linear_algebra.annihilating_polynomial

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

d3e8e0a0

(last sync)

Changes in mathlib3port

mathlib3

mathlib3port

61db041a

bump to nightly-2024-03-17-08

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

22f01ce4

Diff

@@ -204,7 +204,7 @@ theorem monic_generator_eq_minpoly (a : A) (p : 𝕜[X]) (p_monic : p.Monic)
   by
   by_cases h : p = 0
   · rwa [h, ann_ideal_generator_eq_zero_iff, ← p_gen, ideal.span_singleton_eq_bot.mpr]
-  · rw [← span_singleton_ann_ideal_generator, Ideal.span_singleton_eq_span_singleton] at p_gen 
+  · rw [← span_singleton_ann_ideal_generator, Ideal.span_singleton_eq_span_singleton] at p_gen
     rw [eq_comm]
     apply eq_of_monic_of_associated p_monic _ p_gen
     · apply monic_ann_ideal_generator _ _ ((Associated.ne_zero_iff p_gen).mp h)

61db041a

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) 2022 Justin Thomas. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Justin Thomas
 -/
-import Mathbin.FieldTheory.Minpoly.Field
-import Mathbin.RingTheory.PrincipalIdealDomain
+import FieldTheory.Minpoly.Field
+import RingTheory.PrincipalIdealDomain
 
 #align_import linear_algebra.annihilating_polynomial from "leanprover-community/mathlib"@"61db041ab8e4aaf8cb5c7dc10a7d4ff261997536"

61db041a

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) 2022 Justin Thomas. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Justin Thomas
-
-! This file was ported from Lean 3 source module linear_algebra.annihilating_polynomial
-! leanprover-community/mathlib commit 61db041ab8e4aaf8cb5c7dc10a7d4ff261997536
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.FieldTheory.Minpoly.Field
 import Mathbin.RingTheory.PrincipalIdealDomain
 
+#align_import linear_algebra.annihilating_polynomial from "leanprover-community/mathlib"@"61db041ab8e4aaf8cb5c7dc10a7d4ff261997536"
+
 /-!
 # Annihilating Ideal

61db041a

bump to nightly-2023-06-13-21

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

829520ac

Diff

@@ -64,11 +64,13 @@ noncomputable def annIdeal (a : A) : Ideal R[X] :=
 
 variable {R}
 
+#print Polynomial.mem_annIdeal_iff_aeval_eq_zero /-
 /-- It is useful to refer to ideal membership sometimes
  and the annihilation condition other times. -/
 theorem mem_annIdeal_iff_aeval_eq_zero {a : A} {p : R[X]} : p ∈ annIdeal R a ↔ aeval a p = 0 :=
   Iff.rfl
 #align polynomial.mem_ann_ideal_iff_aeval_eq_zero Polynomial.mem_annIdeal_iff_aeval_eq_zero
+-/
 
 end Semiring
 
@@ -97,14 +99,17 @@ section
 
 variable {𝕜}
 
+#print Polynomial.annIdealGenerator_eq_zero_iff /-
 @[simp]
 theorem annIdealGenerator_eq_zero_iff {a : A} : annIdealGenerator 𝕜 a = 0 ↔ annIdeal 𝕜 a = ⊥ := by
   simp only [ann_ideal_generator, mul_eq_zero, is_principal.eq_bot_iff_generator_eq_zero,
     Polynomial.C_eq_zero, inv_eq_zero, Polynomial.leadingCoeff_eq_zero, or_self_iff]
 #align polynomial.ann_ideal_generator_eq_zero_iff Polynomial.annIdealGenerator_eq_zero_iff
+-/
 
 end
 
+#print Polynomial.span_singleton_annIdealGenerator /-
 /-- `ann_ideal_generator 𝕜 a` is indeed a generator. -/
 @[simp]
 theorem span_singleton_annIdealGenerator (a : A) :
@@ -119,22 +124,29 @@ theorem span_singleton_annIdealGenerator (a : A) :
     apply polynomial.leading_coeff_eq_zero.not.mpr
     apply (mul_ne_zero_iff.mp h).1
 #align polynomial.span_singleton_ann_ideal_generator Polynomial.span_singleton_annIdealGenerator
+-/
 
+#print Polynomial.annIdealGenerator_mem /-
 /-- The annihilating ideal generator is a member of the annihilating ideal. -/
 theorem annIdealGenerator_mem (a : A) : annIdealGenerator 𝕜 a ∈ annIdeal 𝕜 a :=
   Ideal.mul_mem_right _ _ (Submodule.IsPrincipal.generator_mem _)
 #align polynomial.ann_ideal_generator_mem Polynomial.annIdealGenerator_mem
+-/
 
+#print Polynomial.mem_iff_eq_smul_annIdealGenerator /-
 theorem mem_iff_eq_smul_annIdealGenerator {p : 𝕜[X]} (a : A) :
     p ∈ annIdeal 𝕜 a ↔ ∃ s : 𝕜[X], p = s • annIdealGenerator 𝕜 a := by
   simp_rw [@eq_comm _ p, ← mem_span_singleton, ← span_singleton_ann_ideal_generator 𝕜 a, Ideal.span]
 #align polynomial.mem_iff_eq_smul_ann_ideal_generator Polynomial.mem_iff_eq_smul_annIdealGenerator
+-/
 
+#print Polynomial.monic_annIdealGenerator /-
 /-- The generator we chose for the annihilating ideal is monic when the ideal is non-zero. -/
 theorem monic_annIdealGenerator (a : A) (hg : annIdealGenerator 𝕜 a ≠ 0) :
     Monic (annIdealGenerator 𝕜 a) :=
   monic_mul_leadingCoeff_inv (mul_ne_zero_iff.mp hg).1
 #align polynomial.monic_ann_ideal_generator Polynomial.monic_annIdealGenerator
+-/
 
 /-! We are working toward showing the generator of the annihilating ideal
 in the field case is the minimal polynomial. We are going to use a uniqueness
@@ -143,26 +155,33 @@ theorem of the minimal polynomial.
 This is the first condition: it must annihilate the original element `a : A`. -/
 
 
+#print Polynomial.annIdealGenerator_aeval_eq_zero /-
 theorem annIdealGenerator_aeval_eq_zero (a : A) : aeval a (annIdealGenerator 𝕜 a) = 0 :=
   mem_annIdeal_iff_aeval_eq_zero.mp (annIdealGenerator_mem 𝕜 a)
 #align polynomial.ann_ideal_generator_aeval_eq_zero Polynomial.annIdealGenerator_aeval_eq_zero
+-/
 
 variable {𝕜}
 
+#print Polynomial.mem_iff_annIdealGenerator_dvd /-
 theorem mem_iff_annIdealGenerator_dvd {p : 𝕜[X]} {a : A} :
     p ∈ annIdeal 𝕜 a ↔ annIdealGenerator 𝕜 a ∣ p := by
   rw [← Ideal.mem_span_singleton, span_singleton_ann_ideal_generator]
 #align polynomial.mem_iff_ann_ideal_generator_dvd Polynomial.mem_iff_annIdealGenerator_dvd
+-/
 
+#print Polynomial.degree_annIdealGenerator_le_of_mem /-
 /-- The generator of the annihilating ideal has minimal degree among
  the non-zero members of the annihilating ideal -/
 theorem degree_annIdealGenerator_le_of_mem (a : A) (p : 𝕜[X]) (hp : p ∈ annIdeal 𝕜 a)
     (hpn0 : p ≠ 0) : degree (annIdealGenerator 𝕜 a) ≤ degree p :=
   degree_le_of_dvd (mem_iff_annIdealGenerator_dvd.1 hp) hpn0
 #align polynomial.degree_ann_ideal_generator_le_of_mem Polynomial.degree_annIdealGenerator_le_of_mem
+-/
 
 variable (𝕜)
 
+#print Polynomial.annIdealGenerator_eq_minpoly /-
 /-- The generator of the annihilating ideal is the minimal polynomial. -/
 theorem annIdealGenerator_eq_minpoly (a : A) : annIdealGenerator 𝕜 a = minpoly 𝕜 a :=
   by
@@ -178,7 +197,9 @@ theorem annIdealGenerator_eq_minpoly (a : A) : annIdealGenerator 𝕜 a = minpol
         degree_ann_ideal_generator_le_of_mem a q (mem_ann_ideal_iff_aeval_eq_zero.mpr hq)
           q_monic.NeZero
 #align polynomial.ann_ideal_generator_eq_minpoly Polynomial.annIdealGenerator_eq_minpoly
+-/
 
+#print Polynomial.monic_generator_eq_minpoly /-
 /-- If a monic generates the annihilating ideal, it must match our choice
  of the annihilating ideal generator. -/
 theorem monic_generator_eq_minpoly (a : A) (p : 𝕜[X]) (p_monic : p.Monic)
@@ -191,6 +212,7 @@ theorem monic_generator_eq_minpoly (a : A) (p : 𝕜[X]) (p_monic : p.Monic)
     apply eq_of_monic_of_associated p_monic _ p_gen
     · apply monic_ann_ideal_generator _ _ ((Associated.ne_zero_iff p_gen).mp h)
 #align polynomial.monic_generator_eq_minpoly Polynomial.monic_generator_eq_minpoly
+-/
 
 end Field

61db041a

bump to nightly-2023-06-01-16

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

b9c87c70

Diff

@@ -186,7 +186,7 @@ theorem monic_generator_eq_minpoly (a : A) (p : 𝕜[X]) (p_monic : p.Monic)
   by
   by_cases h : p = 0
   · rwa [h, ann_ideal_generator_eq_zero_iff, ← p_gen, ideal.span_singleton_eq_bot.mpr]
-  · rw [← span_singleton_ann_ideal_generator, Ideal.span_singleton_eq_span_singleton] at p_gen
+  · rw [← span_singleton_ann_ideal_generator, Ideal.span_singleton_eq_span_singleton] at p_gen 
     rw [eq_comm]
     apply eq_of_monic_of_associated p_monic _ p_gen
     · apply monic_ann_ideal_generator _ _ ((Associated.ne_zero_iff p_gen).mp h)

61db041a

bump to nightly-2023-06-01-04

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

4d9eaa85

Diff

@@ -143,11 +143,9 @@ theorem of the minimal polynomial.
 This is the first condition: it must annihilate the original element `a : A`. -/
 
 
-#print Polynomial.annIdealGenerator_aeval_eq_zero /-
 theorem annIdealGenerator_aeval_eq_zero (a : A) : aeval a (annIdealGenerator 𝕜 a) = 0 :=
   mem_annIdeal_iff_aeval_eq_zero.mp (annIdealGenerator_mem 𝕜 a)
 #align polynomial.ann_ideal_generator_aeval_eq_zero Polynomial.annIdealGenerator_aeval_eq_zero
--/
 
 variable {𝕜}

61db041a

bump to nightly-2023-05-28-18

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

8d353152

Diff

@@ -40,7 +40,7 @@ there are some common specializations which may be more familiar.
 -/
 
 
-open Polynomial
+open scoped Polynomial
 
 namespace Polynomial

61db041a

bump to nightly-2023-05-28-06

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

ba5d8b97

Diff

@@ -64,9 +64,6 @@ noncomputable def annIdeal (a : A) : Ideal R[X] :=
 
 variable {R}
 
-/- warning: polynomial.mem_ann_ideal_iff_aeval_eq_zero -> Polynomial.mem_annIdeal_iff_aeval_eq_zero is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align polynomial.mem_ann_ideal_iff_aeval_eq_zero Polynomial.mem_annIdeal_iff_aeval_eq_zeroₓ'. -/
 /-- It is useful to refer to ideal membership sometimes
  and the annihilation condition other times. -/
 theorem mem_annIdeal_iff_aeval_eq_zero {a : A} {p : R[X]} : p ∈ annIdeal R a ↔ aeval a p = 0 :=
@@ -100,12 +97,6 @@ section
 
 variable {𝕜}
 
-/- warning: polynomial.ann_ideal_generator_eq_zero_iff -> Polynomial.annIdealGenerator_eq_zero_iff is a dubious translation:
-lean 3 declaration is
-  forall {𝕜 : Type.{u1}} {A : Type.{u2}} [_inst_1 : Field.{u1} 𝕜] [_inst_2 : Ring.{u2} A] [_inst_3 : Algebra.{u1, u2} 𝕜 A (Semifield.toCommSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 _inst_1)) (Ring.toSemiring.{u2} A _inst_2)] {a : A}, Iff (Eq.{succ u1} (Polynomial.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1)))) (Polynomial.annIdealGenerator.{u1, u2} 𝕜 A _inst_1 _inst_2 _inst_3 a) (OfNat.ofNat.{u1} (Polynomial.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1)))) 0 (OfNat.mk.{u1} (Polynomial.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1)))) 0 (Zero.zero.{u1} (Polynomial.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1)))) (Polynomial.zero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1)))))))) (Eq.{succ u1} (Ideal.{u1} (Polynomial.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (Semifield.toCommSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 _inst_1)))) (Polynomial.semiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (Semifield.toCommSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 _inst_1))))) (Polynomial.annIdeal.{u1, u2} 𝕜 A (Semifield.toCommSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 _inst_1)) (Ring.toSemiring.{u2} A _inst_2) _inst_3 a) (Bot.bot.{u1} (Ideal.{u1} (Polynomial.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (Semifield.toCommSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 _inst_1)))) (Polynomial.semiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (Semifield.toCommSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 _inst_1))))) (Submodule.hasBot.{u1, u1} (Polynomial.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (Semifield.toCommSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 _inst_1)))) (Polynomial.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (Semifield.toCommSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 _inst_1)))) (Polynomial.semiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (Semifield.toCommSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (Semifield.toCommSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (Semifield.toCommSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (Semifield.toCommSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 _inst_1)))) (Polynomial.semiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (Semifield.toCommSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 _inst_1))))))) (Semiring.toModule.{u1} (Polynomial.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (Semifield.toCommSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 _inst_1)))) (Polynomial.semiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (Semifield.toCommSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 _inst_1))))))))
-but is expected to have type
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-Case conversion may be inaccurate. Consider using '#align polynomial.ann_ideal_generator_eq_zero_iff Polynomial.annIdealGenerator_eq_zero_iffₓ'. -/
 @[simp]
 theorem annIdealGenerator_eq_zero_iff {a : A} : annIdealGenerator 𝕜 a = 0 ↔ annIdeal 𝕜 a = ⊥ := by
   simp only [ann_ideal_generator, mul_eq_zero, is_principal.eq_bot_iff_generator_eq_zero,
@@ -114,12 +105,6 @@ theorem annIdealGenerator_eq_zero_iff {a : A} : annIdealGenerator 𝕜 a = 0 ↔
 
 end
 
-/- warning: polynomial.span_singleton_ann_ideal_generator -> Polynomial.span_singleton_annIdealGenerator is a dubious translation:
-lean 3 declaration is
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-Case conversion may be inaccurate. Consider using '#align polynomial.span_singleton_ann_ideal_generator Polynomial.span_singleton_annIdealGeneratorₓ'. -/
 /-- `ann_ideal_generator 𝕜 a` is indeed a generator. -/
 @[simp]
 theorem span_singleton_annIdealGenerator (a : A) :
@@ -135,34 +120,16 @@ theorem span_singleton_annIdealGenerator (a : A) :
     apply (mul_ne_zero_iff.mp h).1
 #align polynomial.span_singleton_ann_ideal_generator Polynomial.span_singleton_annIdealGenerator
 
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-Case conversion may be inaccurate. Consider using '#align polynomial.ann_ideal_generator_mem Polynomial.annIdealGenerator_memₓ'. -/
 /-- The annihilating ideal generator is a member of the annihilating ideal. -/
 theorem annIdealGenerator_mem (a : A) : annIdealGenerator 𝕜 a ∈ annIdeal 𝕜 a :=
   Ideal.mul_mem_right _ _ (Submodule.IsPrincipal.generator_mem _)
 #align polynomial.ann_ideal_generator_mem Polynomial.annIdealGenerator_mem
 
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-Case conversion may be inaccurate. Consider using '#align polynomial.mem_iff_eq_smul_ann_ideal_generator Polynomial.mem_iff_eq_smul_annIdealGeneratorₓ'. -/
 theorem mem_iff_eq_smul_annIdealGenerator {p : 𝕜[X]} (a : A) :
     p ∈ annIdeal 𝕜 a ↔ ∃ s : 𝕜[X], p = s • annIdealGenerator 𝕜 a := by
   simp_rw [@eq_comm _ p, ← mem_span_singleton, ← span_singleton_ann_ideal_generator 𝕜 a, Ideal.span]
 #align polynomial.mem_iff_eq_smul_ann_ideal_generator Polynomial.mem_iff_eq_smul_annIdealGenerator
 
-/- warning: polynomial.monic_ann_ideal_generator -> Polynomial.monic_annIdealGenerator is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align polynomial.monic_ann_ideal_generator Polynomial.monic_annIdealGeneratorₓ'. -/
 /-- The generator we chose for the annihilating ideal is monic when the ideal is non-zero. -/
 theorem monic_annIdealGenerator (a : A) (hg : annIdealGenerator 𝕜 a ≠ 0) :
     Monic (annIdealGenerator 𝕜 a) :=
@@ -184,23 +151,11 @@ theorem annIdealGenerator_aeval_eq_zero (a : A) : aeval a (annIdealGenerator 
 
 variable {𝕜}
 
-/- warning: polynomial.mem_iff_ann_ideal_generator_dvd -> Polynomial.mem_iff_annIdealGenerator_dvd is a dubious translation:
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-  forall {𝕜 : Type.{u1}} {A : Type.{u2}} [_inst_1 : Field.{u1} 𝕜] [_inst_2 : Ring.{u2} A] [_inst_3 : Algebra.{u1, u2} 𝕜 A (Semifield.toCommSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 _inst_1)) (Ring.toSemiring.{u2} A _inst_2)] {p : Polynomial.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1)))} {a : A}, Iff (Membership.Mem.{u1, u1} (Polynomial.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1)))) (Ideal.{u1} (Polynomial.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (Semifield.toCommSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 _inst_1)))) (Polynomial.semiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (Semifield.toCommSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 _inst_1))))) (SetLike.hasMem.{u1, u1} (Ideal.{u1} (Polynomial.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (Semifield.toCommSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 _inst_1)))) (Polynomial.semiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (Semifield.toCommSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 _inst_1))))) (Polynomial.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (Semifield.toCommSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 _inst_1)))) (Submodule.setLike.{u1, u1} (Polynomial.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (Semifield.toCommSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 _inst_1)))) (Polynomial.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (Semifield.toCommSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 _inst_1)))) (Polynomial.semiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (Semifield.toCommSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (Semifield.toCommSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (Semifield.toCommSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (Semifield.toCommSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 _inst_1)))) (Polynomial.semiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (Semifield.toCommSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 _inst_1))))))) (Semiring.toModule.{u1} (Polynomial.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (Semifield.toCommSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 _inst_1)))) (Polynomial.semiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (Semifield.toCommSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 _inst_1))))))) p (Polynomial.annIdeal.{u1, u2} 𝕜 A (Semifield.toCommSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 _inst_1)) (Ring.toSemiring.{u2} A _inst_2) _inst_3 a)) (Dvd.Dvd.{u1} (Polynomial.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1)))) (semigroupDvd.{u1} (Polynomial.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1)))) (SemigroupWithZero.toSemigroup.{u1} (Polynomial.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1)))) (NonUnitalSemiring.toSemigroupWithZero.{u1} (Polynomial.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1)))) (NonUnitalRing.toNonUnitalSemiring.{u1} (Polynomial.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1)))) (NonUnitalCommRing.toNonUnitalRing.{u1} (Polynomial.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1)))) (CommRing.toNonUnitalCommRing.{u1} (Polynomial.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1)))) (Polynomial.commRing.{u1} 𝕜 (EuclideanDomain.toCommRing.{u1} 𝕜 (Field.toEuclideanDomain.{u1} 𝕜 _inst_1))))))))) (Polynomial.annIdealGenerator.{u1, u2} 𝕜 A _inst_1 _inst_2 _inst_3 a) p)
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-  forall {𝕜 : Type.{u2}} {A : Type.{u1}} [_inst_1 : Field.{u2} 𝕜] [_inst_2 : Ring.{u1} A] [_inst_3 : Algebra.{u2, u1} 𝕜 A (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)) (Ring.toSemiring.{u1} A _inst_2)] {p : Polynomial.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)))} {a : A}, Iff (Membership.mem.{u2, u2} (Polynomial.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)))) (Ideal.{u2} (Polynomial.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)))) (Polynomial.semiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))))) (SetLike.instMembership.{u2, u2} (Ideal.{u2} (Polynomial.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)))) (Polynomial.semiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))))) (Polynomial.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)))) (Submodule.setLike.{u2, u2} (Polynomial.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)))) (Polynomial.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)))) (Polynomial.semiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)))) (Polynomial.semiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))))))) (Semiring.toModule.{u2} (Polynomial.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)))) (Polynomial.semiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))))))) p (Polynomial.annIdeal.{u2, u1} 𝕜 A (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)) (Ring.toSemiring.{u1} A _inst_2) _inst_3 a)) (Dvd.dvd.{u2} (Polynomial.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)))) (semigroupDvd.{u2} (Polynomial.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)))) (SemigroupWithZero.toSemigroup.{u2} (Polynomial.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)))) (NonUnitalSemiring.toSemigroupWithZero.{u2} (Polynomial.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)))) (NonUnitalCommSemiring.toNonUnitalSemiring.{u2} (Polynomial.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)))) (NonUnitalCommRing.toNonUnitalCommSemiring.{u2} (Polynomial.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)))) (CommRing.toNonUnitalCommRing.{u2} (Polynomial.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)))) (Polynomial.commRing.{u2} 𝕜 (EuclideanDomain.toCommRing.{u2} 𝕜 (Field.toEuclideanDomain.{u2} 𝕜 _inst_1))))))))) (Polynomial.annIdealGenerator.{u2, u1} 𝕜 A _inst_1 _inst_2 _inst_3 a) p)
-Case conversion may be inaccurate. Consider using '#align polynomial.mem_iff_ann_ideal_generator_dvd Polynomial.mem_iff_annIdealGenerator_dvdₓ'. -/
 theorem mem_iff_annIdealGenerator_dvd {p : 𝕜[X]} {a : A} :
     p ∈ annIdeal 𝕜 a ↔ annIdealGenerator 𝕜 a ∣ p := by
   rw [← Ideal.mem_span_singleton, span_singleton_ann_ideal_generator]
 #align polynomial.mem_iff_ann_ideal_generator_dvd Polynomial.mem_iff_annIdealGenerator_dvd
 
-/- warning: polynomial.degree_ann_ideal_generator_le_of_mem -> Polynomial.degree_annIdealGenerator_le_of_mem is a dubious translation:
-lean 3 declaration is
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 /-- The generator of the annihilating ideal has minimal degree among
  the non-zero members of the annihilating ideal -/
 theorem degree_annIdealGenerator_le_of_mem (a : A) (p : 𝕜[X]) (hp : p ∈ annIdeal 𝕜 a)
@@ -210,12 +165,6 @@ theorem degree_annIdealGenerator_le_of_mem (a : A) (p : 𝕜[X]) (hp : p ∈ ann
 
 variable (𝕜)
 
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-Case conversion may be inaccurate. Consider using '#align polynomial.ann_ideal_generator_eq_minpoly Polynomial.annIdealGenerator_eq_minpolyₓ'. -/
 /-- The generator of the annihilating ideal is the minimal polynomial. -/
 theorem annIdealGenerator_eq_minpoly (a : A) : annIdealGenerator 𝕜 a = minpoly 𝕜 a :=
   by
@@ -232,12 +181,6 @@ theorem annIdealGenerator_eq_minpoly (a : A) : annIdealGenerator 𝕜 a = minpol
           q_monic.NeZero
 #align polynomial.ann_ideal_generator_eq_minpoly Polynomial.annIdealGenerator_eq_minpoly
 
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 /-- If a monic generates the annihilating ideal, it must match our choice
  of the annihilating ideal generator. -/
 theorem monic_generator_eq_minpoly (a : A) (p : 𝕜[X]) (p_monic : p.Monic)

61db041a

bump to nightly-2023-05-28-03

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

6c6011cf

Diff

@@ -65,10 +65,7 @@ noncomputable def annIdeal (a : A) : Ideal R[X] :=
 variable {R}
 
 /- warning: polynomial.mem_ann_ideal_iff_aeval_eq_zero -> Polynomial.mem_annIdeal_iff_aeval_eq_zero is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align polynomial.mem_ann_ideal_iff_aeval_eq_zero Polynomial.mem_annIdeal_iff_aeval_eq_zeroₓ'. -/
 /-- It is useful to refer to ideal membership sometimes
  and the annihilation condition other times. -/

61db041a

bump to nightly-2023-05-25-04

mathlib commit https://github.com/leanprover-community/mathlib/commit/ef95945cd48c932c9e034872bd25c3c220d9c946

2175c3c2

Diff

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Justin Thomas
 
 ! This file was ported from Lean 3 source module linear_algebra.annihilating_polynomial
-! leanprover-community/mathlib commit d3e8e0a0237c10c2627bf52c246b15ff8e7df4c0
+! leanprover-community/mathlib commit 61db041ab8e4aaf8cb5c7dc10a7d4ff261997536
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -14,6 +14,9 @@ import Mathbin.RingTheory.PrincipalIdealDomain
 /-!
 # Annihilating Ideal
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 Given a commutative ring `R` and an `R`-algebra `A`
 Every element `a : A` defines
 an ideal `polynomial.ann_ideal a ⊆ R[X]`.

d3e8e0a0

bump to nightly-2023-05-24-06

mathlib commit https://github.com/leanprover-community/mathlib/commit/8d33f09cd7089ecf074b4791907588245aec5d1b

fbc7b476

Diff

@@ -65,7 +65,7 @@ variable {R}
 lean 3 declaration is
   forall {R : Type.{u1}} {A : Type.{u2}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : Semiring.{u2} A] [_inst_3 : Algebra.{u1, u2} R A _inst_1 _inst_2] {a : A} {p : Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)}, Iff (Membership.Mem.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Ideal.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (SetLike.hasMem.{u1, u1} (Ideal.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Submodule.setLike.{u1, u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) (Semiring.toModule.{u1} (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1))))) p (Polynomial.annIdeal.{u1, u2} R A _inst_1 _inst_2 _inst_3 a)) (Eq.{succ u2} A (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (AlgHom.{u1, u1, u2} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_2 (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)) _inst_3) (fun (_x : AlgHom.{u1, u1, u2} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_2 (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)) _inst_3) => (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) -> A) ([anonymous].{u1, u1, u2} R (Polynomial.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) A _inst_1 (Polynomial.semiring.{u1} R (CommSemiring.toSemiring.{u1} R _inst_1)) _inst_2 (Polynomial.algebraOfAlgebra.{u1, u1} R R _inst_1 (CommSemiring.toSemiring.{u1} R _inst_1) (Algebra.id.{u1} R _inst_1)) _inst_3) (Polynomial.aeval.{u1, u2} R A _inst_1 _inst_2 _inst_3 a) p) (OfNat.ofNat.{u2} A 0 (OfNat.mk.{u2} A 0 (Zero.zero.{u2} A (MulZeroClass.toHasZero.{u2} A (NonUnitalNonAssocSemiring.toMulZeroClass.{u2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} A (Semiring.toNonAssocSemiring.{u2} A _inst_2))))))))
 but is expected to have type
-  forall {R : Type.{u2}} {A : Type.{u1}} [_inst_1 : CommSemiring.{u2} R] [_inst_2 : Semiring.{u1} A] [_inst_3 : Algebra.{u2, u1} R A _inst_1 _inst_2] {a : A} {p : Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)}, Iff (Membership.mem.{u2, u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Ideal.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (SetLike.instMembership.{u2, u2} (Ideal.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Submodule.setLike.{u2, u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Semiring.toModule.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) p (Polynomial.annIdeal.{u2, u1} R A _inst_1 _inst_2 _inst_3 a)) (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) => A) p) (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} (AlgHom.{u2, u2, u1} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) A _inst_1 (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) _inst_2 (Polynomial.algebraOfAlgebra.{u2, u2} R R _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1)) _inst_3) (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (fun (_x : Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) => A) _x) (SMulHomClass.toFunLike.{max u1 u2, u2, u2, u1} (AlgHom.{u2, u2, u1} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) A _inst_1 (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) _inst_2 (Polynomial.algebraOfAlgebra.{u2, u2} R R _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1)) _inst_3) R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) A (SMulZeroClass.toSMul.{u2, u2} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (AddMonoid.toZero.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))))) (DistribSMul.toSMulZeroClass.{u2, u2} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (AddMonoid.toAddZeroClass.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))))) (DistribMulAction.toDistribSMul.{u2, u2} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (AddCommMonoid.toAddMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))))) (Module.toDistribMulAction.{u2, u2} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Algebra.toModule.{u2, u2} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) _inst_1 (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.algebraOfAlgebra.{u2, u2} R R _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1))))))) (SMulZeroClass.toSMul.{u2, u1} R A (AddMonoid.toZero.{u1} A (AddCommMonoid.toAddMonoid.{u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))))) (DistribSMul.toSMulZeroClass.{u2, u1} R A (AddMonoid.toAddZeroClass.{u1} A (AddCommMonoid.toAddMonoid.{u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))))) (DistribMulAction.toDistribSMul.{u2, u1} R A (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2)))) (Module.toDistribMulAction.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3))))) (DistribMulActionHomClass.toSMulHomClass.{max u1 u2, u2, u2, u1} (AlgHom.{u2, u2, u1} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) A _inst_1 (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) _inst_2 (Polynomial.algebraOfAlgebra.{u2, u2} R R _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1)) _inst_3) R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) A (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (AddCommMonoid.toAddMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))))) (AddCommMonoid.toAddMonoid.{u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2)))) (Module.toDistribMulAction.{u2, u2} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Algebra.toModule.{u2, u2} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) _inst_1 (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.algebraOfAlgebra.{u2, u2} R R _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1)))) (Module.toDistribMulAction.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u1 u2, u2, u2, u1} (AlgHom.{u2, u2, u1} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) A _inst_1 (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) _inst_2 (Polynomial.algebraOfAlgebra.{u2, u2} R R _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1)) _inst_3) R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) A (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2)) (Module.toDistribMulAction.{u2, u2} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Algebra.toModule.{u2, u2} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) _inst_1 (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.algebraOfAlgebra.{u2, u2} R R _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1)))) (Module.toDistribMulAction.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u2, u2, u1, max u1 u2} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) A _inst_1 (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) _inst_2 (Polynomial.algebraOfAlgebra.{u2, u2} R R _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1)) _inst_3 (AlgHom.{u2, u2, u1} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) A _inst_1 (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) _inst_2 (Polynomial.algebraOfAlgebra.{u2, u2} R R _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1)) _inst_3) (AlgHom.algHomClass.{u2, u2, u1} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) A _inst_1 (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) _inst_2 (Polynomial.algebraOfAlgebra.{u2, u2} R R _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1)) _inst_3))))) (Polynomial.aeval.{u2, u1} R A _inst_1 _inst_2 _inst_3 a) p) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) => A) p) 0 (Zero.toOfNat0.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) => A) p) (MonoidWithZero.toZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) => A) p) (Semiring.toMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) => A) p) _inst_2)))))
+  forall {R : Type.{u2}} {A : Type.{u1}} [_inst_1 : CommSemiring.{u2} R] [_inst_2 : Semiring.{u1} A] [_inst_3 : Algebra.{u2, u1} R A _inst_1 _inst_2] {a : A} {p : Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)}, Iff (Membership.mem.{u2, u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Ideal.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (SetLike.instMembership.{u2, u2} (Ideal.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Submodule.setLike.{u2, u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Semiring.toModule.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) p (Polynomial.annIdeal.{u2, u1} R A _inst_1 _inst_2 _inst_3 a)) (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) => A) p) (FunLike.coe.{max (succ u1) (succ u2), succ u2, succ u1} (AlgHom.{u2, u2, u1} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) A _inst_1 (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) _inst_2 (Polynomial.algebraOfAlgebra.{u2, u2} R R _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1)) _inst_3) (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (fun (_x : Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) => A) _x) (SMulHomClass.toFunLike.{max u1 u2, u2, u2, u1} (AlgHom.{u2, u2, u1} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) A _inst_1 (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) _inst_2 (Polynomial.algebraOfAlgebra.{u2, u2} R R _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1)) _inst_3) R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) A (SMulZeroClass.toSMul.{u2, u2} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (AddMonoid.toZero.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))))) (DistribSMul.toSMulZeroClass.{u2, u2} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (AddMonoid.toAddZeroClass.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (AddCommMonoid.toAddMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))))) (DistribMulAction.toDistribSMul.{u2, u2} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (AddCommMonoid.toAddMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))))) (Module.toDistribMulAction.{u2, u2} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Algebra.toModule.{u2, u2} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) _inst_1 (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.algebraOfAlgebra.{u2, u2} R R _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1))))))) (SMulZeroClass.toSMul.{u2, u1} R A (AddMonoid.toZero.{u1} A (AddCommMonoid.toAddMonoid.{u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))))) (DistribSMul.toSMulZeroClass.{u2, u1} R A (AddMonoid.toAddZeroClass.{u1} A (AddCommMonoid.toAddMonoid.{u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))))) (DistribMulAction.toDistribSMul.{u2, u1} R A (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (AddCommMonoid.toAddMonoid.{u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2)))) (Module.toDistribMulAction.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3))))) (DistribMulActionHomClass.toSMulHomClass.{max u1 u2, u2, u2, u1} (AlgHom.{u2, u2, u1} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) A _inst_1 (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) _inst_2 (Polynomial.algebraOfAlgebra.{u2, u2} R R _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1)) _inst_3) R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) A (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (AddCommMonoid.toAddMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))))) (AddCommMonoid.toAddMonoid.{u1} A (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2)))) (Module.toDistribMulAction.{u2, u2} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Algebra.toModule.{u2, u2} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) _inst_1 (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.algebraOfAlgebra.{u2, u2} R R _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1)))) (Module.toDistribMulAction.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (NonUnitalAlgHomClass.toDistribMulActionHomClass.{max u1 u2, u2, u2, u1} (AlgHom.{u2, u2, u1} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) A _inst_1 (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) _inst_2 (Polynomial.algebraOfAlgebra.{u2, u2} R R _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1)) _inst_3) R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) A (MonoidWithZero.toMonoid.{u2} R (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2)) (Module.toDistribMulAction.{u2, u2} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))))) (Algebra.toModule.{u2, u2} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) _inst_1 (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Polynomial.algebraOfAlgebra.{u2, u2} R R _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1)))) (Module.toDistribMulAction.{u2, u1} R A (CommSemiring.toSemiring.{u2} R _inst_1) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} A (Semiring.toNonAssocSemiring.{u1} A _inst_2))) (Algebra.toModule.{u2, u1} R A _inst_1 _inst_2 _inst_3)) (AlgHom.instNonUnitalAlgHomClassToMonoidToMonoidWithZeroToSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToNonUnitalNonAssocSemiringToNonAssocSemiringToDistribMulActionToAddCommMonoidToModuleToDistribMulActionToAddCommMonoidToModule.{u2, u2, u1, max u1 u2} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) A _inst_1 (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) _inst_2 (Polynomial.algebraOfAlgebra.{u2, u2} R R _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1)) _inst_3 (AlgHom.{u2, u2, u1} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) A _inst_1 (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) _inst_2 (Polynomial.algebraOfAlgebra.{u2, u2} R R _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1)) _inst_3) (AlgHom.algHomClass.{u2, u2, u1} R (Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) A _inst_1 (Polynomial.semiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) _inst_2 (Polynomial.algebraOfAlgebra.{u2, u2} R R _inst_1 (CommSemiring.toSemiring.{u2} R _inst_1) (Algebra.id.{u2} R _inst_1)) _inst_3))))) (Polynomial.aeval.{u2, u1} R A _inst_1 _inst_2 _inst_3 a) p) (OfNat.ofNat.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) => A) p) 0 (Zero.toOfNat0.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) => A) p) (MonoidWithZero.toZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) => A) p) (Semiring.toMonoidWithZero.{u1} ((fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : Polynomial.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) => A) p) _inst_2)))))
 Case conversion may be inaccurate. Consider using '#align polynomial.mem_ann_ideal_iff_aeval_eq_zero Polynomial.mem_annIdeal_iff_aeval_eq_zeroₓ'. -/
 /-- It is useful to refer to ideal membership sometimes
  and the annihilation condition other times. -/

d3e8e0a0

bump to nightly-2023-05-23-08

mathlib commit https://github.com/leanprover-community/mathlib/commit/75e7fca56381d056096ce5d05e938f63a6567828

0b6e1728

Diff

@@ -47,6 +47,7 @@ variable {R A : Type _} [CommSemiring R] [Semiring A] [Algebra R A]
 
 variable (R)
 
+#print Polynomial.annIdeal /-
 /-- `ann_ideal R a` is the *annihilating ideal* of all `p : R[X]` such that `p(a) = 0`.
 
 The informal notation `p(a)` stand for `polynomial.aeval a p`.
@@ -56,9 +57,16 @@ The formal definition uses the kernel of the aeval map. -/
 noncomputable def annIdeal (a : A) : Ideal R[X] :=
   ((aeval a).toRingHom : R[X] →+* A).ker
 #align polynomial.ann_ideal Polynomial.annIdeal
+-/
 
 variable {R}
 
+/- warning: polynomial.mem_ann_ideal_iff_aeval_eq_zero -> Polynomial.mem_annIdeal_iff_aeval_eq_zero is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align polynomial.mem_ann_ideal_iff_aeval_eq_zero Polynomial.mem_annIdeal_iff_aeval_eq_zeroₓ'. -/
 /-- It is useful to refer to ideal membership sometimes
  and the annihilation condition other times. -/
 theorem mem_annIdeal_iff_aeval_eq_zero {a : A} {p : R[X]} : p ∈ annIdeal R a ↔ aeval a p = 0 :=
@@ -75,6 +83,7 @@ variable (𝕜)
 
 open Submodule
 
+#print Polynomial.annIdealGenerator /-
 /-- `ann_ideal_generator 𝕜 a` is the monic generator of `ann_ideal 𝕜 a`
 if one exists, otherwise `0`.
 
@@ -85,11 +94,18 @@ noncomputable def annIdealGenerator (a : A) : 𝕜[X] :=
   let g := IsPrincipal.generator <| annIdeal 𝕜 a
   g * C g.leadingCoeff⁻¹
 #align polynomial.ann_ideal_generator Polynomial.annIdealGenerator
+-/
 
 section
 
 variable {𝕜}
 
+/- warning: polynomial.ann_ideal_generator_eq_zero_iff -> Polynomial.annIdealGenerator_eq_zero_iff is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} {A : Type.{u2}} [_inst_1 : Field.{u1} 𝕜] [_inst_2 : Ring.{u2} A] [_inst_3 : Algebra.{u1, u2} 𝕜 A (Semifield.toCommSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 _inst_1)) (Ring.toSemiring.{u2} A _inst_2)] {a : A}, Iff (Eq.{succ u1} (Polynomial.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1)))) (Polynomial.annIdealGenerator.{u1, u2} 𝕜 A _inst_1 _inst_2 _inst_3 a) (OfNat.ofNat.{u1} (Polynomial.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1)))) 0 (OfNat.mk.{u1} (Polynomial.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1)))) 0 (Zero.zero.{u1} (Polynomial.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1)))) (Polynomial.zero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1)))))))) (Eq.{succ u1} (Ideal.{u1} (Polynomial.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (Semifield.toCommSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 _inst_1)))) (Polynomial.semiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (Semifield.toCommSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 _inst_1))))) (Polynomial.annIdeal.{u1, u2} 𝕜 A (Semifield.toCommSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 _inst_1)) (Ring.toSemiring.{u2} A _inst_2) _inst_3 a) (Bot.bot.{u1} (Ideal.{u1} (Polynomial.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (Semifield.toCommSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 _inst_1)))) (Polynomial.semiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (Semifield.toCommSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 _inst_1))))) (Submodule.hasBot.{u1, u1} (Polynomial.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (Semifield.toCommSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 _inst_1)))) (Polynomial.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (Semifield.toCommSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 _inst_1)))) (Polynomial.semiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (Semifield.toCommSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (Semifield.toCommSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (Semifield.toCommSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (Semifield.toCommSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 _inst_1)))) (Polynomial.semiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (Semifield.toCommSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 _inst_1))))))) (Semiring.toModule.{u1} (Polynomial.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (Semifield.toCommSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 _inst_1)))) (Polynomial.semiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (Semifield.toCommSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 _inst_1))))))))
+but is expected to have type
+  forall {𝕜 : Type.{u2}} {A : Type.{u1}} [_inst_1 : Field.{u2} 𝕜] [_inst_2 : Ring.{u1} A] [_inst_3 : Algebra.{u2, u1} 𝕜 A (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)) (Ring.toSemiring.{u1} A _inst_2)] {a : A}, Iff (Eq.{succ u2} (Polynomial.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)))) (Polynomial.annIdealGenerator.{u2, u1} 𝕜 A _inst_1 _inst_2 _inst_3 a) (OfNat.ofNat.{u2} (Polynomial.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)))) 0 (Zero.toOfNat0.{u2} (Polynomial.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)))) (Polynomial.zero.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))))))) (Eq.{succ u2} (Ideal.{u2} (Polynomial.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)))) (Polynomial.semiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))))) (Polynomial.annIdeal.{u2, u1} 𝕜 A (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)) (Ring.toSemiring.{u1} A _inst_2) _inst_3 a) (Bot.bot.{u2} (Ideal.{u2} (Polynomial.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)))) (Polynomial.semiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))))) (Submodule.instBotSubmodule.{u2, u2} (Polynomial.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)))) (Polynomial.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)))) (Polynomial.semiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)))) (Polynomial.semiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))))))) (Semiring.toModule.{u2} (Polynomial.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)))) (Polynomial.semiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))))))))
+Case conversion may be inaccurate. Consider using '#align polynomial.ann_ideal_generator_eq_zero_iff Polynomial.annIdealGenerator_eq_zero_iffₓ'. -/
 @[simp]
 theorem annIdealGenerator_eq_zero_iff {a : A} : annIdealGenerator 𝕜 a = 0 ↔ annIdeal 𝕜 a = ⊥ := by
   simp only [ann_ideal_generator, mul_eq_zero, is_principal.eq_bot_iff_generator_eq_zero,
@@ -98,6 +114,12 @@ theorem annIdealGenerator_eq_zero_iff {a : A} : annIdealGenerator 𝕜 a = 0 ↔
 
 end
 
+/- warning: polynomial.span_singleton_ann_ideal_generator -> Polynomial.span_singleton_annIdealGenerator is a dubious translation:
+lean 3 declaration is
+  forall (𝕜 : Type.{u1}) {A : Type.{u2}} [_inst_1 : Field.{u1} 𝕜] [_inst_2 : Ring.{u2} A] [_inst_3 : Algebra.{u1, u2} 𝕜 A (Semifield.toCommSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 _inst_1)) (Ring.toSemiring.{u2} A _inst_2)] (a : A), Eq.{succ u1} (Ideal.{u1} (Polynomial.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (Semifield.toCommSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 _inst_1)))) (Polynomial.semiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (Semifield.toCommSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 _inst_1))))) (Ideal.span.{u1} (Polynomial.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (Semifield.toCommSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 _inst_1)))) (Polynomial.semiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (Semifield.toCommSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 _inst_1)))) (Singleton.singleton.{u1, u1} (Polynomial.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1)))) (Set.{u1} (Polynomial.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (Semifield.toCommSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 _inst_1))))) (Set.hasSingleton.{u1} (Polynomial.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (Semifield.toCommSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 _inst_1))))) (Polynomial.annIdealGenerator.{u1, u2} 𝕜 A _inst_1 _inst_2 _inst_3 a))) (Polynomial.annIdeal.{u1, u2} 𝕜 A (Semifield.toCommSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 _inst_1)) (Ring.toSemiring.{u2} A _inst_2) _inst_3 a)
+but is expected to have type
+  forall (𝕜 : Type.{u2}) {A : Type.{u1}} [_inst_1 : Field.{u2} 𝕜] [_inst_2 : Ring.{u1} A] [_inst_3 : Algebra.{u2, u1} 𝕜 A (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)) (Ring.toSemiring.{u1} A _inst_2)] (a : A), Eq.{succ u2} (Ideal.{u2} (Polynomial.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)))) (Polynomial.semiring.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))))) (Ideal.span.{u2} (Polynomial.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)))) (Polynomial.semiring.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)))) (Singleton.singleton.{u2, u2} (Polynomial.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)))) (Set.{u2} (Polynomial.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))))) (Set.instSingletonSet.{u2} (Polynomial.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))))) (Polynomial.annIdealGenerator.{u2, u1} 𝕜 A _inst_1 _inst_2 _inst_3 a))) (Polynomial.annIdeal.{u2, u1} 𝕜 A (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)) (Ring.toSemiring.{u1} A _inst_2) _inst_3 a)
+Case conversion may be inaccurate. Consider using '#align polynomial.span_singleton_ann_ideal_generator Polynomial.span_singleton_annIdealGeneratorₓ'. -/
 /-- `ann_ideal_generator 𝕜 a` is indeed a generator. -/
 @[simp]
 theorem span_singleton_annIdealGenerator (a : A) :
@@ -113,16 +135,34 @@ theorem span_singleton_annIdealGenerator (a : A) :
     apply (mul_ne_zero_iff.mp h).1
 #align polynomial.span_singleton_ann_ideal_generator Polynomial.span_singleton_annIdealGenerator
 
+/- warning: polynomial.ann_ideal_generator_mem -> Polynomial.annIdealGenerator_mem is a dubious translation:
+lean 3 declaration is
+  forall (𝕜 : Type.{u1}) {A : Type.{u2}} [_inst_1 : Field.{u1} 𝕜] [_inst_2 : Ring.{u2} A] [_inst_3 : Algebra.{u1, u2} 𝕜 A (Semifield.toCommSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 _inst_1)) (Ring.toSemiring.{u2} A _inst_2)] (a : A), Membership.Mem.{u1, u1} (Polynomial.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1)))) (Ideal.{u1} (Polynomial.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (Semifield.toCommSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 _inst_1)))) (Polynomial.semiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (Semifield.toCommSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 _inst_1))))) (SetLike.hasMem.{u1, u1} (Ideal.{u1} (Polynomial.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (Semifield.toCommSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 _inst_1)))) (Polynomial.semiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (Semifield.toCommSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 _inst_1))))) (Polynomial.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (Semifield.toCommSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 _inst_1)))) (Submodule.setLike.{u1, u1} (Polynomial.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (Semifield.toCommSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 _inst_1)))) (Polynomial.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (Semifield.toCommSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 _inst_1)))) (Polynomial.semiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (Semifield.toCommSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (Semifield.toCommSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (Semifield.toCommSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (Semifield.toCommSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 _inst_1)))) (Polynomial.semiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (Semifield.toCommSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 _inst_1))))))) (Semiring.toModule.{u1} (Polynomial.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (Semifield.toCommSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 _inst_1)))) (Polynomial.semiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (Semifield.toCommSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 _inst_1))))))) (Polynomial.annIdealGenerator.{u1, u2} 𝕜 A _inst_1 _inst_2 _inst_3 a) (Polynomial.annIdeal.{u1, u2} 𝕜 A (Semifield.toCommSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 _inst_1)) (Ring.toSemiring.{u2} A _inst_2) _inst_3 a)
+but is expected to have type
+  forall (𝕜 : Type.{u2}) {A : Type.{u1}} [_inst_1 : Field.{u2} 𝕜] [_inst_2 : Ring.{u1} A] [_inst_3 : Algebra.{u2, u1} 𝕜 A (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)) (Ring.toSemiring.{u1} A _inst_2)] (a : A), Membership.mem.{u2, u2} (Polynomial.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)))) (Ideal.{u2} (Polynomial.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)))) (Polynomial.semiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))))) (SetLike.instMembership.{u2, u2} (Ideal.{u2} (Polynomial.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)))) (Polynomial.semiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))))) (Polynomial.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)))) (Submodule.setLike.{u2, u2} (Polynomial.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)))) (Polynomial.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)))) (Polynomial.semiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)))) (Polynomial.semiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))))))) (Semiring.toModule.{u2} (Polynomial.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)))) (Polynomial.semiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))))))) (Polynomial.annIdealGenerator.{u2, u1} 𝕜 A _inst_1 _inst_2 _inst_3 a) (Polynomial.annIdeal.{u2, u1} 𝕜 A (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)) (Ring.toSemiring.{u1} A _inst_2) _inst_3 a)
+Case conversion may be inaccurate. Consider using '#align polynomial.ann_ideal_generator_mem Polynomial.annIdealGenerator_memₓ'. -/
 /-- The annihilating ideal generator is a member of the annihilating ideal. -/
 theorem annIdealGenerator_mem (a : A) : annIdealGenerator 𝕜 a ∈ annIdeal 𝕜 a :=
   Ideal.mul_mem_right _ _ (Submodule.IsPrincipal.generator_mem _)
 #align polynomial.ann_ideal_generator_mem Polynomial.annIdealGenerator_mem
 
+/- warning: polynomial.mem_iff_eq_smul_ann_ideal_generator -> Polynomial.mem_iff_eq_smul_annIdealGenerator is a dubious translation:
+lean 3 declaration is
+  forall (𝕜 : Type.{u1}) {A : Type.{u2}} [_inst_1 : Field.{u1} 𝕜] [_inst_2 : Ring.{u2} A] [_inst_3 : Algebra.{u1, u2} 𝕜 A (Semifield.toCommSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 _inst_1)) (Ring.toSemiring.{u2} A _inst_2)] {p : Polynomial.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1)))} (a : A), Iff (Membership.Mem.{u1, u1} (Polynomial.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1)))) (Ideal.{u1} (Polynomial.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (Semifield.toCommSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 _inst_1)))) (Polynomial.semiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (Semifield.toCommSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 _inst_1))))) (SetLike.hasMem.{u1, u1} (Ideal.{u1} (Polynomial.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (Semifield.toCommSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 _inst_1)))) (Polynomial.semiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (Semifield.toCommSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 _inst_1))))) (Polynomial.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (Semifield.toCommSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 _inst_1)))) (Submodule.setLike.{u1, u1} (Polynomial.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (Semifield.toCommSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 _inst_1)))) (Polynomial.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (Semifield.toCommSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 _inst_1)))) (Polynomial.semiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (Semifield.toCommSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (Semifield.toCommSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (Semifield.toCommSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (Semifield.toCommSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 _inst_1)))) (Polynomial.semiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (Semifield.toCommSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 _inst_1))))))) (Semiring.toModule.{u1} (Polynomial.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (Semifield.toCommSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 _inst_1)))) (Polynomial.semiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (Semifield.toCommSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 _inst_1))))))) p (Polynomial.annIdeal.{u1, u2} 𝕜 A (Semifield.toCommSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 _inst_1)) (Ring.toSemiring.{u2} A _inst_2) _inst_3 a)) (Exists.{succ u1} (Polynomial.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1)))) (fun (s : Polynomial.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1)))) => Eq.{succ u1} (Polynomial.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1)))) p (SMul.smul.{u1, u1} (Polynomial.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1)))) (Polynomial.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1)))) (Mul.toSMul.{u1} (Polynomial.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1)))) (Polynomial.mul'.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))))) s (Polynomial.annIdealGenerator.{u1, u2} 𝕜 A _inst_1 _inst_2 _inst_3 a))))
+but is expected to have type
+  forall (𝕜 : Type.{u2}) {A : Type.{u1}} [_inst_1 : Field.{u2} 𝕜] [_inst_2 : Ring.{u1} A] [_inst_3 : Algebra.{u2, u1} 𝕜 A (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)) (Ring.toSemiring.{u1} A _inst_2)] {p : Polynomial.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)))} (a : A), Iff (Membership.mem.{u2, u2} (Polynomial.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)))) (Ideal.{u2} (Polynomial.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)))) (Polynomial.semiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))))) (SetLike.instMembership.{u2, u2} (Ideal.{u2} (Polynomial.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)))) (Polynomial.semiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))))) (Polynomial.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)))) (Submodule.setLike.{u2, u2} (Polynomial.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)))) (Polynomial.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)))) (Polynomial.semiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)))) (Polynomial.semiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))))))) (Semiring.toModule.{u2} (Polynomial.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)))) (Polynomial.semiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))))))) p (Polynomial.annIdeal.{u2, u1} 𝕜 A (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)) (Ring.toSemiring.{u1} A _inst_2) _inst_3 a)) (Exists.{succ u2} (Polynomial.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)))) (fun (s : Polynomial.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)))) => Eq.{succ u2} (Polynomial.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)))) p (HSMul.hSMul.{u2, u2, u2} (Polynomial.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)))) (Polynomial.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)))) (Polynomial.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)))) (instHSMul.{u2, u2} (Polynomial.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)))) (Polynomial.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)))) (Algebra.toSMul.{u2, u2} (Polynomial.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)))) (Polynomial.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)))) (Polynomial.commSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) (Polynomial.semiring.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)))) (Algebra.id.{u2} (Polynomial.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)))) (Polynomial.commSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)))))) s (Polynomial.annIdealGenerator.{u2, u1} 𝕜 A _inst_1 _inst_2 _inst_3 a))))
+Case conversion may be inaccurate. Consider using '#align polynomial.mem_iff_eq_smul_ann_ideal_generator Polynomial.mem_iff_eq_smul_annIdealGeneratorₓ'. -/
 theorem mem_iff_eq_smul_annIdealGenerator {p : 𝕜[X]} (a : A) :
     p ∈ annIdeal 𝕜 a ↔ ∃ s : 𝕜[X], p = s • annIdealGenerator 𝕜 a := by
   simp_rw [@eq_comm _ p, ← mem_span_singleton, ← span_singleton_ann_ideal_generator 𝕜 a, Ideal.span]
 #align polynomial.mem_iff_eq_smul_ann_ideal_generator Polynomial.mem_iff_eq_smul_annIdealGenerator
 
+/- warning: polynomial.monic_ann_ideal_generator -> Polynomial.monic_annIdealGenerator is a dubious translation:
+lean 3 declaration is
+  forall (𝕜 : Type.{u1}) {A : Type.{u2}} [_inst_1 : Field.{u1} 𝕜] [_inst_2 : Ring.{u2} A] [_inst_3 : Algebra.{u1, u2} 𝕜 A (Semifield.toCommSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 _inst_1)) (Ring.toSemiring.{u2} A _inst_2)] (a : A), (Ne.{succ u1} (Polynomial.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1)))) (Polynomial.annIdealGenerator.{u1, u2} 𝕜 A _inst_1 _inst_2 _inst_3 a) (OfNat.ofNat.{u1} (Polynomial.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1)))) 0 (OfNat.mk.{u1} (Polynomial.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1)))) 0 (Zero.zero.{u1} (Polynomial.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1)))) (Polynomial.zero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1)))))))) -> (Polynomial.Monic.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))) (Polynomial.annIdealGenerator.{u1, u2} 𝕜 A _inst_1 _inst_2 _inst_3 a))
+but is expected to have type
+  forall (𝕜 : Type.{u2}) {A : Type.{u1}} [_inst_1 : Field.{u2} 𝕜] [_inst_2 : Ring.{u1} A] [_inst_3 : Algebra.{u2, u1} 𝕜 A (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)) (Ring.toSemiring.{u1} A _inst_2)] (a : A), (Ne.{succ u2} (Polynomial.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)))) (Polynomial.annIdealGenerator.{u2, u1} 𝕜 A _inst_1 _inst_2 _inst_3 a) (OfNat.ofNat.{u2} (Polynomial.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)))) 0 (Zero.toOfNat0.{u2} (Polynomial.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)))) (Polynomial.zero.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))))))) -> (Polynomial.Monic.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) (Polynomial.annIdealGenerator.{u2, u1} 𝕜 A _inst_1 _inst_2 _inst_3 a))
+Case conversion may be inaccurate. Consider using '#align polynomial.monic_ann_ideal_generator Polynomial.monic_annIdealGeneratorₓ'. -/
 /-- The generator we chose for the annihilating ideal is monic when the ideal is non-zero. -/
 theorem monic_annIdealGenerator (a : A) (hg : annIdealGenerator 𝕜 a ≠ 0) :
     Monic (annIdealGenerator 𝕜 a) :=
@@ -136,17 +176,31 @@ theorem of the minimal polynomial.
 This is the first condition: it must annihilate the original element `a : A`. -/
 
 
+#print Polynomial.annIdealGenerator_aeval_eq_zero /-
 theorem annIdealGenerator_aeval_eq_zero (a : A) : aeval a (annIdealGenerator 𝕜 a) = 0 :=
   mem_annIdeal_iff_aeval_eq_zero.mp (annIdealGenerator_mem 𝕜 a)
 #align polynomial.ann_ideal_generator_aeval_eq_zero Polynomial.annIdealGenerator_aeval_eq_zero
+-/
 
 variable {𝕜}
 
+/- warning: polynomial.mem_iff_ann_ideal_generator_dvd -> Polynomial.mem_iff_annIdealGenerator_dvd is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align polynomial.mem_iff_ann_ideal_generator_dvd Polynomial.mem_iff_annIdealGenerator_dvdₓ'. -/
 theorem mem_iff_annIdealGenerator_dvd {p : 𝕜[X]} {a : A} :
     p ∈ annIdeal 𝕜 a ↔ annIdealGenerator 𝕜 a ∣ p := by
   rw [← Ideal.mem_span_singleton, span_singleton_ann_ideal_generator]
 #align polynomial.mem_iff_ann_ideal_generator_dvd Polynomial.mem_iff_annIdealGenerator_dvd
 
+/- warning: polynomial.degree_ann_ideal_generator_le_of_mem -> Polynomial.degree_annIdealGenerator_le_of_mem is a dubious translation:
+lean 3 declaration is
+  forall {𝕜 : Type.{u1}} {A : Type.{u2}} [_inst_1 : Field.{u1} 𝕜] [_inst_2 : Ring.{u2} A] [_inst_3 : Algebra.{u1, u2} 𝕜 A (Semifield.toCommSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 _inst_1)) (Ring.toSemiring.{u2} A _inst_2)] (a : A) (p : Polynomial.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1)))), (Membership.Mem.{u1, u1} (Polynomial.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1)))) (Ideal.{u1} (Polynomial.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (Semifield.toCommSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 _inst_1)))) (Polynomial.semiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (Semifield.toCommSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 _inst_1))))) (SetLike.hasMem.{u1, u1} (Ideal.{u1} (Polynomial.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (Semifield.toCommSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 _inst_1)))) (Polynomial.semiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (Semifield.toCommSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 _inst_1))))) (Polynomial.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (Semifield.toCommSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 _inst_1)))) (Submodule.setLike.{u1, u1} (Polynomial.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (Semifield.toCommSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 _inst_1)))) (Polynomial.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (Semifield.toCommSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 _inst_1)))) (Polynomial.semiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (Semifield.toCommSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} (Polynomial.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (Semifield.toCommSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (Polynomial.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (Semifield.toCommSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 _inst_1)))) (Semiring.toNonAssocSemiring.{u1} (Polynomial.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (Semifield.toCommSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 _inst_1)))) (Polynomial.semiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (Semifield.toCommSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 _inst_1))))))) (Semiring.toModule.{u1} (Polynomial.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (Semifield.toCommSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 _inst_1)))) (Polynomial.semiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (Semifield.toCommSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 _inst_1))))))) p (Polynomial.annIdeal.{u1, u2} 𝕜 A (Semifield.toCommSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 _inst_1)) (Ring.toSemiring.{u2} A _inst_2) _inst_3 a)) -> (Ne.{succ u1} (Polynomial.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1)))) p (OfNat.ofNat.{u1} (Polynomial.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1)))) 0 (OfNat.mk.{u1} (Polynomial.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1)))) 0 (Zero.zero.{u1} (Polynomial.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1)))) (Polynomial.zero.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1)))))))) -> (LE.le.{0} (WithBot.{0} Nat) (Preorder.toHasLe.{0} (WithBot.{0} Nat) (WithBot.preorder.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (Polynomial.degree.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))) (Polynomial.annIdealGenerator.{u1, u2} 𝕜 A _inst_1 _inst_2 _inst_3 a)) (Polynomial.degree.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))) p))
+but is expected to have type
+  forall {𝕜 : Type.{u2}} {A : Type.{u1}} [_inst_1 : Field.{u2} 𝕜] [_inst_2 : Ring.{u1} A] [_inst_3 : Algebra.{u2, u1} 𝕜 A (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)) (Ring.toSemiring.{u1} A _inst_2)] (a : A) (p : Polynomial.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)))), (Membership.mem.{u2, u2} (Polynomial.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)))) (Ideal.{u2} (Polynomial.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)))) (Polynomial.semiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))))) (SetLike.instMembership.{u2, u2} (Ideal.{u2} (Polynomial.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)))) (Polynomial.semiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))))) (Polynomial.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)))) (Submodule.setLike.{u2, u2} (Polynomial.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)))) (Polynomial.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)))) (Polynomial.semiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u2} (Polynomial.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} (Polynomial.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)))) (Semiring.toNonAssocSemiring.{u2} (Polynomial.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)))) (Polynomial.semiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))))))) (Semiring.toModule.{u2} (Polynomial.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)))) (Polynomial.semiring.{u2} 𝕜 (CommSemiring.toSemiring.{u2} 𝕜 (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))))))) p (Polynomial.annIdeal.{u2, u1} 𝕜 A (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)) (Ring.toSemiring.{u1} A _inst_2) _inst_3 a)) -> (Ne.{succ u2} (Polynomial.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)))) p (OfNat.ofNat.{u2} (Polynomial.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)))) 0 (Zero.toOfNat0.{u2} (Polynomial.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)))) (Polynomial.zero.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))))))) -> (LE.le.{0} (WithBot.{0} Nat) (Preorder.toLE.{0} (WithBot.{0} Nat) (WithBot.preorder.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)))) (Polynomial.degree.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) (Polynomial.annIdealGenerator.{u2, u1} 𝕜 A _inst_1 _inst_2 _inst_3 a)) (Polynomial.degree.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) p))
+Case conversion may be inaccurate. Consider using '#align polynomial.degree_ann_ideal_generator_le_of_mem Polynomial.degree_annIdealGenerator_le_of_memₓ'. -/
 /-- The generator of the annihilating ideal has minimal degree among
  the non-zero members of the annihilating ideal -/
 theorem degree_annIdealGenerator_le_of_mem (a : A) (p : 𝕜[X]) (hp : p ∈ annIdeal 𝕜 a)
@@ -156,6 +210,12 @@ theorem degree_annIdealGenerator_le_of_mem (a : A) (p : 𝕜[X]) (hp : p ∈ ann
 
 variable (𝕜)
 
+/- warning: polynomial.ann_ideal_generator_eq_minpoly -> Polynomial.annIdealGenerator_eq_minpoly is a dubious translation:
+lean 3 declaration is
+  forall (𝕜 : Type.{u1}) {A : Type.{u2}} [_inst_1 : Field.{u1} 𝕜] [_inst_2 : Ring.{u2} A] [_inst_3 : Algebra.{u1, u2} 𝕜 A (Semifield.toCommSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 _inst_1)) (Ring.toSemiring.{u2} A _inst_2)] (a : A), Eq.{succ u1} (Polynomial.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1)))) (Polynomial.annIdealGenerator.{u1, u2} 𝕜 A _inst_1 _inst_2 _inst_3 a) (minpoly.{u1, u2} 𝕜 A (EuclideanDomain.toCommRing.{u1} 𝕜 (Field.toEuclideanDomain.{u1} 𝕜 _inst_1)) _inst_2 _inst_3 a)
+but is expected to have type
+  forall (𝕜 : Type.{u2}) {A : Type.{u1}} [_inst_1 : Field.{u2} 𝕜] [_inst_2 : Ring.{u1} A] [_inst_3 : Algebra.{u2, u1} 𝕜 A (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)) (Ring.toSemiring.{u1} A _inst_2)] (a : A), Eq.{succ u2} (Polynomial.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)))) (Polynomial.annIdealGenerator.{u2, u1} 𝕜 A _inst_1 _inst_2 _inst_3 a) (minpoly.{u2, u1} 𝕜 A (EuclideanDomain.toCommRing.{u2} 𝕜 (Field.toEuclideanDomain.{u2} 𝕜 _inst_1)) _inst_2 _inst_3 a)
+Case conversion may be inaccurate. Consider using '#align polynomial.ann_ideal_generator_eq_minpoly Polynomial.annIdealGenerator_eq_minpolyₓ'. -/
 /-- The generator of the annihilating ideal is the minimal polynomial. -/
 theorem annIdealGenerator_eq_minpoly (a : A) : annIdealGenerator 𝕜 a = minpoly 𝕜 a :=
   by
@@ -172,6 +232,12 @@ theorem annIdealGenerator_eq_minpoly (a : A) : annIdealGenerator 𝕜 a = minpol
           q_monic.NeZero
 #align polynomial.ann_ideal_generator_eq_minpoly Polynomial.annIdealGenerator_eq_minpoly
 
+/- warning: polynomial.monic_generator_eq_minpoly -> Polynomial.monic_generator_eq_minpoly is a dubious translation:
+lean 3 declaration is
+  forall (𝕜 : Type.{u1}) {A : Type.{u2}} [_inst_1 : Field.{u1} 𝕜] [_inst_2 : Ring.{u2} A] [_inst_3 : Algebra.{u1, u2} 𝕜 A (Semifield.toCommSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 _inst_1)) (Ring.toSemiring.{u2} A _inst_2)] (a : A) (p : Polynomial.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1)))), (Polynomial.Monic.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1))) p) -> (Eq.{succ u1} (Ideal.{u1} (Polynomial.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (Semifield.toCommSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 _inst_1)))) (Polynomial.semiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (Semifield.toCommSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 _inst_1))))) (Ideal.span.{u1} (Polynomial.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (Semifield.toCommSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 _inst_1)))) (Polynomial.semiring.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (Semifield.toCommSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 _inst_1)))) (Singleton.singleton.{u1, u1} (Polynomial.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1)))) (Set.{u1} (Polynomial.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (Semifield.toCommSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 _inst_1))))) (Set.hasSingleton.{u1} (Polynomial.{u1} 𝕜 (CommSemiring.toSemiring.{u1} 𝕜 (Semifield.toCommSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 _inst_1))))) p)) (Polynomial.annIdeal.{u1, u2} 𝕜 A (Semifield.toCommSemiring.{u1} 𝕜 (Field.toSemifield.{u1} 𝕜 _inst_1)) (Ring.toSemiring.{u2} A _inst_2) _inst_3 a)) -> (Eq.{succ u1} (Polynomial.{u1} 𝕜 (Ring.toSemiring.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 _inst_1)))) (Polynomial.annIdealGenerator.{u1, u2} 𝕜 A _inst_1 _inst_2 _inst_3 a) p)
+but is expected to have type
+  forall (𝕜 : Type.{u2}) {A : Type.{u1}} [_inst_1 : Field.{u2} 𝕜] [_inst_2 : Ring.{u1} A] [_inst_3 : Algebra.{u2, u1} 𝕜 A (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)) (Ring.toSemiring.{u1} A _inst_2)] (a : A) (p : Polynomial.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)))), (Polynomial.Monic.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))) p) -> (Eq.{succ u2} (Ideal.{u2} (Polynomial.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)))) (Polynomial.semiring.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))))) (Ideal.span.{u2} (Polynomial.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)))) (Polynomial.semiring.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)))) (Singleton.singleton.{u2, u2} (Polynomial.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)))) (Set.{u2} (Polynomial.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))))) (Set.instSingletonSet.{u2} (Polynomial.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1))))) p)) (Polynomial.annIdeal.{u2, u1} 𝕜 A (Semifield.toCommSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)) (Ring.toSemiring.{u1} A _inst_2) _inst_3 a)) -> (Eq.{succ u2} (Polynomial.{u2} 𝕜 (DivisionSemiring.toSemiring.{u2} 𝕜 (Semifield.toDivisionSemiring.{u2} 𝕜 (Field.toSemifield.{u2} 𝕜 _inst_1)))) (Polynomial.annIdealGenerator.{u2, u1} 𝕜 A _inst_1 _inst_2 _inst_3 a) p)
+Case conversion may be inaccurate. Consider using '#align polynomial.monic_generator_eq_minpoly Polynomial.monic_generator_eq_minpolyₓ'. -/
 /-- If a monic generates the annihilating ideal, it must match our choice
  of the annihilating ideal generator. -/
 theorem monic_generator_eq_minpoly (a : A) (p : 𝕜[X]) (p_monic : p.Monic)

d3e8e0a0

bump to nightly-2023-03-08-10

mathlib commit https://github.com/leanprover-community/mathlib/commit/38f16f960f5006c6c0c2bac7b0aba5273188f4e5

422cc012

Diff

@@ -83,7 +83,7 @@ Since `𝕜[X]` is a principal ideal domain there is a polynomial `g` such that
  We prefer the monic generator of the ideal. -/
 noncomputable def annIdealGenerator (a : A) : 𝕜[X] :=
   let g := IsPrincipal.generator <| annIdeal 𝕜 a
-  g * c g.leadingCoeff⁻¹
+  g * C g.leadingCoeff⁻¹
 #align polynomial.ann_ideal_generator Polynomial.annIdealGenerator
 
 section
@@ -93,7 +93,7 @@ variable {𝕜}
 @[simp]
 theorem annIdealGenerator_eq_zero_iff {a : A} : annIdealGenerator 𝕜 a = 0 ↔ annIdeal 𝕜 a = ⊥ := by
   simp only [ann_ideal_generator, mul_eq_zero, is_principal.eq_bot_iff_generator_eq_zero,
-    Polynomial.c_eq_zero, inv_eq_zero, Polynomial.leadingCoeff_eq_zero, or_self_iff]
+    Polynomial.C_eq_zero, inv_eq_zero, Polynomial.leadingCoeff_eq_zero, or_self_iff]
 #align polynomial.ann_ideal_generator_eq_zero_iff Polynomial.annIdealGenerator_eq_zero_iff
 
 end

d3e8e0a0

bump to nightly-2023-02-21-16

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

1107b979

Changes in mathlib4

mathlib3

mathlib4

d3e8e0a0

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

@@ -41,7 +41,6 @@ namespace Polynomial
 section Semiring
 
 variable {R A : Type*} [CommSemiring R] [Semiring A] [Algebra R A]
-
 variable (R)
 
 /-- `annIdeal R a` is the *annihilating ideal* of all `p : R[X]` such that `p(a) = 0`.
@@ -67,7 +66,6 @@ end Semiring
 section Field
 
 variable {𝕜 A : Type*} [Field 𝕜] [Ring A] [Algebra 𝕜 A]
-
 variable (𝕜)
 
 open Submodule

d3e8e0a0

feat: sum and product of commuting semisimple endomorphisms (#10808)

Prove isSemisimple_of_mem_adjoin: if two commuting endomorphisms of a finite-dimensional vector space over a perfect field are both semisimple, then every endomorphism in the algebra generated by them (in particular their product and sum) is semisimple.
In the same file LinearAlgebra/Semisimple.lean, eq_zero_of_isNilpotent_isSemisimple and isSemisimple_of_squarefree_aeval_eq_zero are golfed, and IsSemisimple.minpoly_squarefree is proved

RingTheory/SimpleModule.lean:

Define IsSemisimpleRing R to mean that R is a semisimple R-module. add properties of simple modules and a characterization (they are exactly the quotients of the ring by maximal left ideals).
The annihilator of a semisimple module is a radical ideal.
Any module over a semisimple ring is semisimple.
A finite product of semisimple rings is semisimple.
Any quotient of a semisimple ring is semisimple.
Add Artin--Wedderburn as a TODO (proof_wanted).
Order/Atoms.lean: add the instance from IsSimpleOrder to ComplementedLattice, so that IsSimpleModule → IsSemisimpleModule is automatically inferred.

Prerequisites for showing a product of semisimple rings is semisimple:

Algebra/Module/Submodule/Map.lean: generalize orderIsoMapComap so that it only requires RingHomSurjective rather than RingHomInvPair
Algebra/Ring/CompTypeclasses.lean, Mathlib/Algebra/Ring/Pi.lean, Algebra/Ring/Prod.lean: add RingHomSurjective instances

RingTheory/Artinian.lean:

quotNilradicalEquivPi: the quotient of a commutative Artinian ring R by its nilradical is isomorphic to the (finite) product of its quotients by maximal ideals (therefore a product of fields). equivPi: if the ring is moreover reduced, then the ring itself is a product of fields. Deduce that R is a semisimple ring and both R and R[X] are decomposition monoids. Requires RingEquiv.quotientBot in RingTheory/Ideal/QuotientOperations.lean.
Data/Polynomial/Eval.lean: the polynomial ring over a finite product of rings is isomorphic to the product of polynomial rings over individual rings. (Used to show R[X] is a decomposition monoid.)

Other necessary results:

FieldTheory/Minpoly/Field.lean: the minimal polynomial of an element in a reduced algebra over a field is radical.
RingTheory/PowerBasis.lean: generalize PowerBasis.finiteDimensional and rename it to .finite.

Annihilator stuff, some of which do not end up being used:

RingTheory/Ideal/Operations.lean: define Module.annihilator and redefine Submodule.annihilator in terms of it; add lemmas, including one that says an arbitrary intersection of radical ideals is radical. The new lemma Ideal.isRadical_iff_pow_one_lt depends on pow_imp_self_of_one_lt in Mathlib/Data/Nat/Interval.lean, which is also used to golf the proof of isRadical_iff_pow_one_lt.
Algebra/Module/Torsion.lean: add a lemma and an instance (unused)
Data/Polynomial/Module/Basic.lean: add a def (unused) and a lemma
LinearAlgebra/AnnihilatingPolynomial.lean: add lemma span_minpoly_eq_annihilator

Some results about idempotent linear maps (projections) and idempotent elements, used to show that any (left) ideal in a semisimple ring is spanned by an idempotent element (unused):

LinearAlgebra/Projection.lean: add def isIdempotentElemEquiv
LinearAlgebra/Span.lean: add two lemmas

Co-authored-by: Junyan Xu <junyanxu.math@gmail.com>

0b52a6a5

Diff

@@ -177,6 +177,11 @@ theorem monic_generator_eq_minpoly (a : A) (p : 𝕜[X]) (p_monic : p.Monic)
     · apply monic_annIdealGenerator _ _ ((Associated.ne_zero_iff p_gen).mp h)
 #align polynomial.monic_generator_eq_minpoly Polynomial.monic_generator_eq_minpoly
 
+theorem span_minpoly_eq_annihilator {M} [AddCommGroup M] [Module 𝕜 M] (f : Module.End 𝕜 M) :
+    Ideal.span {minpoly 𝕜 f} = Module.annihilator 𝕜[X] (Module.AEval' f) := by
+  rw [← annIdealGenerator_eq_minpoly, span_singleton_annIdealGenerator]; ext
+  rw [mem_annIdeal_iff_aeval_eq_zero, DFunLike.ext_iff, Module.mem_annihilator]; rfl
+
 end Field
 
 end Polynomial

d3e8e0a0

chore: update/remove heart beat bumps (#6860)

We clean up heart beat bumps after #6474.

c95f05bd

Diff

@@ -72,7 +72,6 @@ variable (𝕜)
 
 open Submodule
 
-set_option synthInstance.maxHeartbeats 35000 in
 /-- `annIdealGenerator 𝕜 a` is the monic generator of `annIdeal 𝕜 a`
 if one exists, otherwise `0`.

d3e8e0a0

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

@@ -40,7 +40,7 @@ namespace Polynomial
 
 section Semiring
 
-variable {R A : Type _} [CommSemiring R] [Semiring A] [Algebra R A]
+variable {R A : Type*} [CommSemiring R] [Semiring A] [Algebra R A]
 
 variable (R)
 
@@ -66,7 +66,7 @@ end Semiring
 
 section Field
 
-variable {𝕜 A : Type _} [Field 𝕜] [Ring A] [Algebra 𝕜 A]
+variable {𝕜 A : Type*} [Field 𝕜] [Ring A] [Algebra 𝕜 A]
 
 variable (𝕜)

d3e8e0a0

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) 2022 Justin Thomas. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Justin Thomas
-
-! This file was ported from Lean 3 source module linear_algebra.annihilating_polynomial
-! leanprover-community/mathlib commit d3e8e0a0237c10c2627bf52c246b15ff8e7df4c0
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.FieldTheory.Minpoly.Field
 import Mathlib.RingTheory.PrincipalIdealDomain
 
+#align_import linear_algebra.annihilating_polynomial from "leanprover-community/mathlib"@"d3e8e0a0237c10c2627bf52c246b15ff8e7df4c0"
+
 /-!
 # Annihilating Ideal

d3e8e0a0

feat: port LinearAlgebra.AnnihilatingPolynomial (#4252)

c4f284bd

`linear_algebra.annihilating_polynomial` ⟷ `Mathlib.LinearAlgebra.AnnihilatingPolynomial`

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Dependencies 10 + 630

linear_algebra.annihilating_polynomial ⟷ Mathlib.LinearAlgebra.AnnihilatingPolynomial

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Dependencies 10 + 630

`linear_algebra.annihilating_polynomial` ⟷ `Mathlib.LinearAlgebra.AnnihilatingPolynomial`