[Merged by Bors] - feat(Algebra): misc lemmas and cleanup #18431
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PR summary dab732db8a
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| File | Base Count | Head Count | Change |
|---|---|---|---|
| Mathlib.FieldTheory.PrimitiveElement | 1358 | 1350 | -8 (-0.59%) |
| Mathlib.FieldTheory.IsSepClosed | 1374 | 1366 | -8 (-0.58%) |
Import changes for all files
| Files | Import difference |
|---|---|
9 filesMathlib.AlgebraicGeometry.EllipticCurve.J Mathlib.FieldTheory.AbelRuffini Mathlib.FieldTheory.Minpoly.MinpolyDiv Mathlib.FieldTheory.IsSepClosed Mathlib.FieldTheory.KrullTopology Mathlib.FieldTheory.Finite.GaloisField Mathlib.FieldTheory.Galois.Basic Mathlib.FieldTheory.PrimitiveElement Mathlib.FieldTheory.PolynomialGaloisGroup |
-8 |
21 filesMathlib.Analysis.CStarAlgebra.GelfandDuality Mathlib.Analysis.CStarAlgebra.Spectrum Mathlib.Analysis.Normed.Algebra.Spectrum Mathlib.Analysis.CStarAlgebra.Module.Constructions Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Isometric Mathlib.Analysis.CStarAlgebra.Module.Defs Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Integral Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Unique Mathlib.Analysis.CStarAlgebra.ApproximateUnit Mathlib.Analysis.SpecialFunctions.ContinuousFunctionalCalculus.ExpLog Mathlib.Analysis.Complex.Polynomial.Basic Mathlib.FieldTheory.Cardinality Mathlib.Analysis.InnerProductSpace.StarOrder Mathlib.Analysis.Normed.Algebra.Basic Mathlib.RingTheory.Polynomial.Selmer Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Instances Mathlib.Analysis.CStarAlgebra.Hom Mathlib.Analysis.Complex.Polynomial.UnitTrinomial Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Order Mathlib.LinearAlgebra.Matrix.HermitianFunctionalCalculus Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Basic |
-6 |
Declarations diff
+ IsAlgClosure.of_splits
+ Subspace.biUnion_ne_univ_of_top_nmem
+ Subspace.exists_eq_top_of_iUnion_eq_univ
+ Subspace.top_mem_of_biUnion_eq_univ
+ adjoin_ext
+ eq_iff_aeval_eq_zero
+ eq_iff_aeval_minpoly_eq_zero
+ ext_of_eq_adjoin
You can run this locally as follows
## summary with just the declaration names:
./scripts/declarations_diff.sh <optional_commit>
## more verbose report:
./scripts/declarations_diff.sh long <optional_commit>The doc-module for script/declarations_diff.sh contains some details about this script.
2 tasks
Ruben-VandeVelde
approved these changes
Nov 3, 2024
| p = minpoly A x ↔ Polynomial.aeval x p = 0 := | ||
| ⟨(· ▸ aeval A x), (eq_of_irreducible_of_monic hp1 · hp3)⟩ | ||
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| theorem eq_iff_aeval_minpoly_eq_zero [IsDomain B] {C} [Ring C] [Algebra A C] [Nontrivial C] |
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| theorem eq_iff_aeval_minpoly_eq_zero [IsDomain B] {C} [Ring C] [Algebra A C] [Nontrivial C] | |
| theorem eq_iff_aeval_minpoly_eq_zero [IsDomain B] {C : Type*} [Ring C] [Algebra A C] [Nontrivial C] |
There was a problem hiding this comment.
Is it not clear from [Ring C] that C is a Type*? Or are there other concerns? Worried that C may be inferred to be of some fixed universe rather than polymorphic?
| @[deprecated (since := "2024-10-29")] | ||
| alias Subspace.exists_eq_top_of_biUnion_eq_univ := Subspace.top_mem_of_biUnion_eq_univ | ||
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| theorem Subspace.exists_eq_top_of_iUnion_eq_univ {ι} [Finite ι] {p : ι → Subspace k E} |
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| theorem Subspace.exists_eq_top_of_iUnion_eq_univ {ι} [Finite ι] {p : ι → Subspace k E} | |
| theorem Subspace.exists_eq_top_of_iUnion_eq_univ {ι : Type*} [Finite ι] {p : ι → Subspace k E} |
or Sort*?
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Finite allows Sort*. Leaving the type unspecified has the advantage that you don't need to worry about this.
alreadydone
commented
Nov 5, 2024
| p = minpoly A x ↔ Polynomial.aeval x p = 0 := | ||
| ⟨(· ▸ aeval A x), (eq_of_irreducible_of_monic hp1 · hp3)⟩ | ||
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| theorem eq_iff_aeval_minpoly_eq_zero [IsDomain B] {C} [Ring C] [Algebra A C] [Nontrivial C] |
There was a problem hiding this comment.
Is it not clear from [Ring C] that C is a Type*? Or are there other concerns? Worried that C may be inferred to be of some fixed universe rather than polymorphic?
| @[deprecated (since := "2024-10-29")] | ||
| alias Subspace.exists_eq_top_of_biUnion_eq_univ := Subspace.top_mem_of_biUnion_eq_univ | ||
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| theorem Subspace.exists_eq_top_of_iUnion_eq_univ {ι} [Finite ι] {p : ι → Subspace k E} |
There was a problem hiding this comment.
Finite allows Sort*. Leaving the type unspecified has the advantage that you don't need to worry about this.
jcommelin
reviewed
Nov 7, 2024
| p = minpoly A x ↔ Polynomial.aeval x p = 0 := | ||
| ⟨(· ▸ aeval A x), (eq_of_irreducible_of_monic hp1 · hp3)⟩ | ||
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| theorem eq_iff_aeval_minpoly_eq_zero [IsDomain B] {C} [Ring C] [Algebra A C] [Nontrivial C] |
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+ In IsAlgClosed/Basic we add the fact that an algebraic extension E/F is an algebraic closure if all (monic irreducible) polynomials in F[X] split in E. In fact it suffices that every such polynomial has a root in E, but is used to deduce the "split" version in #18412. + Swap the order of `AlgHom.card_of_splits` and `AlgHom.card` in FieldTheory/PrimitiveElement to avoid importing AlgebraicClosure. + Simplify the statements of two theorems in GroupTheory/CosetCover and deduce an easier-to-use form. + Add two extensionality lemmas for AlgHom out of `Algebra.adjoin R s` in RingTheory/Adjoin/Basic. + Add two lemmas to Minpoly/Field and golf `minpoly.eq_of_root` in FieldTheory/Adjoin. Co-authored-by: Junyan Xu <[email protected]>
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In IsAlgClosed/Basic we add the fact that an algebraic extension E/F is an algebraic closure if all (monic irreducible) polynomials in F[X] split in E. In fact it suffices that every such polynomial has a root in E, but is used to deduce the "split" version in feat(FieldTheory): minimal polynomials determine an algebraic extension (Isaacs 1980) #18412.
Swap the order of
AlgHom.card_of_splitsandAlgHom.cardin FieldTheory/PrimitiveElement to avoid importing AlgebraicClosure.Simplify the statements of two theorems in GroupTheory/CosetCover and deduce an easier-to-use form.
Add two extensionality lemmas for AlgHom out of
Algebra.adjoin R sin RingTheory/Adjoin/Basic.Add two lemmas to Minpoly/Field and golf
minpoly.eq_of_rootin FieldTheory/Adjoin.