linear_algebra.quadratic_form.isometry

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

14b69e9f

(last sync)

Changes in mathlib3port

mathlib3

mathlib3port

c2092722

bump to nightly-2024-03-17-08

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

22f01ce4

Diff

@@ -194,7 +194,7 @@ theorem equivalent_weightedSumSquares_units_of_nondegenerate' (Q : QuadraticForm
   by
   obtain ⟨v, hv₁⟩ := exists_orthogonal_basis (associated_is_symm _ Q)
   have hv₂ := hv₁.not_is_ortho_basis_self_of_nondegenerate hQ
-  simp_rw [is_ortho, associated_eq_self_apply] at hv₂ 
+  simp_rw [is_ortho, associated_eq_self_apply] at hv₂
   exact ⟨fun i => Units.mk0 _ (hv₂ i), ⟨Q.isometry_weighted_sum_squares v hv₁⟩⟩
 #align quadratic_form.equivalent_weighted_sum_squares_units_of_nondegenerate' QuadraticForm.equivalent_weightedSumSquares_units_of_nondegenerate'
 -/

c2092722

bump to nightly-2024-02-27-08

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

cca8d078

Diff

@@ -182,7 +182,7 @@ open BilinForm
 #print QuadraticForm.equivalent_weightedSumSquares /-
 theorem equivalent_weightedSumSquares (Q : QuadraticForm K V) :
     ∃ w : Fin (FiniteDimensional.finrank K V) → K, Equivalent Q (weightedSumSquares K w) :=
-  let ⟨v, hv₁⟩ := exists_orthogonal_basis (associated_isSymm _ Q)
+  let ⟨v, hv₁⟩ := LinearMap.BilinForm.exists_orthogonal_basis (associated_isSymm _ Q)
   ⟨_, ⟨Q.isometryEquivWeightedSumSquares v hv₁⟩⟩
 #align quadratic_form.equivalent_weighted_sum_squares QuadraticForm.equivalent_weightedSumSquares
 -/

c2092722

bump to nightly-2023-09-24-06

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

5655435f

Diff

@@ -3,7 +3,7 @@ Copyright (c) 2020 Anne Baanen. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Kexing Ying, Eric Wieser
 -/
-import Mathbin.LinearAlgebra.QuadraticForm.Basic
+import LinearAlgebra.QuadraticForm.Basic
 
 #align_import linear_algebra.quadratic_form.isometry from "leanprover-community/mathlib"@"c20927220ef87bb4962ba08bf6da2ce3cf50a6dd"

c2092722

bump to nightly-2023-08-03-09

mathlib commit https://github.com/leanprover-community/mathlib/commit/48a058d7e39a80ed56858505719a0b2197900999

b7c9a72c

Diff

@@ -35,13 +35,14 @@ variable [AddCommMonoid M] [AddCommMonoid M₁] [AddCommMonoid M₂] [AddCommMon
 
 variable [Module R M] [Module R M₁] [Module R M₂] [Module R M₃]
 
-#print QuadraticForm.Isometry /-
+#print QuadraticForm.IsometryEquiv /-
 /-- An isometry between two quadratic spaces `M₁, Q₁` and `M₂, Q₂` over a ring `R`,
 is a linear equivalence between `M₁` and `M₂` that commutes with the quadratic forms. -/
 @[nolint has_nonempty_instance]
-structure Isometry (Q₁ : QuadraticForm R M₁) (Q₂ : QuadraticForm R M₂) extends M₁ ≃ₗ[R] M₂ where
+structure IsometryEquiv (Q₁ : QuadraticForm R M₁) (Q₂ : QuadraticForm R M₂) extends
+    M₁ ≃ₗ[R] M₂ where
   map_app' : ∀ m, Q₂ (to_fun m) = Q₁ m
-#align quadratic_form.isometry QuadraticForm.Isometry
+#align quadratic_form.isometry QuadraticForm.IsometryEquiv
 -/
 
 #print QuadraticForm.Equivalent /-
@@ -49,7 +50,7 @@ structure Isometry (Q₁ : QuadraticForm R M₁) (Q₂ : QuadraticForm R M₂) e
 if there exists an isometry between them:
 a linear equivalence that transforms one quadratic form into the other. -/
 def Equivalent (Q₁ : QuadraticForm R M₁) (Q₂ : QuadraticForm R M₂) :=
-  Nonempty (Q₁.Isometry Q₂)
+  Nonempty (Q₁.IsometryEquiv Q₂)
 #align quadratic_form.equivalent QuadraticForm.Equivalent
 -/
 
@@ -57,55 +58,55 @@ namespace Isometry
 
 variable {Q₁ : QuadraticForm R M₁} {Q₂ : QuadraticForm R M₂} {Q₃ : QuadraticForm R M₃}
 
-instance : Coe (Q₁.Isometry Q₂) (M₁ ≃ₗ[R] M₂) :=
-  ⟨Isometry.toLinearEquiv⟩
+instance : Coe (Q₁.IsometryEquiv Q₂) (M₁ ≃ₗ[R] M₂) :=
+  ⟨IsometryEquiv.toLinearEquiv⟩
 
 @[simp]
-theorem toLinearEquiv_eq_coe (f : Q₁.Isometry Q₂) : f.toLinearEquiv = f :=
+theorem toLinearEquiv_eq_coe (f : Q₁.IsometryEquiv Q₂) : f.toLinearEquiv = f :=
   rfl
-#align quadratic_form.isometry.to_linear_equiv_eq_coe QuadraticForm.Isometry.toLinearEquiv_eq_coe
+#align quadratic_form.isometry.to_linear_equiv_eq_coe QuadraticForm.IsometryEquiv.toLinearEquiv_eq_coe
 
-instance : CoeFun (Q₁.Isometry Q₂) fun _ => M₁ → M₂ :=
+instance : CoeFun (Q₁.IsometryEquiv Q₂) fun _ => M₁ → M₂ :=
   ⟨fun f => ⇑(f : M₁ ≃ₗ[R] M₂)⟩
 
-#print QuadraticForm.Isometry.coe_toLinearEquiv /-
+#print QuadraticForm.IsometryEquiv.coe_toLinearEquiv /-
 @[simp]
-theorem coe_toLinearEquiv (f : Q₁.Isometry Q₂) : ⇑(f : M₁ ≃ₗ[R] M₂) = f :=
+theorem coe_toLinearEquiv (f : Q₁.IsometryEquiv Q₂) : ⇑(f : M₁ ≃ₗ[R] M₂) = f :=
   rfl
-#align quadratic_form.isometry.coe_to_linear_equiv QuadraticForm.Isometry.coe_toLinearEquiv
+#align quadratic_form.isometry.coe_to_linear_equiv QuadraticForm.IsometryEquiv.coe_toLinearEquiv
 -/
 
-#print QuadraticForm.Isometry.map_app /-
+#print QuadraticForm.IsometryEquiv.map_app /-
 @[simp]
-theorem map_app (f : Q₁.Isometry Q₂) (m : M₁) : Q₂ (f m) = Q₁ m :=
+theorem map_app (f : Q₁.IsometryEquiv Q₂) (m : M₁) : Q₂ (f m) = Q₁ m :=
   f.map_app' m
-#align quadratic_form.isometry.map_app QuadraticForm.Isometry.map_app
+#align quadratic_form.isometry.map_app QuadraticForm.IsometryEquiv.map_app
 -/
 
-#print QuadraticForm.Isometry.refl /-
+#print QuadraticForm.IsometryEquiv.refl /-
 /-- The identity isometry from a quadratic form to itself. -/
 @[refl]
-def refl (Q : QuadraticForm R M) : Q.Isometry Q :=
+def refl (Q : QuadraticForm R M) : Q.IsometryEquiv Q :=
   { LinearEquiv.refl R M with map_app' := fun m => rfl }
-#align quadratic_form.isometry.refl QuadraticForm.Isometry.refl
+#align quadratic_form.isometry.refl QuadraticForm.IsometryEquiv.refl
 -/
 
-#print QuadraticForm.Isometry.symm /-
+#print QuadraticForm.IsometryEquiv.symm /-
 /-- The inverse isometry of an isometry between two quadratic forms. -/
 @[symm]
-def symm (f : Q₁.Isometry Q₂) : Q₂.Isometry Q₁ :=
+def symm (f : Q₁.IsometryEquiv Q₂) : Q₂.IsometryEquiv Q₁ :=
   { (f : M₁ ≃ₗ[R] M₂).symm with
     map_app' := by intro m; rw [← f.map_app]; congr; exact f.to_linear_equiv.apply_symm_apply m }
-#align quadratic_form.isometry.symm QuadraticForm.Isometry.symm
+#align quadratic_form.isometry.symm QuadraticForm.IsometryEquiv.symm
 -/
 
-#print QuadraticForm.Isometry.trans /-
+#print QuadraticForm.IsometryEquiv.trans /-
 /-- The composition of two isometries between quadratic forms. -/
 @[trans]
-def trans (f : Q₁.Isometry Q₂) (g : Q₂.Isometry Q₃) : Q₁.Isometry Q₃ :=
+def trans (f : Q₁.IsometryEquiv Q₂) (g : Q₂.IsometryEquiv Q₃) : Q₁.IsometryEquiv Q₃ :=
   { (f : M₁ ≃ₗ[R] M₂).trans (g : M₂ ≃ₗ[R] M₃) with
     map_app' := by intro m; rw [← f.map_app, ← g.map_app]; rfl }
-#align quadratic_form.isometry.trans QuadraticForm.Isometry.trans
+#align quadratic_form.isometry.trans QuadraticForm.IsometryEquiv.trans
 -/
 
 end Isometry
@@ -117,7 +118,7 @@ variable {Q₁ : QuadraticForm R M₁} {Q₂ : QuadraticForm R M₂} {Q₃ : Qua
 #print QuadraticForm.Equivalent.refl /-
 @[refl]
 theorem refl (Q : QuadraticForm R M) : Q.Equivalent Q :=
-  ⟨Isometry.refl Q⟩
+  ⟨IsometryEquiv.refl Q⟩
 #align quadratic_form.equivalent.refl QuadraticForm.Equivalent.refl
 -/
 
@@ -139,39 +140,39 @@ end Equivalent
 
 variable [Fintype ι] {v : Basis ι R M}
 
-#print QuadraticForm.isometryOfCompLinearEquiv /-
+#print QuadraticForm.isometryEquivOfCompLinearEquiv /-
 /-- A quadratic form composed with a `linear_equiv` is isometric to itself. -/
-def isometryOfCompLinearEquiv (Q : QuadraticForm R M) (f : M₁ ≃ₗ[R] M) :
-    Q.Isometry (Q.comp (f : M₁ →ₗ[R] M)) :=
+def isometryEquivOfCompLinearEquiv (Q : QuadraticForm R M) (f : M₁ ≃ₗ[R] M) :
+    Q.IsometryEquiv (Q.comp (f : M₁ →ₗ[R] M)) :=
   { f.symm with
     map_app' := by
       intro
       simp only [comp_apply, LinearEquiv.coe_coe, LinearEquiv.toFun_eq_coe,
         LinearEquiv.apply_symm_apply, f.apply_symm_apply] }
-#align quadratic_form.isometry_of_comp_linear_equiv QuadraticForm.isometryOfCompLinearEquiv
+#align quadratic_form.isometry_of_comp_linear_equiv QuadraticForm.isometryEquivOfCompLinearEquiv
 -/
 
-#print QuadraticForm.isometryBasisRepr /-
+#print QuadraticForm.isometryEquivBasisRepr /-
 /-- A quadratic form is isometric to its bases representations. -/
-noncomputable def isometryBasisRepr (Q : QuadraticForm R M) (v : Basis ι R M) :
-    Isometry Q (Q.basis_repr v) :=
-  isometryOfCompLinearEquiv Q v.equivFun.symm
-#align quadratic_form.isometry_basis_repr QuadraticForm.isometryBasisRepr
+noncomputable def isometryEquivBasisRepr (Q : QuadraticForm R M) (v : Basis ι R M) :
+    IsometryEquiv Q (Q.basis_repr v) :=
+  isometryEquivOfCompLinearEquiv Q v.equivFun.symm
+#align quadratic_form.isometry_basis_repr QuadraticForm.isometryEquivBasisRepr
 -/
 
 variable [Field K] [Invertible (2 : K)] [AddCommGroup V] [Module K V]
 
-#print QuadraticForm.isometryWeightedSumSquares /-
+#print QuadraticForm.isometryEquivWeightedSumSquares /-
 /-- Given an orthogonal basis, a quadratic form is isometric with a weighted sum of squares. -/
-noncomputable def isometryWeightedSumSquares (Q : QuadraticForm K V)
+noncomputable def isometryEquivWeightedSumSquares (Q : QuadraticForm K V)
     (v : Basis (Fin (FiniteDimensional.finrank K V)) K V) (hv₁ : (associated Q).IsOrthoᵢ v) :
-    Q.Isometry (weightedSumSquares K fun i => Q (v i)) :=
+    Q.IsometryEquiv (weightedSumSquares K fun i => Q (v i)) :=
   by
   let iso := Q.isometry_basis_repr v
   refine' ⟨iso, fun m => _⟩
   convert iso.map_app m
   rw [basis_repr_eq_of_is_Ortho _ _ hv₁]
-#align quadratic_form.isometry_weighted_sum_squares QuadraticForm.isometryWeightedSumSquares
+#align quadratic_form.isometry_weighted_sum_squares QuadraticForm.isometryEquivWeightedSumSquares
 -/
 
 variable [FiniteDimensional K V]
@@ -182,7 +183,7 @@ open BilinForm
 theorem equivalent_weightedSumSquares (Q : QuadraticForm K V) :
     ∃ w : Fin (FiniteDimensional.finrank K V) → K, Equivalent Q (weightedSumSquares K w) :=
   let ⟨v, hv₁⟩ := exists_orthogonal_basis (associated_isSymm _ Q)
-  ⟨_, ⟨Q.isometryWeightedSumSquares v hv₁⟩⟩
+  ⟨_, ⟨Q.isometryEquivWeightedSumSquares v hv₁⟩⟩
 #align quadratic_form.equivalent_weighted_sum_squares QuadraticForm.equivalent_weightedSumSquares
 -/

c2092722

bump to nightly-2023-07-20-09

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

9c56d0dd

Diff

@@ -2,14 +2,11 @@
 Copyright (c) 2020 Anne Baanen. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Kexing Ying, Eric Wieser
-
-! This file was ported from Lean 3 source module linear_algebra.quadratic_form.isometry
-! leanprover-community/mathlib commit c20927220ef87bb4962ba08bf6da2ce3cf50a6dd
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.LinearAlgebra.QuadraticForm.Basic
 
+#align_import linear_algebra.quadratic_form.isometry from "leanprover-community/mathlib"@"c20927220ef87bb4962ba08bf6da2ce3cf50a6dd"
+
 /-!
 # Isometries with respect to quadratic forms

c2092722

bump to nightly-2023-06-13-21

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

829520ac

Diff

@@ -71,15 +71,19 @@ theorem toLinearEquiv_eq_coe (f : Q₁.Isometry Q₂) : f.toLinearEquiv = f :=
 instance : CoeFun (Q₁.Isometry Q₂) fun _ => M₁ → M₂ :=
   ⟨fun f => ⇑(f : M₁ ≃ₗ[R] M₂)⟩
 
+#print QuadraticForm.Isometry.coe_toLinearEquiv /-
 @[simp]
 theorem coe_toLinearEquiv (f : Q₁.Isometry Q₂) : ⇑(f : M₁ ≃ₗ[R] M₂) = f :=
   rfl
 #align quadratic_form.isometry.coe_to_linear_equiv QuadraticForm.Isometry.coe_toLinearEquiv
+-/
 
+#print QuadraticForm.Isometry.map_app /-
 @[simp]
 theorem map_app (f : Q₁.Isometry Q₂) (m : M₁) : Q₂ (f m) = Q₁ m :=
   f.map_app' m
 #align quadratic_form.isometry.map_app QuadraticForm.Isometry.map_app
+-/
 
 #print QuadraticForm.Isometry.refl /-
 /-- The identity isometry from a quadratic form to itself. -/
@@ -113,20 +117,26 @@ namespace Equivalent
 
 variable {Q₁ : QuadraticForm R M₁} {Q₂ : QuadraticForm R M₂} {Q₃ : QuadraticForm R M₃}
 
+#print QuadraticForm.Equivalent.refl /-
 @[refl]
 theorem refl (Q : QuadraticForm R M) : Q.Equivalent Q :=
   ⟨Isometry.refl Q⟩
 #align quadratic_form.equivalent.refl QuadraticForm.Equivalent.refl
+-/
 
+#print QuadraticForm.Equivalent.symm /-
 @[symm]
 theorem symm (h : Q₁.Equivalent Q₂) : Q₂.Equivalent Q₁ :=
   h.elim fun f => ⟨f.symm⟩
 #align quadratic_form.equivalent.symm QuadraticForm.Equivalent.symm
+-/
 
+#print QuadraticForm.Equivalent.trans /-
 @[trans]
 theorem trans (h : Q₁.Equivalent Q₂) (h' : Q₂.Equivalent Q₃) : Q₁.Equivalent Q₃ :=
   h'.elim <| h.elim fun f g => ⟨f.trans g⟩
 #align quadratic_form.equivalent.trans QuadraticForm.Equivalent.trans
+-/
 
 end Equivalent
 
@@ -154,6 +164,7 @@ noncomputable def isometryBasisRepr (Q : QuadraticForm R M) (v : Basis ι R M) :
 
 variable [Field K] [Invertible (2 : K)] [AddCommGroup V] [Module K V]
 
+#print QuadraticForm.isometryWeightedSumSquares /-
 /-- Given an orthogonal basis, a quadratic form is isometric with a weighted sum of squares. -/
 noncomputable def isometryWeightedSumSquares (Q : QuadraticForm K V)
     (v : Basis (Fin (FiniteDimensional.finrank K V)) K V) (hv₁ : (associated Q).IsOrthoᵢ v) :
@@ -164,17 +175,21 @@ noncomputable def isometryWeightedSumSquares (Q : QuadraticForm K V)
   convert iso.map_app m
   rw [basis_repr_eq_of_is_Ortho _ _ hv₁]
 #align quadratic_form.isometry_weighted_sum_squares QuadraticForm.isometryWeightedSumSquares
+-/
 
 variable [FiniteDimensional K V]
 
 open BilinForm
 
+#print QuadraticForm.equivalent_weightedSumSquares /-
 theorem equivalent_weightedSumSquares (Q : QuadraticForm K V) :
     ∃ w : Fin (FiniteDimensional.finrank K V) → K, Equivalent Q (weightedSumSquares K w) :=
   let ⟨v, hv₁⟩ := exists_orthogonal_basis (associated_isSymm _ Q)
   ⟨_, ⟨Q.isometryWeightedSumSquares v hv₁⟩⟩
 #align quadratic_form.equivalent_weighted_sum_squares QuadraticForm.equivalent_weightedSumSquares
+-/
 
+#print QuadraticForm.equivalent_weightedSumSquares_units_of_nondegenerate' /-
 theorem equivalent_weightedSumSquares_units_of_nondegenerate' (Q : QuadraticForm K V)
     (hQ : (associated Q).Nondegenerate) :
     ∃ w : Fin (FiniteDimensional.finrank K V) → Kˣ, Equivalent Q (weightedSumSquares K w) :=
@@ -184,6 +199,7 @@ theorem equivalent_weightedSumSquares_units_of_nondegenerate' (Q : QuadraticForm
   simp_rw [is_ortho, associated_eq_self_apply] at hv₂ 
   exact ⟨fun i => Units.mk0 _ (hv₂ i), ⟨Q.isometry_weighted_sum_squares v hv₁⟩⟩
 #align quadratic_form.equivalent_weighted_sum_squares_units_of_nondegenerate' QuadraticForm.equivalent_weightedSumSquares_units_of_nondegenerate'
+-/
 
 end QuadraticForm

c2092722

bump to nightly-2023-06-08-03

mathlib commit https://github.com/leanprover-community/mathlib/commit/31c24aa72e7b3e5ed97a8412470e904f82b81004

8f04dc2b

Diff

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Kexing Ying, Eric Wieser
 
 ! This file was ported from Lean 3 source module linear_algebra.quadratic_form.isometry
-! leanprover-community/mathlib commit 14b69e9f3c16630440a2cbd46f1ddad0d561dee7
+! leanprover-community/mathlib commit c20927220ef87bb4962ba08bf6da2ce3cf50a6dd
 ! 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.QuadraticForm.Basic
 /-!
 # Isometries with respect to quadratic forms
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 ## Main definitions
 
 * `quadratic_form.isometry`: `linear_equiv`s which map between two different quadratic forms

14b69e9f

bump to nightly-2023-06-06-13

mathlib commit https://github.com/leanprover-community/mathlib/commit/a3209ddf94136d36e5e5c624b10b2a347cc9d090

ccc9a4b3

Diff

@@ -35,19 +35,23 @@ variable [AddCommMonoid M] [AddCommMonoid M₁] [AddCommMonoid M₂] [AddCommMon
 
 variable [Module R M] [Module R M₁] [Module R M₂] [Module R M₃]
 
+#print QuadraticForm.Isometry /-
 /-- An isometry between two quadratic spaces `M₁, Q₁` and `M₂, Q₂` over a ring `R`,
 is a linear equivalence between `M₁` and `M₂` that commutes with the quadratic forms. -/
 @[nolint has_nonempty_instance]
 structure Isometry (Q₁ : QuadraticForm R M₁) (Q₂ : QuadraticForm R M₂) extends M₁ ≃ₗ[R] M₂ where
   map_app' : ∀ m, Q₂ (to_fun m) = Q₁ m
 #align quadratic_form.isometry QuadraticForm.Isometry
+-/
 
+#print QuadraticForm.Equivalent /-
 /-- Two quadratic forms over a ring `R` are equivalent
 if there exists an isometry between them:
 a linear equivalence that transforms one quadratic form into the other. -/
 def Equivalent (Q₁ : QuadraticForm R M₁) (Q₂ : QuadraticForm R M₂) :=
   Nonempty (Q₁.Isometry Q₂)
 #align quadratic_form.equivalent QuadraticForm.Equivalent
+-/
 
 namespace Isometry
 
@@ -65,34 +69,40 @@ instance : CoeFun (Q₁.Isometry Q₂) fun _ => M₁ → M₂ :=
   ⟨fun f => ⇑(f : M₁ ≃ₗ[R] M₂)⟩
 
 @[simp]
-theorem coe_to_linearEquiv (f : Q₁.Isometry Q₂) : ⇑(f : M₁ ≃ₗ[R] M₂) = f :=
+theorem coe_toLinearEquiv (f : Q₁.Isometry Q₂) : ⇑(f : M₁ ≃ₗ[R] M₂) = f :=
   rfl
-#align quadratic_form.isometry.coe_to_linear_equiv QuadraticForm.Isometry.coe_to_linearEquiv
+#align quadratic_form.isometry.coe_to_linear_equiv QuadraticForm.Isometry.coe_toLinearEquiv
 
 @[simp]
 theorem map_app (f : Q₁.Isometry Q₂) (m : M₁) : Q₂ (f m) = Q₁ m :=
   f.map_app' m
 #align quadratic_form.isometry.map_app QuadraticForm.Isometry.map_app
 
+#print QuadraticForm.Isometry.refl /-
 /-- The identity isometry from a quadratic form to itself. -/
 @[refl]
 def refl (Q : QuadraticForm R M) : Q.Isometry Q :=
   { LinearEquiv.refl R M with map_app' := fun m => rfl }
 #align quadratic_form.isometry.refl QuadraticForm.Isometry.refl
+-/
 
+#print QuadraticForm.Isometry.symm /-
 /-- The inverse isometry of an isometry between two quadratic forms. -/
 @[symm]
 def symm (f : Q₁.Isometry Q₂) : Q₂.Isometry Q₁ :=
   { (f : M₁ ≃ₗ[R] M₂).symm with
     map_app' := by intro m; rw [← f.map_app]; congr; exact f.to_linear_equiv.apply_symm_apply m }
 #align quadratic_form.isometry.symm QuadraticForm.Isometry.symm
+-/
 
+#print QuadraticForm.Isometry.trans /-
 /-- The composition of two isometries between quadratic forms. -/
 @[trans]
 def trans (f : Q₁.Isometry Q₂) (g : Q₂.Isometry Q₃) : Q₁.Isometry Q₃ :=
   { (f : M₁ ≃ₗ[R] M₂).trans (g : M₂ ≃ₗ[R] M₃) with
     map_app' := by intro m; rw [← f.map_app, ← g.map_app]; rfl }
 #align quadratic_form.isometry.trans QuadraticForm.Isometry.trans
+-/
 
 end Isometry
 
@@ -119,6 +129,7 @@ end Equivalent
 
 variable [Fintype ι] {v : Basis ι R M}
 
+#print QuadraticForm.isometryOfCompLinearEquiv /-
 /-- A quadratic form composed with a `linear_equiv` is isometric to itself. -/
 def isometryOfCompLinearEquiv (Q : QuadraticForm R M) (f : M₁ ≃ₗ[R] M) :
     Q.Isometry (Q.comp (f : M₁ →ₗ[R] M)) :=
@@ -128,12 +139,15 @@ def isometryOfCompLinearEquiv (Q : QuadraticForm R M) (f : M₁ ≃ₗ[R] M) :
       simp only [comp_apply, LinearEquiv.coe_coe, LinearEquiv.toFun_eq_coe,
         LinearEquiv.apply_symm_apply, f.apply_symm_apply] }
 #align quadratic_form.isometry_of_comp_linear_equiv QuadraticForm.isometryOfCompLinearEquiv
+-/
 
+#print QuadraticForm.isometryBasisRepr /-
 /-- A quadratic form is isometric to its bases representations. -/
 noncomputable def isometryBasisRepr (Q : QuadraticForm R M) (v : Basis ι R M) :
     Isometry Q (Q.basis_repr v) :=
   isometryOfCompLinearEquiv Q v.equivFun.symm
 #align quadratic_form.isometry_basis_repr QuadraticForm.isometryBasisRepr
+-/
 
 variable [Field K] [Invertible (2 : K)] [AddCommGroup V] [Module K V]

14b69e9f

bump to nightly-2023-06-01-16

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

b9c87c70

Diff

@@ -84,7 +84,7 @@ def refl (Q : QuadraticForm R M) : Q.Isometry Q :=
 @[symm]
 def symm (f : Q₁.Isometry Q₂) : Q₂.Isometry Q₁ :=
   { (f : M₁ ≃ₗ[R] M₂).symm with
-    map_app' := by intro m; rw [← f.map_app]; congr ; exact f.to_linear_equiv.apply_symm_apply m }
+    map_app' := by intro m; rw [← f.map_app]; congr; exact f.to_linear_equiv.apply_symm_apply m }
 #align quadratic_form.isometry.symm QuadraticForm.Isometry.symm
 
 /-- The composition of two isometries between quadratic forms. -/
@@ -164,7 +164,7 @@ theorem equivalent_weightedSumSquares_units_of_nondegenerate' (Q : QuadraticForm
   by
   obtain ⟨v, hv₁⟩ := exists_orthogonal_basis (associated_is_symm _ Q)
   have hv₂ := hv₁.not_is_ortho_basis_self_of_nondegenerate hQ
-  simp_rw [is_ortho, associated_eq_self_apply] at hv₂
+  simp_rw [is_ortho, associated_eq_self_apply] at hv₂ 
   exact ⟨fun i => Units.mk0 _ (hv₂ i), ⟨Q.isometry_weighted_sum_squares v hv₁⟩⟩
 #align quadratic_form.equivalent_weighted_sum_squares_units_of_nondegenerate' QuadraticForm.equivalent_weightedSumSquares_units_of_nondegenerate'

14b69e9f

bump to nightly-2023-05-28-04

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

6797a637

Diff

@@ -84,21 +84,14 @@ def refl (Q : QuadraticForm R M) : Q.Isometry Q :=
 @[symm]
 def symm (f : Q₁.Isometry Q₂) : Q₂.Isometry Q₁ :=
   { (f : M₁ ≃ₗ[R] M₂).symm with
-    map_app' := by
-      intro m
-      rw [← f.map_app]
-      congr
-      exact f.to_linear_equiv.apply_symm_apply m }
+    map_app' := by intro m; rw [← f.map_app]; congr ; exact f.to_linear_equiv.apply_symm_apply m }
 #align quadratic_form.isometry.symm QuadraticForm.Isometry.symm
 
 /-- The composition of two isometries between quadratic forms. -/
 @[trans]
 def trans (f : Q₁.Isometry Q₂) (g : Q₂.Isometry Q₃) : Q₁.Isometry Q₃ :=
   { (f : M₁ ≃ₗ[R] M₂).trans (g : M₂ ≃ₗ[R] M₃) with
-    map_app' := by
-      intro m
-      rw [← f.map_app, ← g.map_app]
-      rfl }
+    map_app' := by intro m; rw [← f.map_app, ← g.map_app]; rfl }
 #align quadratic_form.isometry.trans QuadraticForm.Isometry.trans
 
 end Isometry

14b69e9f

bump to nightly-2023-05-23-03

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

ed98987c

Diff

@@ -161,7 +161,7 @@ open BilinForm
 
 theorem equivalent_weightedSumSquares (Q : QuadraticForm K V) :
     ∃ w : Fin (FiniteDimensional.finrank K V) → K, Equivalent Q (weightedSumSquares K w) :=
-  let ⟨v, hv₁⟩ := exists_orthogonal_basis (associatedIsSymm _ Q)
+  let ⟨v, hv₁⟩ := exists_orthogonal_basis (associated_isSymm _ Q)
   ⟨_, ⟨Q.isometryWeightedSumSquares v hv₁⟩⟩
 #align quadratic_form.equivalent_weighted_sum_squares QuadraticForm.equivalent_weightedSumSquares

14b69e9f

bump to nightly-2023-03-22-16

mathlib commit https://github.com/leanprover-community/mathlib/commit/dd6388c44e6f6b4547070b887c5905d5cfe6c9f8

85865d39

Diff

@@ -146,7 +146,7 @@ variable [Field K] [Invertible (2 : K)] [AddCommGroup V] [Module K V]
 
 /-- Given an orthogonal basis, a quadratic form is isometric with a weighted sum of squares. -/
 noncomputable def isometryWeightedSumSquares (Q : QuadraticForm K V)
-    (v : Basis (Fin (FiniteDimensional.finrank K V)) K V) (hv₁ : (associated Q).IsOrthoCat v) :
+    (v : Basis (Fin (FiniteDimensional.finrank K V)) K V) (hv₁ : (associated Q).IsOrthoᵢ v) :
     Q.Isometry (weightedSumSquares K fun i => Q (v i)) :=
   by
   let iso := Q.isometry_basis_repr v

14b69e9f

bump to nightly-2023-02-21-16

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

1107b979

Changes in mathlib4

mathlib3

mathlib4

14b69e9f

chore: classify porting notes referring to missing linters (#12098)

Reference the newly created issues #12094 and #12096, as well as the pre-existing #5171. Change all references to #10927 to #5171. Some of these changes were not labelled as "porting note"; change this for good measure.

c5b5490c

Diff

@@ -33,7 +33,7 @@ variable [Module R M] [Module R M₁] [Module R M₂] [Module R M₃]
 
 /-- An isometric equivalence between two quadratic spaces `M₁, Q₁` and `M₂, Q₂` over a ring `R`,
 is a linear equivalence between `M₁` and `M₂` that commutes with the quadratic forms. -/
--- Porting note: not implemented @[nolint has_nonempty_instance]
+-- Porting note(#5171): linter not ported yet @[nolint has_nonempty_instance]
 structure IsometryEquiv (Q₁ : QuadraticForm R M₁) (Q₂ : QuadraticForm R M₂)
     extends M₁ ≃ₗ[R] M₂ where
   map_app' : ∀ m, Q₂ (toFun m) = Q₁ m

14b69e9f

chore(*): remove empty lines between variable statements (#11418)

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)

75c86f04

Diff

@@ -28,9 +28,7 @@ variable {ι R K M M₁ M₂ M₃ V : Type*}
 namespace QuadraticForm
 
 variable [CommSemiring R]
-
 variable [AddCommMonoid M] [AddCommMonoid M₁] [AddCommMonoid M₂] [AddCommMonoid M₃]
-
 variable [Module R M] [Module R M₁] [Module R M₂] [Module R M₃]
 
 /-- An isometric equivalence between two quadratic spaces `M₁, Q₁` and `M₂, Q₂` over a ring `R`,

14b69e9f

refactor(LinearAlgebra/QuadraticForm): Replace BilinForm with a scalar valued bi LinearMap (#10238)

Following on from #10097, which converted the companion of a quadratic form with a bilinear map, this PR replaces a number of results about quadratic forms and bilinear forms with results about quadratic forms and scalar valued bilinear maps. The long term aim is to be able to consider quadratic maps.

The main change is to LinearAlgebra/QuadraticForm/Basic, but this necessitates changes throughout LinearAlgebra/QuadraticForm/. Minor changes are also required elsewhere:

LinearAlgebra/CliffordAlgebra/
LinearAlgebra/Matrix/PosDef
LinearAlgebra/SesquilinearForm
A number of additional results about tensor products and linear maps are also required.

Co-authored-by: Eric Wieser <wieser.eric@gmail.com> Co-authored-by: Christopher Hoskin <christopher.hoskin@overleaf.com>

9f926b1a

Diff

@@ -153,7 +153,7 @@ variable [Field K] [Invertible (2 : K)] [AddCommGroup V] [Module K V]
 squares. -/
 noncomputable def isometryEquivWeightedSumSquares (Q : QuadraticForm K V)
     (v : Basis (Fin (FiniteDimensional.finrank K V)) K V)
-    (hv₁ : (associated (R := K) Q).iIsOrtho v) :
+    (hv₁ : (associated (R := K) Q).IsOrthoᵢ v) :
     Q.IsometryEquiv (weightedSumSquares K fun i => Q (v i)) := by
   let iso := Q.isometryEquivBasisRepr v
   refine' ⟨iso, fun m => _⟩
@@ -163,7 +163,7 @@ noncomputable def isometryEquivWeightedSumSquares (Q : QuadraticForm K V)
 
 variable [FiniteDimensional K V]
 
-open BilinForm
+open LinearMap.BilinForm
 
 theorem equivalent_weightedSumSquares (Q : QuadraticForm K V) :
     ∃ w : Fin (FiniteDimensional.finrank K V) → K, Equivalent Q (weightedSumSquares K w) :=
@@ -172,11 +172,11 @@ theorem equivalent_weightedSumSquares (Q : QuadraticForm K V) :
 #align quadratic_form.equivalent_weighted_sum_squares QuadraticForm.equivalent_weightedSumSquares
 
 theorem equivalent_weightedSumSquares_units_of_nondegenerate' (Q : QuadraticForm K V)
-    (hQ : (associated (R := K) Q).Nondegenerate) :
+    (hQ : (associated (R := K) Q).SeparatingLeft) :
     ∃ w : Fin (FiniteDimensional.finrank K V) → Kˣ, Equivalent Q (weightedSumSquares K w) := by
   obtain ⟨v, hv₁⟩ := exists_orthogonal_basis (associated_isSymm K Q)
-  have hv₂ := hv₁.not_isOrtho_basis_self_of_nondegenerate hQ
-  simp_rw [BilinForm.IsOrtho, associated_eq_self_apply] at hv₂
+  have hv₂ := hv₁.not_isOrtho_basis_self_of_separatingLeft hQ
+  simp_rw [LinearMap.IsOrtho, associated_eq_self_apply] at hv₂
   exact ⟨fun i => Units.mk0 _ (hv₂ i), ⟨Q.isometryEquivWeightedSumSquares v hv₁⟩⟩
 #align quadratic_form.equivalent_weighted_sum_squares_units_of_nondegenerate' QuadraticForm.equivalent_weightedSumSquares_units_of_nondegenerate'

14b69e9f

chore(LinearAlgebra): Fintype -> Finite (#10722)

ea9e243b

Diff

@@ -129,8 +129,6 @@ theorem trans (h : Q₁.Equivalent Q₂) (h' : Q₂.Equivalent Q₃) : Q₁.Equi
 
 end Equivalent
 
-variable [Fintype ι] {v : Basis ι R M}
-
 /-- A quadratic form composed with a `LinearEquiv` is isometric to itself. -/
 def isometryEquivOfCompLinearEquiv (Q : QuadraticForm R M) (f : M₁ ≃ₗ[R] M) :
     Q.IsometryEquiv (Q.comp (f : M₁ →ₗ[R] M)) :=
@@ -141,6 +139,8 @@ def isometryEquivOfCompLinearEquiv (Q : QuadraticForm R M) (f : M₁ ≃ₗ[R] M
         LinearEquiv.apply_symm_apply, f.apply_symm_apply] }
 #align quadratic_form.isometry_of_comp_linear_equiv QuadraticForm.isometryEquivOfCompLinearEquiv
 
+variable [Finite ι]
+
 /-- A quadratic form is isometrically equivalent to its bases representations. -/
 noncomputable def isometryEquivBasisRepr (Q : QuadraticForm R M) (v : Basis ι R M) :
     IsometryEquiv Q (Q.basisRepr v) :=

14b69e9f

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

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

Zulip thread

Important changes

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

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

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

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

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

Similarly, MyEquivClass should take EquivLike as a parameter.

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

Remaining issues

Slower (failing) search

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

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

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

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

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

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

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

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

`simp` not firing sometimes

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

Missing instances due to unification failing

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

Workaround for issues

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

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

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

c6a73d4f

Diff

@@ -52,12 +52,14 @@ namespace IsometryEquiv
 
 variable {Q₁ : QuadraticForm R M₁} {Q₂ : QuadraticForm R M₂} {Q₃ : QuadraticForm R M₃}
 
-instance : LinearEquivClass (Q₁.IsometryEquiv Q₂) R M₁ M₂ where
+instance : EquivLike (Q₁.IsometryEquiv Q₂) M₁ M₂ where
   coe f := f.toLinearEquiv
   inv f := f.toLinearEquiv.symm
   left_inv f := f.toLinearEquiv.left_inv
   right_inv f := f.toLinearEquiv.right_inv
   coe_injective' f g := by cases f; cases g; simp (config := {contextual := true})
+
+instance : LinearEquivClass (Q₁.IsometryEquiv Q₂) R M₁ M₂ where
   map_add f := map_add f.toLinearEquiv
   map_smulₛₗ f := map_smulₛₗ f.toLinearEquiv

14b69e9f

feat: define QuadraticForm.IsOrtho as Q (x + y) = Q x + Q y (#9141)

This includes some basic API, and the connection with BilinForm.IsOrtho.

The motivation for this definition are the results about vectors commuting in a clifford algebra.

499d5381

Diff

@@ -174,7 +174,7 @@ theorem equivalent_weightedSumSquares_units_of_nondegenerate' (Q : QuadraticForm
     ∃ w : Fin (FiniteDimensional.finrank K V) → Kˣ, Equivalent Q (weightedSumSquares K w) := by
   obtain ⟨v, hv₁⟩ := exists_orthogonal_basis (associated_isSymm K Q)
   have hv₂ := hv₁.not_isOrtho_basis_self_of_nondegenerate hQ
-  simp_rw [IsOrtho, associated_eq_self_apply] at hv₂
+  simp_rw [BilinForm.IsOrtho, associated_eq_self_apply] at hv₂
   exact ⟨fun i => Units.mk0 _ (hv₂ i), ⟨Q.isometryEquivWeightedSumSquares v hv₁⟩⟩
 #align quadratic_form.equivalent_weighted_sum_squares_units_of_nondegenerate' QuadraticForm.equivalent_weightedSumSquares_units_of_nondegenerate'

14b69e9f

refactor(LinearAlgebra/QuadraticForm/Basic): remove non-commutativity support (#7581)

As discussed on Zulip, this generalization seems nonsensical as currently implemented.

There are sensible ways to make this generalization, but they are much larger refactors, and in the meantime the current generalization is useless anyway.

281dea7c

Diff

@@ -27,7 +27,7 @@ variable {ι R K M M₁ M₂ M₃ V : Type*}
 
 namespace QuadraticForm
 
-variable [Semiring R]
+variable [CommSemiring R]
 
 variable [AddCommMonoid M] [AddCommMonoid M₁] [AddCommMonoid M₂] [AddCommMonoid M₃]
 
@@ -151,7 +151,7 @@ variable [Field K] [Invertible (2 : K)] [AddCommGroup V] [Module K V]
 squares. -/
 noncomputable def isometryEquivWeightedSumSquares (Q : QuadraticForm K V)
     (v : Basis (Fin (FiniteDimensional.finrank K V)) K V)
-    (hv₁ : (associated (R₁ := K) Q).iIsOrtho v) :
+    (hv₁ : (associated (R := K) Q).iIsOrtho v) :
     Q.IsometryEquiv (weightedSumSquares K fun i => Q (v i)) := by
   let iso := Q.isometryEquivBasisRepr v
   refine' ⟨iso, fun m => _⟩
@@ -170,7 +170,7 @@ theorem equivalent_weightedSumSquares (Q : QuadraticForm K V) :
 #align quadratic_form.equivalent_weighted_sum_squares QuadraticForm.equivalent_weightedSumSquares
 
 theorem equivalent_weightedSumSquares_units_of_nondegenerate' (Q : QuadraticForm K V)
-    (hQ : (associated (R₁ := K) Q).Nondegenerate) :
+    (hQ : (associated (R := K) Q).Nondegenerate) :
     ∃ w : Fin (FiniteDimensional.finrank K V) → Kˣ, Equivalent Q (weightedSumSquares K w) := by
   obtain ⟨v, hv₁⟩ := exists_orthogonal_basis (associated_isSymm K Q)
   have hv₂ := hv₁.not_isOrtho_basis_self_of_nondegenerate hQ

14b69e9f

feat(LinearAlgebra/QuadraticForm): add QuadraticForm.Isometry (#6984)

Also use it to tidy the API of CliffordAlgebra.map.

351962aa

Diff

@@ -4,6 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Kexing Ying, Eric Wieser
 -/
 import Mathlib.LinearAlgebra.QuadraticForm.Basic
+import Mathlib.LinearAlgebra.QuadraticForm.Isometry
 
 #align_import linear_algebra.quadratic_form.isometry from "leanprover-community/mathlib"@"14b69e9f3c16630440a2cbd46f1ddad0d561dee7"
 
@@ -97,6 +98,12 @@ def trans (f : Q₁.IsometryEquiv Q₂) (g : Q₂.IsometryEquiv Q₃) : Q₁.Iso
     map_app' := by intro m; rw [← f.map_app, ← g.map_app]; rfl }
 #align quadratic_form.isometry.trans QuadraticForm.IsometryEquiv.trans
 
+/-- Isometric equivalences are isometric maps -/
+@[simps]
+def toIsometry (g : Q₁.IsometryEquiv Q₂) : Q₁ →qᵢ Q₂ where
+  toFun x := g x
+  __ := g
+
 end IsometryEquiv
 
 namespace Equivalent

14b69e9f

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

@@ -22,7 +22,7 @@ import Mathlib.LinearAlgebra.QuadraticForm.Basic
 -/
 
 
-variable {ι R K M M₁ M₂ M₃ V : Type _}
+variable {ι R K M M₁ M₂ M₃ V : Type*}
 
 namespace QuadraticForm

14b69e9f

feat: LinearEquivClass QuadraticForm.IsometryEquiv (#6429)

From the lorentz center workshop https://github.com/alexjbest/ant-lorentz

Co-authored-by: Eric Wieser <wieser.eric@gmail.com>

6bef3bc8

Diff

@@ -51,6 +51,15 @@ namespace IsometryEquiv
 
 variable {Q₁ : QuadraticForm R M₁} {Q₂ : QuadraticForm R M₂} {Q₃ : QuadraticForm R M₃}
 
+instance : LinearEquivClass (Q₁.IsometryEquiv Q₂) R M₁ M₂ where
+  coe f := f.toLinearEquiv
+  inv f := f.toLinearEquiv.symm
+  left_inv f := f.toLinearEquiv.left_inv
+  right_inv f := f.toLinearEquiv.right_inv
+  coe_injective' f g := by cases f; cases g; simp (config := {contextual := true})
+  map_add f := map_add f.toLinearEquiv
+  map_smulₛₗ f := map_smulₛₗ f.toLinearEquiv
+
 -- Porting note: was `Coe`
 instance : CoeOut (Q₁.IsometryEquiv Q₂) (M₁ ≃ₗ[R] M₂) :=
   ⟨IsometryEquiv.toLinearEquiv⟩
@@ -58,14 +67,6 @@ instance : CoeOut (Q₁.IsometryEquiv Q₂) (M₁ ≃ₗ[R] M₂) :=
 -- Porting note: syntaut
 #noalign quadratic_form.isometry.to_linear_equiv_eq_coe
 
---Porting note: replace `CoeFun` with `EquivLike`
-instance : EquivLike (Q₁.IsometryEquiv Q₂) M₁ M₂ :=
-  { coe := fun f => ⇑(f : M₁ ≃ₗ[R] M₂),
-    inv := fun f => ⇑(f : M₁ ≃ₗ[R] M₂).symm,
-    left_inv := fun f => (f : M₁ ≃ₗ[R] M₂).left_inv
-    right_inv := fun f => (f : M₁ ≃ₗ[R] M₂).right_inv
-    coe_injective' := fun f g => by cases f; cases g; simp (config := {contextual := true}) }
-
 @[simp]
 theorem coe_toLinearEquiv (f : Q₁.IsometryEquiv Q₂) : ⇑(f : M₁ ≃ₗ[R] M₂) = f :=
   rfl

14b69e9f

refactor(LinearAlgebra/QuadraticForm): rename Isometry to IsometryEquiv (#6305)

This is consistent with LinearIsometryEquiv vs LinearIsometry. The motivation is to make room for QuadraticForm.Isometry as the homomorphism.

b9cabefa

Diff

@@ -8,11 +8,11 @@ import Mathlib.LinearAlgebra.QuadraticForm.Basic
 #align_import linear_algebra.quadratic_form.isometry from "leanprover-community/mathlib"@"14b69e9f3c16630440a2cbd46f1ddad0d561dee7"
 
 /-!
-# Isometries with respect to quadratic forms
+# Isometric equivalences with respect to quadratic forms
 
 ## Main definitions
 
-* `QuadraticForm.Isometry`: `LinearEquiv`s which map between two different quadratic forms
+* `QuadraticForm.IsometryEquiv`: `LinearEquiv`s which map between two different quadratic forms
 * `QuadraticForm.Equivalent`: propositional version of the above
 
 ## Main results
@@ -32,33 +32,34 @@ variable [AddCommMonoid M] [AddCommMonoid M₁] [AddCommMonoid M₂] [AddCommMon
 
 variable [Module R M] [Module R M₁] [Module R M₂] [Module R M₃]
 
-/-- An isometry between two quadratic spaces `M₁, Q₁` and `M₂, Q₂` over a ring `R`,
+/-- An isometric equivalence between two quadratic spaces `M₁, Q₁` and `M₂, Q₂` over a ring `R`,
 is a linear equivalence between `M₁` and `M₂` that commutes with the quadratic forms. -/
 -- Porting note: not implemented @[nolint has_nonempty_instance]
-structure Isometry (Q₁ : QuadraticForm R M₁) (Q₂ : QuadraticForm R M₂) extends M₁ ≃ₗ[R] M₂ where
+structure IsometryEquiv (Q₁ : QuadraticForm R M₁) (Q₂ : QuadraticForm R M₂)
+    extends M₁ ≃ₗ[R] M₂ where
   map_app' : ∀ m, Q₂ (toFun m) = Q₁ m
-#align quadratic_form.isometry QuadraticForm.Isometry
+#align quadratic_form.isometry QuadraticForm.IsometryEquiv
 
 /-- Two quadratic forms over a ring `R` are equivalent
-if there exists an isometry between them:
+if there exists an isometric equivalence between them:
 a linear equivalence that transforms one quadratic form into the other. -/
-def Equivalent (Q₁ : QuadraticForm R M₁) (Q₂ : QuadraticForm R M₂) :=
-  Nonempty (Q₁.Isometry Q₂)
+def Equivalent (Q₁ : QuadraticForm R M₁) (Q₂ : QuadraticForm R M₂) : Prop :=
+  Nonempty (Q₁.IsometryEquiv Q₂)
 #align quadratic_form.equivalent QuadraticForm.Equivalent
 
-namespace Isometry
+namespace IsometryEquiv
 
 variable {Q₁ : QuadraticForm R M₁} {Q₂ : QuadraticForm R M₂} {Q₃ : QuadraticForm R M₃}
 
 -- Porting note: was `Coe`
-instance : CoeOut (Q₁.Isometry Q₂) (M₁ ≃ₗ[R] M₂) :=
-  ⟨Isometry.toLinearEquiv⟩
+instance : CoeOut (Q₁.IsometryEquiv Q₂) (M₁ ≃ₗ[R] M₂) :=
+  ⟨IsometryEquiv.toLinearEquiv⟩
 
 -- Porting note: syntaut
 #noalign quadratic_form.isometry.to_linear_equiv_eq_coe
 
 --Porting note: replace `CoeFun` with `EquivLike`
-instance : EquivLike (Q₁.Isometry Q₂) M₁ M₂ :=
+instance : EquivLike (Q₁.IsometryEquiv Q₂) M₁ M₂ :=
   { coe := fun f => ⇑(f : M₁ ≃ₗ[R] M₂),
     inv := fun f => ⇑(f : M₁ ≃ₗ[R] M₂).symm,
     left_inv := fun f => (f : M₁ ≃ₗ[R] M₂).left_inv
@@ -66,36 +67,36 @@ instance : EquivLike (Q₁.Isometry Q₂) M₁ M₂ :=
     coe_injective' := fun f g => by cases f; cases g; simp (config := {contextual := true}) }
 
 @[simp]
-theorem coe_toLinearEquiv (f : Q₁.Isometry Q₂) : ⇑(f : M₁ ≃ₗ[R] M₂) = f :=
+theorem coe_toLinearEquiv (f : Q₁.IsometryEquiv Q₂) : ⇑(f : M₁ ≃ₗ[R] M₂) = f :=
   rfl
-#align quadratic_form.isometry.coe_to_linear_equiv QuadraticForm.Isometry.coe_toLinearEquiv
+#align quadratic_form.isometry.coe_to_linear_equiv QuadraticForm.IsometryEquiv.coe_toLinearEquiv
 
 @[simp]
-theorem map_app (f : Q₁.Isometry Q₂) (m : M₁) : Q₂ (f m) = Q₁ m :=
+theorem map_app (f : Q₁.IsometryEquiv Q₂) (m : M₁) : Q₂ (f m) = Q₁ m :=
   f.map_app' m
-#align quadratic_form.isometry.map_app QuadraticForm.Isometry.map_app
+#align quadratic_form.isometry.map_app QuadraticForm.IsometryEquiv.map_app
 
-/-- The identity isometry from a quadratic form to itself. -/
+/-- The identity isometric equivalence between a quadratic form and itself. -/
 @[refl]
-def refl (Q : QuadraticForm R M) : Q.Isometry Q :=
+def refl (Q : QuadraticForm R M) : Q.IsometryEquiv Q :=
   { LinearEquiv.refl R M with map_app' := fun _ => rfl }
-#align quadratic_form.isometry.refl QuadraticForm.Isometry.refl
+#align quadratic_form.isometry.refl QuadraticForm.IsometryEquiv.refl
 
-/-- The inverse isometry of an isometry between two quadratic forms. -/
+/-- The inverse isometric equivalence of an isometric equivalence between two quadratic forms. -/
 @[symm]
-def symm (f : Q₁.Isometry Q₂) : Q₂.Isometry Q₁ :=
+def symm (f : Q₁.IsometryEquiv Q₂) : Q₂.IsometryEquiv Q₁ :=
   { (f : M₁ ≃ₗ[R] M₂).symm with
     map_app' := by intro m; rw [← f.map_app]; congr; exact f.toLinearEquiv.apply_symm_apply m }
-#align quadratic_form.isometry.symm QuadraticForm.Isometry.symm
+#align quadratic_form.isometry.symm QuadraticForm.IsometryEquiv.symm
 
-/-- The composition of two isometries between quadratic forms. -/
+/-- The composition of two isometric equivalences between quadratic forms. -/
 @[trans]
-def trans (f : Q₁.Isometry Q₂) (g : Q₂.Isometry Q₃) : Q₁.Isometry Q₃ :=
+def trans (f : Q₁.IsometryEquiv Q₂) (g : Q₂.IsometryEquiv Q₃) : Q₁.IsometryEquiv Q₃ :=
   { (f : M₁ ≃ₗ[R] M₂).trans (g : M₂ ≃ₗ[R] M₃) with
     map_app' := by intro m; rw [← f.map_app, ← g.map_app]; rfl }
-#align quadratic_form.isometry.trans QuadraticForm.Isometry.trans
+#align quadratic_form.isometry.trans QuadraticForm.IsometryEquiv.trans
 
-end Isometry
+end IsometryEquiv
 
 namespace Equivalent
 
@@ -103,7 +104,7 @@ variable {Q₁ : QuadraticForm R M₁} {Q₂ : QuadraticForm R M₂} {Q₃ : Qua
 
 @[refl]
 theorem refl (Q : QuadraticForm R M) : Q.Equivalent Q :=
-  ⟨Isometry.refl Q⟩
+  ⟨IsometryEquiv.refl Q⟩
 #align quadratic_form.equivalent.refl QuadraticForm.Equivalent.refl
 
 @[symm]
@@ -121,33 +122,34 @@ end Equivalent
 variable [Fintype ι] {v : Basis ι R M}
 
 /-- A quadratic form composed with a `LinearEquiv` is isometric to itself. -/
-def isometryOfCompLinearEquiv (Q : QuadraticForm R M) (f : M₁ ≃ₗ[R] M) :
-    Q.Isometry (Q.comp (f : M₁ →ₗ[R] M)) :=
+def isometryEquivOfCompLinearEquiv (Q : QuadraticForm R M) (f : M₁ ≃ₗ[R] M) :
+    Q.IsometryEquiv (Q.comp (f : M₁ →ₗ[R] M)) :=
   { f.symm with
     map_app' := by
       intro
       simp only [comp_apply, LinearEquiv.coe_coe, LinearEquiv.toFun_eq_coe,
         LinearEquiv.apply_symm_apply, f.apply_symm_apply] }
-#align quadratic_form.isometry_of_comp_linear_equiv QuadraticForm.isometryOfCompLinearEquiv
+#align quadratic_form.isometry_of_comp_linear_equiv QuadraticForm.isometryEquivOfCompLinearEquiv
 
-/-- A quadratic form is isometric to its bases representations. -/
-noncomputable def isometryBasisRepr (Q : QuadraticForm R M) (v : Basis ι R M) :
-    Isometry Q (Q.basisRepr v) :=
-  isometryOfCompLinearEquiv Q v.equivFun.symm
-#align quadratic_form.isometry_basis_repr QuadraticForm.isometryBasisRepr
+/-- A quadratic form is isometrically equivalent to its bases representations. -/
+noncomputable def isometryEquivBasisRepr (Q : QuadraticForm R M) (v : Basis ι R M) :
+    IsometryEquiv Q (Q.basisRepr v) :=
+  isometryEquivOfCompLinearEquiv Q v.equivFun.symm
+#align quadratic_form.isometry_basis_repr QuadraticForm.isometryEquivBasisRepr
 
 variable [Field K] [Invertible (2 : K)] [AddCommGroup V] [Module K V]
 
-/-- Given an orthogonal basis, a quadratic form is isometric with a weighted sum of squares. -/
-noncomputable def isometryWeightedSumSquares (Q : QuadraticForm K V)
+/-- Given an orthogonal basis, a quadratic form is isometrically equivalent with a weighted sum of
+squares. -/
+noncomputable def isometryEquivWeightedSumSquares (Q : QuadraticForm K V)
     (v : Basis (Fin (FiniteDimensional.finrank K V)) K V)
     (hv₁ : (associated (R₁ := K) Q).iIsOrtho v) :
-    Q.Isometry (weightedSumSquares K fun i => Q (v i)) := by
-  let iso := Q.isometryBasisRepr v
+    Q.IsometryEquiv (weightedSumSquares K fun i => Q (v i)) := by
+  let iso := Q.isometryEquivBasisRepr v
   refine' ⟨iso, fun m => _⟩
   convert iso.map_app m
   rw [basisRepr_eq_of_iIsOrtho _ _ hv₁]
-#align quadratic_form.isometry_weighted_sum_squares QuadraticForm.isometryWeightedSumSquares
+#align quadratic_form.isometry_weighted_sum_squares QuadraticForm.isometryEquivWeightedSumSquares
 
 variable [FiniteDimensional K V]
 
@@ -156,7 +158,7 @@ open BilinForm
 theorem equivalent_weightedSumSquares (Q : QuadraticForm K V) :
     ∃ w : Fin (FiniteDimensional.finrank K V) → K, Equivalent Q (weightedSumSquares K w) :=
   let ⟨v, hv₁⟩ := exists_orthogonal_basis (associated_isSymm _ Q)
-  ⟨_, ⟨Q.isometryWeightedSumSquares v hv₁⟩⟩
+  ⟨_, ⟨Q.isometryEquivWeightedSumSquares v hv₁⟩⟩
 #align quadratic_form.equivalent_weighted_sum_squares QuadraticForm.equivalent_weightedSumSquares
 
 theorem equivalent_weightedSumSquares_units_of_nondegenerate' (Q : QuadraticForm K V)
@@ -165,7 +167,7 @@ theorem equivalent_weightedSumSquares_units_of_nondegenerate' (Q : QuadraticForm
   obtain ⟨v, hv₁⟩ := exists_orthogonal_basis (associated_isSymm K Q)
   have hv₂ := hv₁.not_isOrtho_basis_self_of_nondegenerate hQ
   simp_rw [IsOrtho, associated_eq_self_apply] at hv₂
-  exact ⟨fun i => Units.mk0 _ (hv₂ i), ⟨Q.isometryWeightedSumSquares v hv₁⟩⟩
+  exact ⟨fun i => Units.mk0 _ (hv₂ i), ⟨Q.isometryEquivWeightedSumSquares v hv₁⟩⟩
 #align quadratic_form.equivalent_weighted_sum_squares_units_of_nondegenerate' QuadraticForm.equivalent_weightedSumSquares_units_of_nondegenerate'
 
 end QuadraticForm

14b69e9f

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

@@ -2,14 +2,11 @@
 Copyright (c) 2020 Anne Baanen. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Kexing Ying, Eric Wieser
-
-! This file was ported from Lean 3 source module linear_algebra.quadratic_form.isometry
-! leanprover-community/mathlib commit 14b69e9f3c16630440a2cbd46f1ddad0d561dee7
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.LinearAlgebra.QuadraticForm.Basic
 
+#align_import linear_algebra.quadratic_form.isometry from "leanprover-community/mathlib"@"14b69e9f3c16630440a2cbd46f1ddad0d561dee7"
+
 /-!
 # Isometries with respect to quadratic forms

14b69e9f

chore: bump to nightly-2023-07-01 (#5409)

depends on: https://github.com/leanprover/std4/pull/163
depends on: #5584
depends on: #5715
depends on: #5729
depends on: https://github.com/leanprover/std4/pull/173

Co-authored-by: Komyyy <pol_tta@outlook.jp> Co-authored-by: Scott Morrison <scott.morrison@gmail.com> Co-authored-by: Scott Morrison <scott.morrison@anu.edu.au> Co-authored-by: Ruben Van de Velde <65514131+Ruben-VandeVelde@users.noreply.github.com> Co-authored-by: Mario Carneiro <di.gama@gmail.com>

906f7221

Diff

@@ -165,7 +165,7 @@ theorem equivalent_weightedSumSquares (Q : QuadraticForm K V) :
 theorem equivalent_weightedSumSquares_units_of_nondegenerate' (Q : QuadraticForm K V)
     (hQ : (associated (R₁ := K) Q).Nondegenerate) :
     ∃ w : Fin (FiniteDimensional.finrank K V) → Kˣ, Equivalent Q (weightedSumSquares K w) := by
-  obtain ⟨v, hv₁⟩ := exists_orthogonal_basis (associated_isSymm _ Q)
+  obtain ⟨v, hv₁⟩ := exists_orthogonal_basis (associated_isSymm K Q)
   have hv₂ := hv₁.not_isOrtho_basis_self_of_nondegenerate hQ
   simp_rw [IsOrtho, associated_eq_self_apply] at hv₂
   exact ⟨fun i => Units.mk0 _ (hv₂ i), ⟨Q.isometryWeightedSumSquares v hv₁⟩⟩

14b69e9f

chore: formatting issues (#4947)

Co-authored-by: Scott Morrison <scott.morrison@anu.edu.au> Co-authored-by: Parcly Taxel <reddeloostw@gmail.com>

5068808d

Diff

@@ -66,7 +66,7 @@ instance : EquivLike (Q₁.Isometry Q₂) M₁ M₂ :=
     inv := fun f => ⇑(f : M₁ ≃ₗ[R] M₂).symm,
     left_inv := fun f => (f : M₁ ≃ₗ[R] M₂).left_inv
     right_inv := fun f => (f : M₁ ≃ₗ[R] M₂).right_inv
-    coe_injective' := fun f g => by cases f; cases g; simp (config:={contextual:=true}) }
+    coe_injective' := fun f g => by cases f; cases g; simp (config := {contextual := true}) }
 
 @[simp]
 theorem coe_toLinearEquiv (f : Q₁.Isometry Q₂) : ⇑(f : M₁ ≃ₗ[R] M₂) = f :=

14b69e9f

feat: port LinearAlgebra.QuadraticForm.Isometry (#4703)

Co-authored-by: Chris Hughes <chrishughes24@gmail.com>

6f0499b5

`linear_algebra.quadratic_form.isometry` ⟷ `Mathlib.LinearAlgebra.QuadraticForm.IsometryEquiv`

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Important changes

Remaining issues

Slower (failing) search

`simp` not firing sometimes

Missing instances due to unification failing

Workaround for issues

Dependencies 10 + 625

linear_algebra.quadratic_form.isometry ⟷ Mathlib.LinearAlgebra.QuadraticForm.IsometryEquiv

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Important changes

Remaining issues

Slower (failing) search

simp not firing sometimes

Missing instances due to unification failing

Workaround for issues

Dependencies 10 + 625

`linear_algebra.quadratic_form.isometry` ⟷ `Mathlib.LinearAlgebra.QuadraticForm.IsometryEquiv`

`simp` not firing sometimes