linear_algebra.quadratic_form.prod | 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

9b2755b9

(last sync)

Changes in mathlib3port

mathlib3

mathlib3port

c2092722

bump to nightly-2024-04-06-08

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

e34029c9

Diff

@@ -3,7 +3,7 @@ Copyright (c) 2021 Eric Wieser. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Eric Wieser
 -/
-import LinearAlgebra.QuadraticForm.Isometry
+import LinearAlgebra.QuadraticForm.IsometryEquiv
 
 #align_import linear_algebra.quadratic_form.prod from "leanprover-community/mathlib"@"c20927220ef87bb4962ba08bf6da2ce3cf50a6dd"

c2092722

bump to nightly-2024-03-17-08

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

22f01ce4

Diff

@@ -87,7 +87,7 @@ theorem anisotropic_of_prod {R} [OrderedRing R] [Module R M₁] [Module R M₂]
     {Q₁ : QuadraticForm R M₁} {Q₂ : QuadraticForm R M₂} (h : (Q₁.Prod Q₂).Anisotropic) :
     Q₁.Anisotropic ∧ Q₂.Anisotropic :=
   by
-  simp_rw [anisotropic, prod_apply, Prod.forall, Prod.mk_eq_zero] at h 
+  simp_rw [anisotropic, prod_apply, Prod.forall, Prod.mk_eq_zero] at h
   constructor
   · intro x hx
     refine' (h x 0 _).1
@@ -125,7 +125,7 @@ theorem posDef_prod_iff {R} [OrderedRing R] [Module R M₁] [Module R M₂] {Q
   · rintro ⟨⟨hle₁, ha₁⟩, ⟨hle₂, ha₂⟩⟩
     refine' ⟨⟨hle₁, hle₂⟩, _⟩
     rintro ⟨x₁, x₂⟩ (hx : Q₁ x₁ + Q₂ x₂ = 0)
-    rw [add_eq_zero_iff' (hle₁ x₁) (hle₂ x₂), ha₁.eq_zero_iff, ha₂.eq_zero_iff] at hx 
+    rw [add_eq_zero_iff' (hle₁ x₁) (hle₂ x₂), ha₁.eq_zero_iff, ha₂.eq_zero_iff] at hx
     rwa [Prod.mk_eq_zero]
 #align quadratic_form.pos_def_prod_iff QuadraticForm.posDef_prod_iff
 -/
@@ -182,11 +182,11 @@ theorem Equivalent.pi [Fintype ι] {Q : ∀ i, QuadraticForm R (Mᵢ i)}
 theorem anisotropic_of_pi [Fintype ι] {R} [OrderedRing R] [∀ i, Module R (Mᵢ i)]
     {Q : ∀ i, QuadraticForm R (Mᵢ i)} (h : (pi Q).Anisotropic) : ∀ i, (Q i).Anisotropic :=
   by
-  simp_rw [anisotropic, pi_apply, Function.funext_iff, Pi.zero_apply] at h 
+  simp_rw [anisotropic, pi_apply, Function.funext_iff, Pi.zero_apply] at h
   intro i x hx
   classical
   have := h (Pi.single i x) _ i
-  · rw [Pi.single_eq_same] at this 
+  · rw [Pi.single_eq_same] at this
     exact this
   apply Finset.sum_eq_zero
   intro j _
@@ -225,7 +225,7 @@ theorem posDef_pi_iff [Fintype ι] {R} [OrderedRing R] [∀ i, Module R (Mᵢ i)
     exact ⟨hle i, anisotropic_of_pi ha i⟩
   · intro h
     refine' ⟨fun i => (h i).1, fun x hx => funext fun i => (h i).2 _ _⟩
-    rw [pi_apply, Finset.sum_eq_zero_iff_of_nonneg fun j hj => _] at hx 
+    rw [pi_apply, Finset.sum_eq_zero_iff_of_nonneg fun j hj => _] at hx
     · exact hx _ (Finset.mem_univ _)
     exact (h j).1 _
 #align quadratic_form.pos_def_pi_iff QuadraticForm.posDef_pi_iff

c2092722

bump to nightly-2024-02-01-06

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

5433bded

Diff

@@ -185,6 +185,14 @@ theorem anisotropic_of_pi [Fintype ι] {R} [OrderedRing R] [∀ i, Module R (M
   simp_rw [anisotropic, pi_apply, Function.funext_iff, Pi.zero_apply] at h 
   intro i x hx
   classical
+  have := h (Pi.single i x) _ i
+  · rw [Pi.single_eq_same] at this 
+    exact this
+  apply Finset.sum_eq_zero
+  intro j _
+  by_cases hji : j = i
+  · subst hji; rw [Pi.single_eq_same, hx]
+  · rw [Pi.single_eq_of_ne hji, map_zero]
 #align quadratic_form.anisotropic_of_pi QuadraticForm.anisotropic_of_pi
 -/
 
@@ -198,6 +206,9 @@ theorem nonneg_pi_iff [Fintype ι] {R} [OrderedRing R] [∀ i, Module R (Mᵢ i)
   -- TODO: does this generalize to a useful lemma independent of `quadratic_form`?
   · intro h i x
     classical
+    convert h (Pi.single i x) using 1
+    rw [Finset.sum_eq_single_of_mem i (Finset.mem_univ _) fun j _ hji => _, Pi.single_eq_same]
+    rw [Pi.single_eq_of_ne hji, map_zero]
   · rintro h x
     exact Finset.sum_nonneg fun i hi => h i (x i)
 #align quadratic_form.nonneg_pi_iff QuadraticForm.nonneg_pi_iff

c2092722

bump to nightly-2024-01-31-06

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

61100fe9

Diff

@@ -185,14 +185,6 @@ theorem anisotropic_of_pi [Fintype ι] {R} [OrderedRing R] [∀ i, Module R (M
   simp_rw [anisotropic, pi_apply, Function.funext_iff, Pi.zero_apply] at h 
   intro i x hx
   classical
-  have := h (Pi.single i x) _ i
-  · rw [Pi.single_eq_same] at this 
-    exact this
-  apply Finset.sum_eq_zero
-  intro j _
-  by_cases hji : j = i
-  · subst hji; rw [Pi.single_eq_same, hx]
-  · rw [Pi.single_eq_of_ne hji, map_zero]
 #align quadratic_form.anisotropic_of_pi QuadraticForm.anisotropic_of_pi
 -/
 
@@ -206,9 +198,6 @@ theorem nonneg_pi_iff [Fintype ι] {R} [OrderedRing R] [∀ i, Module R (Mᵢ i)
   -- TODO: does this generalize to a useful lemma independent of `quadratic_form`?
   · intro h i x
     classical
-    convert h (Pi.single i x) using 1
-    rw [Finset.sum_eq_single_of_mem i (Finset.mem_univ _) fun j _ hji => _, Pi.single_eq_same]
-    rw [Pi.single_eq_of_ne hji, map_zero]
   · rintro h x
     exact Finset.sum_nonneg fun i hi => h i (x i)
 #align quadratic_form.nonneg_pi_iff QuadraticForm.nonneg_pi_iff

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) 2021 Eric Wieser. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Eric Wieser
 -/
-import Mathbin.LinearAlgebra.QuadraticForm.Isometry
+import LinearAlgebra.QuadraticForm.Isometry
 
 #align_import linear_algebra.quadratic_form.prod 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

@@ -60,24 +60,24 @@ def prod (Q₁ : QuadraticForm R M₁) (Q₂ : QuadraticForm R M₂) : Quadratic
 #align quadratic_form.prod QuadraticForm.prod
 -/
 
-#print QuadraticForm.Isometry.prod /-
+#print QuadraticForm.IsometryEquiv.prod /-
 /-- An isometry between quadratic forms generated by `quadratic_form.prod` can be constructed
 from a pair of isometries between the left and right parts. -/
 @[simps toLinearEquiv]
-def Isometry.prod {Q₁ : QuadraticForm R M₁} {Q₂ : QuadraticForm R M₂} {Q₁' : QuadraticForm R N₁}
-    {Q₂' : QuadraticForm R N₂} (e₁ : Q₁.Isometry Q₁') (e₂ : Q₂.Isometry Q₂') :
-    (Q₁.Prod Q₂).Isometry (Q₁'.Prod Q₂')
+def IsometryEquiv.prod {Q₁ : QuadraticForm R M₁} {Q₂ : QuadraticForm R M₂}
+    {Q₁' : QuadraticForm R N₁} {Q₂' : QuadraticForm R N₂} (e₁ : Q₁.IsometryEquiv Q₁')
+    (e₂ : Q₂.IsometryEquiv Q₂') : (Q₁.Prod Q₂).IsometryEquiv (Q₁'.Prod Q₂')
     where
   map_app' x := congr_arg₂ (· + ·) (e₁.map_app x.1) (e₂.map_app x.2)
   toLinearEquiv := LinearEquiv.prod e₁.toLinearEquiv e₂.toLinearEquiv
-#align quadratic_form.isometry.prod QuadraticForm.Isometry.prod
+#align quadratic_form.isometry.prod QuadraticForm.IsometryEquiv.prod
 -/
 
 #print QuadraticForm.Equivalent.prod /-
 theorem Equivalent.prod {Q₁ : QuadraticForm R M₁} {Q₂ : QuadraticForm R M₂}
     {Q₁' : QuadraticForm R N₁} {Q₂' : QuadraticForm R N₂} (e₁ : Q₁.Equivalent Q₁')
     (e₂ : Q₂.Equivalent Q₂') : (Q₁.Prod Q₂).Equivalent (Q₁'.Prod Q₂') :=
-  Nonempty.map2 Isometry.prod e₁ e₂
+  Nonempty.map2 IsometryEquiv.prod e₁ e₂
 #align quadratic_form.equivalent.prod QuadraticForm.Equivalent.prod
 -/
 
@@ -154,25 +154,26 @@ theorem pi_apply [Fintype ι] (Q : ∀ i, QuadraticForm R (Mᵢ i)) (x : ∀ i,
 #align quadratic_form.pi_apply QuadraticForm.pi_apply
 -/
 
-#print QuadraticForm.Isometry.pi /-
+#print QuadraticForm.IsometryEquiv.pi /-
 /-- An isometry between quadratic forms generated by `quadratic_form.prod` can be constructed
 from a pair of isometries between the left and right parts. -/
 @[simps toLinearEquiv]
-def Isometry.pi [Fintype ι] {Q : ∀ i, QuadraticForm R (Mᵢ i)} {Q' : ∀ i, QuadraticForm R (Nᵢ i)}
-    (e : ∀ i, (Q i).Isometry (Q' i)) : (pi Q).Isometry (pi Q')
+def IsometryEquiv.pi [Fintype ι] {Q : ∀ i, QuadraticForm R (Mᵢ i)}
+    {Q' : ∀ i, QuadraticForm R (Nᵢ i)} (e : ∀ i, (Q i).IsometryEquiv (Q' i)) :
+    (pi Q).IsometryEquiv (pi Q')
     where
   map_app' x := by
     simp only [pi_apply, LinearEquiv.piCongrRight, LinearEquiv.toFun_eq_coe,
       isometry.coe_to_linear_equiv, isometry.map_app]
   toLinearEquiv := LinearEquiv.piCongrRight fun i => (e i : Mᵢ i ≃ₗ[R] Nᵢ i)
-#align quadratic_form.isometry.pi QuadraticForm.Isometry.pi
+#align quadratic_form.isometry.pi QuadraticForm.IsometryEquiv.pi
 -/
 
 #print QuadraticForm.Equivalent.pi /-
 theorem Equivalent.pi [Fintype ι] {Q : ∀ i, QuadraticForm R (Mᵢ i)}
     {Q' : ∀ i, QuadraticForm R (Nᵢ i)} (e : ∀ i, (Q i).Equivalent (Q' i)) :
     (pi Q).Equivalent (pi Q') :=
-  ⟨Isometry.pi fun i => Classical.choice (e i)⟩
+  ⟨IsometryEquiv.pi fun i => Classical.choice (e i)⟩
 #align quadratic_form.equivalent.pi QuadraticForm.Equivalent.pi
 -/

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) 2021 Eric Wieser. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Eric Wieser
-
-! This file was ported from Lean 3 source module linear_algebra.quadratic_form.prod
-! 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.Isometry
 
+#align_import linear_algebra.quadratic_form.prod from "leanprover-community/mathlib"@"c20927220ef87bb4962ba08bf6da2ce3cf50a6dd"
+
 /-! # Quadratic form on product and pi types
 
 > THIS FILE IS SYNCHRONIZED WITH MATHLIB4.

c2092722

bump to nightly-2023-06-13-21

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

829520ac

Diff

@@ -54,13 +54,16 @@ variable [∀ i, Module R (Mᵢ i)] [∀ i, Module R (Nᵢ i)]
 
 namespace QuadraticForm
 
+#print QuadraticForm.prod /-
 /-- Construct a quadratic form on a product of two modules from the quadratic form on each module.
 -/
 @[simps]
 def prod (Q₁ : QuadraticForm R M₁) (Q₂ : QuadraticForm R M₂) : QuadraticForm R (M₁ × M₂) :=
   Q₁.comp (LinearMap.fst _ _ _) + Q₂.comp (LinearMap.snd _ _ _)
 #align quadratic_form.prod QuadraticForm.prod
+-/
 
+#print QuadraticForm.Isometry.prod /-
 /-- An isometry between quadratic forms generated by `quadratic_form.prod` can be constructed
 from a pair of isometries between the left and right parts. -/
 @[simps toLinearEquiv]
@@ -71,13 +74,17 @@ def Isometry.prod {Q₁ : QuadraticForm R M₁} {Q₂ : QuadraticForm R M₂} {Q
   map_app' x := congr_arg₂ (· + ·) (e₁.map_app x.1) (e₂.map_app x.2)
   toLinearEquiv := LinearEquiv.prod e₁.toLinearEquiv e₂.toLinearEquiv
 #align quadratic_form.isometry.prod QuadraticForm.Isometry.prod
+-/
 
+#print QuadraticForm.Equivalent.prod /-
 theorem Equivalent.prod {Q₁ : QuadraticForm R M₁} {Q₂ : QuadraticForm R M₂}
     {Q₁' : QuadraticForm R N₁} {Q₂' : QuadraticForm R N₂} (e₁ : Q₁.Equivalent Q₁')
     (e₂ : Q₂.Equivalent Q₂') : (Q₁.Prod Q₂).Equivalent (Q₁'.Prod Q₂') :=
   Nonempty.map2 Isometry.prod e₁ e₂
 #align quadratic_form.equivalent.prod QuadraticForm.Equivalent.prod
+-/
 
+#print QuadraticForm.anisotropic_of_prod /-
 /-- If a product is anisotropic then its components must be. The converse is not true. -/
 theorem anisotropic_of_prod {R} [OrderedRing R] [Module R M₁] [Module R M₂]
     {Q₁ : QuadraticForm R M₁} {Q₂ : QuadraticForm R M₂} (h : (Q₁.Prod Q₂).Anisotropic) :
@@ -92,7 +99,9 @@ theorem anisotropic_of_prod {R} [OrderedRing R] [Module R M₁] [Module R M₂]
     refine' (h 0 x _).2
     rw [hx, add_zero, map_zero]
 #align quadratic_form.anisotropic_of_prod QuadraticForm.anisotropic_of_prod
+-/
 
+#print QuadraticForm.nonneg_prod_iff /-
 theorem nonneg_prod_iff {R} [OrderedRing R] [Module R M₁] [Module R M₂] {Q₁ : QuadraticForm R M₁}
     {Q₂ : QuadraticForm R M₂} : (∀ x, 0 ≤ (Q₁.Prod Q₂) x) ↔ (∀ x, 0 ≤ Q₁ x) ∧ ∀ x, 0 ≤ Q₂ x :=
   by
@@ -105,7 +114,9 @@ theorem nonneg_prod_iff {R} [OrderedRing R] [Module R M₁] [Module R M₂] {Q
   · rintro ⟨h₁, h₂⟩ x₁ x₂
     exact add_nonneg (h₁ x₁) (h₂ x₂)
 #align quadratic_form.nonneg_prod_iff QuadraticForm.nonneg_prod_iff
+-/
 
+#print QuadraticForm.posDef_prod_iff /-
 theorem posDef_prod_iff {R} [OrderedRing R] [Module R M₁] [Module R M₂] {Q₁ : QuadraticForm R M₁}
     {Q₂ : QuadraticForm R M₂} : (Q₁.Prod Q₂).PosDef ↔ Q₁.PosDef ∧ Q₂.PosDef :=
   by
@@ -120,11 +131,14 @@ theorem posDef_prod_iff {R} [OrderedRing R] [Module R M₁] [Module R M₂] {Q
     rw [add_eq_zero_iff' (hle₁ x₁) (hle₂ x₂), ha₁.eq_zero_iff, ha₂.eq_zero_iff] at hx 
     rwa [Prod.mk_eq_zero]
 #align quadratic_form.pos_def_prod_iff QuadraticForm.posDef_prod_iff
+-/
 
+#print QuadraticForm.PosDef.prod /-
 theorem PosDef.prod {R} [OrderedRing R] [Module R M₁] [Module R M₂] {Q₁ : QuadraticForm R M₁}
     {Q₂ : QuadraticForm R M₂} (h₁ : Q₁.PosDef) (h₂ : Q₂.PosDef) : (Q₁.Prod Q₂).PosDef :=
   posDef_prod_iff.mpr ⟨h₁, h₂⟩
 #align quadratic_form.pos_def.prod QuadraticForm.PosDef.prod
+-/
 
 open scoped BigOperators
 
@@ -135,11 +149,13 @@ def pi [Fintype ι] (Q : ∀ i, QuadraticForm R (Mᵢ i)) : QuadraticForm R (∀
 #align quadratic_form.pi QuadraticForm.pi
 -/
 
+#print QuadraticForm.pi_apply /-
 @[simp]
 theorem pi_apply [Fintype ι] (Q : ∀ i, QuadraticForm R (Mᵢ i)) (x : ∀ i, Mᵢ i) :
     pi Q x = ∑ i, Q i (x i) :=
   sum_apply _ _ _
 #align quadratic_form.pi_apply QuadraticForm.pi_apply
+-/
 
 #print QuadraticForm.Isometry.pi /-
 /-- An isometry between quadratic forms generated by `quadratic_form.prod` can be constructed
@@ -155,12 +171,15 @@ def Isometry.pi [Fintype ι] {Q : ∀ i, QuadraticForm R (Mᵢ i)} {Q' : ∀ i,
 #align quadratic_form.isometry.pi QuadraticForm.Isometry.pi
 -/
 
+#print QuadraticForm.Equivalent.pi /-
 theorem Equivalent.pi [Fintype ι] {Q : ∀ i, QuadraticForm R (Mᵢ i)}
     {Q' : ∀ i, QuadraticForm R (Nᵢ i)} (e : ∀ i, (Q i).Equivalent (Q' i)) :
     (pi Q).Equivalent (pi Q') :=
   ⟨Isometry.pi fun i => Classical.choice (e i)⟩
 #align quadratic_form.equivalent.pi QuadraticForm.Equivalent.pi
+-/
 
+#print QuadraticForm.anisotropic_of_pi /-
 /-- If a family is anisotropic then its components must be. The converse is not true. -/
 theorem anisotropic_of_pi [Fintype ι] {R} [OrderedRing R] [∀ i, Module R (Mᵢ i)]
     {Q : ∀ i, QuadraticForm R (Mᵢ i)} (h : (pi Q).Anisotropic) : ∀ i, (Q i).Anisotropic :=
@@ -177,7 +196,9 @@ theorem anisotropic_of_pi [Fintype ι] {R} [OrderedRing R] [∀ i, Module R (M
   · subst hji; rw [Pi.single_eq_same, hx]
   · rw [Pi.single_eq_of_ne hji, map_zero]
 #align quadratic_form.anisotropic_of_pi QuadraticForm.anisotropic_of_pi
+-/
 
+#print QuadraticForm.nonneg_pi_iff /-
 theorem nonneg_pi_iff [Fintype ι] {R} [OrderedRing R] [∀ i, Module R (Mᵢ i)]
     {Q : ∀ i, QuadraticForm R (Mᵢ i)} : (∀ x, 0 ≤ pi Q x) ↔ ∀ i x, 0 ≤ Q i x :=
   by
@@ -193,7 +214,9 @@ theorem nonneg_pi_iff [Fintype ι] {R} [OrderedRing R] [∀ i, Module R (Mᵢ i)
   · rintro h x
     exact Finset.sum_nonneg fun i hi => h i (x i)
 #align quadratic_form.nonneg_pi_iff QuadraticForm.nonneg_pi_iff
+-/
 
+#print QuadraticForm.posDef_pi_iff /-
 theorem posDef_pi_iff [Fintype ι] {R} [OrderedRing R] [∀ i, Module R (Mᵢ i)]
     {Q : ∀ i, QuadraticForm R (Mᵢ i)} : (pi Q).PosDef ↔ ∀ i, (Q i).PosDef :=
   by
@@ -208,6 +231,7 @@ theorem posDef_pi_iff [Fintype ι] {R} [OrderedRing R] [∀ i, Module R (Mᵢ i)
     · exact hx _ (Finset.mem_univ _)
     exact (h j).1 _
 #align quadratic_form.pos_def_pi_iff QuadraticForm.posDef_pi_iff
+-/
 
 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: Eric Wieser
 
 ! This file was ported from Lean 3 source module linear_algebra.quadratic_form.prod
-! leanprover-community/mathlib commit 9b2755b951bc323c962bd072cd447b375cf58101
+! leanprover-community/mathlib commit c20927220ef87bb4962ba08bf6da2ce3cf50a6dd
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -12,6 +12,9 @@ import Mathbin.LinearAlgebra.QuadraticForm.Isometry
 
 /-! # Quadratic form on product and pi types
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 ## Main definitions
 
 * `quadratic_form.prod Q₁ Q₂`: the quadratic form constructed elementwise on a product

9b2755b9

bump to nightly-2023-06-06-17

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

7fcd2dd2

Diff

@@ -125,10 +125,12 @@ theorem PosDef.prod {R} [OrderedRing R] [Module R M₁] [Module R M₂] {Q₁ :
 
 open scoped BigOperators
 
+#print QuadraticForm.pi /-
 /-- Construct a quadratic form on a family of modules from the quadratic form on each module. -/
 def pi [Fintype ι] (Q : ∀ i, QuadraticForm R (Mᵢ i)) : QuadraticForm R (∀ i, Mᵢ i) :=
   ∑ i, (Q i).comp (LinearMap.proj i : _ →ₗ[R] Mᵢ i)
 #align quadratic_form.pi QuadraticForm.pi
+-/
 
 @[simp]
 theorem pi_apply [Fintype ι] (Q : ∀ i, QuadraticForm R (Mᵢ i)) (x : ∀ i, Mᵢ i) :
@@ -136,6 +138,7 @@ theorem pi_apply [Fintype ι] (Q : ∀ i, QuadraticForm R (Mᵢ i)) (x : ∀ i,
   sum_apply _ _ _
 #align quadratic_form.pi_apply QuadraticForm.pi_apply
 
+#print QuadraticForm.Isometry.pi /-
 /-- An isometry between quadratic forms generated by `quadratic_form.prod` can be constructed
 from a pair of isometries between the left and right parts. -/
 @[simps toLinearEquiv]
@@ -147,6 +150,7 @@ def Isometry.pi [Fintype ι] {Q : ∀ i, QuadraticForm R (Mᵢ i)} {Q' : ∀ i,
       isometry.coe_to_linear_equiv, isometry.map_app]
   toLinearEquiv := LinearEquiv.piCongrRight fun i => (e i : Mᵢ i ≃ₗ[R] Nᵢ i)
 #align quadratic_form.isometry.pi QuadraticForm.Isometry.pi
+-/
 
 theorem Equivalent.pi [Fintype ι] {Q : ∀ i, QuadraticForm R (Mᵢ i)}
     {Q' : ∀ i, QuadraticForm R (Nᵢ i)} (e : ∀ i, (Q i).Equivalent (Q' i)) :

9b2755b9

bump to nightly-2023-06-05-16

mathlib commit https://github.com/leanprover-community/mathlib/commit/13361559d66b84f80b6d5a1c4a26aa5054766725

43f0fba3

Diff

@@ -155,7 +155,7 @@ theorem Equivalent.pi [Fintype ι] {Q : ∀ i, QuadraticForm R (Mᵢ i)}
 #align quadratic_form.equivalent.pi QuadraticForm.Equivalent.pi
 
 /-- If a family is anisotropic then its components must be. The converse is not true. -/
-theorem anisotropicOfPi [Fintype ι] {R} [OrderedRing R] [∀ i, Module R (Mᵢ i)]
+theorem anisotropic_of_pi [Fintype ι] {R} [OrderedRing R] [∀ i, Module R (Mᵢ i)]
     {Q : ∀ i, QuadraticForm R (Mᵢ i)} (h : (pi Q).Anisotropic) : ∀ i, (Q i).Anisotropic :=
   by
   simp_rw [anisotropic, pi_apply, Function.funext_iff, Pi.zero_apply] at h 
@@ -169,7 +169,7 @@ theorem anisotropicOfPi [Fintype ι] {R} [OrderedRing R] [∀ i, Module R (Mᵢ
   by_cases hji : j = i
   · subst hji; rw [Pi.single_eq_same, hx]
   · rw [Pi.single_eq_of_ne hji, map_zero]
-#align quadratic_form.anisotropic_of_pi QuadraticForm.anisotropicOfPi
+#align quadratic_form.anisotropic_of_pi QuadraticForm.anisotropic_of_pi
 
 theorem nonneg_pi_iff [Fintype ι] {R} [OrderedRing R] [∀ i, Module R (Mᵢ i)]
     {Q : ∀ i, QuadraticForm R (Mᵢ i)} : (∀ x, 0 ≤ pi Q x) ↔ ∀ i x, 0 ≤ Q i x :=

9b2755b9

bump to nightly-2023-06-04-18

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

3fb4268b

Diff

@@ -161,14 +161,14 @@ theorem anisotropicOfPi [Fintype ι] {R} [OrderedRing R] [∀ i, Module R (Mᵢ
   simp_rw [anisotropic, pi_apply, Function.funext_iff, Pi.zero_apply] at h 
   intro i x hx
   classical
-    have := h (Pi.single i x) _ i
-    · rw [Pi.single_eq_same] at this 
-      exact this
-    apply Finset.sum_eq_zero
-    intro j _
-    by_cases hji : j = i
-    · subst hji; rw [Pi.single_eq_same, hx]
-    · rw [Pi.single_eq_of_ne hji, map_zero]
+  have := h (Pi.single i x) _ i
+  · rw [Pi.single_eq_same] at this 
+    exact this
+  apply Finset.sum_eq_zero
+  intro j _
+  by_cases hji : j = i
+  · subst hji; rw [Pi.single_eq_same, hx]
+  · rw [Pi.single_eq_of_ne hji, map_zero]
 #align quadratic_form.anisotropic_of_pi QuadraticForm.anisotropicOfPi
 
 theorem nonneg_pi_iff [Fintype ι] {R} [OrderedRing R] [∀ i, Module R (Mᵢ i)]
@@ -180,9 +180,9 @@ theorem nonneg_pi_iff [Fintype ι] {R} [OrderedRing R] [∀ i, Module R (Mᵢ i)
   -- TODO: does this generalize to a useful lemma independent of `quadratic_form`?
   · intro h i x
     classical
-      convert h (Pi.single i x) using 1
-      rw [Finset.sum_eq_single_of_mem i (Finset.mem_univ _) fun j _ hji => _, Pi.single_eq_same]
-      rw [Pi.single_eq_of_ne hji, map_zero]
+    convert h (Pi.single i x) using 1
+    rw [Finset.sum_eq_single_of_mem i (Finset.mem_univ _) fun j _ hji => _, Pi.single_eq_same]
+    rw [Pi.single_eq_of_ne hji, map_zero]
   · rintro h x
     exact Finset.sum_nonneg fun i hi => h i (x i)
 #align quadratic_form.nonneg_pi_iff QuadraticForm.nonneg_pi_iff

9b2755b9

bump to nightly-2023-06-01-16

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

b9c87c70

Diff

@@ -80,7 +80,7 @@ theorem anisotropic_of_prod {R} [OrderedRing R] [Module R M₁] [Module R M₂]
     {Q₁ : QuadraticForm R M₁} {Q₂ : QuadraticForm R M₂} (h : (Q₁.Prod Q₂).Anisotropic) :
     Q₁.Anisotropic ∧ Q₂.Anisotropic :=
   by
-  simp_rw [anisotropic, prod_apply, Prod.forall, Prod.mk_eq_zero] at h
+  simp_rw [anisotropic, prod_apply, Prod.forall, Prod.mk_eq_zero] at h 
   constructor
   · intro x hx
     refine' (h x 0 _).1
@@ -114,7 +114,7 @@ theorem posDef_prod_iff {R} [OrderedRing R] [Module R M₁] [Module R M₂] {Q
   · rintro ⟨⟨hle₁, ha₁⟩, ⟨hle₂, ha₂⟩⟩
     refine' ⟨⟨hle₁, hle₂⟩, _⟩
     rintro ⟨x₁, x₂⟩ (hx : Q₁ x₁ + Q₂ x₂ = 0)
-    rw [add_eq_zero_iff' (hle₁ x₁) (hle₂ x₂), ha₁.eq_zero_iff, ha₂.eq_zero_iff] at hx
+    rw [add_eq_zero_iff' (hle₁ x₁) (hle₂ x₂), ha₁.eq_zero_iff, ha₂.eq_zero_iff] at hx 
     rwa [Prod.mk_eq_zero]
 #align quadratic_form.pos_def_prod_iff QuadraticForm.posDef_prod_iff
 
@@ -158,11 +158,11 @@ theorem Equivalent.pi [Fintype ι] {Q : ∀ i, QuadraticForm R (Mᵢ i)}
 theorem anisotropicOfPi [Fintype ι] {R} [OrderedRing R] [∀ i, Module R (Mᵢ i)]
     {Q : ∀ i, QuadraticForm R (Mᵢ i)} (h : (pi Q).Anisotropic) : ∀ i, (Q i).Anisotropic :=
   by
-  simp_rw [anisotropic, pi_apply, Function.funext_iff, Pi.zero_apply] at h
+  simp_rw [anisotropic, pi_apply, Function.funext_iff, Pi.zero_apply] at h 
   intro i x hx
   classical
     have := h (Pi.single i x) _ i
-    · rw [Pi.single_eq_same] at this
+    · rw [Pi.single_eq_same] at this 
       exact this
     apply Finset.sum_eq_zero
     intro j _
@@ -197,7 +197,7 @@ theorem posDef_pi_iff [Fintype ι] {R} [OrderedRing R] [∀ i, Module R (Mᵢ i)
     exact ⟨hle i, anisotropic_of_pi ha i⟩
   · intro h
     refine' ⟨fun i => (h i).1, fun x hx => funext fun i => (h i).2 _ _⟩
-    rw [pi_apply, Finset.sum_eq_zero_iff_of_nonneg fun j hj => _] at hx
+    rw [pi_apply, Finset.sum_eq_zero_iff_of_nonneg fun j hj => _] at hx 
     · exact hx _ (Finset.mem_univ _)
     exact (h j).1 _
 #align quadratic_form.pos_def_pi_iff QuadraticForm.posDef_pi_iff

9b2755b9

bump to nightly-2023-05-28-18

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

8d353152

Diff

@@ -123,7 +123,7 @@ theorem PosDef.prod {R} [OrderedRing R] [Module R M₁] [Module R M₂] {Q₁ :
   posDef_prod_iff.mpr ⟨h₁, h₂⟩
 #align quadratic_form.pos_def.prod QuadraticForm.PosDef.prod
 
-open BigOperators
+open scoped BigOperators
 
 /-- Construct a quadratic form on a family of modules from the quadratic form on each module. -/
 def pi [Fintype ι] (Q : ∀ i, QuadraticForm R (Mᵢ i)) : QuadraticForm R (∀ i, Mᵢ i) :=

9b2755b9

bump to nightly-2023-05-28-04

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

6797a637

Diff

@@ -97,10 +97,8 @@ theorem nonneg_prod_iff {R} [OrderedRing R] [Module R M₁] [Module R M₂] {Q
   constructor
   · intro h
     constructor
-    · intro x
-      simpa only [add_zero, map_zero] using h x 0
-    · intro x
-      simpa only [zero_add, map_zero] using h 0 x
+    · intro x; simpa only [add_zero, map_zero] using h x 0
+    · intro x; simpa only [zero_add, map_zero] using h 0 x
   · rintro ⟨h₁, h₂⟩ x₁ x₂
     exact add_nonneg (h₁ x₁) (h₂ x₂)
 #align quadratic_form.nonneg_prod_iff QuadraticForm.nonneg_prod_iff
@@ -169,8 +167,7 @@ theorem anisotropicOfPi [Fintype ι] {R} [OrderedRing R] [∀ i, Module R (Mᵢ
     apply Finset.sum_eq_zero
     intro j _
     by_cases hji : j = i
-    · subst hji
-      rw [Pi.single_eq_same, hx]
+    · subst hji; rw [Pi.single_eq_same, hx]
     · rw [Pi.single_eq_of_ne hji, map_zero]
 #align quadratic_form.anisotropic_of_pi QuadraticForm.anisotropicOfPi

9b2755b9

bump to nightly-2023-02-21-16

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

1107b979

Changes in mathlib4

mathlib3

mathlib4

9b2755b9

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

@@ -219,15 +219,15 @@ variable [Module R M₁] [Module R M₂]
 
 @[simp] theorem polarBilin_prod (Q₁ : QuadraticForm R M₁) (Q₂ : QuadraticForm R M₂) :
     (Q₁.prod Q₂).polarBilin =
-      Q₁.polarBilin.comp (.fst _ _ _) (.fst _ _ _) +
-      Q₂.polarBilin.comp (.snd _ _ _) (.snd _ _ _) :=
-  BilinForm.ext <| polar_prod _ _
+      Q₁.polarBilin.compl₁₂ (.fst R M₁ M₂) (.fst R M₁ M₂) +
+      Q₂.polarBilin.compl₁₂ (.snd R M₁ M₂) (.snd R M₁ M₂) :=
+  LinearMap.ext₂ <| polar_prod _ _
 
 @[simp] theorem associated_prod [Invertible (2 : R)]
     (Q₁ : QuadraticForm R M₁) (Q₂ : QuadraticForm R M₂) :
     associated (Q₁.prod Q₂) =
-      Q₁.associated.comp (.fst _ _ _) (.fst _ _ _) +
-      Q₂.associated.comp (.snd _ _ _) (.snd _ _ _) := by
+      (associated Q₁).compl₁₂ (.fst R M₁ M₂) (.fst R M₁ M₂) +
+      (associated Q₂).compl₁₂ (.snd R M₁ M₂) (.snd R M₁ M₂) := by
   dsimp [associated, associatedHom]
   rw [polarBilin_prod, smul_add]
   rfl
@@ -370,11 +370,11 @@ variable [Fintype ι]
   simp_rw [Finset.sum_sub_distrib, pi_apply, Pi.add_apply]
 
 @[simp] theorem polarBilin_pi (Q : ∀ i, QuadraticForm R (Mᵢ i)) :
-    (pi Q).polarBilin = ∑ i, (Q i).polarBilin.comp (.proj i) (.proj i) :=
-  BilinForm.ext fun x y => (polar_pi _ _ _).trans <| by simp
+    (pi Q).polarBilin = ∑ i, (Q i).polarBilin.compl₁₂ (.proj i) (.proj i) :=
+  LinearMap.ext₂ fun x y => (polar_pi _ _ _).trans <| by simp
 
 @[simp] theorem associated_pi [Invertible (2 : R)] (Q : ∀ i, QuadraticForm R (Mᵢ i)) :
-    associated (pi Q) = ∑ i, (Q i).associated.comp (.proj i) (.proj i) := by
+    associated (pi Q) = ∑ i, (Q i).associated.compl₁₂ (.proj i) (.proj i) := by
   dsimp [associated, associatedHom]
   rw [polarBilin_pi, Finset.smul_sum]
   rfl

9b2755b9

chore: remove terminal, terminal refines (#10762)

I replaced a few "terminal" refine/refine's with exact.

The strategy was very simple-minded: essentially any refine whose following line had smaller indentation got replaced by exact and then I cleaned up the mess.

This PR certainly leaves some further terminal refines, but maybe the current change is beneficial.

ea36aa7d

Diff

@@ -167,7 +167,7 @@ theorem posDef_prod_iff {R} [OrderedCommRing R] [Module R M₁] [Module R M₂]
   constructor
   · rintro ⟨⟨hle₁, hle₂⟩, ha⟩
     obtain ⟨ha₁, ha₂⟩ := anisotropic_of_prod ha
-    refine' ⟨⟨hle₁, ha₁⟩, ⟨hle₂, ha₂⟩⟩
+    exact ⟨⟨hle₁, ha₁⟩, ⟨hle₂, ha₂⟩⟩
   · rintro ⟨⟨hle₁, ha₁⟩, ⟨hle₂, ha₂⟩⟩
     refine' ⟨⟨hle₁, hle₂⟩, _⟩
     rintro ⟨x₁, x₂⟩ (hx : Q₁ x₁ + Q₂ x₂ = 0)

9b2755b9

feat: add fst and snd for QuadraticForm.Isometry (#10381)

Also adds proj for the Pi variation, along with Isometry.ofEq to make it possible to state the theorems for the Pi type.

7b0f450d

Diff

@@ -77,6 +77,40 @@ def Isometry.inr (Q₁ : QuadraticForm R M₁) (Q₂ : QuadraticForm R M₂) : Q
   toLinearMap := LinearMap.inr R _ _
   map_app' m₁ := by simp
 
+variable (M₂) in
+/-- `LinearMap.fst` as an isometry, when the second space has the zero quadratic form. -/
+@[simps!]
+def Isometry.fst (Q₁ : QuadraticForm R M₁) : (Q₁.prod (0 : QuadraticForm R M₂)) →qᵢ Q₁ where
+  toLinearMap := LinearMap.fst R _ _
+  map_app' m₁ := by simp
+
+variable (M₁) in
+/-- `LinearMap.snd` as an isometry, when the first space has the zero quadratic form. -/
+@[simps!]
+def Isometry.snd (Q₂ : QuadraticForm R M₂) : ((0 : QuadraticForm R M₁).prod Q₂) →qᵢ Q₂ where
+  toLinearMap := LinearMap.snd R _ _
+  map_app' m₁ := by simp
+
+@[simp]
+lemma Isometry.fst_comp_inl (Q₁ : QuadraticForm R M₁) :
+    (fst M₂ Q₁).comp (inl Q₁ (0 : QuadraticForm R M₂)) = .id _ :=
+  ext fun _ => rfl
+
+@[simp]
+lemma Isometry.snd_comp_inr (Q₂ : QuadraticForm R M₂) :
+    (snd M₁ Q₂).comp (inr (0 : QuadraticForm R M₁) Q₂) = .id _ :=
+  ext fun _ => rfl
+
+@[simp]
+lemma Isometry.snd_comp_inl (Q₂ : QuadraticForm R M₂) :
+    (snd M₁ Q₂).comp (inl (0 : QuadraticForm R M₁) Q₂) = 0 :=
+  ext fun _ => rfl
+
+@[simp]
+lemma Isometry.fst_comp_inr (Q₁ : QuadraticForm R M₁) :
+    (fst M₂ Q₁).comp (inr Q₁ (0 : QuadraticForm R M₂)) = 0 :=
+  ext fun _ => rfl
+
 theorem Equivalent.prod {Q₁ : QuadraticForm R M₁} {Q₂ : QuadraticForm R M₂}
     {Q₁' : QuadraticForm R N₁} {Q₂' : QuadraticForm R N₂} (e₁ : Q₁.Equivalent Q₁')
     (e₂ : Q₂.Equivalent Q₂') : (Q₁.prod Q₂).Equivalent (Q₁'.prod Q₂') :=
@@ -247,6 +281,30 @@ def Isometry.single [Fintype ι] [DecidableEq ι] (Q : ∀ i, QuadraticForm R (M
   toLinearMap := LinearMap.single i
   map_app' := pi_apply_single _ _
 
+/-- `LinearMap.proj` as an isometry, when all but one quadratic form is zero. -/
+@[simps!]
+def Isometry.proj [Fintype ι] [DecidableEq ι] (i : ι) (Q : QuadraticForm R (Mᵢ i)) :
+    pi (Pi.single i Q) →qᵢ Q where
+  toLinearMap := LinearMap.proj i
+  map_app' m := by
+    dsimp
+    rw [pi_apply, Fintype.sum_eq_single i (fun j hij => ?_), Pi.single_eq_same]
+    rw [Pi.single_eq_of_ne hij, zero_apply]
+
+/-- Note that `QuadraticForm.Isometry.id` would not be well-typed as the RHS. -/
+@[simp, nolint simpNF]  -- ignore the bogus "Left-hand side does not simplify" lint error
+theorem Isometry.proj_comp_single_of_same [Fintype ι] [DecidableEq ι]
+    (i : ι) (Q : QuadraticForm R (Mᵢ i)) :
+    (proj i Q).comp (single _ i) = .ofEq (Pi.single_eq_same _ _) :=
+  ext fun _ => Pi.single_eq_same _ _
+
+/-- Note that `0 : 0 →qᵢ Q` alone would not be well-typed as the RHS. -/
+@[simp]
+theorem Isometry.proj_comp_single_of_ne [Fintype ι] [DecidableEq ι]
+    {i j : ι} (h : i ≠ j) (Q : QuadraticForm R (Mᵢ i)) :
+    (proj i Q).comp (single _ j) = (0 : 0 →qᵢ Q).comp (ofEq (Pi.single_eq_of_ne h.symm _)) :=
+  ext fun _ => Pi.single_eq_of_ne h _
+
 theorem Equivalent.pi [Fintype ι] {Q : ∀ i, QuadraticForm R (Mᵢ i)}
     {Q' : ∀ i, QuadraticForm R (Nᵢ i)} (e : ∀ i, (Q i).Equivalent (Q' i)) :
     (pi Q).Equivalent (pi Q') :=

9b2755b9

chore(*): drop $/<| before fun (#9361)

Subset of #9319

3694e27d

Diff

@@ -313,7 +313,7 @@ variable [Fintype ι]
 
 @[simp] theorem polarBilin_pi (Q : ∀ i, QuadraticForm R (Mᵢ i)) :
     (pi Q).polarBilin = ∑ i, (Q i).polarBilin.comp (.proj i) (.proj i) :=
-  BilinForm.ext <| fun x y => (polar_pi _ _ _).trans <| by simp
+  BilinForm.ext fun x y => (polar_pi _ _ _).trans <| by simp
 
 @[simp] theorem associated_pi [Invertible (2 : R)] (Q : ∀ i, QuadraticForm R (Mᵢ i)) :
     associated (pi Q) = ∑ i, (Q i).associated.comp (.proj i) (.proj i) := by

9b2755b9

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

@@ -147,6 +147,29 @@ theorem PosDef.prod {R} [OrderedCommRing R] [Module R M₁] [Module R M₂]
   posDef_prod_iff.mpr ⟨h₁, h₂⟩
 #align quadratic_form.pos_def.prod QuadraticForm.PosDef.prod
 
+theorem IsOrtho.prod {Q₁ : QuadraticForm R M₁} {Q₂ : QuadraticForm R M₂}
+    {v w : M₁ × M₂} (h₁ : Q₁.IsOrtho v.1 w.1) (h₂ : Q₂.IsOrtho v.2 w.2) :
+    (Q₁.prod Q₂).IsOrtho v w :=
+  (congr_arg₂ HAdd.hAdd h₁ h₂).trans <| add_add_add_comm _ _ _ _
+
+@[simp] theorem IsOrtho.inl_inr {Q₁ : QuadraticForm R M₁} {Q₂ : QuadraticForm R M₂}
+    (m₁ : M₁) (m₂ : M₂) :
+    (Q₁.prod Q₂).IsOrtho (m₁, 0) (0, m₂) := .prod (.zero_right _) (.zero_left _)
+
+@[simp] theorem IsOrtho.inr_inl {Q₁ : QuadraticForm R M₁} {Q₂ : QuadraticForm R M₂}
+    (m₁ : M₁) (m₂ : M₂) :
+    (Q₁.prod Q₂).IsOrtho (0, m₂) (m₁, 0) := (IsOrtho.inl_inr _ _).symm
+
+@[simp] theorem isOrtho_inl_inl_iff {Q₁ : QuadraticForm R M₁} {Q₂ : QuadraticForm R M₂}
+    (m₁ m₁' : M₁) :
+    (Q₁.prod Q₂).IsOrtho (m₁, 0) (m₁', 0) ↔ Q₁.IsOrtho m₁ m₁' := by
+  simp [isOrtho_def]
+
+@[simp] theorem isOrtho_inr_inr_iff {Q₁ : QuadraticForm R M₁} {Q₂ : QuadraticForm R M₂}
+    (m₂ m₂' : M₂) :
+    (Q₁.prod Q₂).IsOrtho (0, m₂) (0, m₂') ↔ Q₂.IsOrtho m₂ m₂' := by
+  simp [isOrtho_def]
+
 end Semiring
 
 section Ring

9b2755b9

feat(LinearAlgebra/QuadraticForm/Prod): inl, inr, and single are isometries (#7723)

ab701cad

Diff

@@ -65,6 +65,18 @@ def IsometryEquiv.prod
   toLinearEquiv := LinearEquiv.prod e₁.toLinearEquiv e₂.toLinearEquiv
 #align quadratic_form.isometry.prod QuadraticForm.IsometryEquiv.prod
 
+/-- `LinearMap.inl` as an isometry. -/
+@[simps!]
+def Isometry.inl (Q₁ : QuadraticForm R M₁) (Q₂ : QuadraticForm R M₂) : Q₁ →qᵢ (Q₁.prod Q₂) where
+  toLinearMap := LinearMap.inl R _ _
+  map_app' m₁ := by simp
+
+/-- `LinearMap.inr` as an isometry. -/
+@[simps!]
+def Isometry.inr (Q₁ : QuadraticForm R M₁) (Q₂ : QuadraticForm R M₂) : Q₂ →qᵢ (Q₁.prod Q₂) where
+  toLinearMap := LinearMap.inr R _ _
+  map_app' m₁ := by simp
+
 theorem Equivalent.prod {Q₁ : QuadraticForm R M₁} {Q₂ : QuadraticForm R M₂}
     {Q₁' : QuadraticForm R N₁} {Q₂' : QuadraticForm R N₂} (e₁ : Q₁.Equivalent Q₁')
     (e₂ : Q₂.Equivalent Q₂') : (Q₁.prod Q₂).Equivalent (Q₁'.prod Q₂') :=
@@ -187,6 +199,12 @@ theorem pi_apply [Fintype ι] (Q : ∀ i, QuadraticForm R (Mᵢ i)) (x : ∀ i,
   sum_apply _ _ _
 #align quadratic_form.pi_apply QuadraticForm.pi_apply
 
+theorem pi_apply_single [Fintype ι] [DecidableEq ι]
+    (Q : ∀ i, QuadraticForm R (Mᵢ i)) (i : ι) (m : Mᵢ i) :
+    pi Q (Pi.single i m) = Q i m := by
+  rw [pi_apply, Fintype.sum_eq_single i fun j hj => ?_, Pi.single_eq_same]
+  rw [Pi.single_eq_of_ne hj, map_zero]
+
 /-- An isometry between quadratic forms generated by `QuadraticForm.pi` can be constructed
 from a pair of isometries between the left and right parts. -/
 @[simps toLinearEquiv]
@@ -199,6 +217,13 @@ def IsometryEquiv.pi [Fintype ι]
   toLinearEquiv := LinearEquiv.piCongrRight fun i => (e i : Mᵢ i ≃ₗ[R] Nᵢ i)
 #align quadratic_form.isometry.pi QuadraticForm.IsometryEquiv.pi
 
+/-- `LinearMap.single` as an isometry. -/
+@[simps!]
+def Isometry.single [Fintype ι] [DecidableEq ι] (Q : ∀ i, QuadraticForm R (Mᵢ i)) (i : ι) :
+    Q i →qᵢ pi Q where
+  toLinearMap := LinearMap.single i
+  map_app' := pi_apply_single _ _
+
 theorem Equivalent.pi [Fintype ι] {Q : ∀ i, QuadraticForm R (Mᵢ i)}
     {Q' : ∀ i, QuadraticForm R (Nᵢ i)} (e : ∀ i, (Q i).Equivalent (Q' i)) :
     (pi Q).Equivalent (pi Q') :=

9b2755b9

feat(LinearAlgebra/QuadraticForm/Prod): lemmas about polar,polarBilin, and associated (#7664)

This also slightly adjusts the file sectioning in order to introduce the temporary Ring assumption.

cf3ecdf9

Diff

@@ -36,17 +36,15 @@ universe u v w
 
 variable {ι : Type*} {R : Type*} {M₁ M₂ N₁ N₂ : Type*} {Mᵢ Nᵢ : ι → Type*}
 
-variable [CommSemiring R]
-
-variable [AddCommMonoid M₁] [AddCommMonoid M₂] [AddCommMonoid N₁] [AddCommMonoid N₂]
-
-variable [Module R M₁] [Module R M₂] [Module R N₁] [Module R N₂]
 
-variable [∀ i, AddCommMonoid (Mᵢ i)] [∀ i, AddCommMonoid (Nᵢ i)]
+namespace QuadraticForm
 
-variable [∀ i, Module R (Mᵢ i)] [∀ i, Module R (Nᵢ i)]
+section Prod
 
-namespace QuadraticForm
+section Semiring
+variable [CommSemiring R]
+variable [AddCommMonoid M₁] [AddCommMonoid M₂] [AddCommMonoid N₁] [AddCommMonoid N₂]
+variable [Module R M₁] [Module R M₂] [Module R N₁] [Module R N₂]
 
 /-- Construct a quadratic form on a product of two modules from the quadratic form on each module.
 -/
@@ -137,8 +135,47 @@ theorem PosDef.prod {R} [OrderedCommRing R] [Module R M₁] [Module R M₂]
   posDef_prod_iff.mpr ⟨h₁, h₂⟩
 #align quadratic_form.pos_def.prod QuadraticForm.PosDef.prod
 
+end Semiring
+
+section Ring
+
+variable [CommRing R]
+variable [AddCommGroup M₁] [AddCommGroup M₂]
+variable [Module R M₁] [Module R M₂]
+
+@[simp] theorem polar_prod (Q₁ : QuadraticForm R M₁) (Q₂ : QuadraticForm R M₂) (x y : M₁ × M₂) :
+    polar (Q₁.prod Q₂) x y = polar Q₁ x.1 y.1 + polar Q₂ x.2 y.2 := by
+  dsimp [polar]
+  abel
+
+@[simp] theorem polarBilin_prod (Q₁ : QuadraticForm R M₁) (Q₂ : QuadraticForm R M₂) :
+    (Q₁.prod Q₂).polarBilin =
+      Q₁.polarBilin.comp (.fst _ _ _) (.fst _ _ _) +
+      Q₂.polarBilin.comp (.snd _ _ _) (.snd _ _ _) :=
+  BilinForm.ext <| polar_prod _ _
+
+@[simp] theorem associated_prod [Invertible (2 : R)]
+    (Q₁ : QuadraticForm R M₁) (Q₂ : QuadraticForm R M₂) :
+    associated (Q₁.prod Q₂) =
+      Q₁.associated.comp (.fst _ _ _) (.fst _ _ _) +
+      Q₂.associated.comp (.snd _ _ _) (.snd _ _ _) := by
+  dsimp [associated, associatedHom]
+  rw [polarBilin_prod, smul_add]
+  rfl
+
+end Ring
+
+end Prod
+
+section Pi
+
 open scoped BigOperators
 
+section Semiring
+variable [CommSemiring R]
+variable [∀ i, AddCommMonoid (Mᵢ i)] [∀ i, AddCommMonoid (Nᵢ i)]
+variable [∀ i, Module R (Mᵢ i)] [∀ i, Module R (Nᵢ i)]
+
 /-- Construct a quadratic form on a family of modules from the quadratic form on each module. -/
 def pi [Fintype ι] (Q : ∀ i, QuadraticForm R (Mᵢ i)) : QuadraticForm R (∀ i, Mᵢ i) :=
   ∑ i, (Q i).comp (LinearMap.proj i : _ →ₗ[R] Mᵢ i)
@@ -212,4 +249,32 @@ theorem posDef_pi_iff [Fintype ι] {R} [OrderedCommRing R] [∀ i, Module R (M
     exact (h j).1 _
 #align quadratic_form.pos_def_pi_iff QuadraticForm.posDef_pi_iff
 
+end Semiring
+
+namespace Ring
+
+variable [CommRing R]
+variable [∀ i, AddCommGroup (Mᵢ i)] [∀ i, AddCommGroup (Nᵢ i)]
+variable [∀ i, Module R (Mᵢ i)] [∀ i, Module R (Nᵢ i)]
+variable [Fintype ι]
+
+@[simp] theorem polar_pi (Q : ∀ i, QuadraticForm R (Mᵢ i)) (x y : ∀ i, Mᵢ i) :
+    polar (pi Q) x y = ∑ i, polar (Q i) (x i) (y i) := by
+  dsimp [polar]
+  simp_rw [Finset.sum_sub_distrib, pi_apply, Pi.add_apply]
+
+@[simp] theorem polarBilin_pi (Q : ∀ i, QuadraticForm R (Mᵢ i)) :
+    (pi Q).polarBilin = ∑ i, (Q i).polarBilin.comp (.proj i) (.proj i) :=
+  BilinForm.ext <| fun x y => (polar_pi _ _ _).trans <| by simp
+
+@[simp] theorem associated_pi [Invertible (2 : R)] (Q : ∀ i, QuadraticForm R (Mᵢ i)) :
+    associated (pi Q) = ∑ i, (Q i).associated.comp (.proj i) (.proj i) := by
+  dsimp [associated, associatedHom]
+  rw [polarBilin_pi, Finset.smul_sum]
+  rfl
+
+end Ring
+
+end Pi
+
 end QuadraticForm

9b2755b9

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

@@ -36,7 +36,7 @@ universe u v w
 
 variable {ι : Type*} {R : Type*} {M₁ M₂ N₁ N₂ : Type*} {Mᵢ Nᵢ : ι → Type*}
 
-variable [Semiring R]
+variable [CommSemiring R]
 
 variable [AddCommMonoid M₁] [AddCommMonoid M₂] [AddCommMonoid N₁] [AddCommMonoid N₂]
 
@@ -90,7 +90,7 @@ def IsometryEquiv.prodProdProdComm
   map_app' _ := add_add_add_comm _ _ _ _
 
 /-- If a product is anisotropic then its components must be. The converse is not true. -/
-theorem anisotropic_of_prod {R} [OrderedRing R] [Module R M₁] [Module R M₂]
+theorem anisotropic_of_prod {R} [OrderedCommRing R] [Module R M₁] [Module R M₂]
     {Q₁ : QuadraticForm R M₁} {Q₂ : QuadraticForm R M₂} (h : (Q₁.prod Q₂).Anisotropic) :
     Q₁.Anisotropic ∧ Q₂.Anisotropic := by
   simp_rw [Anisotropic, prod_apply, Prod.forall, Prod.mk_eq_zero] at h
@@ -103,8 +103,9 @@ theorem anisotropic_of_prod {R} [OrderedRing R] [Module R M₁] [Module R M₂]
     rw [hx, add_zero, map_zero]
 #align quadratic_form.anisotropic_of_prod QuadraticForm.anisotropic_of_prod
 
-theorem nonneg_prod_iff {R} [OrderedRing R] [Module R M₁] [Module R M₂] {Q₁ : QuadraticForm R M₁}
-    {Q₂ : QuadraticForm R M₂} : (∀ x, 0 ≤ (Q₁.prod Q₂) x) ↔ (∀ x, 0 ≤ Q₁ x) ∧ ∀ x, 0 ≤ Q₂ x := by
+theorem nonneg_prod_iff {R} [OrderedCommRing R] [Module R M₁] [Module R M₂]
+    {Q₁ : QuadraticForm R M₁} {Q₂ : QuadraticForm R M₂} :
+    (∀ x, 0 ≤ (Q₁.prod Q₂) x) ↔ (∀ x, 0 ≤ Q₁ x) ∧ ∀ x, 0 ≤ Q₂ x := by
   simp_rw [Prod.forall, prod_apply]
   constructor
   · intro h
@@ -115,8 +116,9 @@ theorem nonneg_prod_iff {R} [OrderedRing R] [Module R M₁] [Module R M₂] {Q
     exact add_nonneg (h₁ x₁) (h₂ x₂)
 #align quadratic_form.nonneg_prod_iff QuadraticForm.nonneg_prod_iff
 
-theorem posDef_prod_iff {R} [OrderedRing R] [Module R M₁] [Module R M₂] {Q₁ : QuadraticForm R M₁}
-    {Q₂ : QuadraticForm R M₂} : (Q₁.prod Q₂).PosDef ↔ Q₁.PosDef ∧ Q₂.PosDef := by
+theorem posDef_prod_iff {R} [OrderedCommRing R] [Module R M₁] [Module R M₂]
+    {Q₁ : QuadraticForm R M₁} {Q₂ : QuadraticForm R M₂} :
+    (Q₁.prod Q₂).PosDef ↔ Q₁.PosDef ∧ Q₂.PosDef := by
   simp_rw [posDef_iff_nonneg, nonneg_prod_iff]
   constructor
   · rintro ⟨⟨hle₁, hle₂⟩, ha⟩
@@ -129,8 +131,9 @@ theorem posDef_prod_iff {R} [OrderedRing R] [Module R M₁] [Module R M₂] {Q
     rwa [Prod.mk_eq_zero]
 #align quadratic_form.pos_def_prod_iff QuadraticForm.posDef_prod_iff
 
-theorem PosDef.prod {R} [OrderedRing R] [Module R M₁] [Module R M₂] {Q₁ : QuadraticForm R M₁}
-    {Q₂ : QuadraticForm R M₂} (h₁ : Q₁.PosDef) (h₂ : Q₂.PosDef) : (Q₁.prod Q₂).PosDef :=
+theorem PosDef.prod {R} [OrderedCommRing R] [Module R M₁] [Module R M₂]
+    {Q₁ : QuadraticForm R M₁} {Q₂ : QuadraticForm R M₂} (h₁ : Q₁.PosDef) (h₂ : Q₂.PosDef) :
+    (Q₁.prod Q₂).PosDef :=
   posDef_prod_iff.mpr ⟨h₁, h₂⟩
 #align quadratic_form.pos_def.prod QuadraticForm.PosDef.prod
 
@@ -166,7 +169,7 @@ theorem Equivalent.pi [Fintype ι] {Q : ∀ i, QuadraticForm R (Mᵢ i)}
 #align quadratic_form.equivalent.pi QuadraticForm.Equivalent.pi
 
 /-- If a family is anisotropic then its components must be. The converse is not true. -/
-theorem anisotropic_of_pi [Fintype ι] {R} [OrderedRing R] [∀ i, Module R (Mᵢ i)]
+theorem anisotropic_of_pi [Fintype ι] {R} [OrderedCommRing R] [∀ i, Module R (Mᵢ i)]
     {Q : ∀ i, QuadraticForm R (Mᵢ i)} (h : (pi Q).Anisotropic) : ∀ i, (Q i).Anisotropic := by
   simp_rw [Anisotropic, pi_apply, Function.funext_iff, Pi.zero_apply] at h
   intro i x hx
@@ -181,7 +184,7 @@ theorem anisotropic_of_pi [Fintype ι] {R} [OrderedRing R] [∀ i, Module R (M
   · rw [Pi.single_eq_of_ne hji, map_zero]
 #align quadratic_form.anisotropic_of_pi QuadraticForm.anisotropic_of_pi
 
-theorem nonneg_pi_iff [Fintype ι] {R} [OrderedRing R] [∀ i, Module R (Mᵢ i)]
+theorem nonneg_pi_iff [Fintype ι] {R} [OrderedCommRing R] [∀ i, Module R (Mᵢ i)]
     {Q : ∀ i, QuadraticForm R (Mᵢ i)} : (∀ x, 0 ≤ pi Q x) ↔ ∀ i x, 0 ≤ Q i x := by
   simp_rw [pi, sum_apply, comp_apply, LinearMap.proj_apply]
   constructor
@@ -195,7 +198,7 @@ theorem nonneg_pi_iff [Fintype ι] {R} [OrderedRing R] [∀ i, Module R (Mᵢ i)
     exact Finset.sum_nonneg fun i _ => h i (x i)
 #align quadratic_form.nonneg_pi_iff QuadraticForm.nonneg_pi_iff
 
-theorem posDef_pi_iff [Fintype ι] {R} [OrderedRing R] [∀ i, Module R (Mᵢ i)]
+theorem posDef_pi_iff [Fintype ι] {R} [OrderedCommRing R] [∀ i, Module R (Mᵢ i)]
     {Q : ∀ i, QuadraticForm R (Mᵢ i)} : (pi Q).PosDef ↔ ∀ i, (Q i).PosDef := by
   simp_rw [posDef_iff_nonneg, nonneg_pi_iff]
   constructor

9b2755b9

feat(LinearAlgebra/QuadraticForm/Prod): products are commutative up to isomorphism (#7139)

Surprisingly we're missing the whole tower of bundled Equiv.prodAssoc definitions, so this PR omits those too.

e3c514cd

Diff

@@ -73,6 +73,22 @@ theorem Equivalent.prod {Q₁ : QuadraticForm R M₁} {Q₂ : QuadraticForm R M
   Nonempty.map2 IsometryEquiv.prod e₁ e₂
 #align quadratic_form.equivalent.prod QuadraticForm.Equivalent.prod
 
+/-- `LinearEquiv.prodComm` is isometric. -/
+@[simps!]
+def IsometryEquiv.prodComm (Q₁ : QuadraticForm R M₁) (Q₂ : QuadraticForm R M₂) :
+    (Q₁.prod Q₂).IsometryEquiv (Q₂.prod Q₁) where
+  toLinearEquiv := LinearEquiv.prodComm _ _ _
+  map_app' _ := add_comm _ _
+
+/-- `LinearEquiv.prodProdProdComm` is isometric. -/
+@[simps!]
+def IsometryEquiv.prodProdProdComm
+    (Q₁ : QuadraticForm R M₁) (Q₂ : QuadraticForm R M₂)
+    (Q₃ : QuadraticForm R N₁) (Q₄ : QuadraticForm R N₂) :
+    ((Q₁.prod Q₂).prod (Q₃.prod Q₄)).IsometryEquiv ((Q₁.prod Q₃).prod (Q₂.prod Q₄)) where
+  toLinearEquiv := LinearEquiv.prodProdProdComm _ _ _ _ _
+  map_app' _ := add_add_add_comm _ _ _ _
+
 /-- If a product is anisotropic then its components must be. The converse is not true. -/
 theorem anisotropic_of_prod {R} [OrderedRing R] [Module R M₁] [Module R M₂]
     {Q₁ : QuadraticForm R M₁} {Q₂ : QuadraticForm R M₂} (h : (Q₁.prod Q₂).Anisotropic) :

9b2755b9

chore: remove unused simps (#6632)

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

916c75c1

Diff

@@ -168,7 +168,6 @@ theorem anisotropic_of_pi [Fintype ι] {R} [OrderedRing R] [∀ i, Module R (M
 theorem nonneg_pi_iff [Fintype ι] {R} [OrderedRing R] [∀ i, Module R (Mᵢ i)]
     {Q : ∀ i, QuadraticForm R (Mᵢ i)} : (∀ x, 0 ≤ pi Q x) ↔ ∀ i x, 0 ≤ Q i x := by
   simp_rw [pi, sum_apply, comp_apply, LinearMap.proj_apply]
-  dsimp only
   constructor
   -- TODO: does this generalize to a useful lemma independent of `QuadraticForm`?
   · intro h i x

9b2755b9

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

@@ -34,7 +34,7 @@ forms specifically.
 
 universe u v w
 
-variable {ι : Type _} {R : Type _} {M₁ M₂ N₁ N₂ : Type _} {Mᵢ Nᵢ : ι → Type _}
+variable {ι : Type*} {R : Type*} {M₁ M₂ N₁ N₂ : Type*} {Mᵢ Nᵢ : ι → Type*}
 
 variable [Semiring R]

9b2755b9

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

@@ -3,7 +3,7 @@ Copyright (c) 2021 Eric Wieser. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Eric Wieser
 -/
-import Mathlib.LinearAlgebra.QuadraticForm.Isometry
+import Mathlib.LinearAlgebra.QuadraticForm.IsometryEquiv
 
 #align_import linear_algebra.quadratic_form.prod from "leanprover-community/mathlib"@"9b2755b951bc323c962bd072cd447b375cf58101"
 
@@ -58,17 +58,19 @@ def prod (Q₁ : QuadraticForm R M₁) (Q₂ : QuadraticForm R M₂) : Quadratic
 /-- An isometry between quadratic forms generated by `QuadraticForm.prod` can be constructed
 from a pair of isometries between the left and right parts. -/
 @[simps toLinearEquiv]
-def Isometry.prod {Q₁ : QuadraticForm R M₁} {Q₂ : QuadraticForm R M₂} {Q₁' : QuadraticForm R N₁}
-    {Q₂' : QuadraticForm R N₂} (e₁ : Q₁.Isometry Q₁') (e₂ : Q₂.Isometry Q₂') :
-    (Q₁.prod Q₂).Isometry (Q₁'.prod Q₂') where
+def IsometryEquiv.prod
+    {Q₁ : QuadraticForm R M₁} {Q₂ : QuadraticForm R M₂}
+    {Q₁' : QuadraticForm R N₁} {Q₂' : QuadraticForm R N₂}
+    (e₁ : Q₁.IsometryEquiv Q₁') (e₂ : Q₂.IsometryEquiv Q₂') :
+    (Q₁.prod Q₂).IsometryEquiv (Q₁'.prod Q₂') where
   map_app' x := congr_arg₂ (· + ·) (e₁.map_app x.1) (e₂.map_app x.2)
   toLinearEquiv := LinearEquiv.prod e₁.toLinearEquiv e₂.toLinearEquiv
-#align quadratic_form.isometry.prod QuadraticForm.Isometry.prod
+#align quadratic_form.isometry.prod QuadraticForm.IsometryEquiv.prod
 
 theorem Equivalent.prod {Q₁ : QuadraticForm R M₁} {Q₂ : QuadraticForm R M₂}
     {Q₁' : QuadraticForm R N₁} {Q₂' : QuadraticForm R N₂} (e₁ : Q₁.Equivalent Q₁')
     (e₂ : Q₂.Equivalent Q₂') : (Q₁.prod Q₂).Equivalent (Q₁'.prod Q₂') :=
-  Nonempty.map2 Isometry.prod e₁ e₂
+  Nonempty.map2 IsometryEquiv.prod e₁ e₂
 #align quadratic_form.equivalent.prod QuadraticForm.Equivalent.prod
 
 /-- If a product is anisotropic then its components must be. The converse is not true. -/
@@ -132,18 +134,19 @@ theorem pi_apply [Fintype ι] (Q : ∀ i, QuadraticForm R (Mᵢ i)) (x : ∀ i,
 /-- An isometry between quadratic forms generated by `QuadraticForm.pi` can be constructed
 from a pair of isometries between the left and right parts. -/
 @[simps toLinearEquiv]
-def Isometry.pi [Fintype ι] {Q : ∀ i, QuadraticForm R (Mᵢ i)} {Q' : ∀ i, QuadraticForm R (Nᵢ i)}
-    (e : ∀ i, (Q i).Isometry (Q' i)) : (pi Q).Isometry (pi Q') where
+def IsometryEquiv.pi [Fintype ι]
+    {Q : ∀ i, QuadraticForm R (Mᵢ i)} {Q' : ∀ i, QuadraticForm R (Nᵢ i)}
+    (e : ∀ i, (Q i).IsometryEquiv (Q' i)) : (pi Q).IsometryEquiv (pi Q') where
   map_app' x := by
     simp only [pi_apply, LinearEquiv.piCongrRight, LinearEquiv.toFun_eq_coe,
-      Isometry.coe_toLinearEquiv, Isometry.map_app]
+      IsometryEquiv.coe_toLinearEquiv, IsometryEquiv.map_app]
   toLinearEquiv := LinearEquiv.piCongrRight fun i => (e i : Mᵢ i ≃ₗ[R] Nᵢ i)
-#align quadratic_form.isometry.pi QuadraticForm.Isometry.pi
+#align quadratic_form.isometry.pi QuadraticForm.IsometryEquiv.pi
 
 theorem Equivalent.pi [Fintype ι] {Q : ∀ i, QuadraticForm R (Mᵢ i)}
     {Q' : ∀ i, QuadraticForm R (Nᵢ i)} (e : ∀ i, (Q i).Equivalent (Q' i)) :
     (pi Q).Equivalent (pi Q') :=
-  ⟨Isometry.pi fun i => Classical.choice (e i)⟩
+  ⟨IsometryEquiv.pi fun i => Classical.choice (e i)⟩
 #align quadratic_form.equivalent.pi QuadraticForm.Equivalent.pi
 
 /-- If a family is anisotropic then its components must be. The converse is not true. -/

9b2755b9

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) 2021 Eric Wieser. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Eric Wieser
-
-! This file was ported from Lean 3 source module linear_algebra.quadratic_form.prod
-! leanprover-community/mathlib commit 9b2755b951bc323c962bd072cd447b375cf58101
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.LinearAlgebra.QuadraticForm.Isometry
 
+#align_import linear_algebra.quadratic_form.prod from "leanprover-community/mathlib"@"9b2755b951bc323c962bd072cd447b375cf58101"
+
 /-! # Quadratic form on product and pi types
 
 ## Main definitions

9b2755b9

chore: cleanup whitespace (#5988)

Grepping for [^ .:{-] [^ :] and reviewing the results. Once I started I couldn't stop. :-)

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

12343aa5

Diff

@@ -29,7 +29,7 @@ import Mathlib.LinearAlgebra.QuadraticForm.Isometry
 ## Implementation notes
 
 Many of the lemmas in this file could be generalized into results about sums of positive and
-non-negative elements, and would generalize to any map `Q`  where `Q 0 = 0`, not just quadratic
+non-negative elements, and would generalize to any map `Q` where `Q 0 = 0`, not just quadratic
 forms specifically.
 
 -/

9b2755b9

feat: port LinearAlgebra.QuadraticForm.Prod (#4735)

8f95ac4d

`linear_algebra.quadratic_form.prod` ⟷ `Mathlib.LinearAlgebra.QuadraticForm.Prod`

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Dependencies 10 + 626

linear_algebra.quadratic_form.prod ⟷ Mathlib.LinearAlgebra.QuadraticForm.Prod

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Dependencies 10 + 626

`linear_algebra.quadratic_form.prod` ⟷ `Mathlib.LinearAlgebra.QuadraticForm.Prod`