ring_theory.localization.away.adjoin_root
⟷
Mathlib.RingTheory.Localization.Away.AdjoinRoot
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) 2018 Kenny Lau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kenny Lau, Mario Carneiro, Johan Commelin, Amelia Livingston, Anne Baanen
-/
-import Mathbin.RingTheory.AdjoinRoot
-import Mathbin.RingTheory.Localization.Away.Basic
+import RingTheory.AdjoinRoot
+import RingTheory.Localization.Away.Basic
#align_import ring_theory.localization.away.adjoin_root from "leanprover-community/mathlib"@"c20927220ef87bb4962ba08bf6da2ce3cf50a6dd"
mathlib commit https://github.com/leanprover-community/mathlib/commit/8ea5598db6caeddde6cb734aa179cc2408dbd345
@@ -2,15 +2,12 @@
Copyright (c) 2018 Kenny Lau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kenny Lau, Mario Carneiro, Johan Commelin, Amelia Livingston, Anne Baanen
-
-! This file was ported from Lean 3 source module ring_theory.localization.away.adjoin_root
-! leanprover-community/mathlib commit c20927220ef87bb4962ba08bf6da2ce3cf50a6dd
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
-/
import Mathbin.RingTheory.AdjoinRoot
import Mathbin.RingTheory.Localization.Away.Basic
+#align_import ring_theory.localization.away.adjoin_root from "leanprover-community/mathlib"@"c20927220ef87bb4962ba08bf6da2ce3cf50a6dd"
+
/-!
> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
> Any changes to this file require a corresponding PR to mathlib4.
mathlib commit https://github.com/leanprover-community/mathlib/commit/31c24aa72e7b3e5ed97a8412470e904f82b81004
@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kenny Lau, Mario Carneiro, Johan Commelin, Amelia Livingston, Anne Baanen
! This file was ported from Lean 3 source module ring_theory.localization.away.adjoin_root
-! leanprover-community/mathlib commit a7c017d750512a352b623b1824d75da5998457d0
+! leanprover-community/mathlib commit c20927220ef87bb4962ba08bf6da2ce3cf50a6dd
! Please do not edit these lines, except to modify the commit id
! if you have ported upstream changes.
-/
@@ -12,6 +12,9 @@ import Mathbin.RingTheory.AdjoinRoot
import Mathbin.RingTheory.Localization.Away.Basic
/-!
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
The `R`-`alg_equiv` between the localization of `R` away from `r` and
`R` with an inverse of `r` adjoined.
-/
mathlib commit https://github.com/leanprover-community/mathlib/commit/a3209ddf94136d36e5e5c624b10b2a347cc9d090
@@ -23,26 +23,32 @@ variable {R : Type _} [CommRing R]
attribute [local instance] IsLocalization.algHom_subsingleton AdjoinRoot.algHom_subsingleton
+#print Localization.awayEquivAdjoin /-
/-- The `R`-`alg_equiv` between the localization of `R` away from `r` and
`R` with an inverse of `r` adjoined. -/
noncomputable def Localization.awayEquivAdjoin (r : R) : Away r ≃ₐ[R] AdjoinRoot (C r * X - 1) :=
AlgEquiv.ofAlgHom
{ awayLift _ r _ with
commutes' :=
- IsLocalization.Away.AwayMap.lift_eq r (isUnit_of_mul_eq_one _ _ <| root_is_inv r) }
+ IsLocalization.Away.AwayMap.lift_eq r (isUnit_of_mul_eq_one _ _ <| root_isInv r) }
(liftHom _ (IsLocalization.Away.invSelf r) <| by
simp only [map_sub, map_mul, aeval_C, aeval_X, IsLocalization.Away.mul_invSelf, aeval_one,
sub_self])
(Subsingleton.elim _ _) (Subsingleton.elim _ _)
#align localization.away_equiv_adjoin Localization.awayEquivAdjoin
+-/
+#print IsLocalization.adjoin_inv /-
theorem IsLocalization.adjoin_inv (r : R) : IsLocalization.Away r (AdjoinRoot <| C r * X - 1) :=
IsLocalization.isLocalization_of_algEquiv _ (Localization.awayEquivAdjoin r)
#align is_localization.adjoin_inv IsLocalization.adjoin_inv
+-/
+#print IsLocalization.Away.finitePresentation /-
theorem IsLocalization.Away.finitePresentation (r : R) {S} [CommRing S] [Algebra R S]
[IsLocalization.Away r S] : Algebra.FinitePresentation R S :=
(AdjoinRoot.finitePresentation _).Equiv <|
(Localization.awayEquivAdjoin r).symm.trans <| IsLocalization.algEquiv (Submonoid.powers r) _ _
#align is_localization.away.finite_presentation IsLocalization.Away.finitePresentation
+-/
mathlib commit https://github.com/leanprover-community/mathlib/commit/f51de8769c34652d82d1c8e5f8f18f8374782bed
Type _
and Sort _
(#6499)
We remove all possible occurences of Type _
and Sort _
in favor of Type*
and Sort*
.
This has nice performance benefits.
@@ -15,7 +15,7 @@ The `R`-`AlgEquiv` between the localization of `R` away from `r` and
open Polynomial AdjoinRoot Localization
-variable {R : Type _} [CommRing R]
+variable {R : Type*} [CommRing R]
-- Porting note: removed `IsLocalization.algHom_subsingleton` due to
-- `cannot find synthesization order for instance`
@@ -2,15 +2,12 @@
Copyright (c) 2018 Kenny Lau. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kenny Lau, Mario Carneiro, Johan Commelin, Amelia Livingston, Anne Baanen
-
-! This file was ported from Lean 3 source module ring_theory.localization.away.adjoin_root
-! leanprover-community/mathlib commit a7c017d750512a352b623b1824d75da5998457d0
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
-/
import Mathlib.RingTheory.AdjoinRoot
import Mathlib.RingTheory.Localization.Away.Basic
+#align_import ring_theory.localization.away.adjoin_root from "leanprover-community/mathlib"@"a7c017d750512a352b623b1824d75da5998457d0"
+
/-!
The `R`-`AlgEquiv` between the localization of `R` away from `r` and
`R` with an inverse of `r` adjoined.
The unported dependencies are