ring_theory.nullstellensatz | Mathlib porting status

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

9556784a

(last sync)

Changes in mathlib3port

mathlib3

mathlib3port

1a51edf1

bump to nightly-2024-03-17-08

mathlib commit https://github.com/leanprover-community/mathlib/commit/65a1391a0106c9204fe45bc73a039f056558cb83

22f01ce4

Diff

@@ -146,7 +146,7 @@ instance vanishingIdeal_singleton_isMaximal {x : σ → k} :
             ⟨(Ideal.Quotient.mk (vanishing_ideal {x} : Ideal (MvPolynomial σ k))) (C z), by simp⟩⟩
         obtain ⟨q, rfl⟩ := quotient.mk_surjective p
         rwa [Ideal.Quotient.lift_mk, ← mem_vanishing_ideal_singleton_iff, ←
-          quotient.eq_zero_iff_mem] at hp )
+          quotient.eq_zero_iff_mem] at hp)
   rw [← bot_quotient_is_maximal_iff, ring_equiv.bot_maximal_iff this]
   exact bot_is_maximal
 #align mv_polynomial.vanishing_ideal_singleton_is_maximal MvPolynomial.vanishingIdeal_singleton_isMaximal
@@ -158,7 +158,7 @@ theorem radical_le_vanishingIdeal_zeroLocus (I : Ideal (MvPolynomial σ k)) :
   by
   intro p hp x hx
   rw [← mem_vanishing_ideal_singleton_iff]
-  rw [radical_eq_Inf] at hp 
+  rw [radical_eq_Inf] at hp
   refine'
     (mem_Inf.mp hp)
       ⟨le_trans (le_vanishing_ideal_zero_locus I)
@@ -225,7 +225,7 @@ theorem isMaximal_iff_eq_vanishingIdeal_singleton (I : Ideal (MvPolynomial σ k)
   refine' ⟨x, (is_maximal.eq_of_le (by infer_instance) hI.ne_top _).symm⟩
   intro p hp
   rw [← quotient.eq_zero_iff_mem, map_mv_polynomial_eq_eval₂ (Ideal.Quotient.mk I) p, eval₂_eq']
-  rw [mem_vanishing_ideal_singleton_iff, eval_eq'] at hp 
+  rw [mem_vanishing_ideal_singleton_iff, eval_eq'] at hp
   simpa only [ϕ.map_sum, ϕ.map_mul, ϕ.map_prod, ϕ.map_pow, ϕ.map_zero, hx] using congr_arg ϕ hp
 #align mv_polynomial.is_maximal_iff_eq_vanishing_ideal_singleton MvPolynomial.isMaximal_iff_eq_vanishingIdeal_singleton
 -/

1a51edf1

bump to nightly-2023-09-24-06

mathlib commit https://github.com/leanprover-community/mathlib/commit/ce64cd319bb6b3e82f31c2d38e79080d377be451

5655435f

Diff

@@ -3,10 +3,10 @@ Copyright (c) 2021 Devon Tuma. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Devon Tuma
 -/
-import Mathbin.RingTheory.Jacobson
-import Mathbin.FieldTheory.IsAlgClosed.Basic
-import Mathbin.FieldTheory.MvPolynomial
-import Mathbin.AlgebraicGeometry.PrimeSpectrum.Basic
+import RingTheory.Jacobson
+import FieldTheory.IsAlgClosed.Basic
+import FieldTheory.MvPolynomial
+import AlgebraicGeometry.PrimeSpectrum.Basic
 
 #align_import ring_theory.nullstellensatz from "leanprover-community/mathlib"@"1a51edf13debfcbe223fa06b1cb353b9ed9751cc"

1a51edf1

bump to nightly-2023-07-20-09

mathlib commit https://github.com/leanprover-community/mathlib/commit/8ea5598db6caeddde6cb734aa179cc2408dbd345

9c56d0dd

Diff

@@ -2,17 +2,14 @@
 Copyright (c) 2021 Devon Tuma. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Devon Tuma
-
-! This file was ported from Lean 3 source module ring_theory.nullstellensatz
-! 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.RingTheory.Jacobson
 import Mathbin.FieldTheory.IsAlgClosed.Basic
 import Mathbin.FieldTheory.MvPolynomial
 import Mathbin.AlgebraicGeometry.PrimeSpectrum.Basic
 
+#align_import ring_theory.nullstellensatz from "leanprover-community/mathlib"@"1a51edf13debfcbe223fa06b1cb353b9ed9751cc"
+
 /-!
 # Nullstellensatz

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: Devon Tuma
 
 ! This file was ported from Lean 3 source module ring_theory.nullstellensatz
-! leanprover-community/mathlib commit 9556784a5b84697562e9c6acb40500d4a82e675a
+! leanprover-community/mathlib commit 1a51edf13debfcbe223fa06b1cb353b9ed9751cc
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -15,6 +15,9 @@ import Mathbin.AlgebraicGeometry.PrimeSpectrum.Basic
 
 /-!
 # Nullstellensatz
+
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
 This file establishes a version of Hilbert's classical Nullstellensatz for `mv_polynomial`s.
 The main statement of the theorem is `vanishing_ideal_zero_locus_eq_radical`.

9556784a

bump to nightly-2023-07-04-17

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

0dba3a1a

Diff

@@ -40,29 +40,40 @@ variable {k : Type _} [Field k]
 
 variable {σ : Type _}
 
+#print MvPolynomial.zeroLocus /-
 /-- Set of points that are zeroes of all polynomials in an ideal -/
 def zeroLocus (I : Ideal (MvPolynomial σ k)) : Set (σ → k) :=
   {x : σ → k | ∀ p ∈ I, eval x p = 0}
 #align mv_polynomial.zero_locus MvPolynomial.zeroLocus
+-/
 
+#print MvPolynomial.mem_zeroLocus_iff /-
 @[simp]
 theorem mem_zeroLocus_iff {I : Ideal (MvPolynomial σ k)} {x : σ → k} :
     x ∈ zeroLocus I ↔ ∀ p ∈ I, eval x p = 0 :=
   Iff.rfl
 #align mv_polynomial.mem_zero_locus_iff MvPolynomial.mem_zeroLocus_iff
+-/
 
+#print MvPolynomial.zeroLocus_anti_mono /-
 theorem zeroLocus_anti_mono {I J : Ideal (MvPolynomial σ k)} (h : I ≤ J) :
     zeroLocus J ≤ zeroLocus I := fun x hx p hp => hx p <| h hp
 #align mv_polynomial.zero_locus_anti_mono MvPolynomial.zeroLocus_anti_mono
+-/
 
+#print MvPolynomial.zeroLocus_bot /-
 theorem zeroLocus_bot : zeroLocus (⊥ : Ideal (MvPolynomial σ k)) = ⊤ :=
   eq_top_iff.2 fun x hx p hp => trans (congr_arg (eval x) (mem_bot.1 hp)) (eval x).map_zero
 #align mv_polynomial.zero_locus_bot MvPolynomial.zeroLocus_bot
+-/
 
+#print MvPolynomial.zeroLocus_top /-
 theorem zeroLocus_top : zeroLocus (⊤ : Ideal (MvPolynomial σ k)) = ⊥ :=
   eq_bot_iff.2 fun x hx => one_ne_zero ((eval x).map_one ▸ hx 1 Submodule.mem_top : (1 : k) = 0)
 #align mv_polynomial.zero_locus_top MvPolynomial.zeroLocus_top
+-/
 
+#print MvPolynomial.vanishingIdeal /-
 /-- Ideal of polynomials with common zeroes at all elements of a set -/
 def vanishingIdeal (V : Set (σ → k)) : Ideal (MvPolynomial σ k)
     where
@@ -72,41 +83,57 @@ def vanishingIdeal (V : Set (σ → k)) : Ideal (MvPolynomial σ k)
   smul_mem' p q hq x hx := by
     simp only [hq x hx, Algebra.id.smul_eq_mul, MulZeroClass.mul_zero, RingHom.map_mul]
 #align mv_polynomial.vanishing_ideal MvPolynomial.vanishingIdeal
+-/
 
+#print MvPolynomial.mem_vanishingIdeal_iff /-
 @[simp]
 theorem mem_vanishingIdeal_iff {V : Set (σ → k)} {p : MvPolynomial σ k} :
     p ∈ vanishingIdeal V ↔ ∀ x ∈ V, eval x p = 0 :=
   Iff.rfl
 #align mv_polynomial.mem_vanishing_ideal_iff MvPolynomial.mem_vanishingIdeal_iff
+-/
 
+#print MvPolynomial.vanishingIdeal_anti_mono /-
 theorem vanishingIdeal_anti_mono {A B : Set (σ → k)} (h : A ≤ B) :
     vanishingIdeal B ≤ vanishingIdeal A := fun p hp x hx => hp x <| h hx
 #align mv_polynomial.vanishing_ideal_anti_mono MvPolynomial.vanishingIdeal_anti_mono
+-/
 
+#print MvPolynomial.vanishingIdeal_empty /-
 theorem vanishingIdeal_empty : vanishingIdeal (∅ : Set (σ → k)) = ⊤ :=
   le_antisymm le_top fun p hp x hx => absurd hx (Set.not_mem_empty x)
 #align mv_polynomial.vanishing_ideal_empty MvPolynomial.vanishingIdeal_empty
+-/
 
+#print MvPolynomial.le_vanishingIdeal_zeroLocus /-
 theorem le_vanishingIdeal_zeroLocus (I : Ideal (MvPolynomial σ k)) :
     I ≤ vanishingIdeal (zeroLocus I) := fun p hp x hx => hx p hp
 #align mv_polynomial.le_vanishing_ideal_zero_locus MvPolynomial.le_vanishingIdeal_zeroLocus
+-/
 
+#print MvPolynomial.zeroLocus_vanishingIdeal_le /-
 theorem zeroLocus_vanishingIdeal_le (V : Set (σ → k)) : V ≤ zeroLocus (vanishingIdeal V) :=
   fun V hV p hp => hp V hV
 #align mv_polynomial.zero_locus_vanishing_ideal_le MvPolynomial.zeroLocus_vanishingIdeal_le
+-/
 
+#print MvPolynomial.zeroLocus_vanishingIdeal_galoisConnection /-
 theorem zeroLocus_vanishingIdeal_galoisConnection :
     @GaloisConnection (Ideal (MvPolynomial σ k)) (Set (σ → k))ᵒᵈ _ _ zeroLocus vanishingIdeal :=
   fun I V =>
   ⟨fun h => le_trans (le_vanishingIdeal_zeroLocus I) (vanishingIdeal_anti_mono h), fun h =>
     le_trans (zeroLocus_anti_mono h) (zeroLocus_vanishingIdeal_le V)⟩
 #align mv_polynomial.zero_locus_vanishing_ideal_galois_connection MvPolynomial.zeroLocus_vanishingIdeal_galoisConnection
+-/
 
+#print MvPolynomial.mem_vanishingIdeal_singleton_iff /-
 theorem mem_vanishingIdeal_singleton_iff (x : σ → k) (p : MvPolynomial σ k) :
     p ∈ (vanishingIdeal {x} : Ideal (MvPolynomial σ k)) ↔ eval x p = 0 :=
   ⟨fun h => h x rfl, fun hpx y hy => hy.symm ▸ hpx⟩
 #align mv_polynomial.mem_vanishing_ideal_singleton_iff MvPolynomial.mem_vanishingIdeal_singleton_iff
+-/
 
+#print MvPolynomial.vanishingIdeal_singleton_isMaximal /-
 instance vanishingIdeal_singleton_isMaximal {x : σ → k} :
     (vanishingIdeal {x} : Ideal (MvPolynomial σ k)).IsMaximal :=
   by
@@ -123,7 +150,9 @@ instance vanishingIdeal_singleton_isMaximal {x : σ → k} :
   rw [← bot_quotient_is_maximal_iff, ring_equiv.bot_maximal_iff this]
   exact bot_is_maximal
 #align mv_polynomial.vanishing_ideal_singleton_is_maximal MvPolynomial.vanishingIdeal_singleton_isMaximal
+-/
 
+#print MvPolynomial.radical_le_vanishingIdeal_zeroLocus /-
 theorem radical_le_vanishingIdeal_zeroLocus (I : Ideal (MvPolynomial σ k)) :
     I.radical ≤ vanishingIdeal (zeroLocus I) :=
   by
@@ -136,12 +165,16 @@ theorem radical_le_vanishingIdeal_zeroLocus (I : Ideal (MvPolynomial σ k)) :
           (vanishing_ideal_anti_mono fun y hy => hy.symm ▸ hx),
         is_maximal.is_prime' _⟩
 #align mv_polynomial.radical_le_vanishing_ideal_zero_locus MvPolynomial.radical_le_vanishingIdeal_zeroLocus
+-/
 
+#print MvPolynomial.pointToPoint /-
 /-- The point in the prime spectrum assosiated to a given point -/
 def pointToPoint (x : σ → k) : PrimeSpectrum (MvPolynomial σ k) :=
   ⟨(vanishingIdeal {x} : Ideal (MvPolynomial σ k)), by infer_instance⟩
 #align mv_polynomial.point_to_point MvPolynomial.pointToPoint
+-/
 
+#print MvPolynomial.vanishingIdeal_pointToPoint /-
 @[simp]
 theorem vanishingIdeal_pointToPoint (V : Set (σ → k)) :
     PrimeSpectrum.vanishingIdeal (pointToPoint '' V) = MvPolynomial.vanishingIdeal V :=
@@ -155,7 +188,9 @@ theorem vanishingIdeal_pointToPoint (V : Set (σ → k)) :
       let ⟨x, hx⟩ := hI
       hx.2 ▸ fun x' hx' => (Set.mem_singleton_iff.1 hx').symm ▸ hp x hx.1
 #align mv_polynomial.vanishing_ideal_point_to_point MvPolynomial.vanishingIdeal_pointToPoint
+-/
 
+#print MvPolynomial.pointToPoint_zeroLocus_le /-
 theorem pointToPoint_zeroLocus_le (I : Ideal (MvPolynomial σ k)) :
     pointToPoint '' MvPolynomial.zeroLocus I ≤ PrimeSpectrum.zeroLocus ↑I := fun J hJ =>
   let ⟨x, hx⟩ := hJ
@@ -163,9 +198,11 @@ theorem pointToPoint_zeroLocus_le (I : Ideal (MvPolynomial σ k)) :
       (hx.2 ▸ vanishingIdeal_anti_mono (Set.singleton_subset_iff.2 hx.1)) :
     I ≤ J.asIdeal)
 #align mv_polynomial.point_to_point_zero_locus_le MvPolynomial.pointToPoint_zeroLocus_le
+-/
 
 variable [IsAlgClosed k] [Finite σ]
 
+#print MvPolynomial.isMaximal_iff_eq_vanishingIdeal_singleton /-
 theorem isMaximal_iff_eq_vanishingIdeal_singleton (I : Ideal (MvPolynomial σ k)) :
     I.IsMaximal ↔ ∃ x : σ → k, I = vanishingIdeal {x} :=
   by
@@ -191,7 +228,9 @@ theorem isMaximal_iff_eq_vanishingIdeal_singleton (I : Ideal (MvPolynomial σ k)
   rw [mem_vanishing_ideal_singleton_iff, eval_eq'] at hp 
   simpa only [ϕ.map_sum, ϕ.map_mul, ϕ.map_prod, ϕ.map_pow, ϕ.map_zero, hx] using congr_arg ϕ hp
 #align mv_polynomial.is_maximal_iff_eq_vanishing_ideal_singleton MvPolynomial.isMaximal_iff_eq_vanishingIdeal_singleton
+-/
 
+#print MvPolynomial.vanishingIdeal_zeroLocus_eq_radical /-
 /-- Main statement of the Nullstellensatz -/
 @[simp]
 theorem vanishingIdeal_zeroLocus_eq_radical (I : Ideal (MvPolynomial σ k)) :
@@ -211,12 +250,15 @@ theorem vanishingIdeal_zeroLocus_eq_radical (I : Ideal (MvPolynomial σ k)) :
             (vanishing_ideal_anti_mono fun y hy => hy.symm ▸ hx),
           MvPolynomial.vanishingIdeal_singleton_isMaximal⟩
 #align mv_polynomial.vanishing_ideal_zero_locus_eq_radical MvPolynomial.vanishingIdeal_zeroLocus_eq_radical
+-/
 
+#print MvPolynomial.IsPrime.vanishingIdeal_zeroLocus /-
 @[simp]
 theorem IsPrime.vanishingIdeal_zeroLocus (P : Ideal (MvPolynomial σ k)) [h : P.IsPrime] :
     vanishingIdeal (zeroLocus P) = P :=
   trans (vanishingIdeal_zeroLocus_eq_radical P) h.radical
 #align mv_polynomial.is_prime.vanishing_ideal_zero_locus MvPolynomial.IsPrime.vanishingIdeal_zeroLocus
+-/
 
 end MvPolynomial

9556784a

bump to nightly-2023-06-13-09

mathlib commit https://github.com/leanprover-community/mathlib/commit/9fb8964792b4237dac6200193a0d533f1b3f7423

395b4fcf

Diff

@@ -179,7 +179,7 @@ theorem isMaximal_iff_eq_vanishingIdeal_singleton (I : Ideal (MvPolynomial σ k)
   let ϕ : k →+* MvPolynomial σ k ⧸ I := (Ideal.Quotient.mk I).comp C
   have hϕ : Function.Bijective ϕ :=
     ⟨quotient_mk_comp_C_injective _ _ I hI.ne_top,
-      IsAlgClosed.algebra_map_surjective_of_is_integral' ϕ
+      IsAlgClosed.algebraMap_surjective_of_isIntegral' ϕ
         (mv_polynomial.comp_C_integral_of_surjective_of_jacobson _ quotient.mk_surjective)⟩
   obtain ⟨φ, hφ⟩ := Function.Surjective.hasRightInverse hϕ.2
   let x : σ → k := fun s => φ ((Ideal.Quotient.mk I) (X s))

9556784a

bump to nightly-2023-06-04-18

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

3fb4268b

Diff

@@ -42,7 +42,7 @@ variable {σ : Type _}
 
 /-- Set of points that are zeroes of all polynomials in an ideal -/
 def zeroLocus (I : Ideal (MvPolynomial σ k)) : Set (σ → k) :=
-  { x : σ → k | ∀ p ∈ I, eval x p = 0 }
+  {x : σ → k | ∀ p ∈ I, eval x p = 0}
 #align mv_polynomial.zero_locus MvPolynomial.zeroLocus
 
 @[simp]
@@ -66,7 +66,7 @@ theorem zeroLocus_top : zeroLocus (⊤ : Ideal (MvPolynomial σ k)) = ⊥ :=
 /-- Ideal of polynomials with common zeroes at all elements of a set -/
 def vanishingIdeal (V : Set (σ → k)) : Ideal (MvPolynomial σ k)
     where
-  carrier := { p | ∀ x ∈ V, eval x p = 0 }
+  carrier := {p | ∀ x ∈ V, eval x p = 0}
   zero_mem' x hx := RingHom.map_zero _
   add_mem' p q hp hq x hx := by simp only [hq x hx, hp x hx, add_zero, RingHom.map_add]
   smul_mem' p q hq x hx := by

9556784a

bump to nightly-2023-06-01-16

mathlib commit https://github.com/leanprover-community/mathlib/commit/cca40788df1b8755d5baf17ab2f27dacc2e17acb

b9c87c70

Diff

@@ -119,7 +119,7 @@ instance vanishingIdeal_singleton_isMaximal {x : σ → k} :
             ⟨(Ideal.Quotient.mk (vanishing_ideal {x} : Ideal (MvPolynomial σ k))) (C z), by simp⟩⟩
         obtain ⟨q, rfl⟩ := quotient.mk_surjective p
         rwa [Ideal.Quotient.lift_mk, ← mem_vanishing_ideal_singleton_iff, ←
-          quotient.eq_zero_iff_mem] at hp)
+          quotient.eq_zero_iff_mem] at hp )
   rw [← bot_quotient_is_maximal_iff, ring_equiv.bot_maximal_iff this]
   exact bot_is_maximal
 #align mv_polynomial.vanishing_ideal_singleton_is_maximal MvPolynomial.vanishingIdeal_singleton_isMaximal
@@ -129,7 +129,7 @@ theorem radical_le_vanishingIdeal_zeroLocus (I : Ideal (MvPolynomial σ k)) :
   by
   intro p hp x hx
   rw [← mem_vanishing_ideal_singleton_iff]
-  rw [radical_eq_Inf] at hp
+  rw [radical_eq_Inf] at hp 
   refine'
     (mem_Inf.mp hp)
       ⟨le_trans (le_vanishing_ideal_zero_locus I)
@@ -188,7 +188,7 @@ theorem isMaximal_iff_eq_vanishingIdeal_singleton (I : Ideal (MvPolynomial σ k)
   refine' ⟨x, (is_maximal.eq_of_le (by infer_instance) hI.ne_top _).symm⟩
   intro p hp
   rw [← quotient.eq_zero_iff_mem, map_mv_polynomial_eq_eval₂ (Ideal.Quotient.mk I) p, eval₂_eq']
-  rw [mem_vanishing_ideal_singleton_iff, eval_eq'] at hp
+  rw [mem_vanishing_ideal_singleton_iff, eval_eq'] at hp 
   simpa only [ϕ.map_sum, ϕ.map_mul, ϕ.map_prod, ϕ.map_pow, ϕ.map_zero, hx] using congr_arg ϕ hp
 #align mv_polynomial.is_maximal_iff_eq_vanishing_ideal_singleton MvPolynomial.isMaximal_iff_eq_vanishingIdeal_singleton

9556784a

bump to nightly-2023-05-14-08

mathlib commit https://github.com/leanprover-community/mathlib/commit/e3fb84046afd187b710170887195d50bada934ee

d31da313

Diff

@@ -198,7 +198,7 @@ theorem vanishingIdeal_zeroLocus_eq_radical (I : Ideal (MvPolynomial σ k)) :
     vanishingIdeal (zeroLocus I) = I.radical :=
   by
   rw [I.radical_eq_jacobson]
-  refine' le_antisymm (le_infₛ _) fun p hp x hx => _
+  refine' le_antisymm (le_sInf _) fun p hp x hx => _
   · rintro J ⟨hJI, hJ⟩
     obtain ⟨x, hx⟩ := (is_maximal_iff_eq_vanishing_ideal_singleton J).1 hJ
     refine' hx.symm ▸ vanishing_ideal_anti_mono fun y hy p hp => _

9556784a

bump to nightly-2023-03-11-16

mathlib commit https://github.com/leanprover-community/mathlib/commit/3180fab693e2cee3bff62675571264cb8778b212

cd44fb92

Diff

@@ -69,7 +69,8 @@ def vanishingIdeal (V : Set (σ → k)) : Ideal (MvPolynomial σ k)
   carrier := { p | ∀ x ∈ V, eval x p = 0 }
   zero_mem' x hx := RingHom.map_zero _
   add_mem' p q hp hq x hx := by simp only [hq x hx, hp x hx, add_zero, RingHom.map_add]
-  smul_mem' p q hq x hx := by simp only [hq x hx, Algebra.id.smul_eq_mul, mul_zero, RingHom.map_mul]
+  smul_mem' p q hq x hx := by
+    simp only [hq x hx, Algebra.id.smul_eq_mul, MulZeroClass.mul_zero, RingHom.map_mul]
 #align mv_polynomial.vanishing_ideal MvPolynomial.vanishingIdeal
 
 @[simp]

9556784a

bump to nightly-2023-02-21-16

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

1107b979

Changes in mathlib4

mathlib3

mathlib4

9556784a

chore(*): migrate from RingHom.map_* to _root_.map_* (#11660)

Cherry-picked from #9607 Co-authored-by: @semorrison

859f3760

Diff

@@ -191,7 +191,7 @@ theorem isMaximal_iff_eq_vanishingIdeal_singleton (I : Ideal (MvPolynomial σ k)
   intro p hp
   rw [← Quotient.eq_zero_iff_mem, map_mvPolynomial_eq_eval₂ (Ideal.Quotient.mk I) p, eval₂_eq']
   rw [mem_vanishingIdeal_singleton_iff, eval_eq'] at hp
-  simpa only [ϕ.map_sum, ϕ.map_mul, ϕ.map_prod, ϕ.map_pow, ϕ.map_zero, hx] using congr_arg ϕ hp
+  simpa only [map_sum ϕ, ϕ.map_mul, map_prod ϕ, ϕ.map_pow, ϕ.map_zero, hx] using congr_arg ϕ hp
 #align mv_polynomial.is_maximal_iff_eq_vanishing_ideal_singleton MvPolynomial.isMaximal_iff_eq_vanishingIdeal_singleton
 
 /-- Main statement of the Nullstellensatz -/

9556784a

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

@@ -34,7 +34,6 @@ namespace MvPolynomial
 open MvPolynomial
 
 variable {k : Type*} [Field k]
-
 variable {σ : Type*}
 
 /-- Set of points that are zeroes of all polynomials in an ideal -/

9556784a

style: reduce spacing variation in "porting note" comments (#10886)

In this pull request, I have systematically eliminated the leading whitespace preceding the colon (:) within all unlabelled or unclassified porting notes. This adjustment facilitates a more efficient review process for the remaining notes by ensuring no entries are overlooked due to formatting inconsistencies.

86b84c52

Diff

@@ -152,7 +152,7 @@ theorem vanishingIdeal_pointToPoint (V : Set (σ → k)) :
   le_antisymm
     (fun p hp x hx =>
       (((PrimeSpectrum.mem_vanishingIdeal _ _).1 hp) ⟨vanishingIdeal {x}, by infer_instance⟩ <| by
-          exact ⟨x, ⟨hx, rfl⟩⟩) -- Porting note : tactic mode code compiles but term mode does not
+          exact ⟨x, ⟨hx, rfl⟩⟩) -- Porting note: tactic mode code compiles but term mode does not
         x rfl)
     fun p hp =>
     (PrimeSpectrum.mem_vanishingIdeal _ _).2 fun I hI =>
@@ -212,7 +212,7 @@ theorem vanishingIdeal_zeroLocus_eq_radical (I : Ideal (MvPolynomial σ k)) :
         MvPolynomial.vanishingIdeal_singleton_isMaximal⟩
 #align mv_polynomial.vanishing_ideal_zero_locus_eq_radical MvPolynomial.vanishingIdeal_zeroLocus_eq_radical
 
--- Porting note : marked this as high priority to short cut simplifier
+-- Porting note: marked this as high priority to short cut simplifier
 @[simp (high)]
 theorem IsPrime.vanishingIdeal_zeroLocus (P : Ideal (MvPolynomial σ k)) [h : P.IsPrime] :
     vanishingIdeal (zeroLocus P) = P :=

9556784a

chore: remove terminal, terminal refines (#10762)

I replaced a few "terminal" refine/refine's with exact.

The strategy was very simple-minded: essentially any refine whose following line had smaller indentation got replaced by exact and then I cleaned up the mess.

This PR certainly leaves some further terminal refines, but maybe the current change is beneficial.

ea36aa7d

Diff

@@ -205,7 +205,7 @@ theorem vanishingIdeal_zeroLocus_eq_radical (I : Ideal (MvPolynomial σ k)) :
     obtain ⟨x, hx⟩ := (isMaximal_iff_eq_vanishingIdeal_singleton J).1 hJ
     refine' hx.symm ▸ vanishingIdeal_anti_mono fun y hy p hp => _
     rw [← mem_vanishingIdeal_singleton_iff, Set.mem_singleton_iff.1 hy, ← hx]
-    refine' hJI hp
+    exact hJI hp
   · rw [← mem_vanishingIdeal_singleton_iff x p]
     refine' (mem_sInf.mp hp)
       ⟨le_trans (le_vanishingIdeal_zeroLocus I) (vanishingIdeal_anti_mono fun y hy => hy.symm ▸ hx),

9556784a

chore: cleanup some spaces (#7484)

Purely cosmetic PR.

c93575a3

Diff

@@ -124,7 +124,7 @@ instance vanishingIdeal_singleton_isMaximal {x : σ → k} :
             ⟨(Ideal.Quotient.mk (vanishingIdeal {x} : Ideal (MvPolynomial σ k))) (C z), by simp⟩⟩
         obtain ⟨q, rfl⟩ := Quotient.mk_surjective p
         rwa [Ideal.Quotient.lift_mk, ← mem_vanishingIdeal_singleton_iff,
-          ← Quotient.eq_zero_iff_mem] at hp )
+          ← Quotient.eq_zero_iff_mem] at hp)
   rw [← bot_quotient_isMaximal_iff, RingEquiv.bot_maximal_iff this]
   exact bot_isMaximal
 #align mv_polynomial.vanishing_ideal_singleton_is_maximal MvPolynomial.vanishingIdeal_singleton_isMaximal

9556784a

chore: drop MulZeroClass. in mul_zero/zero_mul (#6682)

Search&replace MulZeroClass.mul_zero -> mul_zero, MulZeroClass.zero_mul -> zero_mul.

These were introduced by Mathport, as the full name of mul_zero is actually MulZeroClass.mul_zero (it's exported with the short name).

277dea95

Diff

@@ -68,7 +68,7 @@ def vanishingIdeal (V : Set (σ → k)) : Ideal (MvPolynomial σ k) where
   zero_mem' x _ := RingHom.map_zero _
   add_mem' {p q} hp hq x hx := by simp only [hq x hx, hp x hx, add_zero, RingHom.map_add]
   smul_mem' p q hq x hx := by
-    simp only [hq x hx, Algebra.id.smul_eq_mul, MulZeroClass.mul_zero, RingHom.map_mul]
+    simp only [hq x hx, Algebra.id.smul_eq_mul, mul_zero, RingHom.map_mul]
 #align mv_polynomial.vanishing_ideal MvPolynomial.vanishingIdeal
 
 @[simp]

9556784a

feat: zeroLocus_span and some simp attributes (#6650)

0dd146c2

Diff

@@ -52,10 +52,12 @@ theorem zeroLocus_anti_mono {I J : Ideal (MvPolynomial σ k)} (h : I ≤ J) :
     zeroLocus J ≤ zeroLocus I := fun _ hx p hp => hx p <| h hp
 #align mv_polynomial.zero_locus_anti_mono MvPolynomial.zeroLocus_anti_mono
 
+@[simp]
 theorem zeroLocus_bot : zeroLocus (⊥ : Ideal (MvPolynomial σ k)) = ⊤ :=
   eq_top_iff.2 fun x _ _ hp => Trans.trans (congr_arg (eval x) (mem_bot.1 hp)) (eval x).map_zero
 #align mv_polynomial.zero_locus_bot MvPolynomial.zeroLocus_bot
 
+@[simp]
 theorem zeroLocus_top : zeroLocus (⊤ : Ideal (MvPolynomial σ k)) = ⊥ :=
   eq_bot_iff.2 fun x hx => one_ne_zero ((eval x).map_one ▸ hx 1 Submodule.mem_top : (1 : k) = 0)
 #align mv_polynomial.zero_locus_top MvPolynomial.zeroLocus_top
@@ -93,11 +95,19 @@ theorem zeroLocus_vanishingIdeal_le (V : Set (σ → k)) : V ≤ zeroLocus (vani
 
 theorem zeroLocus_vanishingIdeal_galoisConnection :
     @GaloisConnection (Ideal (MvPolynomial σ k)) (Set (σ → k))ᵒᵈ _ _ zeroLocus vanishingIdeal :=
-  fun I V =>
-  ⟨fun h => le_trans (le_vanishingIdeal_zeroLocus I) (vanishingIdeal_anti_mono h), fun h =>
-    le_trans (zeroLocus_anti_mono h) (zeroLocus_vanishingIdeal_le V)⟩
+  GaloisConnection.monotone_intro (fun _ _ ↦ vanishingIdeal_anti_mono)
+    (fun _ _ ↦ zeroLocus_anti_mono) le_vanishingIdeal_zeroLocus zeroLocus_vanishingIdeal_le
 #align mv_polynomial.zero_locus_vanishing_ideal_galois_connection MvPolynomial.zeroLocus_vanishingIdeal_galoisConnection
 
+theorem le_zeroLocus_iff_le_vanishingIdeal {V : Set (σ → k)} {I : Ideal (MvPolynomial σ k)} :
+    V ≤ zeroLocus I ↔ I ≤ vanishingIdeal V :=
+  zeroLocus_vanishingIdeal_galoisConnection.le_iff_le
+
+theorem zeroLocus_span (S : Set (MvPolynomial σ k)) :
+    zeroLocus (Ideal.span S) = { x | ∀ p ∈ S, eval x p = 0 } :=
+  eq_of_forall_le_iff fun _ => le_zeroLocus_iff_le_vanishingIdeal.trans <|
+    Ideal.span_le.trans forall₂_swap
+
 theorem mem_vanishingIdeal_singleton_iff (x : σ → k) (p : MvPolynomial σ k) :
     p ∈ (vanishingIdeal {x} : Ideal (MvPolynomial σ k)) ↔ eval x p = 0 :=
   ⟨fun h => h x rfl, fun hpx _ hy => hy.symm ▸ hpx⟩

9556784a

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

@@ -33,9 +33,9 @@ namespace MvPolynomial
 
 open MvPolynomial
 
-variable {k : Type _} [Field k]
+variable {k : Type*} [Field k]
 
-variable {σ : Type _}
+variable {σ : Type*}
 
 /-- Set of points that are zeroes of all polynomials in an ideal -/
 def zeroLocus (I : Ideal (MvPolynomial σ k)) : Set (σ → k) :=

9556784a

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

@@ -2,17 +2,14 @@
 Copyright (c) 2021 Devon Tuma. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Devon Tuma
-
-! This file was ported from Lean 3 source module ring_theory.nullstellensatz
-! leanprover-community/mathlib commit 9556784a5b84697562e9c6acb40500d4a82e675a
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.RingTheory.Jacobson
 import Mathlib.FieldTheory.IsAlgClosed.Basic
 import Mathlib.FieldTheory.MvPolynomial
 import Mathlib.AlgebraicGeometry.PrimeSpectrum.Basic
 
+#align_import ring_theory.nullstellensatz from "leanprover-community/mathlib"@"9556784a5b84697562e9c6acb40500d4a82e675a"
+
 /-!
 # Nullstellensatz
 This file establishes a version of Hilbert's classical Nullstellensatz for `MvPolynomial`s.

9556784a

chore: tidy various files (#5840)

6a00552b

Diff

@@ -15,15 +15,15 @@ import Mathlib.AlgebraicGeometry.PrimeSpectrum.Basic
 
 /-!
 # Nullstellensatz
-This file establishes a version of Hilbert's classical Nullstellensatz for `mv_polynomial`s.
-The main statement of the theorem is `vanishing_ideal_zero_locus_eq_radical`.
+This file establishes a version of Hilbert's classical Nullstellensatz for `MvPolynomial`s.
+The main statement of the theorem is `MvPolynomial.vanishingIdeal_zeroLocus_eq_radical`.
 
-The statement is in terms of new definitions `vanishing_ideal` and `zero_locus`.
+The statement is in terms of new definitions `vanishingIdeal` and `zeroLocus`.
 Mathlib already has versions of these in terms of the prime spectrum of a ring,
   but those are not well-suited for expressing this result.
 Suggestions for better ways to state this theorem or organize things are welcome.
 
-The machinery around `vanishing_ideal` and `zero_locus` is also minimal, I only added lemmas
+The machinery around `vanishingIdeal` and `zeroLocus` is also minimal, I only added lemmas
   directly needed in this proof, since I'm not sure if they are the right approach.
 -/

9556784a

feat: port RingTheory.Nullstellensatz (#5686)

6fae06cc

`ring_theory.nullstellensatz` ⟷ `Mathlib.RingTheory.Nullstellensatz`

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Dependencies 11 + 707

ring_theory.nullstellensatz ⟷ Mathlib.RingTheory.Nullstellensatz

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Dependencies 11 + 707

`ring_theory.nullstellensatz` ⟷ `Mathlib.RingTheory.Nullstellensatz`