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

34020e53

(last sync)

Changes in mathlib3port

mathlib3

mathlib3port

1a51edf1

bump to nightly-2023-09-24-06

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

5655435f

Diff

@@ -3,8 +3,8 @@ 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.ExteriorAlgebra.Basic
-import Mathbin.RingTheory.GradedAlgebra.Basic
+import LinearAlgebra.ExteriorAlgebra.Basic
+import RingTheory.GradedAlgebra.Basic
 
 #align_import linear_algebra.exterior_algebra.grading from "leanprover-community/mathlib"@"1a51edf13debfcbe223fa06b1cb353b9ed9751cc"

1a51edf1

bump to nightly-2023-07-20-09

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

9c56d0dd

Diff

@@ -2,15 +2,12 @@
 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.exterior_algebra.grading
-! leanprover-community/mathlib commit 1a51edf13debfcbe223fa06b1cb353b9ed9751cc
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.LinearAlgebra.ExteriorAlgebra.Basic
 import Mathbin.RingTheory.GradedAlgebra.Basic
 
+#align_import linear_algebra.exterior_algebra.grading from "leanprover-community/mathlib"@"1a51edf13debfcbe223fa06b1cb353b9ed9751cc"
+
 /-!
 # Results about the grading structure of the exterior algebra

1a51edf1

bump to nightly-2023-07-09-03

mathlib commit https://github.com/leanprover-community/mathlib/commit/1a51edf13debfcbe223fa06b1cb353b9ed9751cc

e0217a15

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.exterior_algebra.grading
-! leanprover-community/mathlib commit 34020e531ebc4e8aac6d449d9eecbcd1508ea8d0
+! leanprover-community/mathlib commit 1a51edf13debfcbe223fa06b1cb353b9ed9751cc
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -14,6 +14,9 @@ import Mathbin.RingTheory.GradedAlgebra.Basic
 /-!
 # Results about the grading structure of the exterior algebra
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 Many of these results are copied with minimal modification from the tensor algebra.
 
 The main result is `exterior_algebra.graded_algebra`, which says that the exterior algebra is a

34020e53

bump to nightly-2023-07-05-19

mathlib commit https://github.com/leanprover-community/mathlib/commit/5dc6092d09e5e489106865241986f7f2ad28d4c8

ae61fef9

Diff

@@ -29,35 +29,44 @@ variable (R M)
 
 open scoped DirectSum
 
+#print ExteriorAlgebra.GradedAlgebra.ι /-
 /-- A version of `exterior_algebra.ι` that maps directly into the graded structure. This is
 primarily an auxiliary construction used to provide `exterior_algebra.graded_algebra`. -/
 def GradedAlgebra.ι : M →ₗ[R] ⨁ i : ℕ, ↥((ι R : M →ₗ[_] _).range ^ i) :=
   DirectSum.lof R ℕ (fun i => ↥((ι R : M →ₗ[_] _).range ^ i)) 1 ∘ₗ
     (ι R).codRestrict _ fun m => by simpa only [pow_one] using LinearMap.mem_range_self _ m
 #align exterior_algebra.graded_algebra.ι ExteriorAlgebra.GradedAlgebra.ι
+-/
 
+#print ExteriorAlgebra.GradedAlgebra.ι_apply /-
 theorem GradedAlgebra.ι_apply (m : M) :
     GradedAlgebra.ι R M m =
       DirectSum.of (fun i => ↥((ι R : M →ₗ[_] _).range ^ i)) 1
         ⟨ι R m, by simpa only [pow_one] using LinearMap.mem_range_self _ m⟩ :=
   rfl
 #align exterior_algebra.graded_algebra.ι_apply ExteriorAlgebra.GradedAlgebra.ι_apply
+-/
 
+#print ExteriorAlgebra.GradedAlgebra.ι_sq_zero /-
 theorem GradedAlgebra.ι_sq_zero (m : M) : GradedAlgebra.ι R M m * GradedAlgebra.ι R M m = 0 :=
   by
   rw [graded_algebra.ι_apply, DirectSum.of_mul_of]
   refine' dfinsupp.single_eq_zero.mpr (Subtype.ext <| ι_sq_zero _)
 #align exterior_algebra.graded_algebra.ι_sq_zero ExteriorAlgebra.GradedAlgebra.ι_sq_zero
+-/
 
+#print ExteriorAlgebra.GradedAlgebra.liftι /-
 /-- `exterior_algebra.graded_algebra.ι` lifted to exterior algebra. This is
 primarily an auxiliary construction used to provide `exterior_algebra.graded_algebra`. -/
 def GradedAlgebra.liftι :
     ExteriorAlgebra R M →ₐ[R] ⨁ i : ℕ, ↥((ι R).range ^ i : Submodule R (ExteriorAlgebra R M)) :=
   lift R ⟨by apply graded_algebra.ι R M, GradedAlgebra.ι_sq_zero R M⟩
 #align exterior_algebra.graded_algebra.lift_ι ExteriorAlgebra.GradedAlgebra.liftι
+-/
 
 variable (R M)
 
+#print ExteriorAlgebra.GradedAlgebra.liftι_eq /-
 theorem GradedAlgebra.liftι_eq (i : ℕ)
     (x : ((ι R : M →ₗ[R] ExteriorAlgebra R M).range ^ i : Submodule R (ExteriorAlgebra R M))) :
     GradedAlgebra.liftι R M x =
@@ -75,7 +84,9 @@ theorem GradedAlgebra.liftι_eq (i : ℕ)
       DirectSum.of_mul_of]
     exact DirectSum.of_eq_of_gradedMonoid_eq (Sigma.subtype_ext (add_comm _ _) rfl)
 #align exterior_algebra.graded_algebra.lift_ι_eq ExteriorAlgebra.GradedAlgebra.liftι_eq
+-/
 
+#print ExteriorAlgebra.gradedAlgebra /-
 /-- The exterior algebra is graded by the powers of the submodule `(exterior_algebra.ι R).range`. -/
 instance gradedAlgebra :
     GradedAlgebra ((· ^ ·) (ι R : M →ₗ[R] ExteriorAlgebra R M).range : ℕ → Submodule R _) :=
@@ -90,6 +101,7 @@ instance gradedAlgebra :
       rw [lift_ι_apply, graded_algebra.ι_apply R M, DirectSum.coeAlgHom_of, Subtype.coe_mk])
     (by apply graded_algebra.lift_ι_eq R M)
 #align exterior_algebra.graded_algebra ExteriorAlgebra.gradedAlgebra
+-/
 
 end ExteriorAlgebra

34020e53

bump to nightly-2023-05-28-18

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

8d353152

Diff

@@ -27,7 +27,7 @@ variable {R M : Type _} [CommRing R] [AddCommGroup M] [Module R M]
 
 variable (R M)
 
-open DirectSum
+open scoped DirectSum
 
 /-- A version of `exterior_algebra.ι` that maps directly into the graded structure. This is
 primarily an auxiliary construction used to provide `exterior_algebra.graded_algebra`. -/

34020e53

bump to nightly-2023-05-28-04

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

6797a637

Diff

@@ -68,10 +68,8 @@ theorem GradedAlgebra.liftι_eq (i : ℕ)
   refine'
     Submodule.pow_induction_on_left' _ (fun r => _) (fun x y i hx hy ihx ihy => _)
       (fun m hm i x hx ih => _) hx
-  · rw [AlgHom.commutes, DirectSum.algebraMap_apply]
-    rfl
-  · rw [AlgHom.map_add, ihx, ihy, ← map_add]
-    rfl
+  · rw [AlgHom.commutes, DirectSum.algebraMap_apply]; rfl
+  · rw [AlgHom.map_add, ihx, ihy, ← map_add]; rfl
   · obtain ⟨_, rfl⟩ := hm
     rw [AlgHom.map_mul, ih, graded_algebra.lift_ι, lift_ι_apply, graded_algebra.ι_apply R M,
       DirectSum.of_mul_of]

34020e53

bump to nightly-2023-02-21-16

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

1107b979

Changes in mathlib4

mathlib3

mathlib4

34020e53

style: replace '.-/' by '. -/' (#11938)

Purely automatic replacement. If this is in any way controversial; I'm happy to just close this PR.

3556ded2

Diff

@@ -95,7 +95,7 @@ instance gradedAlgebra : GradedAlgebra (fun i : ℕ ↦ ⋀[R]^i M) :=
 #align exterior_algebra.graded_algebra ExteriorAlgebra.gradedAlgebra
 
 /-- The union of the images of the maps `ExteriorAlgebra.ιMulti R n` for `n` running through
-all natural numbers spans the exterior algebra.-/
+all natural numbers spans the exterior algebra. -/
 lemma ιMulti_span :
     Submodule.span R (Set.range fun x : Σ n, (Fin n → M) => ιMulti R x.1 x.2) = ⊤ := by
   rw [Submodule.eq_top_iff']

34020e53

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

@@ -20,7 +20,6 @@ The main result is `ExteriorAlgebra.gradedAlgebra`, which says that the exterior
 namespace ExteriorAlgebra
 
 variable {R M : Type*} [CommRing R] [AddCommGroup M] [Module R M]
-
 variable (R M)
 
 open scoped DirectSum

34020e53

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

@@ -27,7 +27,7 @@ open scoped DirectSum
 
 /-- A version of `ExteriorAlgebra.ι` that maps directly into the graded structure. This is
 primarily an auxiliary construction used to provide `ExteriorAlgebra.gradedAlgebra`. -/
--- porting note: protected
+-- Porting note: protected
 protected def GradedAlgebra.ι :
     M →ₗ[R] ⨁ i : ℕ, ⋀[R]^i M :=
   DirectSum.lof R ℕ (fun i => ⋀[R]^i M) 1 ∘ₗ

34020e53

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

@@ -71,10 +71,10 @@ theorem GradedAlgebra.liftι_eq (i : ℕ) (x : ⋀[R]^i M) :
   --    (fun m hm i x hx ih => ?_) hx
   -- but it created invalid goals
   induction hx using Submodule.pow_induction_on_left' with
-  | hr => simp_rw [AlgHom.commutes, DirectSum.algebraMap_apply]; rfl
+  | algebraMap => simp_rw [AlgHom.commutes, DirectSum.algebraMap_apply]; rfl
   -- FIXME: specialized `map_add` to avoid a (whole-declaration) timeout
-  | hadd _ _ _ _ _ ihx ihy => simp_rw [AlgHom.map_add, ihx, ihy, ← AddMonoidHom.map_add]; rfl
-  | hmul _ hm _ _ _ ih =>
+  | add _ _ _ _ _ ihx ihy => simp_rw [AlgHom.map_add, ihx, ihy, ← AddMonoidHom.map_add]; rfl
+  | mem_mul _ hm _ _ _ ih =>
       obtain ⟨_, rfl⟩ := hm
       simp_rw [AlgHom.map_mul, ih, GradedAlgebra.liftι, lift_ι_apply, GradedAlgebra.ι_apply R M,
         DirectSum.of_mul_of]

34020e53

refactor(LinearAlgebra/ExteriorAlgebra/{Basic,Grading}): add a definition and notation for the exterior powers of a module (#10744)

This is split off from PR #10654 (that actually proves some properties of the exterior powers). It introduces the reducible definition exteriorPower R n M for the nth exterior power of the R-module M; this is of type Submodule R (ExteriorAlgebra R M) and defined as LinearMap.range (ExteriorAlgebra.ι R : M →ₗ[R] ExteriorAlgebra R M) ^ n. It also introduces the notation Λ[R]^n M for exteriorPower R n M.

Note: for a reason that I don't understand, Lean becomes unable to synthesize the SetLike.GradedMonoid instance on fun (i : ℕ) ↦ (Λ[R]^i) M, so I added it manually in ExteriorAlgebra/Graded.lean. I am far from sure that this is the correct solution.

Co-authored-by: Eric Wieser <wieser.eric@gmail.com> Co-authored-by: Richard Copley <buster@buster.me.uk>

a4e76ac4

Diff

@@ -17,7 +17,6 @@ The main result is `ExteriorAlgebra.gradedAlgebra`, which says that the exterior
 ℕ-graded algebra.
 -/
 
-
 namespace ExteriorAlgebra
 
 variable {R M : Type*} [CommRing R] [AddCommGroup M] [Module R M]
@@ -30,18 +29,24 @@ open scoped DirectSum
 primarily an auxiliary construction used to provide `ExteriorAlgebra.gradedAlgebra`. -/
 -- porting note: protected
 protected def GradedAlgebra.ι :
-    M →ₗ[R] ⨁ i : ℕ, ↥(LinearMap.range (ι R : M →ₗ[R] ExteriorAlgebra R M) ^ i) :=
-  DirectSum.lof R ℕ (fun i => ↥(LinearMap.range (ι R : M →ₗ[R] ExteriorAlgebra R M) ^ i)) 1 ∘ₗ
+    M →ₗ[R] ⨁ i : ℕ, ⋀[R]^i M :=
+  DirectSum.lof R ℕ (fun i => ⋀[R]^i M) 1 ∘ₗ
     (ι R).codRestrict _ fun m => by simpa only [pow_one] using LinearMap.mem_range_self _ m
 #align exterior_algebra.graded_algebra.ι ExteriorAlgebra.GradedAlgebra.ι
 
 theorem GradedAlgebra.ι_apply (m : M) :
     GradedAlgebra.ι R M m =
-      DirectSum.of (fun i : ℕ => ↥(LinearMap.range (ι R : M →ₗ[R] ExteriorAlgebra R M) ^ i)) 1
+      DirectSum.of (fun i : ℕ => ⋀[R]^i M) 1
         ⟨ι R m, by simpa only [pow_one] using LinearMap.mem_range_self _ m⟩ :=
   rfl
 #align exterior_algebra.graded_algebra.ι_apply ExteriorAlgebra.GradedAlgebra.ι_apply
 
+-- Defining this instance manually, because Lean doesn't seem to be able to synthesize it.
+-- Strangely, this problem only appears when we use the abbreviation or notation for the
+-- exterior powers.
+instance : SetLike.GradedMonoid fun i : ℕ ↦ ⋀[R]^i M :=
+  Submodule.nat_power_gradedMonoid (LinearMap.range (ι R : M →ₗ[R] ExteriorAlgebra R M))
+
 -- Porting note: Lean needs to be reminded of this instance otherwise it cannot
 -- synthesize 0 in the next theorem
 attribute [instance 1100] MulZeroClass.toZero in
@@ -53,18 +58,12 @@ theorem GradedAlgebra.ι_sq_zero (m : M) : GradedAlgebra.ι R M m * GradedAlgebr
 /-- `ExteriorAlgebra.GradedAlgebra.ι` lifted to exterior algebra. This is
 primarily an auxiliary construction used to provide `ExteriorAlgebra.gradedAlgebra`. -/
 def GradedAlgebra.liftι :
-    ExteriorAlgebra R M →ₐ[R] ⨁ i : ℕ,
-    (LinearMap.range (ι R : M →ₗ[R] ExteriorAlgebra R M) ^ i : Submodule R (ExteriorAlgebra R M)) :=
+    ExteriorAlgebra R M →ₐ[R] ⨁ i : ℕ, ⋀[R]^i M :=
   lift R ⟨by apply GradedAlgebra.ι R M, GradedAlgebra.ι_sq_zero R M⟩
 #align exterior_algebra.graded_algebra.lift_ι ExteriorAlgebra.GradedAlgebra.liftι
 
-theorem GradedAlgebra.liftι_eq (i : ℕ)
-    (x : (LinearMap.range (ι R : M →ₗ[R] ExteriorAlgebra R M) ^ i :
-      Submodule R (ExteriorAlgebra R M))) :
-    GradedAlgebra.liftι R M x =
-    DirectSum.of (fun i =>
-      ↥(LinearMap.range (ι R : M →ₗ[R] ExteriorAlgebra R M) ^ i :
-      Submodule R (ExteriorAlgebra R M))) i x := by
+theorem GradedAlgebra.liftι_eq (i : ℕ) (x : ⋀[R]^i M) :
+    GradedAlgebra.liftι R M x = DirectSum.of (fun i => ⋀[R]^i M) i x := by
   cases' x with x hx
   dsimp only [Subtype.coe_mk, DirectSum.lof_eq_of]
   -- Porting note: original statement was
@@ -83,8 +82,7 @@ theorem GradedAlgebra.liftι_eq (i : ℕ)
 #align exterior_algebra.graded_algebra.lift_ι_eq ExteriorAlgebra.GradedAlgebra.liftι_eq
 
 /-- The exterior algebra is graded by the powers of the submodule `(ExteriorAlgebra.ι R).range`. -/
-instance gradedAlgebra :
-    GradedAlgebra (LinearMap.range (ι R : M →ₗ[R] ExteriorAlgebra R M) ^ · : ℕ → Submodule R _) :=
+instance gradedAlgebra : GradedAlgebra (fun i : ℕ ↦ ⋀[R]^i M) :=
   GradedAlgebra.ofAlgHom _
     (-- while not necessary, the `by apply` makes this elaborate faster
     by apply GradedAlgebra.liftι R M)
@@ -103,8 +101,7 @@ lemma ιMulti_span :
     Submodule.span R (Set.range fun x : Σ n, (Fin n → M) => ιMulti R x.1 x.2) = ⊤ := by
   rw [Submodule.eq_top_iff']
   intro x
-  induction x
-    using DirectSum.Decomposition.inductionOn fun i => LinearMap.range (ι R (M := M)) ^ i with
+  induction x using DirectSum.Decomposition.inductionOn fun i => ⋀[R]^i M with
   | h_zero => exact Submodule.zero_mem _
   | h_add _ _ hm hm' => exact Submodule.add_mem _ hm hm'
   | h_homogeneous hm =>

34020e53

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

@@ -47,7 +47,7 @@ theorem GradedAlgebra.ι_apply (m : M) :
 attribute [instance 1100] MulZeroClass.toZero in
 theorem GradedAlgebra.ι_sq_zero (m : M) : GradedAlgebra.ι R M m * GradedAlgebra.ι R M m = 0 := by
   rw [GradedAlgebra.ι_apply, DirectSum.of_mul_of]
-  refine DFinsupp.single_eq_zero.mpr (Subtype.ext <| ExteriorAlgebra.ι_sq_zero _)
+  exact DFinsupp.single_eq_zero.mpr (Subtype.ext <| ExteriorAlgebra.ι_sq_zero _)
 #align exterior_algebra.graded_algebra.ι_sq_zero ExteriorAlgebra.GradedAlgebra.ι_sq_zero
 
 /-- `ExteriorAlgebra.GradedAlgebra.ι` lifted to exterior algebra. This is

34020e53

feat(LinearAlgebra/{ExteriorAlgebra,CliffordAlgebra}): Functoriality of the exterior algebra and some lemmas about generation (#9718)

This does a few things:

Define the algebra morphism TrivSqZeroExt.map f between trivial square-zero extensions induced by a linear mapf, and establish some of its basic properties (functoriality, composition with the basic maps to/from TrivSqZeroExt). Note that we only consider the case of a commutative base ring, because the case of a general base ring requires morphisms of bimodules, which we do not have.
Define the algebra morphism ExteriorAlgebra.map f between exterior algebras induced by a linear map f. This is a straightforward application of the similar construction for Clifford algebras, but I think it is still useful to have. Basic properties of this construction are proved: functoriality, composition with ExteriorAlgebra.ι, ExteriorAlgebra.ιInv (this part uses the first point) and ExteriorAlgebra.ιMulti. Then exactness properties of the construction is studied:
- If the linear map is surjective, then the map on exterior algebras is also surjective. This actually holds for Clifford algebras, so I added a lemma called CliffordAlgebra.map_surjective in LinearAlgebra/CliffordAlgebra/Basic.lean. For exterior algebras, the converse holds and is also proved.
- If the linear map has a retraction, then the map on exterior algebras is injective. So if the base ring is a field, the map on exterior algebras is injective if the linear map is injective.
Establish some properties of ExteriorAlgebra.ιMulti:
- ExteriorAlgebra.ιMulti_range: The range of ιMulti R n is contained in the nth exterior power (define here as LinearMap.range (ι R : M →ₗ[R] ExteriorAlgebra R M) ^ n).
- ExteriorAlgebra.ιMulti_span_fixedDegree: This range spans the nth exterior power.
- ExteriorAlgebra.ιMulti_span: The union over all n of the range of ιMulti R n spans the whole exterior algebra (this is in LinearAlgebra/ExteriorAlgebra/Grading.lean because the proof uses the graded module structure, but it might be possible to do something simpler).
Construct ExteriorAlgebra.ιMulti_family: This takes a natural number n and a family of vectors v indexed by a linearly ordered type I, and it returns the family of n-fold products of the v i in the exterior algebra, indexed by the set of finsets of I of cardinality n. (The point, to be proved in another PR, is that when v is a basis, then ExteriorAlgebra.ιMulti_family R n v is a basis of the nth exterior power.)

Co-authored-by: morel <smorel@math.princeton.edu> Co-authored-by: smorel394 <67864981+smorel394@users.noreply.github.com>

29c27c39

Diff

@@ -97,4 +97,22 @@ instance gradedAlgebra :
     (by apply GradedAlgebra.liftι_eq R M)
 #align exterior_algebra.graded_algebra ExteriorAlgebra.gradedAlgebra
 
+/-- The union of the images of the maps `ExteriorAlgebra.ιMulti R n` for `n` running through
+all natural numbers spans the exterior algebra.-/
+lemma ιMulti_span :
+    Submodule.span R (Set.range fun x : Σ n, (Fin n → M) => ιMulti R x.1 x.2) = ⊤ := by
+  rw [Submodule.eq_top_iff']
+  intro x
+  induction x
+    using DirectSum.Decomposition.inductionOn fun i => LinearMap.range (ι R (M := M)) ^ i with
+  | h_zero => exact Submodule.zero_mem _
+  | h_add _ _ hm hm' => exact Submodule.add_mem _ hm hm'
+  | h_homogeneous hm =>
+    let ⟨m, hm⟩ := hm
+    apply Set.mem_of_mem_of_subset hm
+    rw [← ιMulti_span_fixedDegree]
+    refine Submodule.span_mono fun _ hx ↦ ?_
+    obtain ⟨y, rfl⟩ := hx
+    exact ⟨⟨_, y⟩, rfl⟩
+
 end ExteriorAlgebra

34020e53

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

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

Zulip thread

Important changes

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

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

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

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

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

Similarly, MyEquivClass should take EquivLike as a parameter.

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

Remaining issues

Slower (failing) search

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

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

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

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

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

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

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

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

`simp` not firing sometimes

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

Missing instances due to unification failing

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

Workaround for issues

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

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

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

c6a73d4f

Diff

@@ -73,7 +73,8 @@ theorem GradedAlgebra.liftι_eq (i : ℕ)
   -- but it created invalid goals
   induction hx using Submodule.pow_induction_on_left' with
   | hr => simp_rw [AlgHom.commutes, DirectSum.algebraMap_apply]; rfl
-  | hadd _ _ _ _ _ ihx ihy => simp_rw [AlgHom.map_add, ihx, ihy, ← map_add]; rfl
+  -- FIXME: specialized `map_add` to avoid a (whole-declaration) timeout
+  | hadd _ _ _ _ _ ihx ihy => simp_rw [AlgHom.map_add, ihx, ihy, ← AddMonoidHom.map_add]; rfl
   | hmul _ hm _ _ _ ih =>
       obtain ⟨_, rfl⟩ := hm
       simp_rw [AlgHom.map_mul, ih, GradedAlgebra.liftι, lift_ι_apply, GradedAlgebra.ι_apply R M,

34020e53

chore(ExteriorAlgebra.Grading): drop ExteriorAlgebra.instZero (#9274)

Locally change the priority of MulZeroClass.toZero instead.

PR contents

This is the supremum of

#8284
#8056
#8023
#8332
#8226 (already approved)
#7834 (already approved)

along with some minor fixes from failures on nightly-testing as Mathlib master is merged into it.

Note that some PRs for changes that are already compatible with the current toolchain and will be necessary have already been split out: #8380.

I am hopeful that in future we will be able to progressively merge adaptation PRs into a bump/v4.X.0 branch, so we never end up with a "big merge" like this. However one of these adaptation PRs (#8056) predates my new scheme for combined CI, and it wasn't possible to keep that PR viable in the meantime.

Lean PRs involved in this bump

In particular this includes adjustments for the Lean PRs

leanprover/lean4#2778

We can get rid of all the

local macro_rules | `($x ^ $y) => `(HPow.hPow $x $y) -- Porting note: See issue [lean4#2220](https://github.com/leanprover/lean4/pull/2220)

macros across Mathlib (and in any projects that want to write natural number powers of reals).

leanprover/lean4#2722

Changes the default behaviour of simp to (config := {decide := false}). This makes simp (and consequentially norm_num) less powerful, but also more consistent, and less likely to blow up in long failures. This requires a variety of changes: changing some previously by simp or norm_num to decide or rfl, or adding (config := {decide := true}).

leanprover/lean4#2783

This changed the behaviour of simp so that simp [f] will only unfold "fully applied" occurrences of f. The old behaviour can be recovered with simp (config := { unfoldPartialApp := true }). We may in future add a syntax for this, e.g. simp [!f]; please provide feedback! In the meantime, we have made the following changes:

switching to using explicit lemmas that have the intended level of application
(config := { unfoldPartialApp := true }) in some places, to recover the old behaviour
Using @[eqns] to manually adjust the equation lemmas for a particular definition, recovering the old behaviour just for that definition. See #8371, where we do this for Function.comp and Function.flip.

This change in Lean may require further changes down the line (e.g. adding the !f syntax, and/or upstreaming the special treatment for Function.comp and Function.flip, and/or removing this special treatment). Please keep an open and skeptical mind about these changes!

Co-authored-by: leanprover-community-mathlib4-bot <leanprover-community-mathlib4-bot@users.noreply.github.com> Co-authored-by: Scott Morrison <scott.morrison@gmail.com> Co-authored-by: Eric Wieser <wieser.eric@gmail.com> Co-authored-by: Mauricio Collares <mauricio@collares.org>

40b64f79

Diff

@@ -37,7 +37,7 @@ protected def GradedAlgebra.ι :
 
 theorem GradedAlgebra.ι_apply (m : M) :
     GradedAlgebra.ι R M m =
-      DirectSum.of (fun i : ℕ => LinearMap.range (ι R : M →ₗ[R] ExteriorAlgebra R M) ^ i) 1
+      DirectSum.of (fun i : ℕ => ↥(LinearMap.range (ι R : M →ₗ[R] ExteriorAlgebra R M) ^ i)) 1
         ⟨ι R m, by simpa only [pow_one] using LinearMap.mem_range_self _ m⟩ :=
   rfl
 #align exterior_algebra.graded_algebra.ι_apply ExteriorAlgebra.GradedAlgebra.ι_apply

34020e53

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

@@ -35,10 +35,9 @@ protected def GradedAlgebra.ι :
     (ι R).codRestrict _ fun m => by simpa only [pow_one] using LinearMap.mem_range_self _ m
 #align exterior_algebra.graded_algebra.ι ExteriorAlgebra.GradedAlgebra.ι
 
--- porting note: replaced coercion to sort with an explicit subtype notation
 theorem GradedAlgebra.ι_apply (m : M) :
     GradedAlgebra.ι R M m =
-      DirectSum.of (fun i => {x // x ∈ (LinearMap.range (ι R : M →ₗ[R] ExteriorAlgebra R M) ^ i)}) 1
+      DirectSum.of (fun i : ℕ => LinearMap.range (ι R : M →ₗ[R] ExteriorAlgebra R M) ^ i) 1
         ⟨ι R m, by simpa only [pow_one] using LinearMap.mem_range_self _ m⟩ :=
   rfl
 #align exterior_algebra.graded_algebra.ι_apply ExteriorAlgebra.GradedAlgebra.ι_apply

34020e53

chore: exactly 4 spaces in subsequent lines for def (#7321)

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

11dbfb2b

Diff

@@ -55,7 +55,7 @@ theorem GradedAlgebra.ι_sq_zero (m : M) : GradedAlgebra.ι R M m * GradedAlgebr
 /-- `ExteriorAlgebra.GradedAlgebra.ι` lifted to exterior algebra. This is
 primarily an auxiliary construction used to provide `ExteriorAlgebra.gradedAlgebra`. -/
 def GradedAlgebra.liftι :
-  ExteriorAlgebra R M →ₐ[R] ⨁ i : ℕ,
+    ExteriorAlgebra R M →ₐ[R] ⨁ i : ℕ,
     (LinearMap.range (ι R : M →ₗ[R] ExteriorAlgebra R M) ^ i : Submodule R (ExteriorAlgebra R M)) :=
   lift R ⟨by apply GradedAlgebra.ι R M, GradedAlgebra.ι_sq_zero R M⟩
 #align exterior_algebra.graded_algebra.lift_ι ExteriorAlgebra.GradedAlgebra.liftι

34020e53

chore: tidy various files (#7137)

cdbcc219

Diff

@@ -89,7 +89,7 @@ instance gradedAlgebra :
   GradedAlgebra.ofAlgHom _
     (-- while not necessary, the `by apply` makes this elaborate faster
     by apply GradedAlgebra.liftι R M)
-    -- the proof from here onward is identical to the `tensor_algebra` case
+    -- the proof from here onward is identical to the `TensorAlgebra` case
     (by
       ext m
       dsimp only [LinearMap.comp_apply, AlgHom.toLinearMap_apply, AlgHom.comp_apply,

34020e53

chore: update/remove heart beat bumps (#6860)

We clean up heart beat bumps after #6474.

c95f05bd

Diff

@@ -52,7 +52,6 @@ theorem GradedAlgebra.ι_sq_zero (m : M) : GradedAlgebra.ι R M m * GradedAlgebr
   refine DFinsupp.single_eq_zero.mpr (Subtype.ext <| ExteriorAlgebra.ι_sq_zero _)
 #align exterior_algebra.graded_algebra.ι_sq_zero ExteriorAlgebra.GradedAlgebra.ι_sq_zero
 
-set_option maxHeartbeats 400000 in
 /-- `ExteriorAlgebra.GradedAlgebra.ι` lifted to exterior algebra. This is
 primarily an auxiliary construction used to provide `ExteriorAlgebra.gradedAlgebra`. -/
 def GradedAlgebra.liftι :
@@ -61,7 +60,6 @@ def GradedAlgebra.liftι :
   lift R ⟨by apply GradedAlgebra.ι R M, GradedAlgebra.ι_sq_zero R M⟩
 #align exterior_algebra.graded_algebra.lift_ι ExteriorAlgebra.GradedAlgebra.liftι
 
-set_option synthInstance.maxHeartbeats 30000 in
 theorem GradedAlgebra.liftι_eq (i : ℕ)
     (x : (LinearMap.range (ι R : M →ₗ[R] ExteriorAlgebra R M) ^ i :
       Submodule R (ExteriorAlgebra R M))) :
@@ -85,7 +83,6 @@ theorem GradedAlgebra.liftι_eq (i : ℕ)
       exact DirectSum.of_eq_of_gradedMonoid_eq (Sigma.subtype_ext (add_comm _ _) rfl)
 #align exterior_algebra.graded_algebra.lift_ι_eq ExteriorAlgebra.GradedAlgebra.liftι_eq
 
-set_option maxHeartbeats 400000 in
 /-- The exterior algebra is graded by the powers of the submodule `(ExteriorAlgebra.ι R).range`. -/
 instance gradedAlgebra :
     GradedAlgebra (LinearMap.range (ι R : M →ₗ[R] ExteriorAlgebra R M) ^ · : ℕ → Submodule R _) :=

34020e53

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

@@ -20,7 +20,7 @@ The main result is `ExteriorAlgebra.gradedAlgebra`, which says that the exterior
 
 namespace ExteriorAlgebra
 
-variable {R M : Type _} [CommRing R] [AddCommGroup M] [Module R M]
+variable {R M : Type*} [CommRing R] [AddCommGroup M] [Module R M]
 
 variable (R M)
 
@@ -45,7 +45,7 @@ theorem GradedAlgebra.ι_apply (m : M) :
 
 -- Porting note: Lean needs to be reminded of this instance otherwise it cannot
 -- synthesize 0 in the next theorem
-instance (α : Type _) [MulZeroClass α] : Zero α := MulZeroClass.toZero
+instance (α : Type*) [MulZeroClass α] : Zero α := MulZeroClass.toZero
 
 theorem GradedAlgebra.ι_sq_zero (m : M) : GradedAlgebra.ι R M m * GradedAlgebra.ι R M m = 0 := by
   rw [GradedAlgebra.ι_apply, DirectSum.of_mul_of]

34020e53

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

@@ -2,15 +2,12 @@
 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.exterior_algebra.grading
-! leanprover-community/mathlib commit 34020e531ebc4e8aac6d449d9eecbcd1508ea8d0
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.LinearAlgebra.ExteriorAlgebra.Basic
 import Mathlib.RingTheory.GradedAlgebra.Basic
 
+#align_import linear_algebra.exterior_algebra.grading from "leanprover-community/mathlib"@"34020e531ebc4e8aac6d449d9eecbcd1508ea8d0"
+
 /-!
 # Results about the grading structure of the exterior algebra

34020e53

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

@@ -81,7 +81,7 @@ theorem GradedAlgebra.liftι_eq (i : ℕ)
   induction hx using Submodule.pow_induction_on_left' with
   | hr => simp_rw [AlgHom.commutes, DirectSum.algebraMap_apply]; rfl
   | hadd _ _ _ _ _ ihx ihy => simp_rw [AlgHom.map_add, ihx, ihy, ← map_add]; rfl
-  | hmul _ hm _ _ _ ih  =>
+  | hmul _ hm _ _ _ ih =>
       obtain ⟨_, rfl⟩ := hm
       simp_rw [AlgHom.map_mul, ih, GradedAlgebra.liftι, lift_ι_apply, GradedAlgebra.ι_apply R M,
         DirectSum.of_mul_of]

34020e53

chore: rename Dfinsupp to DFinsupp (#5822)

See #4354

268b7d43

Diff

@@ -52,7 +52,7 @@ instance (α : Type _) [MulZeroClass α] : Zero α := MulZeroClass.toZero
 
 theorem GradedAlgebra.ι_sq_zero (m : M) : GradedAlgebra.ι R M m * GradedAlgebra.ι R M m = 0 := by
   rw [GradedAlgebra.ι_apply, DirectSum.of_mul_of]
-  refine Dfinsupp.single_eq_zero.mpr (Subtype.ext <| ExteriorAlgebra.ι_sq_zero _)
+  refine DFinsupp.single_eq_zero.mpr (Subtype.ext <| ExteriorAlgebra.ι_sq_zero _)
 #align exterior_algebra.graded_algebra.ι_sq_zero ExteriorAlgebra.GradedAlgebra.ι_sq_zero
 
 set_option maxHeartbeats 400000 in

34020e53

feat: port LinearAlgebra.ExteriorAlgebra.Grading (#5459)

Co-authored-by: Moritz Firsching <firsching@google.com> Co-authored-by: Xavier-François Roblot <46200072+xroblot@users.noreply.github.com>

b83ae2cd

`linear_algebra.exterior_algebra.grading` ⟷ `Mathlib.LinearAlgebra.ExteriorAlgebra.Grading`

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Important changes

Remaining issues

Slower (failing) search

`simp` not firing sometimes

Missing instances due to unification failing

Workaround for issues

PR contents

Lean PRs involved in this bump

leanprover/lean4#2778

leanprover/lean4#2722

leanprover/lean4#2783

Dependencies 10 + 638

linear_algebra.exterior_algebra.grading ⟷ Mathlib.LinearAlgebra.ExteriorAlgebra.Grading

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Important changes

Remaining issues

Slower (failing) search

simp not firing sometimes

Missing instances due to unification failing

Workaround for issues

PR contents

Lean PRs involved in this bump

leanprover/lean4#2778

leanprover/lean4#2722

leanprover/lean4#2783

Dependencies 10 + 638

`linear_algebra.exterior_algebra.grading` ⟷ `Mathlib.LinearAlgebra.ExteriorAlgebra.Grading`

`simp` not firing sometimes