algebra.direct_sum.algebra | 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

e5ba338e

(last sync)

Changes in mathlib3port

mathlib3

mathlib3port

50251fd6

bump to nightly-2023-09-24-06

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

5655435f

Diff

@@ -3,9 +3,9 @@ Copyright (c) 2021 Eric Wieser. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Eric Wieser
 -/
-import Mathbin.Algebra.Algebra.Basic
-import Mathbin.Algebra.DirectSum.Module
-import Mathbin.Algebra.DirectSum.Ring
+import Algebra.Algebra.Basic
+import Algebra.DirectSum.Module
+import Algebra.DirectSum.Ring
 
 #align_import algebra.direct_sum.algebra from "leanprover-community/mathlib"@"50251fd6309cca5ca2e747882ffecd2729f38c5d"

50251fd6

bump to nightly-2023-08-17-09

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

60285dcc

Diff

@@ -54,7 +54,7 @@ with an `R`-algebra structure. -/
 class GAlgebra where
   toFun : R →+ A 0
   map_one : to_fun 1 = GradedMonoid.GOne.one
-  map_mul :
+  map_hMul :
     ∀ r s, GradedMonoid.mk _ (to_fun (r * s)) = ⟨_, GradedMonoid.GMul.mul (to_fun r) (to_fun s)⟩
   commutes : ∀ r x, GradedMonoid.mk _ (to_fun r) * x = x * ⟨_, to_fun r⟩
   smul_def : ∀ (r) (x : GradedMonoid A), GradedMonoid.mk x.1 (r • x.2) = ⟨_, to_fun r⟩ * x
@@ -159,7 +159,7 @@ instance Algebra.directSumGAlgebra {R A : Type _} [DecidableEq ι] [AddMonoid ι
     where
   toFun := (algebraMap R A).toAddMonoidHom
   map_one := (algebraMap R A).map_one
-  map_mul a b := Sigma.ext (zero_add _).symm (hEq_of_eq <| (algebraMap R A).map_mul a b)
+  map_hMul a b := Sigma.ext (zero_add _).symm (hEq_of_eq <| (algebraMap R A).map_hMul a b)
   commutes := fun r ⟨ai, a⟩ =>
     Sigma.ext ((zero_add _).trans (add_zero _).symm) (hEq_of_eq <| Algebra.commutes _ _)
   smul_def := fun r ⟨ai, a⟩ => Sigma.ext (zero_add _).symm (hEq_of_eq <| Algebra.smul_def _ _)

50251fd6

bump to nightly-2023-07-20-09

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

9c56d0dd

Diff

@@ -2,16 +2,13 @@
 Copyright (c) 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 algebra.direct_sum.algebra
-! leanprover-community/mathlib commit 50251fd6309cca5ca2e747882ffecd2729f38c5d
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.Algebra.Algebra.Basic
 import Mathbin.Algebra.DirectSum.Module
 import Mathbin.Algebra.DirectSum.Ring
 
+#align_import algebra.direct_sum.algebra from "leanprover-community/mathlib"@"50251fd6309cca5ca2e747882ffecd2729f38c5d"
+
 /-! # Additively-graded algebra structures on `⨁ i, A i`
 
 > THIS FILE IS SYNCHRONIZED WITH MATHLIB4.

50251fd6

bump to nightly-2023-07-12-07

mathlib commit https://github.com/leanprover-community/mathlib/commit/4e24c4bfcff371c71f7ba22050308aa17815626c

9849f9d1

Diff

@@ -77,7 +77,7 @@ instance : Algebra R (⨁ i, A i)
   map_mul' a b := by
     simp only [AddMonoidHom.comp_apply]
     rw [of_mul_of]
-    apply Dfinsupp.single_eq_of_sigma_eq (galgebra.map_mul a b)
+    apply DFinsupp.single_eq_of_sigma_eq (galgebra.map_mul a b)
   commutes' r x :=
     by
     change AddMonoidHom.mul (DirectSum.of _ _ _) x = add_monoid_hom.mul.flip (DirectSum.of _ _ _) x
@@ -85,7 +85,7 @@ instance : Algebra R (⨁ i, A i)
     ext i xi : 2
     dsimp only [AddMonoidHom.comp_apply, AddMonoidHom.mul_apply, AddMonoidHom.flip_apply]
     rw [of_mul_of, of_mul_of]
-    apply Dfinsupp.single_eq_of_sigma_eq (galgebra.commutes r ⟨i, xi⟩)
+    apply DFinsupp.single_eq_of_sigma_eq (galgebra.commutes r ⟨i, xi⟩)
   smul_def' r x :=
     by
     change DistribMulAction.toAddMonoidHom _ r x = AddMonoidHom.mul (DirectSum.of _ _ _) x
@@ -94,7 +94,7 @@ instance : Algebra R (⨁ i, A i)
     dsimp only [AddMonoidHom.comp_apply, DistribMulAction.toAddMonoidHom_apply,
       AddMonoidHom.mul_apply]
     rw [DirectSum.of_mul_of, ← of_smul]
-    apply Dfinsupp.single_eq_of_sigma_eq (galgebra.smul_def r ⟨i, xi⟩)
+    apply DFinsupp.single_eq_of_sigma_eq (galgebra.smul_def r ⟨i, xi⟩)
 
 #print DirectSum.algebraMap_apply /-
 theorem algebraMap_apply (r : R) :

50251fd6

bump to nightly-2023-06-20-01

mathlib commit https://github.com/leanprover-community/mathlib/commit/2a0ce625dbb0ffbc7d1316597de0b25c1ec75303

9b351f8c

Diff

@@ -82,7 +82,7 @@ instance : Algebra R (⨁ i, A i)
     by
     change AddMonoidHom.mul (DirectSum.of _ _ _) x = add_monoid_hom.mul.flip (DirectSum.of _ _ _) x
     apply AddMonoidHom.congr_fun _ x
-    ext (i xi) : 2
+    ext i xi : 2
     dsimp only [AddMonoidHom.comp_apply, AddMonoidHom.mul_apply, AddMonoidHom.flip_apply]
     rw [of_mul_of, of_mul_of]
     apply Dfinsupp.single_eq_of_sigma_eq (galgebra.commutes r ⟨i, xi⟩)
@@ -90,7 +90,7 @@ instance : Algebra R (⨁ i, A i)
     by
     change DistribMulAction.toAddMonoidHom _ r x = AddMonoidHom.mul (DirectSum.of _ _ _) x
     apply AddMonoidHom.congr_fun _ x
-    ext (i xi) : 2
+    ext i xi : 2
     dsimp only [AddMonoidHom.comp_apply, DistribMulAction.toAddMonoidHom_apply,
       AddMonoidHom.mul_apply]
     rw [DirectSum.of_mul_of, ← of_smul]

50251fd6

bump to nightly-2023-05-28-18

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

8d353152

Diff

@@ -41,7 +41,7 @@ variable {ι : Type uι}
 
 namespace DirectSum
 
-open DirectSum
+open scoped DirectSum
 
 variable (R : Type uR) (A : ι → Type uA) {B : Type uB} [DecidableEq ι]

50251fd6

bump to nightly-2023-05-19-03

mathlib commit https://github.com/leanprover-community/mathlib/commit/95a87616d63b3cb49d3fe678d416fbe9c4217bf4

9a2fedb8

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 algebra.direct_sum.algebra
-! leanprover-community/mathlib commit e5ba338e9ae4e7feae5027fd5198850971f0fa6a
+! leanprover-community/mathlib commit 50251fd6309cca5ca2e747882ffecd2729f38c5d
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -14,6 +14,9 @@ import Mathbin.Algebra.DirectSum.Ring
 
 /-! # Additively-graded algebra structures on `⨁ i, A i`
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 This file provides `R`-algebra structures on external direct sums of `R`-modules.
 
 Recall that if `A i` are a family of `add_comm_monoid`s indexed by an `add_monoid`, then an instance

e5ba338e

bump to nightly-2023-05-17-20

mathlib commit https://github.com/leanprover-community/mathlib/commit/f8c79b0a623404854a2902b836eac32156fd7712

d85f0014

Diff

@@ -48,27 +48,29 @@ variable [AddMonoid ι] [GSemiring A]
 
 section
 
+#print DirectSum.GAlgebra /-
 /-- A graded version of `algebra`. An instance of `direct_sum.galgebra R A` endows `(⨁ i, A i)`
 with an `R`-algebra structure. -/
-class Galgebra where
+class GAlgebra where
   toFun : R →+ A 0
   map_one : to_fun 1 = GradedMonoid.GOne.one
   map_mul :
     ∀ r s, GradedMonoid.mk _ (to_fun (r * s)) = ⟨_, GradedMonoid.GMul.mul (to_fun r) (to_fun s)⟩
   commutes : ∀ r x, GradedMonoid.mk _ (to_fun r) * x = x * ⟨_, to_fun r⟩
   smul_def : ∀ (r) (x : GradedMonoid A), GradedMonoid.mk x.1 (r • x.2) = ⟨_, to_fun r⟩ * x
-#align direct_sum.galgebra DirectSum.Galgebra
+#align direct_sum.galgebra DirectSum.GAlgebra
+-/
 
 end
 
-variable [Semiring B] [Galgebra R A] [Algebra R B]
+variable [Semiring B] [GAlgebra R A] [Algebra R B]
 
 instance : Algebra R (⨁ i, A i)
     where
-  toFun := (DirectSum.of A 0).comp Galgebra.toFun
+  toFun := (DirectSum.of A 0).comp GAlgebra.toFun
   map_zero' := AddMonoidHom.map_zero _
   map_add' := AddMonoidHom.map_add _
-  map_one' := (DirectSum.of A 0).congr_arg Galgebra.map_one
+  map_one' := (DirectSum.of A 0).congr_arg GAlgebra.map_one
   map_mul' a b := by
     simp only [AddMonoidHom.comp_apply]
     rw [of_mul_of]
@@ -91,16 +93,21 @@ instance : Algebra R (⨁ i, A i)
     rw [DirectSum.of_mul_of, ← of_smul]
     apply Dfinsupp.single_eq_of_sigma_eq (galgebra.smul_def r ⟨i, xi⟩)
 
+#print DirectSum.algebraMap_apply /-
 theorem algebraMap_apply (r : R) :
-    algebraMap R (⨁ i, A i) r = DirectSum.of A 0 (Galgebra.toFun r) :=
+    algebraMap R (⨁ i, A i) r = DirectSum.of A 0 (GAlgebra.toFun r) :=
   rfl
 #align direct_sum.algebra_map_apply DirectSum.algebraMap_apply
+-/
 
+#print DirectSum.algebraMap_toAddMonoid_hom /-
 theorem algebraMap_toAddMonoid_hom :
-    ↑(algebraMap R (⨁ i, A i)) = (DirectSum.of A 0).comp (Galgebra.toFun : R →+ A 0) :=
+    ↑(algebraMap R (⨁ i, A i)) = (DirectSum.of A 0).comp (GAlgebra.toFun : R →+ A 0) :=
   rfl
 #align direct_sum.algebra_map_to_add_monoid_hom DirectSum.algebraMap_toAddMonoid_hom
+-/
 
+#print DirectSum.toAlgebra /-
 /-- A family of `linear_map`s preserving `direct_sum.ghas_one.one` and `direct_sum.ghas_mul.mul`
 describes an `alg_hom` on `⨁ i, A i`. This is a stronger version of `direct_sum.to_semiring`.
 
@@ -111,14 +118,16 @@ can be discharged by `rfl`. -/
 @[simps]
 def toAlgebra (f : ∀ i, A i →ₗ[R] B) (hone : f _ GradedMonoid.GOne.one = 1)
     (hmul : ∀ {i j} (ai : A i) (aj : A j), f _ (GradedMonoid.GMul.mul ai aj) = f _ ai * f _ aj)
-    (hcommutes : ∀ r, (f 0) (Galgebra.toFun r) = (algebraMap R B) r) : (⨁ i, A i) →ₐ[R] B :=
+    (hcommutes : ∀ r, (f 0) (GAlgebra.toFun r) = (algebraMap R B) r) : (⨁ i, A i) →ₐ[R] B :=
   {
     toSemiring (fun i => (f i).toAddMonoidHom) hone
       @hmul with
     toFun := toSemiring (fun i => (f i).toAddMonoidHom) hone @hmul
     commutes' := fun r => (DirectSum.toSemiring_of _ _ _ _ _).trans (hcommutes r) }
 #align direct_sum.to_algebra DirectSum.toAlgebra
+-/
 
+#print DirectSum.algHom_ext' /-
 /-- Two `alg_hom`s out of a direct sum are equal if they agree on the generators.
 
 See note [partially-applied ext lemmas]. -/
@@ -127,22 +136,26 @@ theorem algHom_ext' ⦃f g : (⨁ i, A i) →ₐ[R] B⦄
     (h : ∀ i, f.toLinearMap.comp (lof _ _ A i) = g.toLinearMap.comp (lof _ _ A i)) : f = g :=
   AlgHom.toLinearMap_injective <| DirectSum.linearMap_ext _ h
 #align direct_sum.alg_hom_ext' DirectSum.algHom_ext'
+-/
 
+#print DirectSum.algHom_ext /-
 theorem algHom_ext ⦃f g : (⨁ i, A i) →ₐ[R] B⦄ (h : ∀ i x, f (of A i x) = g (of A i x)) : f = g :=
   algHom_ext' R A fun i => LinearMap.ext <| h i
 #align direct_sum.alg_hom_ext DirectSum.algHom_ext
+-/
 
 end DirectSum
 
 /-! ### Concrete instances -/
 
 
+#print Algebra.directSumGAlgebra /-
 /-- A direct sum of copies of a `algebra` inherits the algebra structure.
 
 -/
 @[simps]
-instance Algebra.directSumGalgebra {R A : Type _} [DecidableEq ι] [AddMonoid ι] [CommSemiring R]
-    [Semiring A] [Algebra R A] : DirectSum.Galgebra R fun i : ι => A
+instance Algebra.directSumGAlgebra {R A : Type _} [DecidableEq ι] [AddMonoid ι] [CommSemiring R]
+    [Semiring A] [Algebra R A] : DirectSum.GAlgebra R fun i : ι => A
     where
   toFun := (algebraMap R A).toAddMonoidHom
   map_one := (algebraMap R A).map_one
@@ -150,7 +163,8 @@ instance Algebra.directSumGalgebra {R A : Type _} [DecidableEq ι] [AddMonoid ι
   commutes := fun r ⟨ai, a⟩ =>
     Sigma.ext ((zero_add _).trans (add_zero _).symm) (hEq_of_eq <| Algebra.commutes _ _)
   smul_def := fun r ⟨ai, a⟩ => Sigma.ext (zero_add _).symm (hEq_of_eq <| Algebra.smul_def _ _)
-#align algebra.direct_sum_galgebra Algebra.directSumGalgebra
+#align algebra.direct_sum_galgebra Algebra.directSumGAlgebra
+-/
 
 namespace Submodule

e5ba338e

bump to nightly-2023-05-17-08

mathlib commit https://github.com/leanprover-community/mathlib/commit/f8c79b0a623404854a2902b836eac32156fd7712

311ac93c

Diff

@@ -44,7 +44,7 @@ variable (R : Type uR) (A : ι → Type uA) {B : Type uB} [DecidableEq ι]
 
 variable [CommSemiring R] [∀ i, AddCommMonoid (A i)] [∀ i, Module R (A i)]
 
-variable [AddMonoid ι] [Gsemiring A]
+variable [AddMonoid ι] [GSemiring A]
 
 section

e5ba338e

bump to nightly-2023-02-21-16

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

1107b979

Changes in mathlib4

mathlib3

mathlib4

e5ba338e

chore: split Algebra.Algebra.Basic (#12486)

Splits Algebra.Algebra.Defs off Algebra.Algebra.Basic. Most imports only need the Defs file, which has significantly smaller imports. The remaining Algebra.Algebra.Basic is now a grab-bag of unrelated results, and should probably be split further or rehomed.

This is mostly motivated by the wasted effort during minimization upon encountering Algebra.Algebra.Basic.

Co-authored-by: Scott Morrison <scott.morrison@gmail.com> Co-authored-by: Ruben Van de Velde <65514131+Ruben-VandeVelde@users.noreply.github.com>

d64b17d9

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.Algebra.Algebra.Basic
+import Mathlib.Algebra.Algebra.Defs
 import Mathlib.Algebra.DirectSum.Module
 import Mathlib.Algebra.DirectSum.Ring

e5ba338e

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

@@ -36,9 +36,7 @@ namespace DirectSum
 open DirectSum
 
 variable (R : Type uR) (A : ι → Type uA) {B : Type uB} [DecidableEq ι]
-
 variable [CommSemiring R] [∀ i, AddCommMonoid (A i)] [∀ i, Module R (A i)]
-
 variable [AddMonoid ι] [GSemiring A]
 
 section

e5ba338e

chore: Remove unnecessary "rw"s (#10704)

Remove unnecessary "rw"s.

db5a9376

Diff

@@ -68,7 +68,7 @@ instance _root_.GradedMonoid.isScalarTower_right :
     IsScalarTower R (GradedMonoid A) (GradedMonoid A) where
   smul_assoc s x y := by
     dsimp
-    rw [GAlgebra.smul_def, GAlgebra.smul_def, ← mul_assoc, GAlgebra.commutes, mul_assoc]
+    rw [GAlgebra.smul_def, GAlgebra.smul_def, ← mul_assoc]
 
 instance : Algebra R (⨁ i, A i) where
   toFun := (DirectSum.of A 0).comp GAlgebra.toFun

e5ba338e

chore(*): rename FunLike to DFunLike (#9785)

This prepares for the introduction of a non-dependent synonym of FunLike, which helps a lot with keeping #8386 readable.

This is entirely search-and-replace in 680197f combined with manual fixes in 4145626, e900597 and b8428f8. The commands that generated this change:

sed -i 's/\bFunLike\b/DFunLike/g' {Archive,Counterexamples,Mathlib,test}/**/*.lean
sed -i 's/\btoFunLike\b/toDFunLike/g' {Archive,Counterexamples,Mathlib,test}/**/*.lean
sed -i 's/import Mathlib.Data.DFunLike/import Mathlib.Data.FunLike/g' {Archive,Counterexamples,Mathlib,test}/**/*.lean
sed -i 's/\bHom_FunLike\b/Hom_DFunLike/g' {Archive,Counterexamples,Mathlib,test}/**/*.lean     
sed -i 's/\binstFunLike\b/instDFunLike/g' {Archive,Counterexamples,Mathlib,test}/**/*.lean
sed -i 's/\bfunLike\b/instDFunLike/g' {Archive,Counterexamples,Mathlib,test}/**/*.lean
sed -i 's/\btoo many metavariables to apply `fun_like.has_coe_to_fun`/too many metavariables to apply `DFunLike.hasCoeToFun`/g' {Archive,Counterexamples,Mathlib,test}/**/*.lean

Co-authored-by: Anne Baanen <Vierkantor@users.noreply.github.com>

82656743

Diff

@@ -81,14 +81,14 @@ instance : Algebra R (⨁ i, A i) where
     apply DFinsupp.single_eq_of_sigma_eq (GAlgebra.map_mul a b)
   commutes' r x := by
     change AddMonoidHom.mul (DirectSum.of _ _ _) x = AddMonoidHom.mul.flip (DirectSum.of _ _ _) x
-    apply FunLike.congr_fun _ x
+    apply DFunLike.congr_fun _ x
     ext i xi : 2
     dsimp only [AddMonoidHom.comp_apply, AddMonoidHom.mul_apply, AddMonoidHom.flip_apply]
     rw [of_mul_of, of_mul_of]
     apply DFinsupp.single_eq_of_sigma_eq (GAlgebra.commutes r ⟨i, xi⟩)
   smul_def' r x := by
     change DistribMulAction.toAddMonoidHom _ r x = AddMonoidHom.mul (DirectSum.of _ _ _) x
-    apply FunLike.congr_fun _ x
+    apply DFunLike.congr_fun _ x
     ext i xi : 2
     dsimp only [AddMonoidHom.comp_apply, DistribMulAction.toAddMonoidHom_apply,
       AddMonoidHom.mul_apply]

e5ba338e

chore: space after ← (#8178)

Co-authored-by: Moritz Firsching <firsching@google.com>

5fb9beab

Diff

@@ -62,13 +62,13 @@ instance _root_.GradedMonoid.smulCommClass_right :
     SMulCommClass R (GradedMonoid A) (GradedMonoid A) where
   smul_comm s x y := by
     dsimp
-    rw [GAlgebra.smul_def, GAlgebra.smul_def, ←mul_assoc, GAlgebra.commutes, mul_assoc]
+    rw [GAlgebra.smul_def, GAlgebra.smul_def, ← mul_assoc, GAlgebra.commutes, mul_assoc]
 
 instance _root_.GradedMonoid.isScalarTower_right :
     IsScalarTower R (GradedMonoid A) (GradedMonoid A) where
   smul_assoc s x y := by
     dsimp
-    rw [GAlgebra.smul_def, GAlgebra.smul_def, ←mul_assoc, GAlgebra.commutes, mul_assoc]
+    rw [GAlgebra.smul_def, GAlgebra.smul_def, ← mul_assoc, GAlgebra.commutes, mul_assoc]
 
 instance : Algebra R (⨁ i, A i) where
   toFun := (DirectSum.of A 0).comp GAlgebra.toFun
@@ -121,7 +121,7 @@ def toAlgebra (f : ∀ i, A i →ₗ[R] B) (hone : f _ GradedMonoid.GOne.one = 1
     commutes' := fun r => by
       show toModule R _ _ f (algebraMap R _ r) = _
       rw [Algebra.algebraMap_eq_smul_one, Algebra.algebraMap_eq_smul_one, map_smul, one_def,
-        ←lof_eq_of R, toModule_lof, hone] }
+        ← lof_eq_of R, toModule_lof, hone] }
 #align direct_sum.to_algebra DirectSum.toAlgebra
 
 /-- Two `AlgHom`s out of a direct sum are equal if they agree on the generators.

e5ba338e

chore(Algebra/DirectSum/Algebra): remove a redundant assumption (#7585)

commutes is implied by hone and linearity.

This matches the approach taken by AlgHom.ofLinearMap.

f9c99994

Diff

@@ -114,12 +114,14 @@ coercions such as `Submodule.subtype (A i)`, and the `[GMonoid A]` structure ori
 can be discharged by `rfl`. -/
 @[simps]
 def toAlgebra (f : ∀ i, A i →ₗ[R] B) (hone : f _ GradedMonoid.GOne.one = 1)
-    (hmul : ∀ {i j} (ai : A i) (aj : A j), f _ (GradedMonoid.GMul.mul ai aj) = f _ ai * f _ aj)
-    (hcommutes : ∀ r, (f 0) (GAlgebra.toFun r) = (algebraMap R B) r) : (⨁ i, A i) →ₐ[R] B :=
-  { toSemiring (fun i => (f i).toAddMonoidHom) hone
-      @hmul with
+    (hmul : ∀ {i j} (ai : A i) (aj : A j), f _ (GradedMonoid.GMul.mul ai aj) = f _ ai * f _ aj) :
+    (⨁ i, A i) →ₐ[R] B :=
+  { toSemiring (fun i => (f i).toAddMonoidHom) hone @hmul with
     toFun := toSemiring (fun i => (f i).toAddMonoidHom) hone @hmul
-    commutes' := fun r => (DirectSum.toSemiring_of _ hone hmul _ _).trans (hcommutes r) }
+    commutes' := fun r => by
+      show toModule R _ _ f (algebraMap R _ r) = _
+      rw [Algebra.algebraMap_eq_smul_one, Algebra.algebraMap_eq_smul_one, map_smul, one_def,
+        ←lof_eq_of R, toModule_lof, hone] }
 #align direct_sum.to_algebra DirectSum.toAlgebra
 
 /-- Two `AlgHom`s out of a direct sum are equal if they agree on the generators.

e5ba338e

feat(Algebra/DirectSum/Algebra): graded multiplication as a bilinear map (#7577)

Also adds some missing actions on GradedMonoid which cleans up the definition of DirectSum.GAlgebra slightly.

This also replaces (⟨i, x⟩ : GradedMonoid _) with .mk i x as the former uses Sigma.mk instead of GradedMonoid.mk, which is annoying for rw.

c4753376

Diff

@@ -49,15 +49,27 @@ class GAlgebra where
   toFun : R →+ A 0
   map_one : toFun 1 = GradedMonoid.GOne.one
   map_mul :
-    ∀ r s, GradedMonoid.mk _ (toFun (r * s)) = ⟨_, GradedMonoid.GMul.mul (toFun r) (toFun s)⟩
-  commutes : ∀ r x, GradedMonoid.mk _ (toFun r) * x = x * ⟨_, toFun r⟩
-  smul_def : ∀ (r) (x : GradedMonoid A), GradedMonoid.mk x.1 (r • x.2) = ⟨_, toFun r⟩ * x
+    ∀ r s, GradedMonoid.mk _ (toFun (r * s)) = .mk _ (GradedMonoid.GMul.mul (toFun r) (toFun s))
+  commutes : ∀ (r) (x : GradedMonoid A), .mk _ (toFun r) * x = x * .mk _ (toFun r)
+  smul_def : ∀ (r) (x : GradedMonoid A), r • x = .mk _ (toFun r) * x
 #align direct_sum.galgebra DirectSum.GAlgebra
 
 end
 
 variable [Semiring B] [GAlgebra R A] [Algebra R B]
 
+instance _root_.GradedMonoid.smulCommClass_right :
+    SMulCommClass R (GradedMonoid A) (GradedMonoid A) where
+  smul_comm s x y := by
+    dsimp
+    rw [GAlgebra.smul_def, GAlgebra.smul_def, ←mul_assoc, GAlgebra.commutes, mul_assoc]
+
+instance _root_.GradedMonoid.isScalarTower_right :
+    IsScalarTower R (GradedMonoid A) (GradedMonoid A) where
+  smul_assoc s x y := by
+    dsimp
+    rw [GAlgebra.smul_def, GAlgebra.smul_def, ←mul_assoc, GAlgebra.commutes, mul_assoc]
+
 instance : Algebra R (⨁ i, A i) where
   toFun := (DirectSum.of A 0).comp GAlgebra.toFun
   map_zero' := AddMonoidHom.map_zero _
@@ -123,6 +135,20 @@ theorem algHom_ext ⦃f g : (⨁ i, A i) →ₐ[R] B⦄ (h : ∀ i x, f (of A i
   algHom_ext' R A fun i => LinearMap.ext <| h i
 #align direct_sum.alg_hom_ext DirectSum.algHom_ext
 
+/-- The piecewise multiplication from the `Mul` instance, as a bundled linear homomorphism.
+
+This is the graded version of `LinearMap.mul`, and the linear version of `DirectSum.gMulHom` -/
+@[simps]
+def gMulLHom {i j} : A i →ₗ[R] A j →ₗ[R] A (i + j) where
+  toFun a :=
+    { toFun := fun b => GradedMonoid.GMul.mul a b
+      map_smul' := fun r x => by
+        injection (smul_comm r (GradedMonoid.mk _ a) (GradedMonoid.mk _ x)).symm
+      map_add' := GNonUnitalNonAssocSemiring.mul_add _ }
+  map_smul' r x := LinearMap.ext fun y => by
+    injection smul_assoc r (GradedMonoid.mk _ x) (GradedMonoid.mk _ y)
+  map_add' _ _ := LinearMap.ext fun _ => GNonUnitalNonAssocSemiring.add_mul _ _ _
+
 end DirectSum
 
 /-! ### Concrete instances -/

e5ba338e

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

@@ -132,7 +132,7 @@ end DirectSum
 
 -/
 @[simps]
-instance Algebra.directSumGAlgebra {R A : Type _} [DecidableEq ι] [AddMonoid ι] [CommSemiring R]
+instance Algebra.directSumGAlgebra {R A : Type*} [DecidableEq ι] [AddMonoid ι] [CommSemiring R]
     [Semiring A] [Algebra R A] : DirectSum.GAlgebra R fun _ : ι => A where
   toFun := (algebraMap R A).toAddMonoidHom
   map_one := (algebraMap R A).map_one

e5ba338e

chore: script to replace headers with #align_import statements (#5979)

depends on: #5966

Co-authored-by: Eric Wieser <wieser.eric@gmail.com> Co-authored-by: Scott Morrison <scott.morrison@gmail.com>

89aa3a3b

Diff

@@ -2,16 +2,13 @@
 Copyright (c) 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 algebra.direct_sum.algebra
-! leanprover-community/mathlib commit e5ba338e9ae4e7feae5027fd5198850971f0fa6a
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.Algebra.Algebra.Basic
 import Mathlib.Algebra.DirectSum.Module
 import Mathlib.Algebra.DirectSum.Ring
 
+#align_import algebra.direct_sum.algebra from "leanprover-community/mathlib"@"e5ba338e9ae4e7feae5027fd5198850971f0fa6a"
+
 /-! # Additively-graded algebra structures on `⨁ i, A i`
 
 This file provides `R`-algebra structures on external direct sums of `R`-modules.

e5ba338e

chore: rename Dfinsupp to DFinsupp (#5822)

See #4354

268b7d43

Diff

@@ -69,14 +69,14 @@ instance : Algebra R (⨁ i, A i) where
   map_mul' a b := by
     simp only [AddMonoidHom.comp_apply]
     rw [of_mul_of]
-    apply Dfinsupp.single_eq_of_sigma_eq (GAlgebra.map_mul a b)
+    apply DFinsupp.single_eq_of_sigma_eq (GAlgebra.map_mul a b)
   commutes' r x := by
     change AddMonoidHom.mul (DirectSum.of _ _ _) x = AddMonoidHom.mul.flip (DirectSum.of _ _ _) x
     apply FunLike.congr_fun _ x
     ext i xi : 2
     dsimp only [AddMonoidHom.comp_apply, AddMonoidHom.mul_apply, AddMonoidHom.flip_apply]
     rw [of_mul_of, of_mul_of]
-    apply Dfinsupp.single_eq_of_sigma_eq (GAlgebra.commutes r ⟨i, xi⟩)
+    apply DFinsupp.single_eq_of_sigma_eq (GAlgebra.commutes r ⟨i, xi⟩)
   smul_def' r x := by
     change DistribMulAction.toAddMonoidHom _ r x = AddMonoidHom.mul (DirectSum.of _ _ _) x
     apply FunLike.congr_fun _ x
@@ -84,7 +84,7 @@ instance : Algebra R (⨁ i, A i) where
     dsimp only [AddMonoidHom.comp_apply, DistribMulAction.toAddMonoidHom_apply,
       AddMonoidHom.mul_apply]
     rw [DirectSum.of_mul_of, ← of_smul]
-    apply Dfinsupp.single_eq_of_sigma_eq (GAlgebra.smul_def r ⟨i, xi⟩)
+    apply DFinsupp.single_eq_of_sigma_eq (GAlgebra.smul_def r ⟨i, xi⟩)
 
 theorem algebraMap_apply (r : R) :
     algebraMap R (⨁ i, A i) r = DirectSum.of A 0 (GAlgebra.toFun r) :=

e5ba338e

chore: remove superfluous parentheses in calls to ext (#5258)

Co-authored-by: Xavier Roblot <46200072+xroblot@users.noreply.github.com> Co-authored-by: Joël Riou <joel.riou@universite-paris-saclay.fr> Co-authored-by: Riccardo Brasca <riccardo.brasca@gmail.com> Co-authored-by: Yury G. Kudryashov <urkud@urkud.name> Co-authored-by: Scott Morrison <scott.morrison@anu.edu.au> Co-authored-by: Scott Morrison <scott.morrison@gmail.com> Co-authored-by: Jeremy Tan Jie Rui <reddeloostw@gmail.com> Co-authored-by: Pol'tta / Miyahara Kō <pol_tta@outlook.jp> Co-authored-by: Jason Yuen <jason_yuen2007@hotmail.com> Co-authored-by: Mario Carneiro <di.gama@gmail.com> Co-authored-by: Jireh Loreaux <loreaujy@gmail.com> Co-authored-by: Ruben Van de Velde <65514131+Ruben-VandeVelde@users.noreply.github.com> Co-authored-by: Kyle Miller <kmill31415@gmail.com> Co-authored-by: Heather Macbeth <25316162+hrmacbeth@users.noreply.github.com> Co-authored-by: Jujian Zhang <jujian.zhang1998@outlook.com> Co-authored-by: Yaël Dillies <yael.dillies@gmail.com>

3d6731dc

Diff

@@ -73,14 +73,14 @@ instance : Algebra R (⨁ i, A i) where
   commutes' r x := by
     change AddMonoidHom.mul (DirectSum.of _ _ _) x = AddMonoidHom.mul.flip (DirectSum.of _ _ _) x
     apply FunLike.congr_fun _ x
-    ext (i xi) : 2
+    ext i xi : 2
     dsimp only [AddMonoidHom.comp_apply, AddMonoidHom.mul_apply, AddMonoidHom.flip_apply]
     rw [of_mul_of, of_mul_of]
     apply Dfinsupp.single_eq_of_sigma_eq (GAlgebra.commutes r ⟨i, xi⟩)
   smul_def' r x := by
     change DistribMulAction.toAddMonoidHom _ r x = AddMonoidHom.mul (DirectSum.of _ _ _) x
     apply FunLike.congr_fun _ x
-    ext (i xi) : 2
+    ext i xi : 2
     dsimp only [AddMonoidHom.comp_apply, DistribMulAction.toAddMonoidHom_apply,
       AddMonoidHom.mul_apply]
     rw [DirectSum.of_mul_of, ← of_smul]

e5ba338e

feat: port Algebra.DirectSum.Algebra (#4049)

Deletes a section that was always content-free, as well as a reference to code that was removed in leanprover-community/mathlib#10127.

d995a932

`algebra.direct_sum.algebra` ⟷ `Mathlib.Algebra.DirectSum.Algebra`

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Dependencies 8 + 426

algebra.direct_sum.algebra ⟷ Mathlib.Algebra.DirectSum.Algebra

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Dependencies 8 + 426

`algebra.direct_sum.algebra` ⟷ `Mathlib.Algebra.DirectSum.Algebra`