linear_algebra.tensor_algebra.basic | Mathlib porting status

Changes since the initial port

The following section lists changes to this file in mathlib3 and mathlib4 that occured after the initial port. Most recent changes are shown first. Hovering over a commit will show all commits associated with the same mathlib3 commit.

Changes in mathlib3

b8d2eaa6

(last sync)

Changes in mathlib3port

mathlib3

mathlib3port

7e5137f5

bump to nightly-2024-03-17-08

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

22f01ce4

Diff

@@ -168,7 +168,7 @@ theorem lift_comp_ι {A : Type _} [Semiring A] [Algebra R A] (g : TensorAlgebra
 theorem hom_ext {A : Type _} [Semiring A] [Algebra R A] {f g : TensorAlgebra R M →ₐ[R] A}
     (w : f.toLinearMap.comp (ι R) = g.toLinearMap.comp (ι R)) : f = g :=
   by
-  rw [← lift_symm_apply, ← lift_symm_apply] at w 
+  rw [← lift_symm_apply, ← lift_symm_apply] at w
   exact (lift R).symm.Injective w
 #align tensor_algebra.hom_ext TensorAlgebra.hom_ext
 -/
@@ -303,7 +303,7 @@ theorem ι_eq_algebraMap_iff (x : M) (r : R) : ι R x = algebraMap R _ r ↔ x =
   · letI : Module Rᵐᵒᵖ M := Module.compHom _ ((RingHom.id R).fromOpposite mul_comm)
     haveI : IsCentralScalar R M := ⟨fun r m => rfl⟩
     have hf0 : to_triv_sq_zero_ext (ι R x) = (0, x) := lift_ι_apply _ _
-    rw [h, AlgHom.commutes] at hf0 
+    rw [h, AlgHom.commutes] at hf0
     have : r = 0 ∧ 0 = x := Prod.ext_iff.1 hf0
     exact this.symm.imp_left Eq.symm
   · rintro ⟨rfl, rfl⟩
@@ -328,7 +328,7 @@ theorem ι_range_disjoint_one :
   by
   rw [Submodule.disjoint_def]
   rintro _ ⟨x, hx⟩ ⟨r, rfl : algebraMap _ _ _ = _⟩
-  rw [ι_eq_algebra_map_iff x] at hx 
+  rw [ι_eq_algebra_map_iff x] at hx
   rw [hx.2, RingHom.map_zero]
 #align tensor_algebra.ι_range_disjoint_one TensorAlgebra.ι_range_disjoint_one
 -/

7e5137f5

bump to nightly-2023-09-24-06

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

5655435f

Diff

@@ -3,11 +3,11 @@ Copyright (c) 2020 Adam Topaz. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Adam Topaz
 -/
-import Mathbin.Algebra.FreeAlgebra
-import Mathbin.Algebra.RingQuot
-import Mathbin.Algebra.TrivSqZeroExt
-import Mathbin.Algebra.Algebra.Operations
-import Mathbin.LinearAlgebra.Multilinear.Basic
+import Algebra.FreeAlgebra
+import Algebra.RingQuot
+import Algebra.TrivSqZeroExt
+import Algebra.Algebra.Operations
+import LinearAlgebra.Multilinear.Basic
 
 #align_import linear_algebra.tensor_algebra.basic from "leanprover-community/mathlib"@"7e5137f579de09a059a5ce98f364a04e221aabf0"

7e5137f5

bump to nightly-2023-08-17-09

mathlib commit https://github.com/leanprover-community/mathlib/commit/32a7e535287f9c73f2e4d2aef306a39190f0b504

60285dcc

Diff

@@ -187,7 +187,7 @@ theorem induction {C : TensorAlgebra R M → Prop}
   -- the arguments are enough to construct a subalgebra, and a mapping into it from M
   let s : Subalgebra R (TensorAlgebra R M) :=
     { carrier := C
-      mul_mem' := h_mul
+      hMul_mem' := h_mul
       add_mem' := h_add
       algebraMap_mem' := h_grade0 }
   let of : M →ₗ[R] s := (ι R).codRestrict s.to_submodule h_grade1

7e5137f5

bump to nightly-2023-07-20-09

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

9c56d0dd

Diff

@@ -2,11 +2,6 @@
 Copyright (c) 2020 Adam Topaz. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Adam Topaz
-
-! This file was ported from Lean 3 source module linear_algebra.tensor_algebra.basic
-! leanprover-community/mathlib commit 7e5137f579de09a059a5ce98f364a04e221aabf0
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.Algebra.FreeAlgebra
 import Mathbin.Algebra.RingQuot
@@ -14,6 +9,8 @@ import Mathbin.Algebra.TrivSqZeroExt
 import Mathbin.Algebra.Algebra.Operations
 import Mathbin.LinearAlgebra.Multilinear.Basic
 
+#align_import linear_algebra.tensor_algebra.basic from "leanprover-community/mathlib"@"7e5137f579de09a059a5ce98f364a04e221aabf0"
+
 /-!
 # Tensor Algebras

7e5137f5

bump to nightly-2023-06-13-21

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

829520ac

Diff

@@ -85,6 +85,7 @@ instance {S : Type _} [CommRing S] [Module S M] : Ring (TensorAlgebra S M) :=
 
 variable {M}
 
+#print TensorAlgebra.ι /-
 /-- The canonical linear map `M →ₗ[R] tensor_algebra R M`.
 -/
 irreducible_def ι : M →ₗ[R] TensorAlgebra R M :=
@@ -92,11 +93,15 @@ irreducible_def ι : M →ₗ[R] TensorAlgebra R M :=
     map_add' := fun x y => by rw [← AlgHom.map_add]; exact RingQuot.mkAlgHom_rel R rel.add
     map_smul' := fun r x => by rw [← AlgHom.map_smul]; exact RingQuot.mkAlgHom_rel R rel.smul }
 #align tensor_algebra.ι TensorAlgebra.ι
+-/
 
+#print TensorAlgebra.ringQuot_mkAlgHom_freeAlgebra_ι_eq_ι /-
 theorem ringQuot_mkAlgHom_freeAlgebra_ι_eq_ι (m : M) :
     RingQuot.mkAlgHom R (Rel R M) (FreeAlgebra.ι R m) = ι R m := by rw [ι]; rfl
 #align tensor_algebra.ring_quot_mk_alg_hom_free_algebra_ι_eq_ι TensorAlgebra.ringQuot_mkAlgHom_freeAlgebra_ι_eq_ι
+-/
 
+#print TensorAlgebra.lift /-
 /-- Given a linear map `f : M → A` where `A` is an `R`-algebra, `lift R f` is the unique lift
 of `f` to a morphism of `R`-algebras `tensor_algebra R M → A`.
 -/
@@ -122,26 +127,34 @@ irreducible_def lift {A : Type _} [Semiring A] [Algebra R A] :
             exact
               (RingQuot.liftAlgHom_mkAlgHom_apply _ _ _ _).trans (FreeAlgebra.lift_ι_apply _ _) }
 #align tensor_algebra.lift TensorAlgebra.lift
+-/
 
 variable {R}
 
+#print TensorAlgebra.ι_comp_lift /-
 @[simp]
 theorem ι_comp_lift {A : Type _} [Semiring A] [Algebra R A] (f : M →ₗ[R] A) :
     (lift R f).toLinearMap.comp (ι R) = f := by convert (lift R).symm_apply_apply f;
   simp only [lift, Equiv.coe_fn_symm_mk]
 #align tensor_algebra.ι_comp_lift TensorAlgebra.ι_comp_lift
+-/
 
+#print TensorAlgebra.lift_ι_apply /-
 @[simp]
 theorem lift_ι_apply {A : Type _} [Semiring A] [Algebra R A] (f : M →ₗ[R] A) (x) :
     lift R f (ι R x) = f x := by conv_rhs => rw [← ι_comp_lift f]; rfl
 #align tensor_algebra.lift_ι_apply TensorAlgebra.lift_ι_apply
+-/
 
+#print TensorAlgebra.lift_unique /-
 @[simp]
 theorem lift_unique {A : Type _} [Semiring A] [Algebra R A] (f : M →ₗ[R] A)
     (g : TensorAlgebra R M →ₐ[R] A) : g.toLinearMap.comp (ι R) = f ↔ g = lift R f := by
   rw [← (lift R).symm_apply_eq]; simp only [lift, Equiv.coe_fn_symm_mk]
 #align tensor_algebra.lift_unique TensorAlgebra.lift_unique
+-/
 
+#print TensorAlgebra.lift_comp_ι /-
 -- Marking `tensor_algebra` irreducible makes `ring` instances inaccessible on quotients.
 -- https://leanprover.zulipchat.com/#narrow/stream/113488-general/topic/algebra.2Esemiring_to_ring.20breaks.20semimodule.20typeclass.20lookup/near/212580241
 -- For now, we avoid this by not marking it irreducible.
@@ -150,7 +163,9 @@ theorem lift_comp_ι {A : Type _} [Semiring A] [Algebra R A] (g : TensorAlgebra
     lift R (g.toLinearMap.comp (ι R)) = g := by rw [← lift_symm_apply];
   exact (lift R).apply_symm_apply g
 #align tensor_algebra.lift_comp_ι TensorAlgebra.lift_comp_ι
+-/
 
+#print TensorAlgebra.hom_ext /-
 /-- See note [partially-applied ext lemmas]. -/
 @[ext]
 theorem hom_ext {A : Type _} [Semiring A] [Algebra R A] {f g : TensorAlgebra R M →ₐ[R] A}
@@ -159,7 +174,9 @@ theorem hom_ext {A : Type _} [Semiring A] [Algebra R A] {f g : TensorAlgebra R M
   rw [← lift_symm_apply, ← lift_symm_apply] at w 
   exact (lift R).symm.Injective w
 #align tensor_algebra.hom_ext TensorAlgebra.hom_ext
+-/
 
+#print TensorAlgebra.induction /-
 -- This proof closely follows `free_algebra.induction`
 /-- If `C` holds for the `algebra_map` of `r : R` into `tensor_algebra R M`, the `ι` of `x : M`,
 and is preserved under addition and muliplication, then it holds for all of `tensor_algebra R M`.
@@ -186,50 +203,66 @@ theorem induction {C : TensorAlgebra R M → Prop}
   convert Subtype.prop (lift R of a)
   exact AlgHom.congr_fun of_id a
 #align tensor_algebra.induction TensorAlgebra.induction
+-/
 
+#print TensorAlgebra.algebraMapInv /-
 /-- The left-inverse of `algebra_map`. -/
 def algebraMapInv : TensorAlgebra R M →ₐ[R] R :=
   lift R (0 : M →ₗ[R] R)
 #align tensor_algebra.algebra_map_inv TensorAlgebra.algebraMapInv
+-/
 
 variable (M)
 
+#print TensorAlgebra.algebraMap_leftInverse /-
 theorem algebraMap_leftInverse :
     Function.LeftInverse algebraMapInv (algebraMap R <| TensorAlgebra R M) := fun x => by
   simp [algebra_map_inv]
 #align tensor_algebra.algebra_map_left_inverse TensorAlgebra.algebraMap_leftInverse
+-/
 
+#print TensorAlgebra.algebraMap_inj /-
 @[simp]
 theorem algebraMap_inj (x y : R) :
     algebraMap R (TensorAlgebra R M) x = algebraMap R (TensorAlgebra R M) y ↔ x = y :=
   (algebraMap_leftInverse M).Injective.eq_iff
 #align tensor_algebra.algebra_map_inj TensorAlgebra.algebraMap_inj
+-/
 
+#print TensorAlgebra.algebraMap_eq_zero_iff /-
 @[simp]
 theorem algebraMap_eq_zero_iff (x : R) : algebraMap R (TensorAlgebra R M) x = 0 ↔ x = 0 :=
   map_eq_zero_iff (algebraMap _ _) (algebraMap_leftInverse _).Injective
 #align tensor_algebra.algebra_map_eq_zero_iff TensorAlgebra.algebraMap_eq_zero_iff
+-/
 
+#print TensorAlgebra.algebraMap_eq_one_iff /-
 @[simp]
 theorem algebraMap_eq_one_iff (x : R) : algebraMap R (TensorAlgebra R M) x = 1 ↔ x = 1 :=
   map_eq_one_iff (algebraMap _ _) (algebraMap_leftInverse _).Injective
 #align tensor_algebra.algebra_map_eq_one_iff TensorAlgebra.algebraMap_eq_one_iff
+-/
 
 variable {M}
 
+#print TensorAlgebra.toTrivSqZeroExt /-
 /-- The canonical map from `tensor_algebra R M` into `triv_sq_zero_ext R M` that sends
 `tensor_algebra.ι` to `triv_sq_zero_ext.inr`. -/
 def toTrivSqZeroExt [Module Rᵐᵒᵖ M] [IsCentralScalar R M] :
     TensorAlgebra R M →ₐ[R] TrivSqZeroExt R M :=
   lift R (TrivSqZeroExt.inrHom R M)
 #align tensor_algebra.to_triv_sq_zero_ext TensorAlgebra.toTrivSqZeroExt
+-/
 
+#print TensorAlgebra.toTrivSqZeroExt_ι /-
 @[simp]
 theorem toTrivSqZeroExt_ι (x : M) [Module Rᵐᵒᵖ M] [IsCentralScalar R M] :
     toTrivSqZeroExt (ι R x) = TrivSqZeroExt.inr x :=
   lift_ι_apply _ _
 #align tensor_algebra.to_triv_sq_zero_ext_ι TensorAlgebra.toTrivSqZeroExt_ι
+-/
 
+#print TensorAlgebra.ιInv /-
 /-- The left-inverse of `ι`.
 
 As an implementation detail, we implement this using `triv_sq_zero_ext` which has a suitable
@@ -240,24 +273,32 @@ def ιInv : TensorAlgebra R M →ₗ[R] M :=
   haveI : IsCentralScalar R M := ⟨fun r m => rfl⟩
   exact (TrivSqZeroExt.sndHom R M).comp to_triv_sq_zero_ext.to_linear_map
 #align tensor_algebra.ι_inv TensorAlgebra.ιInv
+-/
 
+#print TensorAlgebra.ι_leftInverse /-
 theorem ι_leftInverse : Function.LeftInverse ιInv (ι R : M → TensorAlgebra R M) := fun x => by
   simp [ι_inv]
 #align tensor_algebra.ι_left_inverse TensorAlgebra.ι_leftInverse
+-/
 
 variable (R)
 
+#print TensorAlgebra.ι_inj /-
 @[simp]
 theorem ι_inj (x y : M) : ι R x = ι R y ↔ x = y :=
   ι_leftInverse.Injective.eq_iff
 #align tensor_algebra.ι_inj TensorAlgebra.ι_inj
+-/
 
+#print TensorAlgebra.ι_eq_zero_iff /-
 @[simp]
 theorem ι_eq_zero_iff (x : M) : ι R x = 0 ↔ x = 0 := by rw [← ι_inj R x 0, LinearMap.map_zero]
 #align tensor_algebra.ι_eq_zero_iff TensorAlgebra.ι_eq_zero_iff
+-/
 
 variable {R}
 
+#print TensorAlgebra.ι_eq_algebraMap_iff /-
 @[simp]
 theorem ι_eq_algebraMap_iff (x : M) (r : R) : ι R x = algebraMap R _ r ↔ x = 0 ∧ r = 0 :=
   by
@@ -271,14 +312,18 @@ theorem ι_eq_algebraMap_iff (x : M) (r : R) : ι R x = algebraMap R _ r ↔ x =
   · rintro ⟨rfl, rfl⟩
     rw [LinearMap.map_zero, RingHom.map_zero]
 #align tensor_algebra.ι_eq_algebra_map_iff TensorAlgebra.ι_eq_algebraMap_iff
+-/
 
+#print TensorAlgebra.ι_ne_one /-
 @[simp]
 theorem ι_ne_one [Nontrivial R] (x : M) : ι R x ≠ 1 :=
   by
   rw [← (algebraMap R (TensorAlgebra R M)).map_one, Ne.def, ι_eq_algebra_map_iff]
   exact one_ne_zero ∘ And.right
 #align tensor_algebra.ι_ne_one TensorAlgebra.ι_ne_one
+-/
 
+#print TensorAlgebra.ι_range_disjoint_one /-
 /-- The generators of the tensor algebra are disjoint from its scalars. -/
 theorem ι_range_disjoint_one :
     Disjoint (LinearMap.range (ι R : M →ₗ[R] TensorAlgebra R M))
@@ -289,20 +334,25 @@ theorem ι_range_disjoint_one :
   rw [ι_eq_algebra_map_iff x] at hx 
   rw [hx.2, RingHom.map_zero]
 #align tensor_algebra.ι_range_disjoint_one TensorAlgebra.ι_range_disjoint_one
+-/
 
 variable (R M)
 
+#print TensorAlgebra.tprod /-
 /-- Construct a product of `n` elements of the module within the tensor algebra.
 
 See also `pi_tensor_product.tprod`. -/
 def tprod (n : ℕ) : MultilinearMap R (fun i : Fin n => M) (TensorAlgebra R M) :=
   (MultilinearMap.mkPiAlgebraFin R n (TensorAlgebra R M)).compLinearMap fun _ => ι R
 #align tensor_algebra.tprod TensorAlgebra.tprod
+-/
 
+#print TensorAlgebra.tprod_apply /-
 @[simp]
 theorem tprod_apply {n : ℕ} (x : Fin n → M) : tprod R M n x = (List.ofFn fun i => ι R (x i)).Prod :=
   rfl
 #align tensor_algebra.tprod_apply TensorAlgebra.tprod_apply
+-/
 
 variable {R M}
 
@@ -312,16 +362,20 @@ namespace FreeAlgebra
 
 variable {R M}
 
+#print FreeAlgebra.toTensor /-
 /-- The canonical image of the `free_algebra` in the `tensor_algebra`, which maps
 `free_algebra.ι R x` to `tensor_algebra.ι R x`. -/
 def toTensor : FreeAlgebra R M →ₐ[R] TensorAlgebra R M :=
   FreeAlgebra.lift R (TensorAlgebra.ι R)
 #align free_algebra.to_tensor FreeAlgebra.toTensor
+-/
 
+#print FreeAlgebra.toTensor_ι /-
 @[simp]
 theorem toTensor_ι (m : M) : (FreeAlgebra.ι R m).toTensor = TensorAlgebra.ι R m := by
   simp [to_tensor]
 #align free_algebra.to_tensor_ι FreeAlgebra.toTensor_ι
+-/
 
 end FreeAlgebra

7e5137f5

bump to nightly-2023-06-09-03

mathlib commit https://github.com/leanprover-community/mathlib/commit/7e5137f579de09a059a5ce98f364a04e221aabf0

fe176e9b

Diff

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Adam Topaz
 
 ! This file was ported from Lean 3 source module linear_algebra.tensor_algebra.basic
-! leanprover-community/mathlib commit b8d2eaa69d69ce8f03179a5cda774fc0cde984e4
+! leanprover-community/mathlib commit 7e5137f579de09a059a5ce98f364a04e221aabf0
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -17,6 +17,9 @@ import Mathbin.LinearAlgebra.Multilinear.Basic
 /-!
 # Tensor Algebras
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 Given a commutative semiring `R`, and an `R`-module `M`, we construct the tensor algebra of `M`.
 This is the free `R`-algebra generated (`R`-linearly) by the module `M`.

b8d2eaa6

bump to nightly-2023-06-07-07

mathlib commit https://github.com/leanprover-community/mathlib/commit/58a272265b5e05f258161260dd2c5d247213cbd3

61dd52a1

Diff

@@ -49,6 +49,7 @@ variable (M : Type _) [AddCommMonoid M] [Module R M]
 
 namespace TensorAlgebra
 
+#print TensorAlgebra.Rel /-
 /-- An inductively defined relation on `pre R M` used to force the initial algebra structure on
 the associated quotient.
 -/
@@ -59,10 +60,12 @@ inductive Rel : FreeAlgebra R M → FreeAlgebra R M → Prop-- force `ι` to be
   smul {r : R} {a : M} :
     Rel (FreeAlgebra.ι R (r • a)) (algebraMap R (FreeAlgebra R M) r * FreeAlgebra.ι R a)
 #align tensor_algebra.rel TensorAlgebra.Rel
+-/
 
 end TensorAlgebra
 
 /- ./././Mathport/Syntax/Translate/Command.lean:43:9: unsupported derive handler algebra[algebra] R -/
+#print TensorAlgebra /-
 /-- The tensor algebra of the module `M` over the commutative semiring `R`.
 -/
 def TensorAlgebra :=
@@ -70,6 +73,7 @@ def TensorAlgebra :=
 deriving Inhabited, Semiring,
   «./././Mathport/Syntax/Translate/Command.lean:43:9: unsupported derive handler algebra[algebra] R»
 #align tensor_algebra TensorAlgebra
+-/
 
 namespace TensorAlgebra

b8d2eaa6

bump to nightly-2023-06-04-18

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

3fb4268b

Diff

@@ -62,13 +62,13 @@ inductive Rel : FreeAlgebra R M → FreeAlgebra R M → Prop-- force `ι` to be
 
 end TensorAlgebra
 
-/- ./././Mathport/Syntax/Translate/Command.lean:42:9: unsupported derive handler algebra[algebra] R -/
+/- ./././Mathport/Syntax/Translate/Command.lean:43:9: unsupported derive handler algebra[algebra] R -/
 /-- The tensor algebra of the module `M` over the commutative semiring `R`.
 -/
 def TensorAlgebra :=
   RingQuot (TensorAlgebra.Rel R M)
 deriving Inhabited, Semiring,
-  «./././Mathport/Syntax/Translate/Command.lean:42:9: unsupported derive handler algebra[algebra] R»
+  «./././Mathport/Syntax/Translate/Command.lean:43:9: unsupported derive handler algebra[algebra] R»
 #align tensor_algebra TensorAlgebra
 
 namespace TensorAlgebra
@@ -95,7 +95,7 @@ of `f` to a morphism of `R`-algebras `tensor_algebra R M → A`.
 -/
 @[simps symm_apply]
 irreducible_def lift {A : Type _} [Semiring A] [Algebra R A] :
-  (M →ₗ[R] A) ≃ (TensorAlgebra R M →ₐ[R] A) :=
+    (M →ₗ[R] A) ≃ (TensorAlgebra R M →ₐ[R] A) :=
   { toFun :=
       RingQuot.liftAlgHom R ∘ fun f =>
         ⟨FreeAlgebra.lift R ⇑f, fun x y (h : Rel R M x y) => by
@@ -120,7 +120,7 @@ variable {R}
 
 @[simp]
 theorem ι_comp_lift {A : Type _} [Semiring A] [Algebra R A] (f : M →ₗ[R] A) :
-    (lift R f).toLinearMap.comp (ι R) = f := by convert(lift R).symm_apply_apply f;
+    (lift R f).toLinearMap.comp (ι R) = f := by convert (lift R).symm_apply_apply f;
   simp only [lift, Equiv.coe_fn_symm_mk]
 #align tensor_algebra.ι_comp_lift TensorAlgebra.ι_comp_lift

b8d2eaa6

bump to nightly-2023-06-01-16

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

b9c87c70

Diff

@@ -66,7 +66,8 @@ end TensorAlgebra
 /-- The tensor algebra of the module `M` over the commutative semiring `R`.
 -/
 def TensorAlgebra :=
-  RingQuot (TensorAlgebra.Rel R M)deriving Inhabited, Semiring,
+  RingQuot (TensorAlgebra.Rel R M)
+deriving Inhabited, Semiring,
   «./././Mathport/Syntax/Translate/Command.lean:42:9: unsupported derive handler algebra[algebra] R»
 #align tensor_algebra TensorAlgebra
 
@@ -148,7 +149,7 @@ theorem lift_comp_ι {A : Type _} [Semiring A] [Algebra R A] (g : TensorAlgebra
 theorem hom_ext {A : Type _} [Semiring A] [Algebra R A] {f g : TensorAlgebra R M →ₐ[R] A}
     (w : f.toLinearMap.comp (ι R) = g.toLinearMap.comp (ι R)) : f = g :=
   by
-  rw [← lift_symm_apply, ← lift_symm_apply] at w
+  rw [← lift_symm_apply, ← lift_symm_apply] at w 
   exact (lift R).symm.Injective w
 #align tensor_algebra.hom_ext TensorAlgebra.hom_ext
 
@@ -257,7 +258,7 @@ theorem ι_eq_algebraMap_iff (x : M) (r : R) : ι R x = algebraMap R _ r ↔ x =
   · letI : Module Rᵐᵒᵖ M := Module.compHom _ ((RingHom.id R).fromOpposite mul_comm)
     haveI : IsCentralScalar R M := ⟨fun r m => rfl⟩
     have hf0 : to_triv_sq_zero_ext (ι R x) = (0, x) := lift_ι_apply _ _
-    rw [h, AlgHom.commutes] at hf0
+    rw [h, AlgHom.commutes] at hf0 
     have : r = 0 ∧ 0 = x := Prod.ext_iff.1 hf0
     exact this.symm.imp_left Eq.symm
   · rintro ⟨rfl, rfl⟩
@@ -278,7 +279,7 @@ theorem ι_range_disjoint_one :
   by
   rw [Submodule.disjoint_def]
   rintro _ ⟨x, hx⟩ ⟨r, rfl : algebraMap _ _ _ = _⟩
-  rw [ι_eq_algebra_map_iff x] at hx
+  rw [ι_eq_algebra_map_iff x] at hx 
   rw [hx.2, RingHom.map_zero]
 #align tensor_algebra.ι_range_disjoint_one TensorAlgebra.ι_range_disjoint_one

b8d2eaa6

bump to nightly-2023-05-28-04

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

6797a637

Diff

@@ -81,19 +81,12 @@ variable {M}
 -/
 irreducible_def ι : M →ₗ[R] TensorAlgebra R M :=
   { toFun := fun m => RingQuot.mkAlgHom R _ (FreeAlgebra.ι R m)
-    map_add' := fun x y => by
-      rw [← AlgHom.map_add]
-      exact RingQuot.mkAlgHom_rel R rel.add
-    map_smul' := fun r x => by
-      rw [← AlgHom.map_smul]
-      exact RingQuot.mkAlgHom_rel R rel.smul }
+    map_add' := fun x y => by rw [← AlgHom.map_add]; exact RingQuot.mkAlgHom_rel R rel.add
+    map_smul' := fun r x => by rw [← AlgHom.map_smul]; exact RingQuot.mkAlgHom_rel R rel.smul }
 #align tensor_algebra.ι TensorAlgebra.ι
 
 theorem ringQuot_mkAlgHom_freeAlgebra_ι_eq_ι (m : M) :
-    RingQuot.mkAlgHom R (Rel R M) (FreeAlgebra.ι R m) = ι R m :=
-  by
-  rw [ι]
-  rfl
+    RingQuot.mkAlgHom R (Rel R M) (FreeAlgebra.ι R m) = ι R m := by rw [ι]; rfl
 #align tensor_algebra.ring_quot_mk_alg_hom_free_algebra_ι_eq_ι TensorAlgebra.ringQuot_mkAlgHom_freeAlgebra_ι_eq_ι
 
 /-- Given a linear map `f : M → A` where `A` is an `R`-algebra, `lift R f` is the unique lift
@@ -126,25 +119,19 @@ variable {R}
 
 @[simp]
 theorem ι_comp_lift {A : Type _} [Semiring A] [Algebra R A] (f : M →ₗ[R] A) :
-    (lift R f).toLinearMap.comp (ι R) = f :=
-  by
-  convert(lift R).symm_apply_apply f
+    (lift R f).toLinearMap.comp (ι R) = f := by convert(lift R).symm_apply_apply f;
   simp only [lift, Equiv.coe_fn_symm_mk]
 #align tensor_algebra.ι_comp_lift TensorAlgebra.ι_comp_lift
 
 @[simp]
 theorem lift_ι_apply {A : Type _} [Semiring A] [Algebra R A] (f : M →ₗ[R] A) (x) :
-    lift R f (ι R x) = f x := by
-  conv_rhs => rw [← ι_comp_lift f]
-  rfl
+    lift R f (ι R x) = f x := by conv_rhs => rw [← ι_comp_lift f]; rfl
 #align tensor_algebra.lift_ι_apply TensorAlgebra.lift_ι_apply
 
 @[simp]
 theorem lift_unique {A : Type _} [Semiring A] [Algebra R A] (f : M →ₗ[R] A)
-    (g : TensorAlgebra R M →ₐ[R] A) : g.toLinearMap.comp (ι R) = f ↔ g = lift R f :=
-  by
-  rw [← (lift R).symm_apply_eq]
-  simp only [lift, Equiv.coe_fn_symm_mk]
+    (g : TensorAlgebra R M →ₐ[R] A) : g.toLinearMap.comp (ι R) = f ↔ g = lift R f := by
+  rw [← (lift R).symm_apply_eq]; simp only [lift, Equiv.coe_fn_symm_mk]
 #align tensor_algebra.lift_unique TensorAlgebra.lift_unique
 
 -- Marking `tensor_algebra` irreducible makes `ring` instances inaccessible on quotients.
@@ -152,9 +139,7 @@ theorem lift_unique {A : Type _} [Semiring A] [Algebra R A] (f : M →ₗ[R] A)
 -- For now, we avoid this by not marking it irreducible.
 @[simp]
 theorem lift_comp_ι {A : Type _} [Semiring A] [Algebra R A] (g : TensorAlgebra R M →ₐ[R] A) :
-    lift R (g.toLinearMap.comp (ι R)) = g :=
-  by
-  rw [← lift_symm_apply]
+    lift R (g.toLinearMap.comp (ι R)) = g := by rw [← lift_symm_apply];
   exact (lift R).apply_symm_apply g
 #align tensor_algebra.lift_comp_ι TensorAlgebra.lift_comp_ι

b8d2eaa6

bump to nightly-2023-03-17-00

mathlib commit https://github.com/leanprover-community/mathlib/commit/ce7e9d53d4bbc38065db3b595cd5bd73c323bc1d

c85864d4

Diff

@@ -128,7 +128,7 @@ variable {R}
 theorem ι_comp_lift {A : Type _} [Semiring A] [Algebra R A] (f : M →ₗ[R] A) :
     (lift R f).toLinearMap.comp (ι R) = f :=
   by
-  convert (lift R).symm_apply_apply f
+  convert(lift R).symm_apply_apply f
   simp only [lift, Equiv.coe_fn_symm_mk]
 #align tensor_algebra.ι_comp_lift TensorAlgebra.ι_comp_lift

b8d2eaa6

bump to nightly-2023-02-24-03

mathlib commit https://github.com/leanprover-community/mathlib/commit/22131150f88a2d125713ffa0f4693e3355b1eb49

2d8bd121

Diff

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Adam Topaz
 
 ! This file was ported from Lean 3 source module linear_algebra.tensor_algebra.basic
-! leanprover-community/mathlib commit 565eb991e264d0db702722b4bde52ee5173c9950
+! leanprover-community/mathlib commit b8d2eaa69d69ce8f03179a5cda774fc0cde984e4
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -226,12 +226,14 @@ variable {M}
 
 /-- The canonical map from `tensor_algebra R M` into `triv_sq_zero_ext R M` that sends
 `tensor_algebra.ι` to `triv_sq_zero_ext.inr`. -/
-def toTrivSqZeroExt : TensorAlgebra R M →ₐ[R] TrivSqZeroExt R M :=
+def toTrivSqZeroExt [Module Rᵐᵒᵖ M] [IsCentralScalar R M] :
+    TensorAlgebra R M →ₐ[R] TrivSqZeroExt R M :=
   lift R (TrivSqZeroExt.inrHom R M)
 #align tensor_algebra.to_triv_sq_zero_ext TensorAlgebra.toTrivSqZeroExt
 
 @[simp]
-theorem toTrivSqZeroExt_ι (x : M) : toTrivSqZeroExt (ι R x) = TrivSqZeroExt.inr x :=
+theorem toTrivSqZeroExt_ι (x : M) [Module Rᵐᵒᵖ M] [IsCentralScalar R M] :
+    toTrivSqZeroExt (ι R x) = TrivSqZeroExt.inr x :=
   lift_ι_apply _ _
 #align tensor_algebra.to_triv_sq_zero_ext_ι TensorAlgebra.toTrivSqZeroExt_ι
 
@@ -240,7 +242,10 @@ theorem toTrivSqZeroExt_ι (x : M) : toTrivSqZeroExt (ι R x) = TrivSqZeroExt.in
 As an implementation detail, we implement this using `triv_sq_zero_ext` which has a suitable
 algebra structure. -/
 def ιInv : TensorAlgebra R M →ₗ[R] M :=
-  (TrivSqZeroExt.sndHom R M).comp toTrivSqZeroExt.toLinearMap
+  by
+  letI : Module Rᵐᵒᵖ M := Module.compHom _ ((RingHom.id R).fromOpposite mul_comm)
+  haveI : IsCentralScalar R M := ⟨fun r m => rfl⟩
+  exact (TrivSqZeroExt.sndHom R M).comp to_triv_sq_zero_ext.to_linear_map
 #align tensor_algebra.ι_inv TensorAlgebra.ιInv
 
 theorem ι_leftInverse : Function.LeftInverse ιInv (ι R : M → TensorAlgebra R M) := fun x => by
@@ -264,7 +269,9 @@ variable {R}
 theorem ι_eq_algebraMap_iff (x : M) (r : R) : ι R x = algebraMap R _ r ↔ x = 0 ∧ r = 0 :=
   by
   refine' ⟨fun h => _, _⟩
-  · have hf0 : to_triv_sq_zero_ext (ι R x) = (0, x) := lift_ι_apply _ _
+  · letI : Module Rᵐᵒᵖ M := Module.compHom _ ((RingHom.id R).fromOpposite mul_comm)
+    haveI : IsCentralScalar R M := ⟨fun r m => rfl⟩
+    have hf0 : to_triv_sq_zero_ext (ι R x) = (0, x) := lift_ι_apply _ _
     rw [h, AlgHom.commutes] at hf0
     have : r = 0 ∧ 0 = x := Prod.ext_iff.1 hf0
     exact this.symm.imp_left Eq.symm

565eb991

bump to nightly-2023-02-21-16

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

1107b979

Changes in mathlib4

mathlib3

mathlib4

b8d2eaa6

chore: avoid Ne.def (adaptation for nightly-2024-03-27) (#11801)

1b40c7bc

Diff

@@ -305,7 +305,7 @@ theorem ι_eq_algebraMap_iff (x : M) (r : R) : ι R x = algebraMap R _ r ↔ x =
 
 @[simp]
 theorem ι_ne_one [Nontrivial R] (x : M) : ι R x ≠ 1 := by
-  rw [← (algebraMap R (TensorAlgebra R M)).map_one, Ne.def, ι_eq_algebraMap_iff]
+  rw [← (algebraMap R (TensorAlgebra R M)).map_one, Ne, ι_eq_algebraMap_iff]
   exact one_ne_zero ∘ And.right
 #align tensor_algebra.ι_ne_one TensorAlgebra.ι_ne_one

b8d2eaa6

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

@@ -41,7 +41,6 @@ modulo the additional relations making the inclusion of `M` into an `R`-linear m
 
 
 variable (R : Type*) [CommSemiring R]
-
 variable (M : Type*) [AddCommMonoid M] [Module R M]
 
 namespace TensorAlgebra

b8d2eaa6

chore: resolve some porting notes which are fixed now (#11317)

It started with the one in Convex/Combination and spiralled into revisiting all notes with needs in them. The ToLin changes overlap with #11171.

5e218f10

Diff

@@ -274,9 +274,8 @@ def ιInv : TensorAlgebra R M →ₗ[R] M := by
   exact (TrivSqZeroExt.sndHom R M).comp toTrivSqZeroExt.toLinearMap
 #align tensor_algebra.ι_inv TensorAlgebra.ιInv
 
-theorem ι_leftInverse : Function.LeftInverse ιInv (ι R : M → TensorAlgebra R M) := fun x => by
-  -- Porting note: needs the last two `simp` lemmas explicitly in order to use them
-  simp [ιInv, (AlgHom.toLinearMap_apply), toTrivSqZeroExt_ι _]
+theorem ι_leftInverse : Function.LeftInverse ιInv (ι R : M → TensorAlgebra R M) := fun x ↦ by
+  simp [ιInv]
 #align tensor_algebra.ι_left_inverse TensorAlgebra.ι_leftInverse
 
 variable (R)

b8d2eaa6

style: homogenise porting notes (#11145)

Homogenises porting notes via capitalisation and addition of whitespace.

It makes the following changes:

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

8be0b69c

Diff

@@ -202,7 +202,7 @@ theorem induction {C : TensorAlgebra R M → Prop}
       mul_mem' := @mul
       add_mem' := @add
       algebraMap_mem' := algebraMap }
-  -- porting note: Added `h`. `h` is needed for `of`.
+  -- Porting note: Added `h`. `h` is needed for `of`.
   let h : AddCommMonoid s := inferInstanceAs (AddCommMonoid (Subalgebra.toSubmodule s))
   let of : M →ₗ[R] s := (TensorAlgebra.ι R).codRestrict (Subalgebra.toSubmodule s) ι
   -- the mapping through the subalgebra is the identity
@@ -275,7 +275,7 @@ def ιInv : TensorAlgebra R M →ₗ[R] M := by
 #align tensor_algebra.ι_inv TensorAlgebra.ιInv
 
 theorem ι_leftInverse : Function.LeftInverse ιInv (ι R : M → TensorAlgebra R M) := fun x => by
-  -- porting note: needs the last two `simp` lemmas explicitly in order to use them
+  -- Porting note: needs the last two `simp` lemmas explicitly in order to use them
   simp [ιInv, (AlgHom.toLinearMap_apply), toTrivSqZeroExt_ι _]
 #align tensor_algebra.ι_left_inverse TensorAlgebra.ι_leftInverse

b8d2eaa6

chore: rename induction principle arguments around CliffordAlgebra (#10908)

In order to improve the ergonomics of the induction tactic, this renames the arguments of:

ExteriorAlgebra.induction
TensorAlgebra.induction
CliffordAlgebra.induction
CliffordAlgebra.left_induction
CliffordAlgebra.right_induction
CliffordAlgebra.even_induction
CliffordAlgebra.odd_induction
Submodule.iSup_induction'
Submodule.pow_induction_on_left'
Submodule.pow_induction_on_right'

This is slightly awkward for name-resolution within these induction principles, as the argument names end up clashing with the function they are about. Thankfully, this pain is not transferred to the caller using induction _ using _.

0257770c

Diff

@@ -193,18 +193,18 @@ and is preserved under addition and muliplication, then it holds for all of `Ten
 -/
 @[elab_as_elim]
 theorem induction {C : TensorAlgebra R M → Prop}
-    (h_grade0 : ∀ r, C (algebraMap R (TensorAlgebra R M) r)) (h_grade1 : ∀ x, C (ι R x))
-    (h_mul : ∀ a b, C a → C b → C (a * b)) (h_add : ∀ a b, C a → C b → C (a + b))
+    (algebraMap : ∀ r, C (algebraMap R (TensorAlgebra R M) r)) (ι : ∀ x, C (ι R x))
+    (mul : ∀ a b, C a → C b → C (a * b)) (add : ∀ a b, C a → C b → C (a + b))
     (a : TensorAlgebra R M) : C a := by
   -- the arguments are enough to construct a subalgebra, and a mapping into it from M
   let s : Subalgebra R (TensorAlgebra R M) :=
     { carrier := C
-      mul_mem' := @h_mul
-      add_mem' := @h_add
-      algebraMap_mem' := h_grade0 }
+      mul_mem' := @mul
+      add_mem' := @add
+      algebraMap_mem' := algebraMap }
   -- porting note: Added `h`. `h` is needed for `of`.
   let h : AddCommMonoid s := inferInstanceAs (AddCommMonoid (Subalgebra.toSubmodule s))
-  let of : M →ₗ[R] s := (ι R).codRestrict (Subalgebra.toSubmodule s) h_grade1
+  let of : M →ₗ[R] s := (TensorAlgebra.ι R).codRestrict (Subalgebra.toSubmodule s) ι
   -- the mapping through the subalgebra is the identity
   have of_id : AlgHom.id R (TensorAlgebra R M) = s.val.comp (lift R of) := by
     ext

b8d2eaa6

chore(diamonds): appropriate transparency levels for diamond checks (#10910)

Currently, we have multiple "no-diamond" tests of the form

example : x = y := rfl

where X and Y are instances of some class. The problem is that since simp and type class synthesis operate at reducible_and_instances transparency this check means little.

We went through all the mentions of diamonds and either added with_reducible_and_instancse or added a reference to the issue #10906.

Co-authored-by: Kevin Buzzard <k.buzzard@imperial.ac.uk>

29c854d2

Diff

@@ -77,6 +77,7 @@ instance instAlgebra {R A M} [CommSemiring R] [AddCommMonoid M] [CommSemiring A]
   RingQuot.instAlgebra _
 
 -- verify there is no diamond
+-- but doesn't work at `reducible_and_instances` #10906
 example : (algebraNat : Algebra ℕ (TensorAlgebra R M)) = instAlgebra := rfl
 
 instance {R S A M} [CommSemiring R] [CommSemiring S] [AddCommMonoid M] [CommSemiring A]
@@ -97,6 +98,7 @@ instance {S : Type*} [CommRing S] [Module S M] : Ring (TensorAlgebra S M) :=
   RingQuot.instRing (Rel S M)
 
 -- verify there is no diamond
+-- but doesn't work at `reducible_and_instances` #10906
 variable (S M : Type) [CommRing S] [AddCommGroup M] [Module S M] in
 example : (algebraInt _ : Algebra ℤ (TensorAlgebra S M)) = instAlgebra := rfl

b8d2eaa6

feat: tensor algebra of free module over integral domain is a domain (#9890)

Provide instances

Nontrivial (TensorAlgebra R M) when M is a module over a nontrivial semiring R
NoZeroDivisors (FreeAlgebra R X) when R is a commutative semiring with no zero-divisors and X any type
IsDomain (FreeAlgebra R X) when R is an integral domain and X is any type
TwoUniqueProds (FreeMonoid X) where X is any type (this provides NoZeroDivisors (MonoidAlgebra R (FreeMonoid X)) when R is a semiring and X any type, via TwoUniqueProds.toUniqueProds and MonoidAlgebra.instNoZeroDivisorsOfUniqueProds)
NoZeroDivisors (TensorAlgebra R M) when M is a free module over a commutative semiring R with no zero-divisors
IsDomain (TensorAlgebra R M) when M is a free module over an integral domain R

In Algebra.Group.UniqueProds:

Rename UniqueProds.mulHom_image_of_injective to UniqueProds.of_injective_mulHom.
New lemmas UniqueMul.of_mulHom_image, UniqueProds.of_mulHom, TwoUniqueProds.of_mulHom show the relevant property holds in the domain of a multiplicative homomorphism if it holds in the codomain, under a certain hypothesis on the homomorphism.

Co-authored-by: Richard Copley <rcopley@gmail.com> Co-authored-by: Eric Wieser <wieser.eric@gmail.com> Co-authored-by: Junyan Xu <junyanxu.math@gmail.com>

6d578c58

Diff

@@ -243,6 +243,10 @@ theorem algebraMap_eq_one_iff (x : R) : algebraMap R (TensorAlgebra R M) x = 1 
   map_eq_one_iff (algebraMap _ _) (algebraMap_leftInverse _).injective
 #align tensor_algebra.algebra_map_eq_one_iff TensorAlgebra.algebraMap_eq_one_iff
 
+/-- A `TensorAlgebra` over a nontrivial semiring is nontrivial. -/
+instance [Nontrivial R] : Nontrivial (TensorAlgebra R M) :=
+  (algebraMap_leftInverse M).injective.nontrivial
+
 variable {M}
 
 /-- The canonical map from `TensorAlgebra R M` into `TrivSqZeroExt R M` that sends

b8d2eaa6

perf(FunLike.Basic): beta reduce CoeFun.coe (#7905)

This eliminates (fun a ↦ β) α in the type when applying a FunLike.

Co-authored-by: Matthew Ballard <matt@mrb.email> Co-authored-by: Eric Wieser <wieser.eric@gmail.com>

e194c756

Diff

@@ -107,10 +107,10 @@ variable {M}
 irreducible_def ι : M →ₗ[R] TensorAlgebra R M :=
   { toFun := fun m => RingQuot.mkAlgHom R _ (FreeAlgebra.ι R m)
     map_add' := fun x y => by
-      rw [← AlgHom.map_add]
+      rw [← (RingQuot.mkAlgHom R (Rel R M)).map_add]
       exact RingQuot.mkAlgHom_rel R Rel.add
     map_smul' := fun r x => by
-      rw [← AlgHom.map_smul]
+      rw [← (RingQuot.mkAlgHom R (Rel R M)).map_smul]
       exact RingQuot.mkAlgHom_rel R Rel.smul }
 #align tensor_algebra.ι TensorAlgebra.ι

b8d2eaa6

fix(LinearAlgebra/{Free,Tensor,Clifford}Algebra): remove an unused SMulCommClass argument (#8373)

SMulCommClass R S A is always true when Algebra R A and Algebra S A and A is commutative, since the two actions factor via multiplication in A. I don't think mathlib actually knows this fact yet, but in this particular case it's also true by definition.

30d39f9a

Diff

@@ -81,7 +81,7 @@ example : (algebraNat : Algebra ℕ (TensorAlgebra R M)) = instAlgebra := rfl
 
 instance {R S A M} [CommSemiring R] [CommSemiring S] [AddCommMonoid M] [CommSemiring A]
     [Algebra R A] [Algebra S A] [Module R M] [Module S M] [Module A M]
-    [IsScalarTower R A M] [IsScalarTower S A M] [SMulCommClass R S A] :
+    [IsScalarTower R A M] [IsScalarTower S A M] :
     SMulCommClass R S (TensorAlgebra A M) :=
   RingQuot.instSMulCommClass _

b8d2eaa6

chore: fix nonterminal simps (#7497)

Fixes the nonterminal simps identified by #7496

19ca95b1

Diff

@@ -206,7 +206,9 @@ theorem induction {C : TensorAlgebra R M → Prop}
   -- the mapping through the subalgebra is the identity
   have of_id : AlgHom.id R (TensorAlgebra R M) = s.val.comp (lift R of) := by
     ext
-    simp
+    simp only [AlgHom.toLinearMap_id, LinearMap.id_comp, AlgHom.comp_toLinearMap,
+      LinearMap.coe_comp, Function.comp_apply, AlgHom.toLinearMap_apply, lift_ι_apply,
+      Subalgebra.coe_val]
     erw [LinearMap.codRestrict_apply]
   -- finding a proof is finding an element of the subalgebra
   rw [← AlgHom.id_apply (R := R) a, of_id]

b8d2eaa6

chore: tidy various files (#6838)

cda5caa7

Diff

@@ -65,7 +65,7 @@ def TensorAlgebra :=
 #align tensor_algebra TensorAlgebra
 
 -- Porting note: Expanded `deriving Inhabited, Semiring, Algebra`
-instance : Inhabited (TensorAlgebra R M) := RingQuot.instInhabitedRingQuot _
+instance : Inhabited (TensorAlgebra R M) := RingQuot.instInhabited _
 instance : Semiring (TensorAlgebra R M) := RingQuot.instSemiring _
 
 -- `IsScalarTower` is not needed, but the instance isn't really canonical without it.
@@ -74,7 +74,7 @@ instance instAlgebra {R A M} [CommSemiring R] [AddCommMonoid M] [CommSemiring A]
     [Algebra R A] [Module R M] [Module A M]
     [IsScalarTower R A M] :
     Algebra R (TensorAlgebra A M) :=
-  RingQuot.instAlgebraRingQuot _
+  RingQuot.instAlgebra _
 
 -- verify there is no diamond
 example : (algebraNat : Algebra ℕ (TensorAlgebra R M)) = instAlgebra := rfl
@@ -83,13 +83,13 @@ instance {R S A M} [CommSemiring R] [CommSemiring S] [AddCommMonoid M] [CommSemi
     [Algebra R A] [Algebra S A] [Module R M] [Module S M] [Module A M]
     [IsScalarTower R A M] [IsScalarTower S A M] [SMulCommClass R S A] :
     SMulCommClass R S (TensorAlgebra A M) :=
-  RingQuot.instSMulCommClassRingQuot _
+  RingQuot.instSMulCommClass _
 
 instance {R S A M} [CommSemiring R] [CommSemiring S] [AddCommMonoid M] [CommSemiring A]
     [SMul R S] [Algebra R A] [Algebra S A] [Module R M] [Module S M] [Module A M]
     [IsScalarTower R A M] [IsScalarTower S A M] [IsScalarTower R S A] :
     IsScalarTower R S (TensorAlgebra A M) :=
-  RingQuot.instIsScalarTowerRingQuot _
+  RingQuot.instIsScalarTower _
 
 namespace TensorAlgebra

b8d2eaa6

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

@@ -40,9 +40,9 @@ modulo the additional relations making the inclusion of `M` into an `R`-linear m
 -/
 
 
-variable (R : Type _) [CommSemiring R]
+variable (R : Type*) [CommSemiring R]
 
-variable (M : Type _) [AddCommMonoid M] [Module R M]
+variable (M : Type*) [AddCommMonoid M] [Module R M]
 
 namespace TensorAlgebra
 
@@ -93,7 +93,7 @@ instance {R S A M} [CommSemiring R] [CommSemiring S] [AddCommMonoid M] [CommSemi
 
 namespace TensorAlgebra
 
-instance {S : Type _} [CommRing S] [Module S M] : Ring (TensorAlgebra S M) :=
+instance {S : Type*} [CommRing S] [Module S M] : Ring (TensorAlgebra S M) :=
   RingQuot.instRing (Rel S M)
 
 -- verify there is no diamond
@@ -125,7 +125,7 @@ theorem ringQuot_mkAlgHom_freeAlgebra_ι_eq_ι (m : M) :
 of `f` to a morphism of `R`-algebras `TensorAlgebra R M → A`.
 -/
 @[simps symm_apply]
-def lift {A : Type _} [Semiring A] [Algebra R A] : (M →ₗ[R] A) ≃ (TensorAlgebra R M →ₐ[R] A) :=
+def lift {A : Type*} [Semiring A] [Algebra R A] : (M →ₗ[R] A) ≃ (TensorAlgebra R M →ₐ[R] A) :=
   { toFun :=
       RingQuot.liftAlgHom R ∘ fun f =>
         ⟨FreeAlgebra.lift R (⇑f), fun x y (h : Rel R M x y) => by
@@ -149,19 +149,19 @@ def lift {A : Type _} [Semiring A] [Algebra R A] : (M →ₗ[R] A) ≃ (TensorAl
 variable {R}
 
 @[simp]
-theorem ι_comp_lift {A : Type _} [Semiring A] [Algebra R A] (f : M →ₗ[R] A) :
+theorem ι_comp_lift {A : Type*} [Semiring A] [Algebra R A] (f : M →ₗ[R] A) :
     (lift R f).toLinearMap.comp (ι R) = f := by
   convert (lift R).symm_apply_apply f
 #align tensor_algebra.ι_comp_lift TensorAlgebra.ι_comp_lift
 
 @[simp]
-theorem lift_ι_apply {A : Type _} [Semiring A] [Algebra R A] (f : M →ₗ[R] A) (x) :
+theorem lift_ι_apply {A : Type*} [Semiring A] [Algebra R A] (f : M →ₗ[R] A) (x) :
     lift R f (ι R x) = f x := by
   conv_rhs => rw [← ι_comp_lift f]
 #align tensor_algebra.lift_ι_apply TensorAlgebra.lift_ι_apply
 
 @[simp]
-theorem lift_unique {A : Type _} [Semiring A] [Algebra R A] (f : M →ₗ[R] A)
+theorem lift_unique {A : Type*} [Semiring A] [Algebra R A] (f : M →ₗ[R] A)
     (g : TensorAlgebra R M →ₐ[R] A) : g.toLinearMap.comp (ι R) = f ↔ g = lift R f := by
   rw [← (lift R).symm_apply_eq]
   simp only [lift, Equiv.coe_fn_symm_mk]
@@ -171,7 +171,7 @@ theorem lift_unique {A : Type _} [Semiring A] [Algebra R A] (f : M →ₗ[R] A)
 -- https://leanprover.zulipchat.com/#narrow/stream/113488-general/topic/algebra.2Esemiring_to_ring.20breaks.20semimodule.20typeclass.20lookup/near/212580241
 -- For now, we avoid this by not marking it irreducible.
 @[simp]
-theorem lift_comp_ι {A : Type _} [Semiring A] [Algebra R A] (g : TensorAlgebra R M →ₐ[R] A) :
+theorem lift_comp_ι {A : Type*} [Semiring A] [Algebra R A] (g : TensorAlgebra R M →ₐ[R] A) :
     lift R (g.toLinearMap.comp (ι R)) = g := by
   rw [← lift_symm_apply]
   exact (lift R).apply_symm_apply g
@@ -179,7 +179,7 @@ theorem lift_comp_ι {A : Type _} [Semiring A] [Algebra R A] (g : TensorAlgebra
 
 /-- See note [partially-applied ext lemmas]. -/
 @[ext]
-theorem hom_ext {A : Type _} [Semiring A] [Algebra R A] {f g : TensorAlgebra R M →ₐ[R] A}
+theorem hom_ext {A : Type*} [Semiring A] [Algebra R A] {f g : TensorAlgebra R M →ₐ[R] A}
     (w : f.toLinearMap.comp (ι R) = g.toLinearMap.comp (ι R)) : f = g := by
   rw [← lift_symm_apply, ← lift_symm_apply] at w
   exact (lift R).symm.injective w

b8d2eaa6

chore: ensure all instances referred to directly have explicit names (#6423)

Per https://github.com/leanprover/lean4/issues/2343, we are going to need to change the automatic generation of instance names, as they become too long.

This PR ensures that everywhere in Mathlib that refers to an instance by name, that name is given explicitly, rather than being automatically generated.

There are four exceptions, which are now commented, with links to https://github.com/leanprover/lean4/issues/2343.

This was implemented by running Mathlib against a modified Lean that appended _ᾰ to all automatically generated names, and fixing everything.

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

65a35f78

Diff

@@ -74,7 +74,7 @@ instance instAlgebra {R A M} [CommSemiring R] [AddCommMonoid M] [CommSemiring A]
     [Algebra R A] [Module R M] [Module A M]
     [IsScalarTower R A M] :
     Algebra R (TensorAlgebra A M) :=
-  RingQuot.instAlgebraRingQuotInstSemiring _
+  RingQuot.instAlgebraRingQuot _
 
 -- verify there is no diamond
 example : (algebraNat : Algebra ℕ (TensorAlgebra R M)) = instAlgebra := rfl
@@ -83,13 +83,13 @@ instance {R S A M} [CommSemiring R] [CommSemiring S] [AddCommMonoid M] [CommSemi
     [Algebra R A] [Algebra S A] [Module R M] [Module S M] [Module A M]
     [IsScalarTower R A M] [IsScalarTower S A M] [SMulCommClass R S A] :
     SMulCommClass R S (TensorAlgebra A M) :=
-  RingQuot.instSMulCommClassRingQuotInstSMulRingQuotInstSMulRingQuot _
+  RingQuot.instSMulCommClassRingQuot _
 
 instance {R S A M} [CommSemiring R] [CommSemiring S] [AddCommMonoid M] [CommSemiring A]
     [SMul R S] [Algebra R A] [Algebra S A] [Module R M] [Module S M] [Module A M]
     [IsScalarTower R A M] [IsScalarTower S A M] [IsScalarTower R S A] :
     IsScalarTower R S (TensorAlgebra A M) :=
-  RingQuot.instIsScalarTowerRingQuotInstSMulRingQuotInstSMulRingQuot _
+  RingQuot.instIsScalarTowerRingQuot _
 
 namespace TensorAlgebra

b8d2eaa6

feat(Algebra/TensorAlgebra): support towers of algebras (#6073)

This is pre-work towards a base-change of clifford algebras.

The main result here is

@[nolint unusedArguments]
instance instAlgebra {R A M} [CommSemiring R] [AddCommMonoid M] [CommSemiring A]
    [Algebra R A] [Module R M] [Module A M]
    [IsScalarTower R A M] :
    Algebra R (TensorAlgebra A M)

Note that strictly the IsScalarTower R A M argument isn't needed, but I'd claim the instance doesn't make any sense without it.

In order to prevent diamonds in the algebraMap fields of the Int and Nat algebra instances, we have stop having natCast as an irreducible_def, and we have to add a missing intCast customization for RingQuot. In order to prevent diamonds in the smul fields there and elsewhere (such as a complex tensor algebra being a real algebra), we have to stop having the smul definition as an irreducible_def. We already had to make a similar refactor to prevent diamonds for Algebra R (Polynomial A).

If we backport any of this to mathlib3, we'd additionally have to change the smul definition to not use pattern matching. Thankfully, structure eta in Lean 4 makes that unnecessary.

These diamonds are tested with inline examples.

4f0b2d5b

Diff

@@ -67,13 +67,39 @@ def TensorAlgebra :=
 -- Porting note: Expanded `deriving Inhabited, Semiring, Algebra`
 instance : Inhabited (TensorAlgebra R M) := RingQuot.instInhabitedRingQuot _
 instance : Semiring (TensorAlgebra R M) := RingQuot.instSemiring _
-instance : Algebra R (TensorAlgebra R M) := RingQuot.instAlgebraRingQuotInstSemiring _
+
+-- `IsScalarTower` is not needed, but the instance isn't really canonical without it.
+@[nolint unusedArguments]
+instance instAlgebra {R A M} [CommSemiring R] [AddCommMonoid M] [CommSemiring A]
+    [Algebra R A] [Module R M] [Module A M]
+    [IsScalarTower R A M] :
+    Algebra R (TensorAlgebra A M) :=
+  RingQuot.instAlgebraRingQuotInstSemiring _
+
+-- verify there is no diamond
+example : (algebraNat : Algebra ℕ (TensorAlgebra R M)) = instAlgebra := rfl
+
+instance {R S A M} [CommSemiring R] [CommSemiring S] [AddCommMonoid M] [CommSemiring A]
+    [Algebra R A] [Algebra S A] [Module R M] [Module S M] [Module A M]
+    [IsScalarTower R A M] [IsScalarTower S A M] [SMulCommClass R S A] :
+    SMulCommClass R S (TensorAlgebra A M) :=
+  RingQuot.instSMulCommClassRingQuotInstSMulRingQuotInstSMulRingQuot _
+
+instance {R S A M} [CommSemiring R] [CommSemiring S] [AddCommMonoid M] [CommSemiring A]
+    [SMul R S] [Algebra R A] [Algebra S A] [Module R M] [Module S M] [Module A M]
+    [IsScalarTower R A M] [IsScalarTower S A M] [IsScalarTower R S A] :
+    IsScalarTower R S (TensorAlgebra A M) :=
+  RingQuot.instIsScalarTowerRingQuotInstSMulRingQuotInstSMulRingQuot _
 
 namespace TensorAlgebra
 
 instance {S : Type _} [CommRing S] [Module S M] : Ring (TensorAlgebra S M) :=
   RingQuot.instRing (Rel S M)
 
+-- verify there is no diamond
+variable (S M : Type) [CommRing S] [AddCommGroup M] [Module S M] in
+example : (algebraInt _ : Algebra ℤ (TensorAlgebra S M)) = instAlgebra := rfl
+
 variable {M}
 
 /-- The canonical linear map `M →ₗ[R] TensorAlgebra R M`.

b8d2eaa6

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

@@ -2,11 +2,6 @@
 Copyright (c) 2020 Adam Topaz. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Adam Topaz
-
-! This file was ported from Lean 3 source module linear_algebra.tensor_algebra.basic
-! leanprover-community/mathlib commit b8d2eaa69d69ce8f03179a5cda774fc0cde984e4
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.Algebra.FreeAlgebra
 import Mathlib.Algebra.RingQuot
@@ -14,6 +9,8 @@ import Mathlib.Algebra.TrivSqZeroExt
 import Mathlib.Algebra.Algebra.Operations
 import Mathlib.LinearAlgebra.Multilinear.Basic
 
+#align_import linear_algebra.tensor_algebra.basic from "leanprover-community/mathlib"@"b8d2eaa69d69ce8f03179a5cda774fc0cde984e4"
+
 /-!
 # Tensor Algebras

b8d2eaa6

feat: port LinearAlgebra.TensorAlgebra.Basic (#3600)

Co-authored-by: Eric Wieser <wieser.eric@gmail.com> Co-authored-by: ChrisHughes24 <chrishughes24@gmail.com> Co-authored-by: Jeremy Tan Jie Rui <reddeloostw@gmail.com>

159e04e7

`linear_algebra.tensor_algebra.basic` ⟷ `Mathlib.LinearAlgebra.TensorAlgebra.Basic`

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Dependencies 8 + 463

linear_algebra.tensor_algebra.basic ⟷ Mathlib.LinearAlgebra.TensorAlgebra.Basic

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Dependencies 8 + 463

`linear_algebra.tensor_algebra.basic` ⟷ `Mathlib.LinearAlgebra.TensorAlgebra.Basic`