ring_theory.localization.normMathlib.RingTheory.Localization.NormTrace

This file has been ported!

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.

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Changes in mathlib3port

mathlib3
mathlib3port
Diff
@@ -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"
 
Diff
@@ -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
Diff
@@ -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
Diff
@@ -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
+-/
 
Diff
@@ -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
Diff
@@ -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.
 -/
Diff
@@ -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]
 

Changes in mathlib4

mathlib3
mathlib4
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)
Diff
@@ -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) :
fix: attribute [simp] ... in -> attribute [local simp] ... in (#7678)

Mathlib.Logic.Unique contains the line attribute [simp] eq_iff_true_of_subsingleton in ...:

https://github.com/leanprover-community/mathlib4/blob/96a11c7aac574c00370c2b3dab483cb676405c5d/Mathlib/Logic/Unique.lean#L255-L256

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 simps. 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.

https://github.com/leanprover-community/mathlib4/blob/bc49eb9ba756a233370b4b68bcdedd60402f71ed/Mathlib/CategoryTheory/Monoidal/Subcategory.lean#L118-L119

Diff
@@ -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),
chore: only four spaces for subsequent lines (#7286)

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

Diff
@@ -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]
feat: add Algebra.discr_localizationLocalization (#6422)

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).

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.

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

Open in Gitpod

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

Diff
@@ -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
feat: port RingTheory.Localization.Norm (#5299)

Dependencies 10 + 712

713 files ported (98.6%)
290843 lines ported (98.8%)
Show graph

The unported dependencies are