linear_algebra.tensor_algebra.to_tensor_power

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

d97a0c9f

(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.TensorAlgebra.Basic
-import Mathbin.LinearAlgebra.TensorPower
+import LinearAlgebra.TensorAlgebra.Basic
+import LinearAlgebra.TensorPower
 
 #align_import linear_algebra.tensor_algebra.to_tensor_power from "leanprover-community/mathlib"@"1a51edf13debfcbe223fa06b1cb353b9ed9751cc"

1a51edf1

bump to nightly-2023-09-17-06

mathlib commit https://github.com/leanprover-community/mathlib/commit/001ffdc42920050657fd45bd2b8bfbec8eaaeb29

a754d78a

Diff

@@ -176,7 +176,7 @@ theorem TensorPower.list_prod_gradedMonoid_mk_single (n : ℕ) (x : Fin n → M)
     simp_rw [Fin.append_left_eq_cons, Function.comp]
     congr 1 with i
     congr 1
-    rw [Fin.castIso_trans, Fin.castIso_refl, OrderIso.refl_apply]
+    rw [Fin.cast_trans, Fin.castIso_refl, OrderIso.refl_apply]
 #align tensor_power.list_prod_graded_monoid_mk_single TensorPower.list_prod_gradedMonoid_mk_single
 -/

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.tensor_algebra.to_tensor_power
-! 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.TensorAlgebra.Basic
 import Mathbin.LinearAlgebra.TensorPower
 
+#align_import linear_algebra.tensor_algebra.to_tensor_power from "leanprover-community/mathlib"@"1a51edf13debfcbe223fa06b1cb353b9ed9751cc"
+
 /-!
 # Tensor algebras as direct sums of tensor powers

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.tensor_algebra.to_tensor_power
-! leanprover-community/mathlib commit d97a0c9f7a7efe6d76d652c5a6b7c9c634b70e0a
+! 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.LinearAlgebra.TensorPower
 /-!
 # Tensor algebras as direct sums of tensor powers
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 In this file we show that `tensor_algebra R M` is isomorphic to a direct sum of tensor powers, as
 `tensor_algebra.equiv_direct_sum`.
 -/

d97a0c9f

bump to nightly-2023-07-06-17

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

ebc47879

Diff

@@ -25,23 +25,30 @@ variable {R M : Type _} [CommSemiring R] [AddCommMonoid M] [Module R M]
 
 namespace TensorPower
 
+#print TensorPower.toTensorAlgebra /-
 /-- The canonical embedding from a tensor power to the tensor algebra -/
 def toTensorAlgebra {n} : (⨂[R]^n) M →ₗ[R] TensorAlgebra R M :=
   PiTensorProduct.lift (TensorAlgebra.tprod R M n)
 #align tensor_power.to_tensor_algebra TensorPower.toTensorAlgebra
+-/
 
+#print TensorPower.toTensorAlgebra_tprod /-
 @[simp]
 theorem toTensorAlgebra_tprod {n} (x : Fin n → M) :
     TensorPower.toTensorAlgebra (PiTensorProduct.tprod R x) = TensorAlgebra.tprod R M n x :=
   PiTensorProduct.lift.tprod _
 #align tensor_power.to_tensor_algebra_tprod TensorPower.toTensorAlgebra_tprod
+-/
 
+#print TensorPower.toTensorAlgebra_gOne /-
 @[simp]
 theorem toTensorAlgebra_gOne :
     (@GradedMonoid.GOne.one _ (fun n => (⨂[R]^n) M) _ _).toTensorAlgebra = 1 :=
   TensorPower.toTensorAlgebra_tprod _
 #align tensor_power.to_tensor_algebra_ghas_one TensorPower.toTensorAlgebra_gOne
+-/
 
+#print TensorPower.toTensorAlgebra_gMul /-
 @[simp]
 theorem toTensorAlgebra_gMul {i j} (a : (⨂[R]^i) M) (b : (⨂[R]^j) M) :
     (@GradedMonoid.GMul.mul _ (fun n => (⨂[R]^n) M) _ _ _ _ a b).toTensorAlgebra =
@@ -62,7 +69,9 @@ theorem toTensorAlgebra_gMul {i j} (a : (⨂[R]^i) M) (b : (⨂[R]^j) M) :
   rw [← List.map_ofFn _ (TensorAlgebra.ι R), ← List.map_ofFn _ (TensorAlgebra.ι R), ←
     List.map_ofFn _ (TensorAlgebra.ι R), ← List.map_append, List.ofFn_fin_append]
 #align tensor_power.to_tensor_algebra_ghas_mul TensorPower.toTensorAlgebra_gMul
+-/
 
+#print TensorPower.toTensorAlgebra_galgebra_toFun /-
 @[simp]
 theorem toTensorAlgebra_galgebra_toFun (r : R) :
     (@DirectSum.GAlgebra.toFun _ R (fun n => (⨂[R]^n) M) _ _ _ _ _ _ _ r).toTensorAlgebra =
@@ -71,63 +80,81 @@ theorem toTensorAlgebra_galgebra_toFun (r : R) :
   rw [TensorPower.galgebra_toFun_def, TensorPower.algebraMap₀_eq_smul_one, LinearMap.map_smul,
     TensorPower.toTensorAlgebra_gOne, Algebra.algebraMap_eq_smul_one]
 #align tensor_power.to_tensor_algebra_galgebra_to_fun TensorPower.toTensorAlgebra_galgebra_toFun
+-/
 
 end TensorPower
 
 namespace TensorAlgebra
 
+#print TensorAlgebra.ofDirectSum /-
 /-- The canonical map from a direct sum of tensor powers to the tensor algebra. -/
 def ofDirectSum : (⨁ n, (⨂[R]^n) M) →ₐ[R] TensorAlgebra R M :=
   DirectSum.toAlgebra _ _ (fun n => TensorPower.toTensorAlgebra) TensorPower.toTensorAlgebra_gOne
     (fun i j => TensorPower.toTensorAlgebra_gMul) TensorPower.toTensorAlgebra_galgebra_toFun
 #align tensor_algebra.of_direct_sum TensorAlgebra.ofDirectSum
+-/
 
+#print TensorAlgebra.ofDirectSum_of_tprod /-
 @[simp]
 theorem ofDirectSum_of_tprod {n} (x : Fin n → M) :
     ofDirectSum (DirectSum.of _ n (PiTensorProduct.tprod R x)) = tprod R M n x :=
   (DirectSum.toAddMonoid_of _ _ _).trans (TensorPower.toTensorAlgebra_tprod _)
 #align tensor_algebra.of_direct_sum_of_tprod TensorAlgebra.ofDirectSum_of_tprod
+-/
 
+#print TensorAlgebra.toDirectSum /-
 /-- The canonical map from the tensor algebra to a direct sum of tensor powers. -/
 def toDirectSum : TensorAlgebra R M →ₐ[R] ⨁ n, (⨂[R]^n) M :=
   TensorAlgebra.lift R <|
     DirectSum.lof R ℕ (fun n => (⨂[R]^n) M) _ ∘ₗ
       (LinearEquiv.symm <| PiTensorProduct.subsingletonEquiv (0 : Fin 1) : M ≃ₗ[R] _).toLinearMap
 #align tensor_algebra.to_direct_sum TensorAlgebra.toDirectSum
+-/
 
+#print TensorAlgebra.toDirectSum_ι /-
 @[simp]
 theorem toDirectSum_ι (x : M) :
     toDirectSum (ι R x) =
       DirectSum.of (fun n => (⨂[R]^n) M) _ (PiTensorProduct.tprod R fun _ : Fin 1 => x) :=
   TensorAlgebra.lift_ι_apply _ _
 #align tensor_algebra.to_direct_sum_ι TensorAlgebra.toDirectSum_ι
+-/
 
+#print TensorAlgebra.ofDirectSum_comp_toDirectSum /-
 theorem ofDirectSum_comp_toDirectSum :
     ofDirectSum.comp toDirectSum = AlgHom.id R (TensorAlgebra R M) :=
   by
   ext
   simp [DirectSum.lof_eq_of, tprod_apply]
 #align tensor_algebra.of_direct_sum_comp_to_direct_sum TensorAlgebra.ofDirectSum_comp_toDirectSum
+-/
 
+#print TensorAlgebra.ofDirectSum_toDirectSum /-
 @[simp]
 theorem ofDirectSum_toDirectSum (x : TensorAlgebra R M) : ofDirectSum x.toDirectSum = x :=
   AlgHom.congr_fun ofDirectSum_comp_toDirectSum x
 #align tensor_algebra.of_direct_sum_to_direct_sum TensorAlgebra.ofDirectSum_toDirectSum
+-/
 
+#print TensorAlgebra.mk_reindex_cast /-
 @[simp]
 theorem mk_reindex_cast {n m : ℕ} (h : n = m) (x : (⨂[R]^n) M) :
     GradedMonoid.mk m (PiTensorProduct.reindex R M (Equiv.cast <| congr_arg Fin h) x) =
       GradedMonoid.mk n x :=
   Eq.symm (PiTensorProduct.gradedMonoid_eq_of_reindex_cast h rfl)
 #align tensor_algebra.mk_reindex_cast TensorAlgebra.mk_reindex_cast
+-/
 
+#print TensorAlgebra.mk_reindex_fin_cast /-
 @[simp]
-theorem mk_reindex_fin_castIso {n m : ℕ} (h : n = m) (x : (⨂[R]^n) M) :
+theorem mk_reindex_fin_cast {n m : ℕ} (h : n = m) (x : (⨂[R]^n) M) :
     GradedMonoid.mk m (PiTensorProduct.reindex R M (Fin.castIso h).toEquiv x) =
       GradedMonoid.mk n x :=
   by rw [Fin.castIso_to_equiv, mk_reindex_cast h]
-#align tensor_algebra.mk_reindex_fin_cast TensorAlgebra.mk_reindex_fin_castIso
+#align tensor_algebra.mk_reindex_fin_cast TensorAlgebra.mk_reindex_fin_cast
+-/
 
+#print TensorPower.list_prod_gradedMonoid_mk_single /-
 /-- The product of tensor products made of a single vector is the same as a single product of
 all the vectors. -/
 theorem TensorPower.list_prod_gradedMonoid_mk_single (n : ℕ) (x : Fin n → M) :
@@ -151,7 +178,9 @@ theorem TensorPower.list_prod_gradedMonoid_mk_single (n : ℕ) (x : Fin n → M)
     congr 1
     rw [Fin.castIso_trans, Fin.castIso_refl, OrderIso.refl_apply]
 #align tensor_power.list_prod_graded_monoid_mk_single TensorPower.list_prod_gradedMonoid_mk_single
+-/
 
+#print TensorAlgebra.toDirectSum_tensorPower_tprod /-
 theorem toDirectSum_tensorPower_tprod {n} (x : Fin n → M) :
     toDirectSum (tprod R M n x) = DirectSum.of _ n (PiTensorProduct.tprod R x) :=
   by
@@ -163,25 +192,32 @@ theorem toDirectSum_tensorPower_tprod {n} (x : Fin n → M) :
   rw [GradedMonoid.mk_list_dProd]
   rw [TensorPower.list_prod_gradedMonoid_mk_single]
 #align tensor_algebra.to_direct_sum_tensor_power_tprod TensorAlgebra.toDirectSum_tensorPower_tprod
+-/
 
+#print TensorAlgebra.toDirectSum_comp_ofDirectSum /-
 theorem toDirectSum_comp_ofDirectSum :
     toDirectSum.comp ofDirectSum = AlgHom.id R (⨁ n, (⨂[R]^n) M) :=
   by
   ext
   simp [DirectSum.lof_eq_of, -tprod_apply, to_direct_sum_tensor_power_tprod]
 #align tensor_algebra.to_direct_sum_comp_of_direct_sum TensorAlgebra.toDirectSum_comp_ofDirectSum
+-/
 
+#print TensorAlgebra.toDirectSum_ofDirectSum /-
 @[simp]
 theorem toDirectSum_ofDirectSum (x : ⨁ n, (⨂[R]^n) M) : (ofDirectSum x).toDirectSum = x :=
   AlgHom.congr_fun toDirectSum_comp_ofDirectSum x
 #align tensor_algebra.to_direct_sum_of_direct_sum TensorAlgebra.toDirectSum_ofDirectSum
+-/
 
+#print TensorAlgebra.equivDirectSum /-
 /-- The tensor algebra is isomorphic to a direct sum of tensor powers. -/
 @[simps]
 def equivDirectSum : TensorAlgebra R M ≃ₐ[R] ⨁ n, (⨂[R]^n) M :=
   AlgEquiv.ofAlgHom toDirectSum ofDirectSum toDirectSum_comp_ofDirectSum
     ofDirectSum_comp_toDirectSum
 #align tensor_algebra.equiv_direct_sum TensorAlgebra.equivDirectSum
+-/
 
 end TensorAlgebra

d97a0c9f

bump to nightly-2023-07-04-19

mathlib commit https://github.com/leanprover-community/mathlib/commit/728ef9dbb281241906f25cbeb30f90d83e0bb451

4217d5f4

Diff

@@ -122,10 +122,11 @@ theorem mk_reindex_cast {n m : ℕ} (h : n = m) (x : (⨂[R]^n) M) :
 #align tensor_algebra.mk_reindex_cast TensorAlgebra.mk_reindex_cast
 
 @[simp]
-theorem mk_reindex_fin_cast {n m : ℕ} (h : n = m) (x : (⨂[R]^n) M) :
-    GradedMonoid.mk m (PiTensorProduct.reindex R M (Fin.cast h).toEquiv x) = GradedMonoid.mk n x :=
-  by rw [Fin.cast_to_equiv, mk_reindex_cast h]
-#align tensor_algebra.mk_reindex_fin_cast TensorAlgebra.mk_reindex_fin_cast
+theorem mk_reindex_fin_castIso {n m : ℕ} (h : n = m) (x : (⨂[R]^n) M) :
+    GradedMonoid.mk m (PiTensorProduct.reindex R M (Fin.castIso h).toEquiv x) =
+      GradedMonoid.mk n x :=
+  by rw [Fin.castIso_to_equiv, mk_reindex_cast h]
+#align tensor_algebra.mk_reindex_fin_cast TensorAlgebra.mk_reindex_fin_castIso
 
 /-- The product of tensor products made of a single vector is the same as a single product of
 all the vectors. -/
@@ -148,7 +149,7 @@ theorem TensorPower.list_prod_gradedMonoid_mk_single (n : ℕ) (x : Fin n → M)
     simp_rw [Fin.append_left_eq_cons, Function.comp]
     congr 1 with i
     congr 1
-    rw [Fin.cast_trans, Fin.cast_refl, OrderIso.refl_apply]
+    rw [Fin.castIso_trans, Fin.castIso_refl, OrderIso.refl_apply]
 #align tensor_power.list_prod_graded_monoid_mk_single TensorPower.list_prod_gradedMonoid_mk_single
 
 theorem toDirectSum_tensorPower_tprod {n} (x : Fin n → M) :

d97a0c9f

bump to nightly-2023-06-20-01

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

9b351f8c

Diff

@@ -52,7 +52,7 @@ theorem toTensorAlgebra_gMul {i j} (a : (⨂[R]^i) M) (b : (⨂[R]^j) M) :
     LinearMap.compl₂_apply, ← LinearMap.comp_apply]
   refine' LinearMap.congr_fun (LinearMap.congr_fun _ a) b
   clear a b
-  ext (a b)
+  ext a b
   simp only [LinearMap.compr₂_apply, LinearMap.mul_apply', LinearMap.compl₂_apply,
     LinearMap.comp_apply, LinearMap.compMultilinearMap_apply, PiTensorProduct.lift.tprod,
     TensorPower.tprod_mul_tprod, TensorPower.toTensorAlgebra_tprod, TensorAlgebra.tprod_apply, ←

d97a0c9f

bump to nightly-2023-06-04-18

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

3fb4268b

Diff

@@ -37,18 +37,18 @@ theorem toTensorAlgebra_tprod {n} (x : Fin n → M) :
 #align tensor_power.to_tensor_algebra_tprod TensorPower.toTensorAlgebra_tprod
 
 @[simp]
-theorem toTensorAlgebra_ghasOne :
+theorem toTensorAlgebra_gOne :
     (@GradedMonoid.GOne.one _ (fun n => (⨂[R]^n) M) _ _).toTensorAlgebra = 1 :=
   TensorPower.toTensorAlgebra_tprod _
-#align tensor_power.to_tensor_algebra_ghas_one TensorPower.toTensorAlgebra_ghasOne
+#align tensor_power.to_tensor_algebra_ghas_one TensorPower.toTensorAlgebra_gOne
 
 @[simp]
-theorem toTensorAlgebra_ghasMul {i j} (a : (⨂[R]^i) M) (b : (⨂[R]^j) M) :
+theorem toTensorAlgebra_gMul {i j} (a : (⨂[R]^i) M) (b : (⨂[R]^j) M) :
     (@GradedMonoid.GMul.mul _ (fun n => (⨂[R]^n) M) _ _ _ _ a b).toTensorAlgebra =
       a.toTensorAlgebra * b.toTensorAlgebra :=
   by
   -- change `a` and `b` to `tprod R a` and `tprod R b`
-  rw [TensorPower.ghasMul_eq_coe_linearMap, ← LinearMap.compr₂_apply, ← @LinearMap.mul_apply' R, ←
+  rw [TensorPower.gMul_eq_coe_linearMap, ← LinearMap.compr₂_apply, ← @LinearMap.mul_apply' R, ←
     LinearMap.compl₂_apply, ← LinearMap.comp_apply]
   refine' LinearMap.congr_fun (LinearMap.congr_fun _ a) b
   clear a b
@@ -61,7 +61,7 @@ theorem toTensorAlgebra_ghasMul {i j} (a : (⨂[R]^i) M) (b : (⨂[R]^j) M) :
   congr
   rw [← List.map_ofFn _ (TensorAlgebra.ι R), ← List.map_ofFn _ (TensorAlgebra.ι R), ←
     List.map_ofFn _ (TensorAlgebra.ι R), ← List.map_append, List.ofFn_fin_append]
-#align tensor_power.to_tensor_algebra_ghas_mul TensorPower.toTensorAlgebra_ghasMul
+#align tensor_power.to_tensor_algebra_ghas_mul TensorPower.toTensorAlgebra_gMul
 
 @[simp]
 theorem toTensorAlgebra_galgebra_toFun (r : R) :
@@ -69,7 +69,7 @@ theorem toTensorAlgebra_galgebra_toFun (r : R) :
       algebraMap _ _ r :=
   by
   rw [TensorPower.galgebra_toFun_def, TensorPower.algebraMap₀_eq_smul_one, LinearMap.map_smul,
-    TensorPower.toTensorAlgebra_ghasOne, Algebra.algebraMap_eq_smul_one]
+    TensorPower.toTensorAlgebra_gOne, Algebra.algebraMap_eq_smul_one]
 #align tensor_power.to_tensor_algebra_galgebra_to_fun TensorPower.toTensorAlgebra_galgebra_toFun
 
 end TensorPower
@@ -78,8 +78,8 @@ namespace TensorAlgebra
 
 /-- The canonical map from a direct sum of tensor powers to the tensor algebra. -/
 def ofDirectSum : (⨁ n, (⨂[R]^n) M) →ₐ[R] TensorAlgebra R M :=
-  DirectSum.toAlgebra _ _ (fun n => TensorPower.toTensorAlgebra) TensorPower.toTensorAlgebra_ghasOne
-    (fun i j => TensorPower.toTensorAlgebra_ghasMul) TensorPower.toTensorAlgebra_galgebra_toFun
+  DirectSum.toAlgebra _ _ (fun n => TensorPower.toTensorAlgebra) TensorPower.toTensorAlgebra_gOne
+    (fun i j => TensorPower.toTensorAlgebra_gMul) TensorPower.toTensorAlgebra_galgebra_toFun
 #align tensor_algebra.of_direct_sum TensorAlgebra.ofDirectSum
 
 @[simp]

d97a0c9f

bump to nightly-2023-05-28-18

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

8d353152

Diff

@@ -19,7 +19,7 @@ In this file we show that `tensor_algebra R M` is isomorphic to a direct sum of
 -/
 
 
-open DirectSum TensorProduct
+open scoped DirectSum TensorProduct
 
 variable {R M : Type _} [CommSemiring R] [AddCommMonoid M] [Module R M]

d97a0c9f

bump to nightly-2023-05-17-20

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

d85f0014

Diff

@@ -65,7 +65,7 @@ theorem toTensorAlgebra_ghasMul {i j} (a : (⨂[R]^i) M) (b : (⨂[R]^j) M) :
 
 @[simp]
 theorem toTensorAlgebra_galgebra_toFun (r : R) :
-    (@DirectSum.Galgebra.toFun _ R (fun n => (⨂[R]^n) M) _ _ _ _ _ _ _ r).toTensorAlgebra =
+    (@DirectSum.GAlgebra.toFun _ R (fun n => (⨂[R]^n) M) _ _ _ _ _ _ _ r).toTensorAlgebra =
       algebraMap _ _ r :=
   by
   rw [TensorPower.galgebra_toFun_def, TensorPower.algebraMap₀_eq_smul_one, LinearMap.map_smul,

d97a0c9f

bump to nightly-2023-03-31-02

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

c3ffa91f

Changes in mathlib4

mathlib3

mathlib4

d97a0c9f

chore: remove a few miscellaneous now-resolved porting notes (#12127)

fd252837

Diff

@@ -58,8 +58,7 @@ theorem toTensorAlgebra_gMul {i j} (a : (⨂[R]^i) M) (b : (⨂[R]^j) M) :
     TensorPower.tprod_mul_tprod, TensorPower.toTensorAlgebra_tprod, TensorAlgebra.tprod_apply, ←
     gMul_eq_coe_linearMap]
   refine' Eq.trans _ List.prod_append
-  -- Porting note: was `congr`
-  apply congr_arg
+  congr
   -- Porting note: `erw` for `Function.comp`
   erw [← List.map_ofFn _ (TensorAlgebra.ι R), ← List.map_ofFn _ (TensorAlgebra.ι R), ←
     List.map_ofFn _ (TensorAlgebra.ι R), ← List.map_append, List.ofFn_fin_append]

d97a0c9f

fix(LinearAlgebra/TensorPower): correct notation precedence (#11062)

This removes some ugly parens that were introduced during porting

2353c4e3

Diff

@@ -24,7 +24,7 @@ variable {R M : Type*} [CommSemiring R] [AddCommMonoid M] [Module R M]
 namespace TensorPower
 
 /-- The canonical embedding from a tensor power to the tensor algebra -/
-def toTensorAlgebra {n} : (⨂[R]^n) M →ₗ[R] TensorAlgebra R M :=
+def toTensorAlgebra {n} : ⨂[R]^n M →ₗ[R] TensorAlgebra R M :=
   PiTensorProduct.lift (TensorAlgebra.tprod R M n)
 #align tensor_power.to_tensor_algebra TensorPower.toTensorAlgebra
 
@@ -36,13 +36,13 @@ theorem toTensorAlgebra_tprod {n} (x : Fin n → M) :
 
 @[simp]
 theorem toTensorAlgebra_gOne :
-    TensorPower.toTensorAlgebra (@GradedMonoid.GOne.one _ (fun n => (⨂[R]^n) M) _ _) = 1 :=
+    TensorPower.toTensorAlgebra (@GradedMonoid.GOne.one _ (fun n => ⨂[R]^n M) _ _) = 1 :=
   TensorPower.toTensorAlgebra_tprod _
 #align tensor_power.to_tensor_algebra_ghas_one TensorPower.toTensorAlgebra_gOne
 
 @[simp]
 theorem toTensorAlgebra_gMul {i j} (a : (⨂[R]^i) M) (b : (⨂[R]^j) M) :
-    TensorPower.toTensorAlgebra (@GradedMonoid.GMul.mul _ (fun n => (⨂[R]^n) M) _ _ _ _ a b) =
+    TensorPower.toTensorAlgebra (@GradedMonoid.GMul.mul _ (fun n => ⨂[R]^n M) _ _ _ _ a b) =
       TensorPower.toTensorAlgebra a * TensorPower.toTensorAlgebra b := by
   -- change `a` and `b` to `tprod R a` and `tprod R b`
   rw [TensorPower.gMul_eq_coe_linearMap, ← LinearMap.compr₂_apply, ← @LinearMap.mul_apply' R, ←
@@ -67,7 +67,7 @@ theorem toTensorAlgebra_gMul {i j} (a : (⨂[R]^i) M) (b : (⨂[R]^j) M) :
 
 @[simp]
 theorem toTensorAlgebra_galgebra_toFun (r : R) :
-    TensorPower.toTensorAlgebra (DirectSum.GAlgebra.toFun (R := R) (A := fun n => (⨂[R]^n) M) r) =
+    TensorPower.toTensorAlgebra (DirectSum.GAlgebra.toFun (R := R) (A := fun n => ⨂[R]^n M) r) =
       algebraMap _ _ r := by
   rw [TensorPower.galgebra_toFun_def, TensorPower.algebraMap₀_eq_smul_one, LinearMap.map_smul,
     TensorPower.toTensorAlgebra_gOne, Algebra.algebraMap_eq_smul_one]
@@ -78,7 +78,7 @@ end TensorPower
 namespace TensorAlgebra
 
 /-- The canonical map from a direct sum of tensor powers to the tensor algebra. -/
-def ofDirectSum : (⨁ n, (⨂[R]^n) M) →ₐ[R] TensorAlgebra R M :=
+def ofDirectSum : (⨁ n, ⨂[R]^n M) →ₐ[R] TensorAlgebra R M :=
   DirectSum.toAlgebra _ _ (fun _ => TensorPower.toTensorAlgebra) TensorPower.toTensorAlgebra_gOne
     (fun {_ _} => TensorPower.toTensorAlgebra_gMul)
 #align tensor_algebra.of_direct_sum TensorAlgebra.ofDirectSum
@@ -92,16 +92,16 @@ theorem ofDirectSum_of_tprod {n} (x : Fin n → M) :
 #align tensor_algebra.of_direct_sum_of_tprod TensorAlgebra.ofDirectSum_of_tprod
 
 /-- The canonical map from the tensor algebra to a direct sum of tensor powers. -/
-def toDirectSum : TensorAlgebra R M →ₐ[R] ⨁ n, (⨂[R]^n) M :=
+def toDirectSum : TensorAlgebra R M →ₐ[R] ⨁ n, ⨂[R]^n M :=
   TensorAlgebra.lift R <|
-    DirectSum.lof R ℕ (fun n => (⨂[R]^n) M) _ ∘ₗ
+    DirectSum.lof R ℕ (fun n => ⨂[R]^n M) _ ∘ₗ
       (LinearEquiv.symm <| PiTensorProduct.subsingletonEquiv (0 : Fin 1) : M ≃ₗ[R] _).toLinearMap
 #align tensor_algebra.to_direct_sum TensorAlgebra.toDirectSum
 
 @[simp]
 theorem toDirectSum_ι (x : M) :
     toDirectSum (ι R x) =
-      DirectSum.of (fun n => (⨂[R]^n) M) _ (PiTensorProduct.tprod R fun _ : Fin 1 => x) :=
+      DirectSum.of (fun n => ⨂[R]^n M) _ (PiTensorProduct.tprod R fun _ : Fin 1 => x) :=
   TensorAlgebra.lift_ι_apply _ _
 #align tensor_algebra.to_direct_sum_ι TensorAlgebra.toDirectSum_ι
 
@@ -118,7 +118,7 @@ theorem ofDirectSum_toDirectSum (x : TensorAlgebra R M) :
 #align tensor_algebra.of_direct_sum_to_direct_sum TensorAlgebra.ofDirectSum_toDirectSum
 
 @[simp, nolint simpNF] -- see std4#365 for the simpNF issue
-theorem mk_reindex_cast {n m : ℕ} (h : n = m) (x : (⨂[R]^n) M) :
+theorem mk_reindex_cast {n m : ℕ} (h : n = m) (x : ⨂[R]^n M) :
     GradedMonoid.mk (A := fun i => (⨂[R]^i) M) m
     (PiTensorProduct.reindex R (fun _ ↦ M) (Equiv.cast <| congr_arg Fin h) x) =
     GradedMonoid.mk n x :=
@@ -126,7 +126,7 @@ theorem mk_reindex_cast {n m : ℕ} (h : n = m) (x : (⨂[R]^n) M) :
 #align tensor_algebra.mk_reindex_cast TensorAlgebra.mk_reindex_cast
 
 @[simp]
-theorem mk_reindex_fin_cast {n m : ℕ} (h : n = m) (x : (⨂[R]^n) M) :
+theorem mk_reindex_fin_cast {n m : ℕ} (h : n = m) (x : ⨂[R]^n M) :
     GradedMonoid.mk (A := fun i => (⨂[R]^i) M) m
     (PiTensorProduct.reindex R (fun _ ↦ M) (Fin.castIso h).toEquiv x) = GradedMonoid.mk n x := by
   rw [Fin.castIso_to_equiv, mk_reindex_cast h]
@@ -137,7 +137,7 @@ all the vectors. -/
 theorem _root_.TensorPower.list_prod_gradedMonoid_mk_single (n : ℕ) (x : Fin n → M) :
     ((List.finRange n).map fun a =>
           (GradedMonoid.mk _ (PiTensorProduct.tprod R fun _ : Fin 1 => x a) :
-            GradedMonoid fun n => (⨂[R]^n) M)).prod =
+            GradedMonoid fun n => ⨂[R]^n M)).prod =
       GradedMonoid.mk n (PiTensorProduct.tprod R x) := by
   refine' Fin.consInduction _ _ x <;> clear x
   · rw [List.finRange_zero, List.map_nil, List.prod_nil]
@@ -164,20 +164,20 @@ theorem toDirectSum_tensorPower_tprod {n} (x : Fin n → M) :
 #align tensor_algebra.to_direct_sum_tensor_power_tprod TensorAlgebra.toDirectSum_tensorPower_tprod
 
 theorem toDirectSum_comp_ofDirectSum :
-    toDirectSum.comp ofDirectSum = AlgHom.id R (⨁ n, (⨂[R]^n) M) := by
+    toDirectSum.comp ofDirectSum = AlgHom.id R (⨁ n, ⨂[R]^n M) := by
   ext
   simp [DirectSum.lof_eq_of, -tprod_apply, toDirectSum_tensorPower_tprod]
 #align tensor_algebra.to_direct_sum_comp_of_direct_sum TensorAlgebra.toDirectSum_comp_ofDirectSum
 
 @[simp]
-theorem toDirectSum_ofDirectSum (x : ⨁ n, (⨂[R]^n) M) :
+theorem toDirectSum_ofDirectSum (x : ⨁ n, ⨂[R]^n M) :
     TensorAlgebra.toDirectSum (ofDirectSum x) = x :=
   AlgHom.congr_fun toDirectSum_comp_ofDirectSum x
 #align tensor_algebra.to_direct_sum_of_direct_sum TensorAlgebra.toDirectSum_ofDirectSum
 
 /-- The tensor algebra is isomorphic to a direct sum of tensor powers. -/
 @[simps!]
-def equivDirectSum : TensorAlgebra R M ≃ₐ[R] ⨁ n, (⨂[R]^n) M :=
+def equivDirectSum : TensorAlgebra R M ≃ₐ[R] ⨁ n, ⨂[R]^n M :=
   AlgEquiv.ofAlgHom toDirectSum ofDirectSum toDirectSum_comp_ofDirectSum
     ofDirectSum_comp_toDirectSum
 #align tensor_algebra.equiv_direct_sum TensorAlgebra.equivDirectSum

d97a0c9f

feat(LinearAlgebra/PiTensorProduct): make reindex dependently typed (#9445)

used to be (⨂[R] _ : ι, M) ≃ₗ[R] ⨂[R] _ : ι₂, M, now M can vary according to the indexing set.

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

3846d4de

Diff

@@ -120,7 +120,7 @@ theorem ofDirectSum_toDirectSum (x : TensorAlgebra R M) :
 @[simp, nolint simpNF] -- see std4#365 for the simpNF issue
 theorem mk_reindex_cast {n m : ℕ} (h : n = m) (x : (⨂[R]^n) M) :
     GradedMonoid.mk (A := fun i => (⨂[R]^i) M) m
-    (PiTensorProduct.reindex R M (Equiv.cast <| congr_arg Fin h) x) =
+    (PiTensorProduct.reindex R (fun _ ↦ M) (Equiv.cast <| congr_arg Fin h) x) =
     GradedMonoid.mk n x :=
   Eq.symm (PiTensorProduct.gradedMonoid_eq_of_reindex_cast h rfl)
 #align tensor_algebra.mk_reindex_cast TensorAlgebra.mk_reindex_cast
@@ -128,7 +128,7 @@ theorem mk_reindex_cast {n m : ℕ} (h : n = m) (x : (⨂[R]^n) M) :
 @[simp]
 theorem mk_reindex_fin_cast {n m : ℕ} (h : n = m) (x : (⨂[R]^n) M) :
     GradedMonoid.mk (A := fun i => (⨂[R]^i) M) m
-    (PiTensorProduct.reindex R M (Fin.castIso h).toEquiv x) = GradedMonoid.mk n x := by
+    (PiTensorProduct.reindex R (fun _ ↦ M) (Fin.castIso h).toEquiv x) = GradedMonoid.mk n x := by
   rw [Fin.castIso_to_equiv, mk_reindex_cast h]
 #align tensor_algebra.mk_reindex_fin_cast TensorAlgebra.mk_reindex_fin_cast

d97a0c9f

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

@@ -117,7 +117,7 @@ theorem ofDirectSum_toDirectSum (x : TensorAlgebra R M) :
   AlgHom.congr_fun ofDirectSum_comp_toDirectSum x
 #align tensor_algebra.of_direct_sum_to_direct_sum TensorAlgebra.ofDirectSum_toDirectSum
 
-@[simp]
+@[simp, nolint simpNF] -- see std4#365 for the simpNF issue
 theorem mk_reindex_cast {n m : ℕ} (h : n = m) (x : (⨂[R]^n) M) :
     GradedMonoid.mk (A := fun i => (⨂[R]^i) M) m
     (PiTensorProduct.reindex R M (Equiv.cast <| congr_arg Fin h) x) =
@@ -128,8 +128,8 @@ theorem mk_reindex_cast {n m : ℕ} (h : n = m) (x : (⨂[R]^n) M) :
 @[simp]
 theorem mk_reindex_fin_cast {n m : ℕ} (h : n = m) (x : (⨂[R]^n) M) :
     GradedMonoid.mk (A := fun i => (⨂[R]^i) M) m
-    (PiTensorProduct.reindex R M (Fin.castIso h).toEquiv x) = GradedMonoid.mk n x :=
-  by rw [Fin.castIso_to_equiv, mk_reindex_cast h]
+    (PiTensorProduct.reindex R M (Fin.castIso h).toEquiv x) = GradedMonoid.mk n x := by
+  rw [Fin.castIso_to_equiv, mk_reindex_cast h]
 #align tensor_algebra.mk_reindex_fin_cast TensorAlgebra.mk_reindex_fin_cast
 
 /-- The product of tensor products made of a single vector is the same as a single product of

d97a0c9f

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

@@ -80,7 +80,7 @@ namespace TensorAlgebra
 /-- The canonical map from a direct sum of tensor powers to the tensor algebra. -/
 def ofDirectSum : (⨁ n, (⨂[R]^n) M) →ₐ[R] TensorAlgebra R M :=
   DirectSum.toAlgebra _ _ (fun _ => TensorPower.toTensorAlgebra) TensorPower.toTensorAlgebra_gOne
-    (fun {_ _} => TensorPower.toTensorAlgebra_gMul) TensorPower.toTensorAlgebra_galgebra_toFun
+    (fun {_ _} => TensorPower.toTensorAlgebra_gMul)
 #align tensor_algebra.of_direct_sum TensorAlgebra.ofDirectSum
 
 @[simp]

d97a0c9f

feat: use suppress_compilation in tensor products (#7504)

More principled version of #7281.

9ff5b6f1

Diff

@@ -15,6 +15,7 @@ In this file we show that `TensorAlgebra R M` is isomorphic to a direct sum of t
 `TensorAlgebra.equivDirectSum`.
 -/
 
+suppress_compilation
 
 open scoped DirectSum TensorProduct

d97a0c9f

chore: remove unused simps (#6632)

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

916c75c1

Diff

@@ -156,7 +156,6 @@ theorem toDirectSum_tensorPower_tprod {n} (x : Fin n → M) :
     toDirectSum (tprod R M n x) = DirectSum.of _ n (PiTensorProduct.tprod R x) := by
   rw [tprod_apply, AlgHom.map_list_prod, List.map_ofFn]
   simp_rw [Function.comp, toDirectSum_ι]
-  dsimp only
   rw [DirectSum.list_prod_ofFn_of_eq_dProd]
   apply DirectSum.of_eq_of_gradedMonoid_eq
   rw [GradedMonoid.mk_list_dProd]

d97a0c9f

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

@@ -18,7 +18,7 @@ In this file we show that `TensorAlgebra R M` is isomorphic to a direct sum of t
 
 open scoped DirectSum TensorProduct
 
-variable {R M : Type _} [CommSemiring R] [AddCommMonoid M] [Module R M]
+variable {R M : Type*} [CommSemiring R] [AddCommMonoid M] [Module R M]
 
 namespace TensorPower

d97a0c9f

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.tensor_algebra.to_tensor_power
-! leanprover-community/mathlib commit d97a0c9f7a7efe6d76d652c5a6b7c9c634b70e0a
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.LinearAlgebra.TensorAlgebra.Basic
 import Mathlib.LinearAlgebra.TensorPower
 
+#align_import linear_algebra.tensor_algebra.to_tensor_power from "leanprover-community/mathlib"@"d97a0c9f7a7efe6d76d652c5a6b7c9c634b70e0a"
+
 /-!
 # Tensor algebras as direct sums of tensor powers

d97a0c9f

feat: port LinearAlgebra.TensorAlgebra.ToTensorPower (#4876)

Co-authored-by: Kevin Buzzard <k.buzzard@imperial.ac.uk> Co-authored-by: Johan Commelin <johan@commelin.net>

8793f093

`linear_algebra.tensor_algebra.to_tensor_power` ⟷ `Mathlib.LinearAlgebra.TensorAlgebra.ToTensorPower`

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Dependencies 8 + 474

linear_algebra.tensor_algebra.to_tensor_power ⟷ Mathlib.LinearAlgebra.TensorAlgebra.ToTensorPower

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Dependencies 8 + 474

`linear_algebra.tensor_algebra.to_tensor_power` ⟷ `Mathlib.LinearAlgebra.TensorAlgebra.ToTensorPower`