ring_theory.localization.norm
⟷
Mathlib.RingTheory.Localization.NormTrace
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.
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mathlib commit https://github.com/leanprover-community/mathlib/commit/ce64cd319bb6b3e82f31c2d38e79080d377be451
@@ -3,8 +3,8 @@ Copyright (c) 2023 Anne Baanen. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Anne Baanen
-/
-import Mathbin.RingTheory.Localization.Module
-import Mathbin.RingTheory.Norm
+import RingTheory.Localization.Module
+import RingTheory.Norm
#align_import ring_theory.localization.norm from "leanprover-community/mathlib"@"e8e130de9dba4ed6897183c3193c752ffadbcc77"
mathlib commit https://github.com/leanprover-community/mathlib/commit/8ea5598db6caeddde6cb734aa179cc2408dbd345
@@ -2,15 +2,12 @@
Copyright (c) 2023 Anne Baanen. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Anne Baanen
-
-! This file was ported from Lean 3 source module ring_theory.localization.norm
-! leanprover-community/mathlib commit e8e130de9dba4ed6897183c3193c752ffadbcc77
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
-/
import Mathbin.RingTheory.Localization.Module
import Mathbin.RingTheory.Norm
+#align_import ring_theory.localization.norm from "leanprover-community/mathlib"@"e8e130de9dba4ed6897183c3193c752ffadbcc77"
+
/-!
# Field/algebra norm and localization
mathlib commit https://github.com/leanprover-community/mathlib/commit/6285167a053ad0990fc88e56c48ccd9fae6550eb
@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
Authors: Anne Baanen
! This file was ported from Lean 3 source module ring_theory.localization.norm
-! leanprover-community/mathlib commit 2e59a6de168f95d16b16d217b808a36290398c0a
+! leanprover-community/mathlib commit e8e130de9dba4ed6897183c3193c752ffadbcc77
! Please do not edit these lines, except to modify the commit id
! if you have ported upstream changes.
-/
@@ -15,6 +15,9 @@ import Mathbin.RingTheory.Norm
# Field/algebra norm and localization
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
This file contains results on the combination of `algebra.norm` and `is_localization`.
## Main results
mathlib commit https://github.com/leanprover-community/mathlib/commit/0723536a0522d24fc2f159a096fb3304bef77472
@@ -42,6 +42,7 @@ variable [IsLocalization M Rₘ] [IsLocalization (Algebra.algebraMapSubmonoid S
variable [Algebra Rₘ Sₘ] [Algebra R Sₘ] [IsScalarTower R Rₘ Sₘ] [IsScalarTower R S Sₘ]
+#print Algebra.norm_localization /-
/-- Let `S` be an extension of `R` and `Rₘ Sₘ` be localizations at `M` of `R S` respectively.
Then the norm of `a : Sₘ` over `Rₘ` is the norm of `a : S` over `R` if `S` is free as `R`-module.
-/
@@ -61,4 +62,5 @@ theorem Algebra.norm_localization [Module.Free R S] [Module.Finite R S] (a : S)
Basis.localizationLocalization_apply, ← _root_.map_mul]
apply Basis.localizationLocalization_repr_algebraMap
#align algebra.norm_localization Algebra.norm_localization
+-/
mathlib commit https://github.com/leanprover-community/mathlib/commit/2a0ce625dbb0ffbc7d1316597de0b25c1ec75303
@@ -56,7 +56,7 @@ theorem Algebra.norm_localization [Module.Free R S] [Module.Finite R S] (a : S)
rw [Algebra.norm_eq_matrix_det (b.localization_localization Rₘ M Sₘ),
Algebra.norm_eq_matrix_det b, RingHom.map_det]
congr
- ext (i j)
+ ext i j
simp only [Matrix.map_apply, RingHom.mapMatrix_apply, Algebra.leftMulMatrix_eq_repr_mul,
Basis.localizationLocalization_apply, ← _root_.map_mul]
apply Basis.localizationLocalization_repr_algebraMap
mathlib commit https://github.com/leanprover-community/mathlib/commit/9fb8964792b4237dac6200193a0d533f1b3f7423
@@ -42,8 +42,6 @@ variable [IsLocalization M Rₘ] [IsLocalization (Algebra.algebraMapSubmonoid S
variable [Algebra Rₘ Sₘ] [Algebra R Sₘ] [IsScalarTower R Rₘ Sₘ] [IsScalarTower R S Sₘ]
-include M
-
/-- Let `S` be an extension of `R` and `Rₘ Sₘ` be localizations at `M` of `R S` respectively.
Then the norm of `a : Sₘ` over `Rₘ` is the norm of `a : S` over `R` if `S` is free as `R`-module.
-/
mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb
@@ -30,7 +30,7 @@ field norm, algebra norm, localization
-/
-open nonZeroDivisors
+open scoped nonZeroDivisors
variable (R : Type _) {S : Type _} [CommRing R] [CommRing S] [Algebra R S]
mathlib commit https://github.com/leanprover-community/mathlib/commit/bd9851ca476957ea4549eb19b40e7b5ade9428cc
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)
@@ -40,13 +40,9 @@ field norm, algebra norm, localization
open scoped nonZeroDivisors
variable (R : Type*) {S : Type*} [CommRing R] [CommRing S] [Algebra R S]
-
variable {Rₘ Sₘ : Type*} [CommRing Rₘ] [Algebra R Rₘ] [CommRing Sₘ] [Algebra S Sₘ]
-
variable (M : Submonoid R)
-
variable [IsLocalization M Rₘ] [IsLocalization (Algebra.algebraMapSubmonoid S M) Sₘ]
-
variable [Algebra Rₘ Sₘ] [Algebra R Sₘ] [IsScalarTower R Rₘ Sₘ] [IsScalarTower R S Sₘ]
open Algebra
@@ -90,11 +86,8 @@ theorem Algebra.trace_localization [Module.Free R S] [Module.Finite R S] (a : S)
section LocalizationLocalization
variable (Sₘ : Type*) [CommRing Sₘ] [Algebra S Sₘ] [Algebra Rₘ Sₘ] [Algebra R Sₘ]
-
variable [IsScalarTower R Rₘ Sₘ] [IsScalarTower R S Sₘ]
-
variable [IsLocalization (Algebra.algebraMapSubmonoid S M) Sₘ]
-
variable {ι : Type*} [Fintype ι] [DecidableEq ι]
theorem Algebra.traceMatrix_localizationLocalization (b : Basis ι R S) :
attribute [simp] ... in
-> attribute [local simp] ... in
(#7678)
Mathlib.Logic.Unique contains the line attribute [simp] eq_iff_true_of_subsingleton in ...
:
Despite what the in
part may imply, this adds the lemma to the simp set "globally", including for downstream files; it is likely that attribute [local simp] eq_iff_true_of_subsingleton in ...
was meant instead (or maybe scoped simp
, but I think "scoped" refers to the current namespace). Indeed, the relevant lemma is not marked with @[simp]
for possible slowness: https://github.com/leanprover/std4/blob/846e9e1d6bb534774d1acd2dc430e70987da3c18/Std/Logic.lean#L749. Adding it to the simp set causes the example at https://leanprover.zulipchat.com/#narrow/stream/287929-mathlib4/topic/Regression.20in.20simp to slow down.
This PR changes this and fixes the relevant downstream simp
s. There was also one ocurrence of attribute [simp] FullSubcategory.comp_def FullSubcategory.id_def in
in Mathlib.CategoryTheory.Monoidal.Subcategory but that was much easier to fix.
@@ -66,7 +66,7 @@ theorem Algebra.norm_localization [Module.Free R S] [Module.Finite R S] (a : S)
Algebra.norm Rₘ (algebraMap S Sₘ a) = algebraMap R Rₘ (Algebra.norm R a) := by
cases subsingleton_or_nontrivial R
· haveI : Subsingleton Rₘ := Module.subsingleton R Rₘ
- simp
+ simp [eq_iff_true_of_subsingleton]
let b := Module.Free.chooseBasis R S
letI := Classical.decEq (Module.Free.ChooseBasisIndex R S)
rw [Algebra.norm_eq_matrix_det (b.localizationLocalization Rₘ M Sₘ),
@@ -80,7 +80,7 @@ theorem Algebra.trace_localization [Module.Free R S] [Module.Finite R S] (a : S)
Algebra.trace Rₘ Sₘ (algebraMap S Sₘ a) = algebraMap R Rₘ (Algebra.trace R S a) := by
cases subsingleton_or_nontrivial R
· haveI : Subsingleton Rₘ := Module.subsingleton R Rₘ
- simp
+ simp [eq_iff_true_of_subsingleton]
let b := Module.Free.chooseBasis R S
letI := Classical.decEq (Module.Free.ChooseBasisIndex R S)
rw [Algebra.trace_eq_matrix_trace (b.localizationLocalization Rₘ M Sₘ),
@@ -112,7 +112,7 @@ theorem Algebra.traceMatrix_localizationLocalization (b : Basis ι R S) :
discriminant of `b`.
-/
theorem Algebra.discr_localizationLocalization (b : Basis ι R S) :
- Algebra.discr Rₘ (b.localizationLocalization Rₘ M Sₘ) =
+ Algebra.discr Rₘ (b.localizationLocalization Rₘ M Sₘ) =
algebraMap R Rₘ (Algebra.discr R b) := by
rw [Algebra.discr_def, Algebra.discr_def, RingHom.map_det,
Algebra.traceMatrix_localizationLocalization]
We prove
theorem Algebra.discr_localizationLocalization (b : Basis ι R S) :
Algebra.discr Rₘ (b.localizationLocalization Rₘ M Aₘ) = algebraMap R Rₘ (Algebra.discr R b)
We need for that to prove the analogue for the trace of Algebra.norm_localization
(that was the only result in RingTheory.Localization.Norm
). Since the results are added to this file, it is renamed to RingTheory.Localization.NormTrace
(not sure about the name though).
Type _
and Sort _
(#6499)
We remove all possible occurences of Type _
and Sort _
in favor of Type*
and Sort*
.
This has nice performance benefits.
@@ -29,9 +29,9 @@ field norm, algebra norm, localization
open scoped nonZeroDivisors
-variable (R : Type _) {S : Type _} [CommRing R] [CommRing S] [Algebra R S]
+variable (R : Type*) {S : Type*} [CommRing R] [CommRing S] [Algebra R S]
-variable {Rₘ Sₘ : Type _} [CommRing Rₘ] [Algebra R Rₘ] [CommRing Sₘ] [Algebra S Sₘ]
+variable {Rₘ Sₘ : Type*} [CommRing Rₘ] [Algebra R Rₘ] [CommRing Sₘ] [Algebra S Sₘ]
variable (M : Submonoid R)
@@ -2,15 +2,12 @@
Copyright (c) 2023 Anne Baanen. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Anne Baanen
-
-! This file was ported from Lean 3 source module ring_theory.localization.norm
-! leanprover-community/mathlib commit 2e59a6de168f95d16b16d217b808a36290398c0a
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
-/
import Mathlib.RingTheory.Localization.Module
import Mathlib.RingTheory.Norm
+#align_import ring_theory.localization.norm from "leanprover-community/mathlib"@"2e59a6de168f95d16b16d217b808a36290398c0a"
+
/-!
# Field/algebra norm and localization
The unported dependencies are