linear_algebra.matrix.invariant_basis_number
⟷
Mathlib.LinearAlgebra.Matrix.InvariantBasisNumber
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.
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mathlib commit https://github.com/leanprover-community/mathlib/commit/ce64cd319bb6b3e82f31c2d38e79080d377be451
@@ -3,8 +3,8 @@ Copyright (c) 2022 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison
-/
-import Mathbin.LinearAlgebra.Matrix.ToLin
-import Mathbin.LinearAlgebra.InvariantBasisNumber
+import LinearAlgebra.Matrix.ToLin
+import LinearAlgebra.InvariantBasisNumber
#align_import linear_algebra.matrix.invariant_basis_number from "leanprover-community/mathlib"@"f2b757fc5c341d88741b9c4630b1e8ba973c5726"
mathlib commit https://github.com/leanprover-community/mathlib/commit/8ea5598db6caeddde6cb734aa179cc2408dbd345
@@ -2,15 +2,12 @@
Copyright (c) 2022 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.invariant_basis_number
-! leanprover-community/mathlib commit f2b757fc5c341d88741b9c4630b1e8ba973c5726
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
-/
import Mathbin.LinearAlgebra.Matrix.ToLin
import Mathbin.LinearAlgebra.InvariantBasisNumber
+#align_import linear_algebra.matrix.invariant_basis_number from "leanprover-community/mathlib"@"f2b757fc5c341d88741b9c4630b1e8ba973c5726"
+
/-!
# Invertible matrices over a ring with invariant basis number are square.
mathlib commit https://github.com/leanprover-community/mathlib/commit/9fb8964792b4237dac6200193a0d533f1b3f7423
@@ -25,8 +25,10 @@ variable {R : Type _} [Semiring R] [InvariantBasisNumber R]
open scoped Matrix
+#print Matrix.square_of_invertible /-
theorem Matrix.square_of_invertible (M : Matrix n m R) (N : Matrix m n R) (h : M ⬝ N = 1)
(h' : N ⬝ M = 1) : Fintype.card n = Fintype.card m :=
card_eq_of_linearEquiv R (Matrix.toLinearEquivRight'OfInv h' h)
#align matrix.square_of_invertible Matrix.square_of_invertible
+-/
mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb
@@ -23,7 +23,7 @@ variable {n m : Type _} [Fintype n] [DecidableEq n] [Fintype m] [DecidableEq m]
variable {R : Type _} [Semiring R] [InvariantBasisNumber R]
-open Matrix
+open scoped Matrix
theorem Matrix.square_of_invertible (M : Matrix n m R) (N : Matrix m n R) (h : M ⬝ N = 1)
(h' : N ⬝ M = 1) : Fintype.card n = Fintype.card m :=
mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb
@@ -25,12 +25,6 @@ variable {R : Type _} [Semiring R] [InvariantBasisNumber R]
open Matrix
-/- warning: matrix.square_of_invertible -> Matrix.square_of_invertible is a dubious translation:
-lean 3 declaration is
- forall {n : Type.{u1}} {m : Type.{u2}} [_inst_1 : Fintype.{u1} n] [_inst_2 : DecidableEq.{succ u1} n] [_inst_3 : Fintype.{u2} m] [_inst_4 : DecidableEq.{succ u2} m] {R : Type.{u3}} [_inst_5 : Semiring.{u3} R] [_inst_6 : InvariantBasisNumber.{u3} R _inst_5] (M : Matrix.{u1, u2, u3} n m R) (N : Matrix.{u2, u1, u3} m n R), (Eq.{succ (max u1 u3)} (Matrix.{u1, u1, u3} n n R) (Matrix.mul.{u3, u1, u2, u1} n m n R _inst_3 (Distrib.toHasMul.{u3} R (NonUnitalNonAssocSemiring.toDistrib.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_5)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_5))) M N) (OfNat.ofNat.{max u1 u3} (Matrix.{u1, u1, u3} n n R) 1 (OfNat.mk.{max u1 u3} (Matrix.{u1, u1, u3} n n R) 1 (One.one.{max u1 u3} (Matrix.{u1, u1, u3} n n R) (Matrix.hasOne.{u3, u1} n R (fun (a : n) (b : n) => _inst_2 a b) (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_5)))) (AddMonoidWithOne.toOne.{u3} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} R (NonAssocSemiring.toAddCommMonoidWithOne.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_5))))))))) -> (Eq.{succ (max u2 u3)} (Matrix.{u2, u2, u3} m m R) (Matrix.mul.{u3, u2, u1, u2} m n m R _inst_1 (Distrib.toHasMul.{u3} R (NonUnitalNonAssocSemiring.toDistrib.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_5)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_5))) N M) (OfNat.ofNat.{max u2 u3} (Matrix.{u2, u2, u3} m m R) 1 (OfNat.mk.{max u2 u3} (Matrix.{u2, u2, u3} m m R) 1 (One.one.{max u2 u3} (Matrix.{u2, u2, u3} m m R) (Matrix.hasOne.{u3, u2} m R (fun (a : m) (b : m) => _inst_4 a b) (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_5)))) (AddMonoidWithOne.toOne.{u3} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} R (NonAssocSemiring.toAddCommMonoidWithOne.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_5))))))))) -> (Eq.{1} Nat (Fintype.card.{u1} n _inst_1) (Fintype.card.{u2} m _inst_3))
-but is expected to have type
- forall {n : Type.{u3}} {m : Type.{u2}} [_inst_1 : Fintype.{u3} n] [_inst_2 : DecidableEq.{succ u3} n] [_inst_3 : Fintype.{u2} m] [_inst_4 : DecidableEq.{succ u2} m] {R : Type.{u1}} [_inst_5 : Semiring.{u1} R] [_inst_6 : InvariantBasisNumber.{u1} R _inst_5] (M : Matrix.{u3, u2, u1} n m R) (N : Matrix.{u2, u3, u1} m n R), (Eq.{max (succ u3) (succ u1)} (Matrix.{u3, u3, u1} n n R) (Matrix.mul.{u1, u3, u2, u3} n m n R _inst_3 (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_5))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_5))) M N) (OfNat.ofNat.{max u3 u1} (Matrix.{u3, u3, u1} n n R) 1 (One.toOfNat1.{max u3 u1} (Matrix.{u3, u3, u1} n n R) (Matrix.one.{u1, u3} n R (fun (a : n) (b : n) => _inst_2 a b) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_5)) (Semiring.toOne.{u1} R _inst_5))))) -> (Eq.{max (succ u2) (succ u1)} (Matrix.{u2, u2, u1} m m R) (Matrix.mul.{u1, u2, u3, u2} m n m R _inst_1 (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_5))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_5))) N M) (OfNat.ofNat.{max u2 u1} (Matrix.{u2, u2, u1} m m R) 1 (One.toOfNat1.{max u2 u1} (Matrix.{u2, u2, u1} m m R) (Matrix.one.{u1, u2} m R (fun (a : m) (b : m) => _inst_4 a b) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_5)) (Semiring.toOne.{u1} R _inst_5))))) -> (Eq.{1} Nat (Fintype.card.{u3} n _inst_1) (Fintype.card.{u2} m _inst_3))
-Case conversion may be inaccurate. Consider using '#align matrix.square_of_invertible Matrix.square_of_invertibleₓ'. -/
theorem Matrix.square_of_invertible (M : Matrix n m R) (N : Matrix m n R) (h : M ⬝ N = 1)
(h' : N ⬝ M = 1) : Fintype.card n = Fintype.card m :=
card_eq_of_linearEquiv R (Matrix.toLinearEquivRight'OfInv h' h)
mathlib commit https://github.com/leanprover-community/mathlib/commit/86d04064ca33ee3d3405fbfc497d494fd2dd4796
@@ -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.invariant_basis_number
-! leanprover-community/mathlib commit 843240b048bbb19942c581fd64caecbbe96337be
+! leanprover-community/mathlib commit f2b757fc5c341d88741b9c4630b1e8ba973c5726
! Please do not edit these lines, except to modify the commit id
! if you have ported upstream changes.
-/
@@ -13,6 +13,9 @@ import Mathbin.LinearAlgebra.InvariantBasisNumber
/-!
# Invertible matrices over a ring with invariant basis number are square.
+
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
-/
mathlib commit https://github.com/leanprover-community/mathlib/commit/fa78268d4d77cb2b2fbc89f0527e2e7807763780
@@ -22,6 +22,12 @@ variable {R : Type _} [Semiring R] [InvariantBasisNumber R]
open Matrix
+/- warning: matrix.square_of_invertible -> Matrix.square_of_invertible is a dubious translation:
+lean 3 declaration is
+ forall {n : Type.{u1}} {m : Type.{u2}} [_inst_1 : Fintype.{u1} n] [_inst_2 : DecidableEq.{succ u1} n] [_inst_3 : Fintype.{u2} m] [_inst_4 : DecidableEq.{succ u2} m] {R : Type.{u3}} [_inst_5 : Semiring.{u3} R] [_inst_6 : InvariantBasisNumber.{u3} R _inst_5] (M : Matrix.{u1, u2, u3} n m R) (N : Matrix.{u2, u1, u3} m n R), (Eq.{succ (max u1 u3)} (Matrix.{u1, u1, u3} n n R) (Matrix.mul.{u3, u1, u2, u1} n m n R _inst_3 (Distrib.toHasMul.{u3} R (NonUnitalNonAssocSemiring.toDistrib.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_5)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_5))) M N) (OfNat.ofNat.{max u1 u3} (Matrix.{u1, u1, u3} n n R) 1 (OfNat.mk.{max u1 u3} (Matrix.{u1, u1, u3} n n R) 1 (One.one.{max u1 u3} (Matrix.{u1, u1, u3} n n R) (Matrix.hasOne.{u3, u1} n R (fun (a : n) (b : n) => _inst_2 a b) (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_5)))) (AddMonoidWithOne.toOne.{u3} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} R (NonAssocSemiring.toAddCommMonoidWithOne.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_5))))))))) -> (Eq.{succ (max u2 u3)} (Matrix.{u2, u2, u3} m m R) (Matrix.mul.{u3, u2, u1, u2} m n m R _inst_1 (Distrib.toHasMul.{u3} R (NonUnitalNonAssocSemiring.toDistrib.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_5)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_5))) N M) (OfNat.ofNat.{max u2 u3} (Matrix.{u2, u2, u3} m m R) 1 (OfNat.mk.{max u2 u3} (Matrix.{u2, u2, u3} m m R) 1 (One.one.{max u2 u3} (Matrix.{u2, u2, u3} m m R) (Matrix.hasOne.{u3, u2} m R (fun (a : m) (b : m) => _inst_4 a b) (MulZeroClass.toHasZero.{u3} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_5)))) (AddMonoidWithOne.toOne.{u3} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u3} R (NonAssocSemiring.toAddCommMonoidWithOne.{u3} R (Semiring.toNonAssocSemiring.{u3} R _inst_5))))))))) -> (Eq.{1} Nat (Fintype.card.{u1} n _inst_1) (Fintype.card.{u2} m _inst_3))
+but is expected to have type
+ forall {n : Type.{u3}} {m : Type.{u2}} [_inst_1 : Fintype.{u3} n] [_inst_2 : DecidableEq.{succ u3} n] [_inst_3 : Fintype.{u2} m] [_inst_4 : DecidableEq.{succ u2} m] {R : Type.{u1}} [_inst_5 : Semiring.{u1} R] [_inst_6 : InvariantBasisNumber.{u1} R _inst_5] (M : Matrix.{u3, u2, u1} n m R) (N : Matrix.{u2, u3, u1} m n R), (Eq.{max (succ u3) (succ u1)} (Matrix.{u3, u3, u1} n n R) (Matrix.mul.{u1, u3, u2, u3} n m n R _inst_3 (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_5))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_5))) M N) (OfNat.ofNat.{max u3 u1} (Matrix.{u3, u3, u1} n n R) 1 (One.toOfNat1.{max u3 u1} (Matrix.{u3, u3, u1} n n R) (Matrix.one.{u1, u3} n R (fun (a : n) (b : n) => _inst_2 a b) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_5)) (Semiring.toOne.{u1} R _inst_5))))) -> (Eq.{max (succ u2) (succ u1)} (Matrix.{u2, u2, u1} m m R) (Matrix.mul.{u1, u2, u3, u2} m n m R _inst_1 (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_5))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_5))) N M) (OfNat.ofNat.{max u2 u1} (Matrix.{u2, u2, u1} m m R) 1 (One.toOfNat1.{max u2 u1} (Matrix.{u2, u2, u1} m m R) (Matrix.one.{u1, u2} m R (fun (a : m) (b : m) => _inst_4 a b) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_5)) (Semiring.toOne.{u1} R _inst_5))))) -> (Eq.{1} Nat (Fintype.card.{u3} n _inst_1) (Fintype.card.{u2} m _inst_3))
+Case conversion may be inaccurate. Consider using '#align matrix.square_of_invertible Matrix.square_of_invertibleₓ'. -/
theorem Matrix.square_of_invertible (M : Matrix n m R) (N : Matrix m n R) (h : M ⬝ N = 1)
(h' : N ⬝ M = 1) : Fintype.card n = Fintype.card m :=
card_eq_of_linearEquiv R (Matrix.toLinearEquivRight'OfInv h' h)
mathlib commit https://github.com/leanprover-community/mathlib/commit/dd6388c44e6f6b4547070b887c5905d5cfe6c9f8
@@ -24,6 +24,6 @@ open Matrix
theorem Matrix.square_of_invertible (M : Matrix n m R) (N : Matrix m n R) (h : M ⬝ N = 1)
(h' : N ⬝ M = 1) : Fintype.card n = Fintype.card m :=
- card_eq_of_lequiv R (Matrix.toLinearEquivRight'OfInv h' h)
+ card_eq_of_linearEquiv R (Matrix.toLinearEquivRight'OfInv h' h)
#align matrix.square_of_invertible Matrix.square_of_invertible
mathlib commit https://github.com/leanprover-community/mathlib/commit/bd9851ca476957ea4549eb19b40e7b5ade9428cc
Empty lines were removed by executing the following Python script twice
import os
import re
# Loop through each file in the repository
for dir_path, dirs, files in os.walk('.'):
for filename in files:
if filename.endswith('.lean'):
file_path = os.path.join(dir_path, filename)
# Open the file and read its contents
with open(file_path, 'r') as file:
content = file.read()
# Use a regular expression to replace sequences of "variable" lines separated by empty lines
# with sequences without empty lines
modified_content = re.sub(r'(variable.*\n)\n(variable(?! .* in))', r'\1\2', content)
# Write the modified content back to the file
with open(file_path, 'w') as file:
file.write(modified_content)
@@ -14,7 +14,6 @@ import Mathlib.LinearAlgebra.InvariantBasisNumber
variable {n m : Type*} [Fintype n] [DecidableEq n] [Fintype m] [DecidableEq m]
-
variable {R : Type*} [Semiring R] [InvariantBasisNumber R]
open Matrix
⬝
notation in favor of HMul
(#6487)
The main difficulty here is that *
has a slightly difference precedence to ⬝
. notably around smul
and neg
.
The other annoyance is that ↑U ⬝ A ⬝ ↑U⁻¹ : Matrix m m 𝔸
now has to be written U.val * A * (U⁻¹).val
in order to typecheck.
A downside of this change to consider: if you have a goal of A * (B * C) = (A * B) * C
, mul_assoc
now gives the illusion of matching, when in fact Matrix.mul_assoc
is needed. Previously the distinct symbol made it easy to avoid this mistake.
On the flipside, there is now no need to rewrite by Matrix.mul_eq_mul
all the time (indeed, the lemma is now removed).
@@ -19,8 +19,7 @@ variable {R : Type*} [Semiring R] [InvariantBasisNumber R]
open Matrix
-theorem Matrix.square_of_invertible (M : Matrix n m R) (N : Matrix m n R) (h : M ⬝ N = 1)
- (h' : N ⬝ M = 1) : Fintype.card n = Fintype.card m :=
+theorem Matrix.square_of_invertible (M : Matrix n m R) (N : Matrix m n R) (h : M * N = 1)
+ (h' : N * M = 1) : Fintype.card n = Fintype.card m :=
card_eq_of_linearEquiv R (Matrix.toLinearEquivRight'OfInv h' h)
#align matrix.square_of_invertible Matrix.square_of_invertible
-
Type _
and Sort _
(#6499)
We remove all possible occurences of Type _
and Sort _
in favor of Type*
and Sort*
.
This has nice performance benefits.
@@ -13,9 +13,9 @@ import Mathlib.LinearAlgebra.InvariantBasisNumber
-/
-variable {n m : Type _} [Fintype n] [DecidableEq n] [Fintype m] [DecidableEq m]
+variable {n m : Type*} [Fintype n] [DecidableEq n] [Fintype m] [DecidableEq m]
-variable {R : Type _} [Semiring R] [InvariantBasisNumber R]
+variable {R : Type*} [Semiring R] [InvariantBasisNumber R]
open Matrix
@@ -2,15 +2,12 @@
Copyright (c) 2022 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.invariant_basis_number
-! leanprover-community/mathlib commit 843240b048bbb19942c581fd64caecbbe96337be
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
-/
import Mathlib.LinearAlgebra.Matrix.ToLin
import Mathlib.LinearAlgebra.InvariantBasisNumber
+#align_import linear_algebra.matrix.invariant_basis_number from "leanprover-community/mathlib"@"843240b048bbb19942c581fd64caecbbe96337be"
+
/-!
# Invertible matrices over a ring with invariant basis number are square.
-/
The unported dependencies are