linear_algebra.matrix.charpoly.finite_field

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

b95b8c7a

(last sync)

Changes in mathlib3port

mathlib3

mathlib3port

af471b9e

bump to nightly-2024-03-17-08

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

22f01ce4

Diff

@@ -34,7 +34,7 @@ theorem FiniteField.Matrix.charpoly_pow_card {K : Type _} [Field K] [Fintype K]
   · cases' CharP.exists K with p hp; letI := hp
     rcases FiniteField.card K p with ⟨⟨k, kpos⟩, ⟨hp, hk⟩⟩
     haveI : Fact p.prime := ⟨hp⟩
-    dsimp at hk ; rw [hk] at *
+    dsimp at hk; rw [hk] at *
     apply (frobenius_inj K[X] p).iterate k
     repeat' rw [iterate_frobenius]; rw [← hk]
     rw [← FiniteField.expand_card]
@@ -53,7 +53,7 @@ theorem FiniteField.Matrix.charpoly_pow_card {K : Type _} [Field K] [Fintype K]
 @[simp]
 theorem ZMod.charpoly_pow_card {p : ℕ} [Fact p.Prime] (M : Matrix n n (ZMod p)) :
     (M ^ p).charpoly = M.charpoly := by have h := FiniteField.Matrix.charpoly_pow_card M;
-  rwa [ZMod.card] at h 
+  rwa [ZMod.card] at h
 #align zmod.charpoly_pow_card ZMod.charpoly_pow_card
 -/
 
@@ -70,7 +70,7 @@ theorem FiniteField.trace_pow_card {K : Type _} [Field K] [Fintype K] (M : Matri
 
 #print ZMod.trace_pow_card /-
 theorem ZMod.trace_pow_card {p : ℕ} [Fact p.Prime] (M : Matrix n n (ZMod p)) :
-    trace (M ^ p) = trace M ^ p := by have h := FiniteField.trace_pow_card M; rwa [ZMod.card] at h 
+    trace (M ^ p) = trace M ^ p := by have h := FiniteField.trace_pow_card M; rwa [ZMod.card] at h
 #align zmod.trace_pow_card ZMod.trace_pow_card
 -/

af471b9e

bump to nightly-2024-02-17-08

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

42bef5c2

Diff

@@ -42,8 +42,8 @@ theorem FiniteField.Matrix.charpoly_pow_card {K : Type _} [Field K] [Fintype K]
     rw [AlgHom.map_det, ← coe_det_monoid_hom, ← (det_monoid_hom : Matrix n n K[X] →* K[X]).map_pow]
     apply congr_arg det
     refine' mat_poly_equiv.injective _
-    rw [AlgEquiv.map_pow, matPolyEquiv_charmatrix, hk, sub_pow_char_pow_of_commute, ← C_pow]
-    · exact (id (matPolyEquiv_eq_x_pow_sub_c (p ^ k) M) : _)
+    rw [AlgEquiv.map_pow, Matrix.matPolyEquiv_charmatrix, hk, sub_pow_char_pow_of_commute, ← C_pow]
+    · exact (id (matPolyEquiv_eq_X_pow_sub_C (p ^ k) M) : _)
     · exact (C M).commute_X
   · exact congr_arg _ (Subsingleton.elim _ _)
 #align finite_field.matrix.charpoly_pow_card FiniteField.Matrix.charpoly_pow_card

af471b9e

bump to nightly-2023-09-24-06

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

5655435f

Diff

@@ -3,9 +3,9 @@ Copyright (c) 2020 Aaron Anderson, Jalex Stark. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Aaron Anderson, Jalex Stark
 -/
-import Mathbin.LinearAlgebra.Matrix.Charpoly.Coeff
-import Mathbin.FieldTheory.Finite.Basic
-import Mathbin.Data.Matrix.CharP
+import LinearAlgebra.Matrix.Charpoly.Coeff
+import FieldTheory.Finite.Basic
+import Data.Matrix.CharP
 
 #align_import linear_algebra.matrix.charpoly.finite_field from "leanprover-community/mathlib"@"af471b9e3ce868f296626d33189b4ce730fa4c00"

af471b9e

bump to nightly-2023-07-20-09

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

9c56d0dd

Diff

@@ -2,16 +2,13 @@
 Copyright (c) 2020 Aaron Anderson, Jalex Stark. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Aaron Anderson, Jalex Stark
-
-! This file was ported from Lean 3 source module linear_algebra.matrix.charpoly.finite_field
-! leanprover-community/mathlib commit af471b9e3ce868f296626d33189b4ce730fa4c00
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.LinearAlgebra.Matrix.Charpoly.Coeff
 import Mathbin.FieldTheory.Finite.Basic
 import Mathbin.Data.Matrix.CharP
 
+#align_import linear_algebra.matrix.charpoly.finite_field from "leanprover-community/mathlib"@"af471b9e3ce868f296626d33189b4ce730fa4c00"
+
 /-!
 # Results on characteristic polynomials and traces over finite fields.

af471b9e

bump to nightly-2023-06-13-21

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

829520ac

Diff

@@ -28,6 +28,7 @@ open scoped Polynomial
 
 variable {n : Type _} [DecidableEq n] [Fintype n]
 
+#print FiniteField.Matrix.charpoly_pow_card /-
 @[simp]
 theorem FiniteField.Matrix.charpoly_pow_card {K : Type _} [Field K] [Fintype K] (M : Matrix n n K) :
     (M ^ Fintype.card K).charpoly = M.charpoly :=
@@ -49,13 +50,17 @@ theorem FiniteField.Matrix.charpoly_pow_card {K : Type _} [Field K] [Fintype K]
     · exact (C M).commute_X
   · exact congr_arg _ (Subsingleton.elim _ _)
 #align finite_field.matrix.charpoly_pow_card FiniteField.Matrix.charpoly_pow_card
+-/
 
+#print ZMod.charpoly_pow_card /-
 @[simp]
 theorem ZMod.charpoly_pow_card {p : ℕ} [Fact p.Prime] (M : Matrix n n (ZMod p)) :
     (M ^ p).charpoly = M.charpoly := by have h := FiniteField.Matrix.charpoly_pow_card M;
   rwa [ZMod.card] at h 
 #align zmod.charpoly_pow_card ZMod.charpoly_pow_card
+-/
 
+#print FiniteField.trace_pow_card /-
 theorem FiniteField.trace_pow_card {K : Type _} [Field K] [Fintype K] (M : Matrix n n K) :
     trace (M ^ Fintype.card K) = trace M ^ Fintype.card K :=
   by
@@ -64,8 +69,11 @@ theorem FiniteField.trace_pow_card {K : Type _} [Field K] [Fintype K] (M : Matri
   rw [Matrix.trace_eq_neg_charpoly_coeff, Matrix.trace_eq_neg_charpoly_coeff,
     FiniteField.Matrix.charpoly_pow_card, FiniteField.pow_card]
 #align finite_field.trace_pow_card FiniteField.trace_pow_card
+-/
 
+#print ZMod.trace_pow_card /-
 theorem ZMod.trace_pow_card {p : ℕ} [Fact p.Prime] (M : Matrix n n (ZMod p)) :
     trace (M ^ p) = trace M ^ p := by have h := FiniteField.trace_pow_card M; rwa [ZMod.card] at h 
 #align zmod.trace_pow_card ZMod.trace_pow_card
+-/

af471b9e

bump to nightly-2023-06-04-18

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

3fb4268b

Diff

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Aaron Anderson, Jalex Stark
 
 ! This file was ported from Lean 3 source module linear_algebra.matrix.charpoly.finite_field
-! leanprover-community/mathlib commit b95b8c7a484a298228805c72c142f6b062eb0d70
+! leanprover-community/mathlib commit af471b9e3ce868f296626d33189b4ce730fa4c00
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -14,6 +14,9 @@ import Mathbin.Data.Matrix.CharP
 
 /-!
 # Results on characteristic polynomials and traces over finite fields.
+
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
 -/

b95b8c7a

bump to nightly-2023-06-01-16

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

b9c87c70

Diff

@@ -33,7 +33,7 @@ theorem FiniteField.Matrix.charpoly_pow_card {K : Type _} [Field K] [Fintype K]
   · cases' CharP.exists K with p hp; letI := hp
     rcases FiniteField.card K p with ⟨⟨k, kpos⟩, ⟨hp, hk⟩⟩
     haveI : Fact p.prime := ⟨hp⟩
-    dsimp at hk; rw [hk] at *
+    dsimp at hk ; rw [hk] at *
     apply (frobenius_inj K[X] p).iterate k
     repeat' rw [iterate_frobenius]; rw [← hk]
     rw [← FiniteField.expand_card]
@@ -50,7 +50,7 @@ theorem FiniteField.Matrix.charpoly_pow_card {K : Type _} [Field K] [Fintype K]
 @[simp]
 theorem ZMod.charpoly_pow_card {p : ℕ} [Fact p.Prime] (M : Matrix n n (ZMod p)) :
     (M ^ p).charpoly = M.charpoly := by have h := FiniteField.Matrix.charpoly_pow_card M;
-  rwa [ZMod.card] at h
+  rwa [ZMod.card] at h 
 #align zmod.charpoly_pow_card ZMod.charpoly_pow_card
 
 theorem FiniteField.trace_pow_card {K : Type _} [Field K] [Fintype K] (M : Matrix n n K) :
@@ -63,6 +63,6 @@ theorem FiniteField.trace_pow_card {K : Type _} [Field K] [Fintype K] (M : Matri
 #align finite_field.trace_pow_card FiniteField.trace_pow_card
 
 theorem ZMod.trace_pow_card {p : ℕ} [Fact p.Prime] (M : Matrix n n (ZMod p)) :
-    trace (M ^ p) = trace M ^ p := by have h := FiniteField.trace_pow_card M; rwa [ZMod.card] at h
+    trace (M ^ p) = trace M ^ p := by have h := FiniteField.trace_pow_card M; rwa [ZMod.card] at h 
 #align zmod.trace_pow_card ZMod.trace_pow_card

b95b8c7a

bump to nightly-2023-05-28-18

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

8d353152

Diff

@@ -21,7 +21,7 @@ noncomputable section
 
 open Polynomial Matrix
 
-open Polynomial
+open scoped Polynomial
 
 variable {n : Type _} [DecidableEq n] [Fintype n]

b95b8c7a

bump to nightly-2023-05-28-04

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

6797a637

Diff

@@ -30,16 +30,14 @@ theorem FiniteField.Matrix.charpoly_pow_card {K : Type _} [Field K] [Fintype K]
     (M ^ Fintype.card K).charpoly = M.charpoly :=
   by
   cases (isEmpty_or_nonempty n).symm
-  · cases' CharP.exists K with p hp
-    letI := hp
+  · cases' CharP.exists K with p hp; letI := hp
     rcases FiniteField.card K p with ⟨⟨k, kpos⟩, ⟨hp, hk⟩⟩
     haveI : Fact p.prime := ⟨hp⟩
-    dsimp at hk
-    rw [hk] at *
+    dsimp at hk; rw [hk] at *
     apply (frobenius_inj K[X] p).iterate k
     repeat' rw [iterate_frobenius]; rw [← hk]
     rw [← FiniteField.expand_card]
-    unfold charpoly
+    unfold charpoly;
     rw [AlgHom.map_det, ← coe_det_monoid_hom, ← (det_monoid_hom : Matrix n n K[X] →* K[X]).map_pow]
     apply congr_arg det
     refine' mat_poly_equiv.injective _
@@ -51,9 +49,7 @@ theorem FiniteField.Matrix.charpoly_pow_card {K : Type _} [Field K] [Fintype K]
 
 @[simp]
 theorem ZMod.charpoly_pow_card {p : ℕ} [Fact p.Prime] (M : Matrix n n (ZMod p)) :
-    (M ^ p).charpoly = M.charpoly :=
-  by
-  have h := FiniteField.Matrix.charpoly_pow_card M
+    (M ^ p).charpoly = M.charpoly := by have h := FiniteField.Matrix.charpoly_pow_card M;
   rwa [ZMod.card] at h
 #align zmod.charpoly_pow_card ZMod.charpoly_pow_card
 
@@ -67,9 +63,6 @@ theorem FiniteField.trace_pow_card {K : Type _} [Field K] [Fintype K] (M : Matri
 #align finite_field.trace_pow_card FiniteField.trace_pow_card
 
 theorem ZMod.trace_pow_card {p : ℕ} [Fact p.Prime] (M : Matrix n n (ZMod p)) :
-    trace (M ^ p) = trace M ^ p :=
-  by
-  have h := FiniteField.trace_pow_card M
-  rwa [ZMod.card] at h
+    trace (M ^ p) = trace M ^ p := by have h := FiniteField.trace_pow_card M; rwa [ZMod.card] at h
 #align zmod.trace_pow_card ZMod.trace_pow_card

b95b8c7a

bump to nightly-2023-03-08-10

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

422cc012

Diff

@@ -45,7 +45,7 @@ theorem FiniteField.Matrix.charpoly_pow_card {K : Type _} [Field K] [Fintype K]
     refine' mat_poly_equiv.injective _
     rw [AlgEquiv.map_pow, matPolyEquiv_charmatrix, hk, sub_pow_char_pow_of_commute, ← C_pow]
     · exact (id (matPolyEquiv_eq_x_pow_sub_c (p ^ k) M) : _)
-    · exact (C M).commute_x
+    · exact (C M).commute_X
   · exact congr_arg _ (Subsingleton.elim _ _)
 #align finite_field.matrix.charpoly_pow_card FiniteField.Matrix.charpoly_pow_card

b95b8c7a

bump to nightly-2023-02-21-16

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

1107b979

Changes in mathlib4

mathlib3

mathlib4

b95b8c7a

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

9f7fef49

Diff

@@ -38,7 +38,7 @@ theorem FiniteField.Matrix.charpoly_pow_card {K : Type*} [Field K] [Fintype K] (
     apply congr_arg det
     refine' matPolyEquiv.injective _
     rw [AlgEquiv.map_pow, matPolyEquiv_charmatrix, hk, sub_pow_char_pow_of_commute, ← C_pow]
-    · exact (id (matPolyEquiv_eq_x_pow_sub_c (p ^ k) M) : _)
+    · exact (id (matPolyEquiv_eq_X_pow_sub_C (p ^ k) M) : _)
     · exact (C M).commute_X
   · exact congr_arg _ (Subsingleton.elim _ _)
 #align finite_field.matrix.charpoly_pow_card FiniteField.Matrix.charpoly_pow_card

b95b8c7a

feat: nilpotent matrices have nilpotent trace (#6588)

Also some related results

Co-authored-by: damiano <adomani@gmail.com>

351431b2

Diff

@@ -53,7 +53,7 @@ theorem ZMod.charpoly_pow_card {p : ℕ} [Fact p.Prime] (M : Matrix n n (ZMod p)
 theorem FiniteField.trace_pow_card {K : Type*} [Field K] [Fintype K] (M : Matrix n n K) :
     trace (M ^ Fintype.card K) = trace M ^ Fintype.card K := by
   cases isEmpty_or_nonempty n
-  · simp [Matrix.trace]; rw [zero_pow Fintype.card_pos]
+  · simp [Matrix.trace]
   rw [Matrix.trace_eq_neg_charpoly_coeff, Matrix.trace_eq_neg_charpoly_coeff,
     FiniteField.Matrix.charpoly_pow_card, FiniteField.pow_card]
 #align finite_field.trace_pow_card FiniteField.trace_pow_card

b95b8c7a

chore: banish Type _ and Sort _ (#6499)

We remove all possible occurences of Type _ and Sort _ in favor of Type* and Sort*.

This has nice performance benefits.

32de3f67

Diff

@@ -20,10 +20,10 @@ open Polynomial Matrix
 
 open scoped Polynomial
 
-variable {n : Type _} [DecidableEq n] [Fintype n]
+variable {n : Type*} [DecidableEq n] [Fintype n]
 
 @[simp]
-theorem FiniteField.Matrix.charpoly_pow_card {K : Type _} [Field K] [Fintype K] (M : Matrix n n K) :
+theorem FiniteField.Matrix.charpoly_pow_card {K : Type*} [Field K] [Fintype K] (M : Matrix n n K) :
     (M ^ Fintype.card K).charpoly = M.charpoly := by
   cases (isEmpty_or_nonempty n).symm
   · cases' CharP.exists K with p hp; letI := hp
@@ -50,7 +50,7 @@ theorem ZMod.charpoly_pow_card {p : ℕ} [Fact p.Prime] (M : Matrix n n (ZMod p)
   rwa [ZMod.card] at h
 #align zmod.charpoly_pow_card ZMod.charpoly_pow_card
 
-theorem FiniteField.trace_pow_card {K : Type _} [Field K] [Fintype K] (M : Matrix n n K) :
+theorem FiniteField.trace_pow_card {K : Type*} [Field K] [Fintype K] (M : Matrix n n K) :
     trace (M ^ Fintype.card K) = trace M ^ Fintype.card K := by
   cases isEmpty_or_nonempty n
   · simp [Matrix.trace]; rw [zero_pow Fintype.card_pos]

b95b8c7a

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

@@ -2,16 +2,13 @@
 Copyright (c) 2020 Aaron Anderson, Jalex Stark. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Aaron Anderson, Jalex Stark
-
-! This file was ported from Lean 3 source module linear_algebra.matrix.charpoly.finite_field
-! leanprover-community/mathlib commit b95b8c7a484a298228805c72c142f6b062eb0d70
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.LinearAlgebra.Matrix.Charpoly.Coeff
 import Mathlib.FieldTheory.Finite.Basic
 import Mathlib.Data.Matrix.CharP
 
+#align_import linear_algebra.matrix.charpoly.finite_field from "leanprover-community/mathlib"@"b95b8c7a484a298228805c72c142f6b062eb0d70"
+
 /-!
 # Results on characteristic polynomials and traces over finite fields.
 -/

b95b8c7a

feat: port LinearAlgebra.Matrix.Charpoly.FiniteField (#4601)

22a37712

`linear_algebra.matrix.charpoly.finite_field` ⟷ `Mathlib.LinearAlgebra.Matrix.Charpoly.FiniteField`

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Dependencies 10 + 661

linear_algebra.matrix.charpoly.finite_field ⟷ Mathlib.LinearAlgebra.Matrix.Charpoly.FiniteField

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Dependencies 10 + 661

`linear_algebra.matrix.charpoly.finite_field` ⟷ `Mathlib.LinearAlgebra.Matrix.Charpoly.FiniteField`