.toCommSemiring.{u1} R _inst_1) n (fun (a : n) (b : n) => _inst_2 a b) _inst_3) (charmatrix.{u1, u2} R _inst_1 n (fun (a : n) (b : n) => _inst_2 a b) _inst_3 M)) (HSub.hSub.{max u2 u1, max u2 u1, max u2 u1} (Polynomial.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (Polynomial.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (Polynomial.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (instHSub.{max u2 u1} (Polynomial.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (Polynomial.sub.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.ring.{u1, u2} n R _inst_3 (fun (a : n) (b : n) => _inst_2 a b) (CommRing.toRing.{u1} R _inst_1)))) (Polynomial.X.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (coeFn.{succ (max u2 u1), succ (max u2 u1)} (RingHom.{max u2 u1, max u2 u1} (Matrix.{u2, u2, u1} n n R) (Polynomial.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (Semiring.toNonAssocSemiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (Semiring.toNonAssocSemiring.{max u2 u1} (Polynomial.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))))) (fun (_x : RingHom.{max u2 u1, max u2 u1} (Matrix.{u2, u2, u1} n n R) (Polynomial.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (Semiring.toNonAssocSemiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (Semiring.toNonAssocSemiring.{max u2 u1} (Polynomial.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))))) => (Matrix.{u2, u2, u1} n n R) -> (Polynomial.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b)))) (RingHom.hasCoeToFun.{max u2 u1, max u2 u1} (Matrix.{u2, u2, u1} n n R) (Polynomial.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (Semiring.toNonAssocSemiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (Semiring.toNonAssocSemiring.{max u2 u1} (Polynomial.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))))) (Polynomial.C.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) M))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_1 : CommRing.{u1} R] {n : Type.{u2}} [_inst_2 : DecidableEq.{succ u2} n] [_inst_3 : Fintype.{u2} n] (M : Matrix.{u2, u2, u1} n n R), Eq.{max (succ u1) (succ u2)} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) => Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (charmatrix.{u1, u2} R _inst_1 n (fun (a : n) (b : n) => _inst_2 a b) _inst_3 M)) (FunLike.coe.{max (succ u1) (succ u2), max (succ u1) (succ u2), max (succ u1) (succ u2)} (AlgEquiv.{u1, max u1 u2, max u1 u2} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (CommRing.toCommSemiring.{u1} R _inst_1) (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) _inst_3 (fun (a : n) (b : n) => _inst_2 a b)) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) _inst_3 (fun (a : n) (b : n) => _inst_2 a b) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) 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_inst_1)))) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) => Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) _x) (SMulHomClass.toFunLike.{max u1 u2, u1, max u1 u2, max u1 u2} (AlgEquiv.{u1, max u1 u2, max u1 u2} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (CommRing.toCommSemiring.{u1} R _inst_1) (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) _inst_3 (fun (a : n) (b : n) => _inst_2 a b)) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) _inst_3 (fun (a : n) (b : n) => _inst_2 a b) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, max u2 u1} R (Matrix.{u2, u2, u1} n n R) (CommRing.toCommSemiring.{u1} R _inst_1) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b)) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R R _inst_3 (fun (a : n) (b : n) => _inst_2 a b) (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (SMulZeroClass.toSMul.{u1, max u1 u2} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddMonoid.toZero.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))))))) (DistribSMul.toSMulZeroClass.{u1, max u1 u2} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddMonoid.toAddZeroClass.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))))))) (DistribMulAction.toDistribSMul.{u1, max u1 u2} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) _inst_3 (fun (a : n) (b : n) => _inst_2 a b)))))) (Module.toDistribMulAction.{u1, max u1 u2} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))))) (Algebra.toModule.{u1, max u1 u2} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) _inst_3 (fun (a : n) (b : n) => _inst_2 a b)) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) _inst_3 (fun (a : n) (b : n) => _inst_2 a b) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))))) (SMulZeroClass.toSMul.{u1, max u1 u2} R (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (AddMonoid.toZero.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (AddCommMonoid.toAddMonoid.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (Semiring.toNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b)))))))) (DistribSMul.toSMulZeroClass.{u1, max u1 u2} R (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (AddMonoid.toAddZeroClass.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (AddCommMonoid.toAddMonoid.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (Semiring.toNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b)))))))) (DistribMulAction.toDistribSMul.{u1, max u1 u2} R (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (Semiring.toNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))))))) (Module.toDistribMulAction.{u1, max u1 u2} R (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (Semiring.toNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b)))))) (Algebra.toModule.{u1, max u1 u2} R (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (Polynomial.algebraOfAlgebra.{u1, max u2 u1} R (Matrix.{u2, u2, u1} n n R) (CommRing.toCommSemiring.{u1} R _inst_1) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b)) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R R _inst_3 (fun (a : n) (b : n) => _inst_2 a b) (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))))))) (DistribMulActionHomClass.toSMulHomClass.{max u1 u2, u1, max u1 u2, max u1 u2} (AlgEquiv.{u1, max u1 u2, max u1 u2} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (CommRing.toCommSemiring.{u1} R _inst_1) (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) _inst_3 (fun (a : n) (b : n) => _inst_2 a b)) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) _inst_3 (fun (a : n) (b : n) => _inst_2 a b) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, max u2 u1} R (Matrix.{u2, u2, u1} n n R) (CommRing.toCommSemiring.{u1} R _inst_1) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b)) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R R _inst_3 (fun (a : n) (b : n) => _inst_2 a b) (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (AddCommMonoid.toAddMonoid.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) _inst_3 (fun (a : n) (b : n) => _inst_2 a b)))))) (AddCommMonoid.toAddMonoid.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (Semiring.toNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))))))) (Module.toDistribMulAction.{u1, max u1 u2} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))))) (Algebra.toModule.{u1, max u1 u2} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) _inst_3 (fun (a : n) (b : n) => _inst_2 a b)) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) _inst_3 (fun (a : n) (b : n) => _inst_2 a b) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Module.toDistribMulAction.{u1, max u1 u2} R (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (Semiring.toNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b)))))) (Algebra.toModule.{u1, max u1 u2} R (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (Polynomial.algebraOfAlgebra.{u1, max u2 u1} R (Matrix.{u2, u2, u1} n n R) (CommRing.toCommSemiring.{u1} R _inst_1) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b)) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R R _inst_3 (fun (a : n) (b : n) => _inst_2 a b) (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u1 u2, u1, max u1 u2, max u1 u2} (AlgEquiv.{u1, max u1 u2, max u1 u2} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (CommRing.toCommSemiring.{u1} R _inst_1) (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) _inst_3 (fun (a : n) (b : n) => _inst_2 a b)) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) _inst_3 (fun (a : n) (b : n) => _inst_2 a b) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Polynomial.algebraOfAlgebra.{u1, max u2 u1} R (Matrix.{u2, u2, u1} n n R) (CommRing.toCommSemiring.{u1} R _inst_1) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b)) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R R _inst_3 (fun (a : n) (b : n) => _inst_2 a b) (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))))) R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) _inst_3 (fun (a : n) (b : n) => _inst_2 a b)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (Semiring.toNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (Polynomial.semiring.{max u2 u1} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))))) (Module.toDistribMulAction.{u1, max u1 u2} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Semiring.toNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))))) (Algebra.toModule.{u1, max u1 u2} R (Matrix.{u2, u2, u1} n n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))) (CommRing.toCommSemiring.{u1} R _inst_1) (Matrix.semiring.{u1, u2} n (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) _inst_3 (fun (a : n) (b : n) => _inst_2 a b)) (Matrix.instAlgebraMatrixSemiring.{u1, u2, u1} n R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) _inst_3 (fun (a : n) (b : n) => _inst_2 a b) (CommRing.toCommSemiring.{u1} R _inst_1) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1))) (Polynomial.algebraOfAlgebra.{u1, u1} R R (CommRing.toCommSemiring.{u1} R _inst_1) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (Algebra.id.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)))))) (Module.toDistribMulAction.{u1, max u1 u2} R (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R 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(charmatrix.{u1, u2} R _inst_1 n (fun (a : n) (b : n) => _inst_2 a b) _inst_3 M)) (instHSub.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (Polynomial.sub.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.instRingMatrix.{u1, u2} n R _inst_3 (fun (a : n) (b : n) => _inst_2 a b) (CommRing.toRing.{u1} R _inst_1)))) (Polynomial.X.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (FunLike.coe.{succ (max u1 u2), succ (max u1 u2), succ (max u1 u2)} (RingHom.{max u1 u2, max u1 u2} (Matrix.{u2, u2, u1} n n R) (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (Semiring.toNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (Semiring.toNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (Polynomial.semiring.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))))) (Matrix.{u2, u2, u1} n n R) (fun (_x : Matrix.{u2, u2, u1} n n R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : Matrix.{u2, u2, u1} n n R) => Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) _x) (MulHomClass.toFunLike.{max u1 u2, max u1 u2, max u1 u2} (RingHom.{max u1 u2, max u1 u2} (Matrix.{u2, u2, u1} n n R) (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (Semiring.toNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (Semiring.toNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (Polynomial.semiring.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))))) (Matrix.{u2, u2, u1} n n R) (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (NonUnitalNonAssocSemiring.toMul.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Semiring.toNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))))) (NonUnitalNonAssocSemiring.toMul.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (Semiring.toNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (Polynomial.semiring.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b)))))) (NonUnitalRingHomClass.toMulHomClass.{max u1 u2, max u1 u2, max u1 u2} (RingHom.{max u1 u2, max u1 u2} (Matrix.{u2, u2, u1} n n R) (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (Semiring.toNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (Semiring.toNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (Polynomial.semiring.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))))) (Matrix.{u2, u2, u1} n n R) (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Semiring.toNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (Semiring.toNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (Polynomial.semiring.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))))) (RingHomClass.toNonUnitalRingHomClass.{max u1 u2, max u1 u2, max u1 u2} (RingHom.{max u1 u2, max u1 u2} (Matrix.{u2, u2, u1} n n R) (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (Semiring.toNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (Semiring.toNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (Polynomial.semiring.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))))) (Matrix.{u2, u2, u1} n n R) (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (Semiring.toNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (Semiring.toNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (Polynomial.semiring.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b)))) (RingHom.instRingHomClassRingHom.{max u1 u2, max u1 u2} (Matrix.{u2, u2, u1} n n R) (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (Semiring.toNonAssocSemiring.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (Semiring.toNonAssocSemiring.{max u1 u2} (Polynomial.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) (Polynomial.semiring.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b)))))))) (Polynomial.C.{max u1 u2} (Matrix.{u2, u2, u1} n n R) (Matrix.semiring.{u1, u2} n R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) _inst_3 (fun (a : n) (b : n) => _inst_2 a b))) M))
+Case conversion may be inaccurate. Consider using '#align mat_poly_equiv_charmatrix matPolyEquiv_charmatrixₓ'. -/
 theorem matPolyEquiv_charmatrix (M : Matrix n n R) : matPolyEquiv (charmatrix M) = X - C M :=
   by
   ext (k i j)
@@ -84,6 +110,7 @@ theorem matPolyEquiv_charmatrix (M : Matrix n n R) : matPolyEquiv (charmatrix M)
     split_ifs <;> simp [h]
 #align mat_poly_equiv_charmatrix matPolyEquiv_charmatrix
 
+#print charmatrix_reindex /-
 theorem charmatrix_reindex {m : Type v} [DecidableEq m] [Fintype m] (e : n ≃ m) (M : Matrix n n R) :
     charmatrix (reindex e e M) = reindex e e (charmatrix M) :=
   by
@@ -91,20 +118,26 @@ theorem charmatrix_reindex {m : Type v} [DecidableEq m] [Fintype m] (e : n ≃ m
   by_cases h : i = j
   all_goals simp [h]
 #align charmatrix_reindex charmatrix_reindex
+-/
 
+#print Matrix.charpoly /-
 /-- The characteristic polynomial of a matrix `M` is given by $\det (t I - M)$.
 -/
 def Matrix.charpoly (M : Matrix n n R) : R[X] :=
   (charmatrix M).det
 #align matrix.charpoly Matrix.charpoly
+-/
 
+#print Matrix.charpoly_reindex /-
 theorem Matrix.charpoly_reindex {m : Type v} [DecidableEq m] [Fintype m] (e : n ≃ m)
     (M : Matrix n n R) : (reindex e e M).charpoly = M.charpoly :=
   by
   unfold Matrix.charpoly
   rw [charmatrix_reindex, Matrix.det_reindex_self]
 #align matrix.charpoly_reindex Matrix.charpoly_reindex
+-/
 
+#print Matrix.aeval_self_charpoly /-
 -- This proof follows http://drorbn.net/AcademicPensieve/2015-12/CayleyHamilton.pdf
 /-- The **Cayley-Hamilton Theorem**, that the characteristic polynomial of a matrix,
 applied to the matrix itself, is zero.
@@ -136,4 +169,5 @@ theorem Matrix.aeval_self_charpoly (M : Matrix n n R) : aeval M M.charpoly = 0 :
   -- Thus we have $χ_M(M) = 0$, which is the desired result.
   exact h
 #align matrix.aeval_self_charpoly Matrix.aeval_self_charpoly
+-/

70fd9563

bump to nightly-2023-03-08-10

mathlib commit https://github.com/leanprover-community/mathlib/commit/38f16f960f5006c6c0c2bac7b0aba5273188f4e5

422cc012

Diff

@@ -49,29 +49,29 @@ open Finset
 The determinant of this matrix is the characteristic polynomial.
 -/
 def charmatrix (M : Matrix n n R) : Matrix n n R[X] :=
-  Matrix.scalar n (x : R[X]) - (c : R →+* R[X]).mapMatrix M
+  Matrix.scalar n (X : R[X]) - (C : R →+* R[X]).mapMatrix M
 #align charmatrix charmatrix
 
 theorem charmatrix_apply (M : Matrix n n R) (i j : n) :
-    charmatrix M i j = x * (1 : Matrix n n R[X]) i j - c (M i j) :=
+    charmatrix M i j = X * (1 : Matrix n n R[X]) i j - C (M i j) :=
   rfl
 #align charmatrix_apply charmatrix_apply
 
 @[simp]
 theorem charmatrix_apply_eq (M : Matrix n n R) (i : n) :
-    charmatrix M i i = (x : R[X]) - c (M i i) := by
+    charmatrix M i i = (X : R[X]) - C (M i i) := by
   simp only [charmatrix, sub_left_inj, Pi.sub_apply, scalar_apply_eq, RingHom.mapMatrix_apply,
     map_apply, DMatrix.sub_apply]
 #align charmatrix_apply_eq charmatrix_apply_eq
 
 @[simp]
 theorem charmatrix_apply_ne (M : Matrix n n R) (i j : n) (h : i ≠ j) :
-    charmatrix M i j = -c (M i j) := by
+    charmatrix M i j = -C (M i j) := by
   simp only [charmatrix, Pi.sub_apply, scalar_apply_ne _ _ _ h, zero_sub, RingHom.mapMatrix_apply,
     map_apply, DMatrix.sub_apply]
 #align charmatrix_apply_ne charmatrix_apply_ne
 
-theorem matPolyEquiv_charmatrix (M : Matrix n n R) : matPolyEquiv (charmatrix M) = x - c M :=
+theorem matPolyEquiv_charmatrix (M : Matrix n n R) : matPolyEquiv (charmatrix M) = X - C M :=
   by
   ext (k i j)
   simp only [matPolyEquiv_coeff_apply, coeff_sub, Pi.sub_apply]

70fd9563

bump to nightly-2023-02-21-16

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

1107b979

Changes in mathlib4

mathlib3

mathlib4

70fd9563

chore: tidy various files (#12316)

dbc20eec

Diff

@@ -25,10 +25,6 @@ See the file `Mathlib/LinearAlgebra/Matrix/Charpoly/Coeff.lean` for corollaries
 We follow a nice proof from http://drorbn.net/AcademicPensieve/2015-12/CayleyHamilton.pdf
 -/
 
--- Porting note: these imports are no longer needed
---import Mathlib.Tactic.ApplyFun
---import Mathlib.Tactic.Squeeze
-
 noncomputable section
 
 universe u v w
@@ -112,8 +108,8 @@ theorem charpoly_reindex (e : n ≃ m)
 
 lemma charpoly_map (M : Matrix n n R) (f : R →+* S) :
     (M.map f).charpoly = M.charpoly.map f := by
-  rw [charpoly, charmatrix_map, ← Polynomial.coe_mapRingHom, charpoly, RingHom.map_det]
-  rfl
+  rw [charpoly, charmatrix_map, ← Polynomial.coe_mapRingHom, charpoly, RingHom.map_det,
+    RingHom.mapMatrix_apply]
 
 @[simp]
 lemma charpoly_fromBlocks_zero₁₂ :

70fd9563

chore(LinearAlgebra/Matrix/Charpoly): fix swapped lines (#12162)

58b254ee

Diff

@@ -114,8 +114,8 @@ lemma charpoly_map (M : Matrix n n R) (f : R →+* S) :
     (M.map f).charpoly = M.charpoly.map f := by
   rw [charpoly, charmatrix_map, ← Polynomial.coe_mapRingHom, charpoly, RingHom.map_det]
   rfl
-@[simp]
 
+@[simp]
 lemma charpoly_fromBlocks_zero₁₂ :
     (fromBlocks M₁₁ 0 M₂₁ M₂₂).charpoly = (M₁₁.charpoly * M₂₂.charpoly) := by
   simp only [charpoly, charmatrix_fromBlocks, Matrix.map_zero _ (Polynomial.C_0), neg_zero,

70fd9563

style: homogenise porting notes (#11145)

Homogenises porting notes via capitalisation and addition of whitespace.

It makes the following changes:

converts "--porting note" into "-- Porting note";
converts "porting note" into "Porting note".

8be0b69c

Diff

@@ -25,7 +25,7 @@ See the file `Mathlib/LinearAlgebra/Matrix/Charpoly/Coeff.lean` for corollaries
 We follow a nice proof from http://drorbn.net/AcademicPensieve/2015-12/CayleyHamilton.pdf
 -/
 
--- porting note: these imports are no longer needed
+-- Porting note: these imports are no longer needed
 --import Mathlib.Tactic.ApplyFun
 --import Mathlib.Tactic.Squeeze

70fd9563

chore(LinearAlgebra/Matrix/Charpoly): place more decls in Matrix namespace (#10488)

9f7fef49

Diff

@@ -33,39 +33,40 @@ noncomputable section
 
 universe u v w
 
-open Polynomial Matrix BigOperators Polynomial
+namespace Matrix
+
+open BigOperators Finset Matrix Polynomial
 
 variable {R S : Type*} [CommRing R] [CommRing S]
 variable {m n : Type*} [DecidableEq m] [DecidableEq n] [Fintype m] [Fintype n]
 variable (M₁₁ : Matrix m m R) (M₁₂ : Matrix m n R) (M₂₁ : Matrix n m R) (M₂₂ M : Matrix n n R)
 variable (i j : n)
 
-open Finset
 
 /-- The "characteristic matrix" of `M : Matrix n n R` is the matrix of polynomials $t I - M$.
 The determinant of this matrix is the characteristic polynomial.
 -/
 def charmatrix (M : Matrix n n R) : Matrix n n R[X] :=
   Matrix.scalar n (X : R[X]) - (C : R →+* R[X]).mapMatrix M
-#align charmatrix charmatrix
+#align charmatrix Matrix.charmatrix
 
 theorem charmatrix_apply :
     charmatrix M i j = (Matrix.diagonal fun _ : n => X) i j - C (M i j) :=
   rfl
-#align charmatrix_apply charmatrix_apply
+#align charmatrix_apply Matrix.charmatrix_apply
 
 @[simp]
 theorem charmatrix_apply_eq : charmatrix M i i = (X : R[X]) - C (M i i) := by
   simp only [charmatrix, RingHom.mapMatrix_apply, sub_apply, scalar_apply, map_apply,
     diagonal_apply_eq]
 
-#align charmatrix_apply_eq charmatrix_apply_eq
+#align charmatrix_apply_eq Matrix.charmatrix_apply_eq
 
 @[simp]
 theorem charmatrix_apply_ne (h : i ≠ j) : charmatrix M i j = -C (M i j) := by
   simp only [charmatrix, RingHom.mapMatrix_apply, sub_apply, scalar_apply, diagonal_apply_ne _ h,
     map_apply, sub_eq_neg_self]
-#align charmatrix_apply_ne charmatrix_apply_ne
+#align charmatrix_apply_ne Matrix.charmatrix_apply_ne
 
 theorem matPolyEquiv_charmatrix : matPolyEquiv (charmatrix M) = X - C M := by
   ext k i j
@@ -77,14 +78,14 @@ theorem matPolyEquiv_charmatrix : matPolyEquiv (charmatrix M) = X - C M := by
     split_ifs <;> simp
   · rw [charmatrix_apply_ne _ _ _ h, coeff_X, coeff_neg, coeff_C, coeff_C]
     split_ifs <;> simp [h]
-#align mat_poly_equiv_charmatrix matPolyEquiv_charmatrix
+#align mat_poly_equiv_charmatrix Matrix.matPolyEquiv_charmatrix
 
 theorem charmatrix_reindex (e : n ≃ m) :
     charmatrix (reindex e e M) = reindex e e (charmatrix M) := by
   ext i j x
   by_cases h : i = j
   all_goals simp [h]
-#align charmatrix_reindex charmatrix_reindex
+#align charmatrix_reindex Matrix.charmatrix_reindex
 
 lemma charmatrix_map (M : Matrix n n R) (f : R →+* S) :
     charmatrix (M.map f) = (charmatrix M).map (Polynomial.map f) := by
@@ -97,8 +98,6 @@ lemma charmatrix_fromBlocks :
   simp only [charmatrix]
   ext (i|i) (j|j) : 2 <;> simp [diagonal]
 
-namespace Matrix
-
 /-- The characteristic polynomial of a matrix `M` is given by $\det (t I - M)$.
 -/
 def charpoly (M : Matrix n n R) : R[X] :=

70fd9563

feat(LinearAlgebra/Charpoly): the universal characteristic polynomial (#10358)

72068a15

Diff

@@ -35,7 +35,7 @@ universe u v w
 
 open Polynomial Matrix BigOperators Polynomial
 
-variable {R : Type u} [CommRing R]
+variable {R S : Type*} [CommRing R] [CommRing S]
 variable {m n : Type*} [DecidableEq m] [DecidableEq n] [Fintype m] [Fintype n]
 variable (M₁₁ : Matrix m m R) (M₁₂ : Matrix m n R) (M₂₁ : Matrix n m R) (M₂₂ M : Matrix n n R)
 variable (i j : n)
@@ -86,6 +86,11 @@ theorem charmatrix_reindex (e : n ≃ m) :
   all_goals simp [h]
 #align charmatrix_reindex charmatrix_reindex
 
+lemma charmatrix_map (M : Matrix n n R) (f : R →+* S) :
+    charmatrix (M.map f) = (charmatrix M).map (Polynomial.map f) := by
+  ext i j
+  by_cases h : i = j <;> simp [h, charmatrix, diagonal]
+
 lemma charmatrix_fromBlocks :
     charmatrix (fromBlocks M₁₁ M₁₂ M₂₁ M₂₂) =
       fromBlocks (charmatrix M₁₁) (- M₁₂.map C) (- M₂₁.map C) (charmatrix M₂₂) := by
@@ -106,7 +111,12 @@ theorem charpoly_reindex (e : n ≃ m)
   rw [charmatrix_reindex, Matrix.det_reindex_self]
 #align matrix.charpoly_reindex Matrix.charpoly_reindex
 
+lemma charpoly_map (M : Matrix n n R) (f : R →+* S) :
+    (M.map f).charpoly = M.charpoly.map f := by
+  rw [charpoly, charmatrix_map, ← Polynomial.coe_mapRingHom, charpoly, RingHom.map_det]
+  rfl
 @[simp]
+
 lemma charpoly_fromBlocks_zero₁₂ :
     (fromBlocks M₁₁ 0 M₂₁ M₂₂).charpoly = (M₁₁.charpoly * M₂₂.charpoly) := by
   simp only [charpoly, charmatrix_fromBlocks, Matrix.map_zero _ (Polynomial.C_0), neg_zero,

70fd9563

chore(LinearAlgebra/Matrix/Charpoly): charpoly of block matrix (#10480)

34661a71

Diff

@@ -36,8 +36,9 @@ universe u v w
 open Polynomial Matrix BigOperators Polynomial
 
 variable {R : Type u} [CommRing R]
-
-variable {n : Type w} [DecidableEq n] [Fintype n]
+variable {m n : Type*} [DecidableEq m] [DecidableEq n] [Fintype m] [Fintype n]
+variable (M₁₁ : Matrix m m R) (M₁₂ : Matrix m n R) (M₂₁ : Matrix n m R) (M₂₂ M : Matrix n n R)
+variable (i j : n)
 
 open Finset
 
@@ -48,27 +49,25 @@ def charmatrix (M : Matrix n n R) : Matrix n n R[X] :=
   Matrix.scalar n (X : R[X]) - (C : R →+* R[X]).mapMatrix M
 #align charmatrix charmatrix
 
-theorem charmatrix_apply (M : Matrix n n R) (i j : n) :
+theorem charmatrix_apply :
     charmatrix M i j = (Matrix.diagonal fun _ : n => X) i j - C (M i j) :=
   rfl
 #align charmatrix_apply charmatrix_apply
 
 @[simp]
-theorem charmatrix_apply_eq (M : Matrix n n R) (i : n) :
-    charmatrix M i i = (X : R[X]) - C (M i i) := by
+theorem charmatrix_apply_eq : charmatrix M i i = (X : R[X]) - C (M i i) := by
   simp only [charmatrix, RingHom.mapMatrix_apply, sub_apply, scalar_apply, map_apply,
     diagonal_apply_eq]
 
 #align charmatrix_apply_eq charmatrix_apply_eq
 
 @[simp]
-theorem charmatrix_apply_ne (M : Matrix n n R) (i j : n) (h : i ≠ j) :
-    charmatrix M i j = -C (M i j) := by
+theorem charmatrix_apply_ne (h : i ≠ j) : charmatrix M i j = -C (M i j) := by
   simp only [charmatrix, RingHom.mapMatrix_apply, sub_apply, scalar_apply, diagonal_apply_ne _ h,
     map_apply, sub_eq_neg_self]
 #align charmatrix_apply_ne charmatrix_apply_ne
 
-theorem matPolyEquiv_charmatrix (M : Matrix n n R) : matPolyEquiv (charmatrix M) = X - C M := by
+theorem matPolyEquiv_charmatrix : matPolyEquiv (charmatrix M) = X - C M := by
   ext k i j
   simp only [matPolyEquiv_coeff_apply, coeff_sub, Pi.sub_apply]
   by_cases h : i = j
@@ -80,25 +79,45 @@ theorem matPolyEquiv_charmatrix (M : Matrix n n R) : matPolyEquiv (charmatrix M)
     split_ifs <;> simp [h]
 #align mat_poly_equiv_charmatrix matPolyEquiv_charmatrix
 
-theorem charmatrix_reindex {m : Type v} [DecidableEq m] [Fintype m] (e : n ≃ m) (M : Matrix n n R) :
+theorem charmatrix_reindex (e : n ≃ m) :
     charmatrix (reindex e e M) = reindex e e (charmatrix M) := by
   ext i j x
   by_cases h : i = j
   all_goals simp [h]
 #align charmatrix_reindex charmatrix_reindex
 
+lemma charmatrix_fromBlocks :
+    charmatrix (fromBlocks M₁₁ M₁₂ M₂₁ M₂₂) =
+      fromBlocks (charmatrix M₁₁) (- M₁₂.map C) (- M₂₁.map C) (charmatrix M₂₂) := by
+  simp only [charmatrix]
+  ext (i|i) (j|j) : 2 <;> simp [diagonal]
+
+namespace Matrix
+
 /-- The characteristic polynomial of a matrix `M` is given by $\det (t I - M)$.
 -/
-def Matrix.charpoly (M : Matrix n n R) : R[X] :=
+def charpoly (M : Matrix n n R) : R[X] :=
   (charmatrix M).det
 #align matrix.charpoly Matrix.charpoly
 
-theorem Matrix.charpoly_reindex {m : Type v} [DecidableEq m] [Fintype m] (e : n ≃ m)
+theorem charpoly_reindex (e : n ≃ m)
     (M : Matrix n n R) : (reindex e e M).charpoly = M.charpoly := by
   unfold Matrix.charpoly
   rw [charmatrix_reindex, Matrix.det_reindex_self]
 #align matrix.charpoly_reindex Matrix.charpoly_reindex
 
+@[simp]
+lemma charpoly_fromBlocks_zero₁₂ :
+    (fromBlocks M₁₁ 0 M₂₁ M₂₂).charpoly = (M₁₁.charpoly * M₂₂.charpoly) := by
+  simp only [charpoly, charmatrix_fromBlocks, Matrix.map_zero _ (Polynomial.C_0), neg_zero,
+    det_fromBlocks_zero₁₂]
+
+@[simp]
+lemma charpoly_fromBlocks_zero₂₁ :
+    (fromBlocks M₁₁ M₁₂ 0 M₂₂).charpoly = (M₁₁.charpoly * M₂₂.charpoly) := by
+  simp only [charpoly, charmatrix_fromBlocks, Matrix.map_zero _ (Polynomial.C_0), neg_zero,
+    det_fromBlocks_zero₂₁]
+
 -- This proof follows http://drorbn.net/AcademicPensieve/2015-12/CayleyHamilton.pdf
 /-- The **Cayley-Hamilton Theorem**, that the characteristic polynomial of a matrix,
 applied to the matrix itself, is zero.
@@ -107,7 +126,7 @@ This holds over any commutative ring.
 
 See `LinearMap.aeval_self_charpoly` for the equivalent statement about endomorphisms.
 -/
-theorem Matrix.aeval_self_charpoly (M : Matrix n n R) : aeval M M.charpoly = 0 := by
+theorem aeval_self_charpoly (M : Matrix n n R) : aeval M M.charpoly = 0 := by
   -- We begin with the fact $χ_M(t) I = adjugate (t I - M) * (t I - M)$,
   -- as an identity in `Matrix n n R[X]`.
   have h : M.charpoly • (1 : Matrix n n R[X]) = adjugate (charmatrix M) * charmatrix M :=
@@ -129,3 +148,5 @@ theorem Matrix.aeval_self_charpoly (M : Matrix n n R) : aeval M M.charpoly = 0 :
   -- Thus we have $χ_M(M) = 0$, which is the desired result.
   exact h
 #align matrix.aeval_self_charpoly Matrix.aeval_self_charpoly
+
+end Matrix

70fd9563

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

@@ -49,22 +49,23 @@ def charmatrix (M : Matrix n n R) : Matrix n n R[X] :=
 #align charmatrix charmatrix
 
 theorem charmatrix_apply (M : Matrix n n R) (i j : n) :
-    charmatrix M i j = X * (1 : Matrix n n R[X]) i j - C (M i j) :=
+    charmatrix M i j = (Matrix.diagonal fun _ : n => X) i j - C (M i j) :=
   rfl
 #align charmatrix_apply charmatrix_apply
 
 @[simp]
 theorem charmatrix_apply_eq (M : Matrix n n R) (i : n) :
     charmatrix M i i = (X : R[X]) - C (M i i) := by
-  simp only [charmatrix, RingHom.mapMatrix_apply, sub_apply, scalar_apply_eq, map_apply]
+  simp only [charmatrix, RingHom.mapMatrix_apply, sub_apply, scalar_apply, map_apply,
+    diagonal_apply_eq]
 
 #align charmatrix_apply_eq charmatrix_apply_eq
 
 @[simp]
 theorem charmatrix_apply_ne (M : Matrix n n R) (i j : n) (h : i ≠ j) :
     charmatrix M i j = -C (M i j) := by
-  simp only [charmatrix, RingHom.mapMatrix_apply, sub_apply, scalar_apply_ne _ _ _ h, map_apply,
-    sub_eq_neg_self]
+  simp only [charmatrix, RingHom.mapMatrix_apply, sub_apply, scalar_apply, diagonal_apply_ne _ h,
+    map_apply, sub_eq_neg_self]
 #align charmatrix_apply_ne charmatrix_apply_ne
 
 theorem matPolyEquiv_charmatrix (M : Matrix n n R) : matPolyEquiv (charmatrix M) = X - C M := by

70fd9563

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) 2020 Scott Morrison. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Scott Morrison
-
-! This file was ported from Lean 3 source module linear_algebra.matrix.charpoly.basic
-! leanprover-community/mathlib commit 70fd9563a21e7b963887c9360bd29b2393e6225a
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.LinearAlgebra.Matrix.Adjugate
 import Mathlib.RingTheory.PolynomialAlgebra
 
+#align_import linear_algebra.matrix.charpoly.basic from "leanprover-community/mathlib"@"70fd9563a21e7b963887c9360bd29b2393e6225a"
+
 /-!
 # Characteristic polynomials and the Cayley-Hamilton theorem

70fd9563

chore: clean up spacing around at and goals (#5387)

Changes are of the form

some_tactic at h⊢ -> some_tactic at h ⊢
some_tactic at h -> some_tactic at h

2a870323

Diff

@@ -116,14 +116,14 @@ theorem Matrix.aeval_self_charpoly (M : Matrix n n R) : aeval M M.charpoly = 0 :
     (adjugate_mul _).symm
   -- Using the algebra isomorphism `Matrix n n R[X] ≃ₐ[R] Polynomial (Matrix n n R)`,
   -- we have the same identity in `Polynomial (Matrix n n R)`.
-  apply_fun matPolyEquiv  at h
+  apply_fun matPolyEquiv at h
   simp only [matPolyEquiv.map_mul, matPolyEquiv_charmatrix] at h
   -- Because the coefficient ring `Matrix n n R` is non-commutative,
   -- evaluation at `M` is not multiplicative.
   -- However, any polynomial which is a product of the form $N * (t I - M)$
   -- is sent to zero, because the evaluation function puts the polynomial variable
   -- to the right of any coefficients, so everything telescopes.
-  apply_fun fun p => p.eval M  at h
+  apply_fun fun p => p.eval M at h
   rw [eval_mul_X_sub_C] at h
   -- Now $χ_M (t) I$, when thought of as a polynomial of matrices
   -- and evaluated at some `N` is exactly $χ_M (N)$.

70fd9563

chore: remove superfluous parentheses in calls to ext (#5258)

Co-authored-by: Xavier Roblot <46200072+xroblot@users.noreply.github.com> Co-authored-by: Joël Riou <joel.riou@universite-paris-saclay.fr> Co-authored-by: Riccardo Brasca <riccardo.brasca@gmail.com> Co-authored-by: Yury G. Kudryashov <urkud@urkud.name> Co-authored-by: Scott Morrison <scott.morrison@anu.edu.au> Co-authored-by: Scott Morrison <scott.morrison@gmail.com> Co-authored-by: Jeremy Tan Jie Rui <reddeloostw@gmail.com> Co-authored-by: Pol'tta / Miyahara Kō <pol_tta@outlook.jp> Co-authored-by: Jason Yuen <jason_yuen2007@hotmail.com> Co-authored-by: Mario Carneiro <di.gama@gmail.com> Co-authored-by: Jireh Loreaux <loreaujy@gmail.com> Co-authored-by: Ruben Van de Velde <65514131+Ruben-VandeVelde@users.noreply.github.com> Co-authored-by: Kyle Miller <kmill31415@gmail.com> Co-authored-by: Heather Macbeth <25316162+hrmacbeth@users.noreply.github.com> Co-authored-by: Jujian Zhang <jujian.zhang1998@outlook.com> Co-authored-by: Yaël Dillies <yael.dillies@gmail.com>

3d6731dc

Diff

@@ -71,7 +71,7 @@ theorem charmatrix_apply_ne (M : Matrix n n R) (i j : n) (h : i ≠ j) :
 #align charmatrix_apply_ne charmatrix_apply_ne
 
 theorem matPolyEquiv_charmatrix (M : Matrix n n R) : matPolyEquiv (charmatrix M) = X - C M := by
-  ext (k i j)
+  ext k i j
   simp only [matPolyEquiv_coeff_apply, coeff_sub, Pi.sub_apply]
   by_cases h : i = j
   · subst h
@@ -84,7 +84,7 @@ theorem matPolyEquiv_charmatrix (M : Matrix n n R) : matPolyEquiv (charmatrix M)
 
 theorem charmatrix_reindex {m : Type v} [DecidableEq m] [Fintype m] (e : n ≃ m) (M : Matrix n n R) :
     charmatrix (reindex e e M) = reindex e e (charmatrix M) := by
-  ext (i j x)
+  ext i j x
   by_cases h : i = j
   all_goals simp [h]
 #align charmatrix_reindex charmatrix_reindex

70fd9563

chore: tidy various files (#4757)

ea80818c

Diff

@@ -17,7 +17,7 @@ import Mathlib.RingTheory.PolynomialAlgebra
 We define characteristic polynomials of matrices and
 prove the Cayley–Hamilton theorem over arbitrary commutative rings.
 
-See the file `matrix/charpoly/coeff` for corollaries of this theorem.
+See the file `Mathlib/LinearAlgebra/Matrix/Charpoly/Coeff.lean` for corollaries of this theorem.
 
 ## Main definitions
 
@@ -36,9 +36,7 @@ noncomputable section
 
 universe u v w
 
-open Polynomial Matrix
-
-open BigOperators Polynomial
+open Polynomial Matrix BigOperators Polynomial
 
 variable {R : Type u} [CommRing R]

70fd9563

chore: fix upper/lowercase in comments (#4360)

Run a non-interactive version of fix-comments.py on all files.
Go through the diff and manually add/discard/edit chunks.

27d257fc

Diff

@@ -21,7 +21,7 @@ See the file `matrix/charpoly/coeff` for corollaries of this theorem.
 
 ## Main definitions
 
-* `matrix.charpoly` is the characteristic polynomial of a matrix.
+* `Matrix.charpoly` is the characteristic polynomial of a matrix.
 
 ## Implementation details
 
@@ -46,7 +46,7 @@ variable {n : Type w} [DecidableEq n] [Fintype n]
 
 open Finset
 
-/-- The "characteristic matrix" of `M : matrix n n R` is the matrix of polynomials $t I - M$.
+/-- The "characteristic matrix" of `M : Matrix n n R` is the matrix of polynomials $t I - M$.
 The determinant of this matrix is the characteristic polynomial.
 -/
 def charmatrix (M : Matrix n n R) : Matrix n n R[X] :=
@@ -109,18 +109,18 @@ applied to the matrix itself, is zero.
 
 This holds over any commutative ring.
 
-See `linear_map.aeval_self_charpoly` for the equivalent statement about endomorphisms.
+See `LinearMap.aeval_self_charpoly` for the equivalent statement about endomorphisms.
 -/
 theorem Matrix.aeval_self_charpoly (M : Matrix n n R) : aeval M M.charpoly = 0 := by
   -- We begin with the fact $χ_M(t) I = adjugate (t I - M) * (t I - M)$,
-  -- as an identity in `matrix n n R[X]`.
+  -- as an identity in `Matrix n n R[X]`.
   have h : M.charpoly • (1 : Matrix n n R[X]) = adjugate (charmatrix M) * charmatrix M :=
     (adjugate_mul _).symm
-  -- Using the algebra isomorphism `matrix n n R[X] ≃ₐ[R] polynomial (matrix n n R)`,
-  -- we have the same identity in `polynomial (matrix n n R)`.
+  -- Using the algebra isomorphism `Matrix n n R[X] ≃ₐ[R] Polynomial (Matrix n n R)`,
+  -- we have the same identity in `Polynomial (Matrix n n R)`.
   apply_fun matPolyEquiv  at h
   simp only [matPolyEquiv.map_mul, matPolyEquiv_charmatrix] at h
-  -- Because the coefficient ring `matrix n n R` is non-commutative,
+  -- Because the coefficient ring `Matrix n n R` is non-commutative,
   -- evaluation at `M` is not multiplicative.
   -- However, any polynomial which is a product of the form $N * (t I - M)$
   -- is sent to zero, because the evaluation function puts the polynomial variable

70fd9563

feat: port LinearAlgebra.Matrix.Charpoly.Basic (#4118)

Very few fixes were needed for this file!

Co-authored-by: ChrisHughes24 <chrishughes24@gmail.com> Co-authored-by: Parcly Taxel <reddeloostw@gmail.com>

542f2e56

`linear_algebra.matrix.charpoly.basic` ⟷ `Mathlib.LinearAlgebra.Matrix.Charpoly.Basic`

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Dependencies 10 + 608

linear_algebra.matrix.charpoly.basic ⟷ Mathlib.LinearAlgebra.Matrix.Charpoly.Basic

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Dependencies 10 + 608

`linear_algebra.matrix.charpoly.basic` ⟷ `Mathlib.LinearAlgebra.Matrix.Charpoly.Basic`