linear_algebra.exterior_algebra.of_alternating

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

ce11c3c2

(last sync)

Changes in mathlib3port

mathlib3

mathlib3port

08b63ab5

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) 2022 Eric Wieser. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Eric Wieser
 -/
-import Mathbin.LinearAlgebra.CliffordAlgebra.Fold
-import Mathbin.LinearAlgebra.ExteriorAlgebra.Basic
+import LinearAlgebra.CliffordAlgebra.Fold
+import LinearAlgebra.ExteriorAlgebra.Basic
 
 #align_import linear_algebra.exterior_algebra.of_alternating from "leanprover-community/mathlib"@"08b63ab58a6ec1157ebeafcbbe6c7a3fb3c9f6d5"

08b63ab5

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) 2022 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.of_alternating
-! leanprover-community/mathlib commit 08b63ab58a6ec1157ebeafcbbe6c7a3fb3c9f6d5
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.LinearAlgebra.CliffordAlgebra.Fold
 import Mathbin.LinearAlgebra.ExteriorAlgebra.Basic
 
+#align_import linear_algebra.exterior_algebra.of_alternating from "leanprover-community/mathlib"@"08b63ab58a6ec1157ebeafcbbe6c7a3fb3c9f6d5"
+
 /-!
 # Extending an alternating map to the exterior algebra

08b63ab5

bump to nightly-2023-07-01-17

mathlib commit https://github.com/leanprover-community/mathlib/commit/9240e8be927a0955b9a82c6c85ef499ee3a626b8

a0c14df7

Diff

@@ -37,11 +37,11 @@ variable [CommRing R] [AddCommGroup M] [AddCommGroup N] [AddCommGroup N']
 
 variable [Module R M] [Module R N] [Module R N']
 
-#print AlternatingMap.ModuleAddCommGroup /-
+#print AlternatingMap.instModuleAddCommGroup /-
 -- This instance can't be found where it's needed if we don't remind lean that it exists.
-instance AlternatingMap.ModuleAddCommGroup {ι : Type _} : Module R (AlternatingMap R M N ι) := by
-  infer_instance
-#align alternating_map.module_add_comm_group AlternatingMap.ModuleAddCommGroup
+instance AlternatingMap.instModuleAddCommGroup {ι : Type _} : Module R (AlternatingMap R M N ι) :=
+  by infer_instance
+#align alternating_map.module_add_comm_group AlternatingMap.instModuleAddCommGroup
 -/
 
 namespace ExteriorAlgebra

08b63ab5

bump to nightly-2023-06-30-03

mathlib commit https://github.com/leanprover-community/mathlib/commit/9240e8be927a0955b9a82c6c85ef499ee3a626b8

397a8f48

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.of_alternating
-! leanprover-community/mathlib commit ce11c3c2a285bbe6937e26d9792fda4e51f3fe1a
+! leanprover-community/mathlib commit 08b63ab58a6ec1157ebeafcbbe6c7a3fb3c9f6d5
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -14,6 +14,9 @@ import Mathbin.LinearAlgebra.ExteriorAlgebra.Basic
 /-!
 # Extending an alternating map to the exterior algebra
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 ## Main definitions
 
 * `exterior_algebra.lift_alternating`: construct a linear map out of the exterior algebra

ce11c3c2

bump to nightly-2023-06-26-03

mathlib commit https://github.com/leanprover-community/mathlib/commit/fdc286cc6967a012f41b87f76dcd2797b53152af

f06bc311

Diff

@@ -34,15 +34,18 @@ variable [CommRing R] [AddCommGroup M] [AddCommGroup N] [AddCommGroup N']
 
 variable [Module R M] [Module R N] [Module R N']
 
+#print AlternatingMap.ModuleAddCommGroup /-
 -- This instance can't be found where it's needed if we don't remind lean that it exists.
-instance AlternatingMap.moduleAddCommGroup {ι : Type _} : Module R (AlternatingMap R M N ι) := by
+instance AlternatingMap.ModuleAddCommGroup {ι : Type _} : Module R (AlternatingMap R M N ι) := by
   infer_instance
-#align alternating_map.module_add_comm_group AlternatingMap.moduleAddCommGroup
+#align alternating_map.module_add_comm_group AlternatingMap.ModuleAddCommGroup
+-/
 
 namespace ExteriorAlgebra
 
 open CliffordAlgebra hiding ι
 
+#print ExteriorAlgebra.liftAlternating /-
 /-- Build a map out of the exterior algebra given a collection of alternating maps acting on each
 exterior power -/
 def liftAlternating : (∀ i, AlternatingMap R M N (Fin i)) →ₗ[R] ExteriorAlgebra R M →ₗ[R] N :=
@@ -69,7 +72,9 @@ def liftAlternating : (∀ i, AlternatingMap R M N (Fin i)) →ₗ[R] ExteriorAl
     ext i : 1
     exact AlternatingMap.curryLeft_same _ _
 #align exterior_algebra.lift_alternating ExteriorAlgebra.liftAlternating
+-/
 
+#print ExteriorAlgebra.liftAlternating_ι /-
 @[simp]
 theorem liftAlternating_ι (f : ∀ i, AlternatingMap R M N (Fin i)) (m : M) :
     liftAlternating f (ι R m) = f 1 ![m] :=
@@ -78,7 +83,9 @@ theorem liftAlternating_ι (f : ∀ i, AlternatingMap R M N (Fin i)) (m : M) :
   rw [foldl_ι, LinearMap.mk₂_apply, AlternatingMap.curryLeft_apply_apply]
   congr
 #align exterior_algebra.lift_alternating_ι ExteriorAlgebra.liftAlternating_ι
+-/
 
+#print ExteriorAlgebra.liftAlternating_ι_mul /-
 theorem liftAlternating_ι_mul (f : ∀ i, AlternatingMap R M N (Fin i)) (m : M)
     (x : ExteriorAlgebra R M) :
     liftAlternating f (ι R m * x) = liftAlternating (fun i => (f i.succ).curryLeft m) x :=
@@ -87,7 +94,9 @@ theorem liftAlternating_ι_mul (f : ∀ i, AlternatingMap R M N (Fin i)) (m : M)
   rw [foldl_mul, foldl_ι]
   rfl
 #align exterior_algebra.lift_alternating_ι_mul ExteriorAlgebra.liftAlternating_ι_mul
+-/
 
+#print ExteriorAlgebra.liftAlternating_one /-
 @[simp]
 theorem liftAlternating_one (f : ∀ i, AlternatingMap R M N (Fin i)) :
     liftAlternating f (1 : ExteriorAlgebra R M) = f 0 0 :=
@@ -95,13 +104,17 @@ theorem liftAlternating_one (f : ∀ i, AlternatingMap R M N (Fin i)) :
   dsimp [lift_alternating]
   rw [foldl_one]
 #align exterior_algebra.lift_alternating_one ExteriorAlgebra.liftAlternating_one
+-/
 
+#print ExteriorAlgebra.liftAlternating_algebraMap /-
 @[simp]
 theorem liftAlternating_algebraMap (f : ∀ i, AlternatingMap R M N (Fin i)) (r : R) :
     liftAlternating f (algebraMap _ (ExteriorAlgebra R M) r) = r • f 0 0 := by
   rw [Algebra.algebraMap_eq_smul_one, map_smul, lift_alternating_one]
 #align exterior_algebra.lift_alternating_algebra_map ExteriorAlgebra.liftAlternating_algebraMap
+-/
 
+#print ExteriorAlgebra.liftAlternating_apply_ιMulti /-
 @[simp]
 theorem liftAlternating_apply_ιMulti {n : ℕ} (f : ∀ i, AlternatingMap R M N (Fin i))
     (v : Fin n → M) : liftAlternating f (ιMulti R n v) = f n v :=
@@ -114,13 +127,17 @@ theorem liftAlternating_apply_ιMulti {n : ℕ} (f : ∀ i, AlternatingMap R M N
     congr
     exact Matrix.cons_head_tail _
 #align exterior_algebra.lift_alternating_apply_ι_multi ExteriorAlgebra.liftAlternating_apply_ιMulti
+-/
 
+#print ExteriorAlgebra.liftAlternating_comp_ιMulti /-
 @[simp]
 theorem liftAlternating_comp_ιMulti {n : ℕ} (f : ∀ i, AlternatingMap R M N (Fin i)) :
     (liftAlternating f).compAlternatingMap (ιMulti R n) = f n :=
   AlternatingMap.ext <| liftAlternating_apply_ιMulti f
 #align exterior_algebra.lift_alternating_comp_ι_multi ExteriorAlgebra.liftAlternating_comp_ιMulti
+-/
 
+#print ExteriorAlgebra.liftAlternating_comp /-
 @[simp]
 theorem liftAlternating_comp (g : N →ₗ[R] N') (f : ∀ i, AlternatingMap R M N (Fin i)) :
     (liftAlternating fun i => g.compAlternatingMap (f i)) = g ∘ₗ liftAlternating f :=
@@ -135,7 +152,9 @@ theorem liftAlternating_comp (g : N →ₗ[R] N') (f : ∀ i, AlternatingMap R M
   · rw [lift_alternating_ι_mul, lift_alternating_ι_mul, ← hx]
     simp_rw [AlternatingMap.curryLeft_compAlternatingMap]
 #align exterior_algebra.lift_alternating_comp ExteriorAlgebra.liftAlternating_comp
+-/
 
+#print ExteriorAlgebra.liftAlternating_ιMulti /-
 @[simp]
 theorem liftAlternating_ιMulti :
     liftAlternating (ι_multi R) = (LinearMap.id : ExteriorAlgebra R M →ₗ[R] ExteriorAlgebra R M) :=
@@ -149,7 +168,9 @@ theorem liftAlternating_ιMulti :
     simp_rw [lift_alternating_ι_mul, ι_multi_succ_curry_left, lift_alternating_comp,
       LinearMap.comp_apply, LinearMap.mulLeft_apply, hx]
 #align exterior_algebra.lift_alternating_ι_multi ExteriorAlgebra.liftAlternating_ιMulti
+-/
 
+#print ExteriorAlgebra.liftAlternatingEquiv /-
 /-- `exterior_algebra.lift_alternating` is an equivalence. -/
 @[simps apply symm_apply]
 def liftAlternatingEquiv : (∀ i, AlternatingMap R M N (Fin i)) ≃ₗ[R] ExteriorAlgebra R M →ₗ[R] N
@@ -162,7 +183,9 @@ def liftAlternatingEquiv : (∀ i, AlternatingMap R M N (Fin i)) ≃ₗ[R] Exter
   right_inv F :=
     (liftAlternating_comp _ _).trans <| by rw [lift_alternating_ι_multi, LinearMap.comp_id]
 #align exterior_algebra.lift_alternating_equiv ExteriorAlgebra.liftAlternatingEquiv
+-/
 
+#print ExteriorAlgebra.lhom_ext /-
 /-- To show that two linear maps from the exterior algebra agree, it suffices to show they agree on
 the exterior powers.
 
@@ -172,6 +195,7 @@ theorem lhom_ext ⦃f g : ExteriorAlgebra R M →ₗ[R] N⦄
     (h : ∀ i, f.compAlternatingMap (ιMulti R i) = g.compAlternatingMap (ιMulti R i)) : f = g :=
   liftAlternatingEquiv.symm.Injective <| funext h
 #align exterior_algebra.lhom_ext ExteriorAlgebra.lhom_ext
+-/
 
 end ExteriorAlgebra

ce11c3c2

bump to nightly-2023-06-05-16

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

43f0fba3

Diff

@@ -127,7 +127,7 @@ theorem liftAlternating_comp (g : N →ₗ[R] N') (f : ∀ i, AlternatingMap R M
   by
   ext v
   rw [LinearMap.comp_apply]
-  induction' v using CliffordAlgebra.leftInduction with r x y hx hy x m hx generalizing f
+  induction' v using CliffordAlgebra.left_induction with r x y hx hy x m hx generalizing f
   ·
     rw [lift_alternating_algebra_map, lift_alternating_algebra_map, map_smul,
       LinearMap.compAlternatingMap_apply]
@@ -142,7 +142,7 @@ theorem liftAlternating_ιMulti :
   by
   ext v
   dsimp
-  induction' v using CliffordAlgebra.leftInduction with r x y hx hy x m hx
+  induction' v using CliffordAlgebra.left_induction with r x y hx hy x m hx
   · rw [lift_alternating_algebra_map, ι_multi_zero_apply, Algebra.algebraMap_eq_smul_one]
   · rw [map_add, hx, hy]
   ·

ce11c3c2

bump to nightly-2023-03-31-02

mathlib commit https://github.com/leanprover-community/mathlib/commit/ce11c3c2a285bbe6937e26d9792fda4e51f3fe1a

c3ffa91f

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.of_alternating
-! leanprover-community/mathlib commit 9264b15ee696b7ca83f13c8ad67c83d6eb70b730
+! leanprover-community/mathlib commit ce11c3c2a285bbe6937e26d9792fda4e51f3fe1a
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -35,8 +35,8 @@ variable [CommRing R] [AddCommGroup M] [AddCommGroup N] [AddCommGroup N']
 variable [Module R M] [Module R N] [Module R N']
 
 -- This instance can't be found where it's needed if we don't remind lean that it exists.
-instance AlternatingMap.moduleAddCommGroup {ι : Type _} [DecidableEq ι] :
-    Module R (AlternatingMap R M N ι) := by infer_instance
+instance AlternatingMap.moduleAddCommGroup {ι : Type _} : Module R (AlternatingMap R M N ι) := by
+  infer_instance
 #align alternating_map.module_add_comm_group AlternatingMap.moduleAddCommGroup
 
 namespace ExteriorAlgebra

9264b15e

bump to nightly-2023-02-21-16

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

1107b979

Changes in mathlib4

mathlib3

mathlib4

ce11c3c2

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

@@ -26,9 +26,7 @@ import Mathlib.LinearAlgebra.ExteriorAlgebra.Basic
 
 
 variable {R M N N' : Type*}
-
 variable [CommRing R] [AddCommGroup M] [AddCommGroup N] [AddCommGroup N']
-
 variable [Module R M] [Module R N] [Module R N']
 
 -- This instance can't be found where it's needed if we don't remind lean that it exists.

ce11c3c2

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

@@ -72,7 +72,7 @@ theorem liftAlternating_ι (f : ∀ i, M [⋀^Fin i]→ₗ[R] N) (m : M) :
   dsimp [liftAlternating]
   rw [foldl_ι, LinearMap.mk₂_apply, AlternatingMap.curryLeft_apply_apply]
   congr
-  -- porting note: In Lean 3, `congr` could use the `[Subsingleton (Fin 0 → M)]` instance to finish
+  -- Porting note: In Lean 3, `congr` could use the `[Subsingleton (Fin 0 → M)]` instance to finish
   -- the proof. Here, the instance can be synthesized but `congr` does not use it so the following
   -- line is provided.
   rw [Matrix.zero_empty]
@@ -105,9 +105,9 @@ theorem liftAlternating_algebraMap (f : ∀ i, M [⋀^Fin i]→ₗ[R] N) (r : R)
 theorem liftAlternating_apply_ιMulti {n : ℕ} (f : ∀ i, M [⋀^Fin i]→ₗ[R] N)
     (v : Fin n → M) : liftAlternating (R := R) (M := M) (N := N) f (ιMulti R n v) = f n v := by
   rw [ιMulti_apply]
-  -- porting note: `v` is generalized automatically so it was removed from the next line
+  -- Porting note: `v` is generalized automatically so it was removed from the next line
   induction' n with n ih generalizing f
-  · -- porting note: Lean does not automatically synthesize the instance
+  · -- Porting note: Lean does not automatically synthesize the instance
     -- `[Subsingleton (Fin 0 → M)]` which is needed for `Subsingleton.elim 0 v` on line 114.
     letI : Subsingleton (Fin 0 → M) := by infer_instance
     rw [List.ofFn_zero, List.prod_nil, liftAlternating_one, Subsingleton.elim 0 v]

ce11c3c2

fix: denote alternating map by ⋀, not Λ (#11064)

That is, \bigwedge, not \Lambda

Co-authored-by: Richard Copley <rcopley@gmail.com> Co-authored-by: Patrick Massot <patrickmassot@free.fr>

008d6e96

Diff

@@ -33,7 +33,7 @@ variable [Module R M] [Module R N] [Module R N']
 
 -- This instance can't be found where it's needed if we don't remind lean that it exists.
 instance AlternatingMap.instModuleAddCommGroup {ι : Type*} :
-    Module R (M [Λ^ι]→ₗ[R] N) := by
+    Module R (M [⋀^ι]→ₗ[R] N) := by
   infer_instance
 #align alternating_map.module_add_comm_group AlternatingMap.instModuleAddCommGroup
 
@@ -43,10 +43,10 @@ open CliffordAlgebra hiding ι
 
 /-- Build a map out of the exterior algebra given a collection of alternating maps acting on each
 exterior power -/
-def liftAlternating : (∀ i, M [Λ^Fin i]→ₗ[R] N) →ₗ[R] ExteriorAlgebra R M →ₗ[R] N := by
+def liftAlternating : (∀ i, M [⋀^Fin i]→ₗ[R] N) →ₗ[R] ExteriorAlgebra R M →ₗ[R] N := by
   suffices
-    (∀ i, M [Λ^Fin i]→ₗ[R] N) →ₗ[R]
-      ExteriorAlgebra R M →ₗ[R] ∀ i, M [Λ^Fin i]→ₗ[R] N by
+    (∀ i, M [⋀^Fin i]→ₗ[R] N) →ₗ[R]
+      ExteriorAlgebra R M →ₗ[R] ∀ i, M [⋀^Fin i]→ₗ[R] N by
     refine' LinearMap.compr₂ this _
     refine' (LinearEquiv.toLinearMap _).comp (LinearMap.proj 0)
     exact AlternatingMap.constLinearEquivOfIsEmpty.symm
@@ -67,7 +67,7 @@ def liftAlternating : (∀ i, M [Λ^Fin i]→ₗ[R] N) →ₗ[R] ExteriorAlgebra
 #align exterior_algebra.lift_alternating ExteriorAlgebra.liftAlternating
 
 @[simp]
-theorem liftAlternating_ι (f : ∀ i, M [Λ^Fin i]→ₗ[R] N) (m : M) :
+theorem liftAlternating_ι (f : ∀ i, M [⋀^Fin i]→ₗ[R] N) (m : M) :
     liftAlternating (R := R) (M := M) (N := N) f (ι R m) = f 1 ![m] := by
   dsimp [liftAlternating]
   rw [foldl_ι, LinearMap.mk₂_apply, AlternatingMap.curryLeft_apply_apply]
@@ -78,7 +78,7 @@ theorem liftAlternating_ι (f : ∀ i, M [Λ^Fin i]→ₗ[R] N) (m : M) :
   rw [Matrix.zero_empty]
 #align exterior_algebra.lift_alternating_ι ExteriorAlgebra.liftAlternating_ι
 
-theorem liftAlternating_ι_mul (f : ∀ i, M [Λ^Fin i]→ₗ[R] N) (m : M)
+theorem liftAlternating_ι_mul (f : ∀ i, M [⋀^Fin i]→ₗ[R] N) (m : M)
     (x : ExteriorAlgebra R M) :
     liftAlternating (R := R) (M := M) (N := N) f (ι R m * x) =
     liftAlternating (R := R) (M := M) (N := N) (fun i => (f i.succ).curryLeft m) x := by
@@ -88,21 +88,21 @@ theorem liftAlternating_ι_mul (f : ∀ i, M [Λ^Fin i]→ₗ[R] N) (m : M)
 #align exterior_algebra.lift_alternating_ι_mul ExteriorAlgebra.liftAlternating_ι_mul
 
 @[simp]
-theorem liftAlternating_one (f : ∀ i, M [Λ^Fin i]→ₗ[R] N) :
+theorem liftAlternating_one (f : ∀ i, M [⋀^Fin i]→ₗ[R] N) :
     liftAlternating (R := R) (M := M) (N := N) f (1 : ExteriorAlgebra R M) = f 0 0 := by
   dsimp [liftAlternating]
   rw [foldl_one]
 #align exterior_algebra.lift_alternating_one ExteriorAlgebra.liftAlternating_one
 
 @[simp]
-theorem liftAlternating_algebraMap (f : ∀ i, M [Λ^Fin i]→ₗ[R] N) (r : R) :
+theorem liftAlternating_algebraMap (f : ∀ i, M [⋀^Fin i]→ₗ[R] N) (r : R) :
     liftAlternating (R := R) (M := M) (N := N) f (algebraMap _ (ExteriorAlgebra R M) r) =
     r • f 0 0 := by
   rw [Algebra.algebraMap_eq_smul_one, map_smul, liftAlternating_one]
 #align exterior_algebra.lift_alternating_algebra_map ExteriorAlgebra.liftAlternating_algebraMap
 
 @[simp]
-theorem liftAlternating_apply_ιMulti {n : ℕ} (f : ∀ i, M [Λ^Fin i]→ₗ[R] N)
+theorem liftAlternating_apply_ιMulti {n : ℕ} (f : ∀ i, M [⋀^Fin i]→ₗ[R] N)
     (v : Fin n → M) : liftAlternating (R := R) (M := M) (N := N) f (ιMulti R n v) = f n v := by
   rw [ιMulti_apply]
   -- porting note: `v` is generalized automatically so it was removed from the next line
@@ -118,13 +118,13 @@ theorem liftAlternating_apply_ιMulti {n : ℕ} (f : ∀ i, M [Λ^Fin i]→ₗ[R
 #align exterior_algebra.lift_alternating_apply_ι_multi ExteriorAlgebra.liftAlternating_apply_ιMulti
 
 @[simp]
-theorem liftAlternating_comp_ιMulti {n : ℕ} (f : ∀ i, M [Λ^Fin i]→ₗ[R] N) :
+theorem liftAlternating_comp_ιMulti {n : ℕ} (f : ∀ i, M [⋀^Fin i]→ₗ[R] N) :
     (liftAlternating (R := R) (M := M) (N := N) f).compAlternatingMap (ιMulti R n) = f n :=
   AlternatingMap.ext <| liftAlternating_apply_ιMulti f
 #align exterior_algebra.lift_alternating_comp_ι_multi ExteriorAlgebra.liftAlternating_comp_ιMulti
 
 @[simp]
-theorem liftAlternating_comp (g : N →ₗ[R] N') (f : ∀ i, M [Λ^Fin i]→ₗ[R] N) :
+theorem liftAlternating_comp (g : N →ₗ[R] N') (f : ∀ i, M [⋀^Fin i]→ₗ[R] N) :
     (liftAlternating (R := R) (M := M) (N := N') fun i => g.compAlternatingMap (f i)) =
     g ∘ₗ liftAlternating (R := R) (M := M) (N := N) f := by
   ext v
@@ -152,7 +152,7 @@ theorem liftAlternating_ιMulti :
 
 /-- `ExteriorAlgebra.liftAlternating` is an equivalence. -/
 @[simps apply symm_apply]
-def liftAlternatingEquiv : (∀ i, M [Λ^Fin i]→ₗ[R] N) ≃ₗ[R] ExteriorAlgebra R M →ₗ[R] N
+def liftAlternatingEquiv : (∀ i, M [⋀^Fin i]→ₗ[R] N) ≃ₗ[R] ExteriorAlgebra R M →ₗ[R] N
     where
   toFun := liftAlternating (R := R)
   map_add' := map_add _

ce11c3c2

chore: introduce notation for AlternatingMap (#8697)

Use M [Λ^ι]→ₗ[R] N for AlternatingMap R M N ι, similarly to the existing notation M [Λ^ι]→L[R] N for ContinuousAlternatingMap R M N ι.

ae010c18

Diff

@@ -33,7 +33,7 @@ variable [Module R M] [Module R N] [Module R N']
 
 -- This instance can't be found where it's needed if we don't remind lean that it exists.
 instance AlternatingMap.instModuleAddCommGroup {ι : Type*} :
-    Module R (AlternatingMap R M N ι) := by
+    Module R (M [Λ^ι]→ₗ[R] N) := by
   infer_instance
 #align alternating_map.module_add_comm_group AlternatingMap.instModuleAddCommGroup
 
@@ -43,10 +43,10 @@ open CliffordAlgebra hiding ι
 
 /-- Build a map out of the exterior algebra given a collection of alternating maps acting on each
 exterior power -/
-def liftAlternating : (∀ i, AlternatingMap R M N (Fin i)) →ₗ[R] ExteriorAlgebra R M →ₗ[R] N := by
+def liftAlternating : (∀ i, M [Λ^Fin i]→ₗ[R] N) →ₗ[R] ExteriorAlgebra R M →ₗ[R] N := by
   suffices
-    (∀ i, AlternatingMap R M N (Fin i)) →ₗ[R]
-      ExteriorAlgebra R M →ₗ[R] ∀ i, AlternatingMap R M N (Fin i) by
+    (∀ i, M [Λ^Fin i]→ₗ[R] N) →ₗ[R]
+      ExteriorAlgebra R M →ₗ[R] ∀ i, M [Λ^Fin i]→ₗ[R] N by
     refine' LinearMap.compr₂ this _
     refine' (LinearEquiv.toLinearMap _).comp (LinearMap.proj 0)
     exact AlternatingMap.constLinearEquivOfIsEmpty.symm
@@ -67,7 +67,7 @@ def liftAlternating : (∀ i, AlternatingMap R M N (Fin i)) →ₗ[R] ExteriorAl
 #align exterior_algebra.lift_alternating ExteriorAlgebra.liftAlternating
 
 @[simp]
-theorem liftAlternating_ι (f : ∀ i, AlternatingMap R M N (Fin i)) (m : M) :
+theorem liftAlternating_ι (f : ∀ i, M [Λ^Fin i]→ₗ[R] N) (m : M) :
     liftAlternating (R := R) (M := M) (N := N) f (ι R m) = f 1 ![m] := by
   dsimp [liftAlternating]
   rw [foldl_ι, LinearMap.mk₂_apply, AlternatingMap.curryLeft_apply_apply]
@@ -78,7 +78,7 @@ theorem liftAlternating_ι (f : ∀ i, AlternatingMap R M N (Fin i)) (m : M) :
   rw [Matrix.zero_empty]
 #align exterior_algebra.lift_alternating_ι ExteriorAlgebra.liftAlternating_ι
 
-theorem liftAlternating_ι_mul (f : ∀ i, AlternatingMap R M N (Fin i)) (m : M)
+theorem liftAlternating_ι_mul (f : ∀ i, M [Λ^Fin i]→ₗ[R] N) (m : M)
     (x : ExteriorAlgebra R M) :
     liftAlternating (R := R) (M := M) (N := N) f (ι R m * x) =
     liftAlternating (R := R) (M := M) (N := N) (fun i => (f i.succ).curryLeft m) x := by
@@ -88,21 +88,21 @@ theorem liftAlternating_ι_mul (f : ∀ i, AlternatingMap R M N (Fin i)) (m : M)
 #align exterior_algebra.lift_alternating_ι_mul ExteriorAlgebra.liftAlternating_ι_mul
 
 @[simp]
-theorem liftAlternating_one (f : ∀ i, AlternatingMap R M N (Fin i)) :
+theorem liftAlternating_one (f : ∀ i, M [Λ^Fin i]→ₗ[R] N) :
     liftAlternating (R := R) (M := M) (N := N) f (1 : ExteriorAlgebra R M) = f 0 0 := by
   dsimp [liftAlternating]
   rw [foldl_one]
 #align exterior_algebra.lift_alternating_one ExteriorAlgebra.liftAlternating_one
 
 @[simp]
-theorem liftAlternating_algebraMap (f : ∀ i, AlternatingMap R M N (Fin i)) (r : R) :
+theorem liftAlternating_algebraMap (f : ∀ i, M [Λ^Fin i]→ₗ[R] N) (r : R) :
     liftAlternating (R := R) (M := M) (N := N) f (algebraMap _ (ExteriorAlgebra R M) r) =
     r • f 0 0 := by
   rw [Algebra.algebraMap_eq_smul_one, map_smul, liftAlternating_one]
 #align exterior_algebra.lift_alternating_algebra_map ExteriorAlgebra.liftAlternating_algebraMap
 
 @[simp]
-theorem liftAlternating_apply_ιMulti {n : ℕ} (f : ∀ i, AlternatingMap R M N (Fin i))
+theorem liftAlternating_apply_ιMulti {n : ℕ} (f : ∀ i, M [Λ^Fin i]→ₗ[R] N)
     (v : Fin n → M) : liftAlternating (R := R) (M := M) (N := N) f (ιMulti R n v) = f n v := by
   rw [ιMulti_apply]
   -- porting note: `v` is generalized automatically so it was removed from the next line
@@ -118,13 +118,13 @@ theorem liftAlternating_apply_ιMulti {n : ℕ} (f : ∀ i, AlternatingMap R M N
 #align exterior_algebra.lift_alternating_apply_ι_multi ExteriorAlgebra.liftAlternating_apply_ιMulti
 
 @[simp]
-theorem liftAlternating_comp_ιMulti {n : ℕ} (f : ∀ i, AlternatingMap R M N (Fin i)) :
+theorem liftAlternating_comp_ιMulti {n : ℕ} (f : ∀ i, M [Λ^Fin i]→ₗ[R] N) :
     (liftAlternating (R := R) (M := M) (N := N) f).compAlternatingMap (ιMulti R n) = f n :=
   AlternatingMap.ext <| liftAlternating_apply_ιMulti f
 #align exterior_algebra.lift_alternating_comp_ι_multi ExteriorAlgebra.liftAlternating_comp_ιMulti
 
 @[simp]
-theorem liftAlternating_comp (g : N →ₗ[R] N') (f : ∀ i, AlternatingMap R M N (Fin i)) :
+theorem liftAlternating_comp (g : N →ₗ[R] N') (f : ∀ i, M [Λ^Fin i]→ₗ[R] N) :
     (liftAlternating (R := R) (M := M) (N := N') fun i => g.compAlternatingMap (f i)) =
     g ∘ₗ liftAlternating (R := R) (M := M) (N := N) f := by
   ext v
@@ -152,7 +152,7 @@ theorem liftAlternating_ιMulti :
 
 /-- `ExteriorAlgebra.liftAlternating` is an equivalence. -/
 @[simps apply symm_apply]
-def liftAlternatingEquiv : (∀ i, AlternatingMap R M N (Fin i)) ≃ₗ[R] ExteriorAlgebra R M →ₗ[R] N
+def liftAlternatingEquiv : (∀ i, M [Λ^Fin i]→ₗ[R] N) ≃ₗ[R] ExteriorAlgebra R M →ₗ[R] N
     where
   toFun := liftAlternating (R := R)
   map_add' := map_add _

ce11c3c2

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

@@ -25,14 +25,14 @@ import Mathlib.LinearAlgebra.ExteriorAlgebra.Basic
 -/
 
 
-variable {R M N N' : Type _}
+variable {R M N N' : Type*}
 
 variable [CommRing R] [AddCommGroup M] [AddCommGroup N] [AddCommGroup N']
 
 variable [Module R M] [Module R N] [Module R N']
 
 -- This instance can't be found where it's needed if we don't remind lean that it exists.
-instance AlternatingMap.instModuleAddCommGroup {ι : Type _} :
+instance AlternatingMap.instModuleAddCommGroup {ι : Type*} :
     Module R (AlternatingMap R M N ι) := by
   infer_instance
 #align alternating_map.module_add_comm_group AlternatingMap.instModuleAddCommGroup

ce11c3c2

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) 2022 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.of_alternating
-! leanprover-community/mathlib commit ce11c3c2a285bbe6937e26d9792fda4e51f3fe1a
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.LinearAlgebra.CliffordAlgebra.Fold
 import Mathlib.LinearAlgebra.ExteriorAlgebra.Basic
 
+#align_import linear_algebra.exterior_algebra.of_alternating from "leanprover-community/mathlib"@"ce11c3c2a285bbe6937e26d9792fda4e51f3fe1a"
+
 /-!
 # Extending an alternating map to the exterior algebra

ce11c3c2

chore: tidy various files (#5628)

3282e2f7

Diff

@@ -35,9 +35,10 @@ variable [CommRing R] [AddCommGroup M] [AddCommGroup N] [AddCommGroup N']
 variable [Module R M] [Module R N] [Module R N']
 
 -- This instance can't be found where it's needed if we don't remind lean that it exists.
-instance AlternatingMap.ModuleAddCommGroup {ι : Type _} : Module R (AlternatingMap R M N ι) := by
+instance AlternatingMap.instModuleAddCommGroup {ι : Type _} :
+    Module R (AlternatingMap R M N ι) := by
   infer_instance
-#align alternating_map.module_add_comm_group AlternatingMap.ModuleAddCommGroup
+#align alternating_map.module_add_comm_group AlternatingMap.instModuleAddCommGroup
 
 namespace ExteriorAlgebra

ce11c3c2

feat: port LinearAlgebra.ExteriorAlgebra.OfAlternating (#5465)

01e12e77

`linear_algebra.exterior_algebra.of_alternating` ⟷ `Mathlib.LinearAlgebra.ExteriorAlgebra.OfAlternating`

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Dependencies 10 + 643

linear_algebra.exterior_algebra.of_alternating ⟷ Mathlib.LinearAlgebra.ExteriorAlgebra.OfAlternating

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Dependencies 10 + 643

`linear_algebra.exterior_algebra.of_alternating` ⟷ `Mathlib.LinearAlgebra.ExteriorAlgebra.OfAlternating`