[Merged by Bors] - feat(Combinatorics/Nullstellensatz): Alon's combinatorial Nullstellensatz - #20495
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[Merged by Bors] - feat(Combinatorics/Nullstellensatz): Alon's combinatorial Nullstellensatz#20495AntoineChambert-Loir wants to merge 168 commits into
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Co-authored-by: Yaël Dillies <yael.dillies@gmail.com>
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Looks all good to me. I'll let @b-mehta do the final call.
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LGTM since Bhavik is seemingly unavailable maintainer merge |
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🚀 Pull request has been placed on the maintainer queue by YaelDillies. |
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This looks very nice, thank you! And my sincerest apologies for the delay.
bors d+
| f.sum_option_index _ (fun _ => zero_smul _ _) fun _ _ _ => add_smul _ _ _ | ||
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| theorem eq_option_embedding_update_none_iff [Zero M] {n : Option α →₀ M} {m : α →₀ M} {i : M} : | ||
| (n = (embDomain Embedding.some m).update none i) ↔ |
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| (n = (embDomain Embedding.some m).update none i) ↔ | |
| n = (embDomain Embedding.some m).update none i ↔ |
| ext m | ||
| simp only [coeff_zero, optionEquivLeft_coeff_coeff] | ||
| set n := (embDomain Function.Embedding.some m).update none d with hn | ||
| -- set n := embDomain Function.Embedding.some m + Finsupp.single none d with hn |
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| -- set n := embDomain Function.Embedding.some m + Finsupp.single none d with hn |
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| ∃ (h : σ →₀ MvPolynomial σ R) | ||
| (_ : ∀ i, ((∏ s ∈ S i, (X i - C s)) * h i).totalDegree ≤ f.totalDegree), | ||
| f = linearCombination (MvPolynomial σ R) (fun i ↦ ∏ r ∈ S i, (X i - C r)) h := by |
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Perhaps I'm missing something, but it looks like this should be written as ∃ (h : σ →₀ MvPolynomial σ R), then the conjunction of the two statements, rather than a double-exists? That is, the rhs of exists_prop rather than the lhs.
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| · rw [← hj] | ||
| exact h' |
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| · rw [← hj] | |
| exact h' | |
| · rwa [← hj] |
optional and untested, but it appears cleaner here!
| (f : MvPolynomial σ R) | ||
| (t : σ →₀ ℕ) (ht : f.coeff t ≠ 0) (ht' : f.totalDegree = t.degree) | ||
| (S : σ → Finset R) (htS : ∀ i, t i < #(S i)) : | ||
| ∃ (s : σ → R) (_ : ∀ i, s i ∈ S i), eval s f ≠ 0 := by |
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bors r+
Le 6 avril 2025 21:29:20 GMT+02:00, "mathlib-bors[bot]" ***@***.***> a écrit :
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…satz (#20495) This is a formalization of Alon's Combinatorial Nullstellensatz. Meanwhile, prove several results * a multivariate polynomial that vanishes on a too large product set vanishes identically Probably, this file should belong to the `RingTheory.MvPolynomial` hierarchy.
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…satz (#20495) This is a formalization of Alon's Combinatorial Nullstellensatz. Meanwhile, prove several results * a multivariate polynomial that vanishes on a too large product set vanishes identically Probably, this file should belong to the `RingTheory.MvPolynomial` hierarchy.
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Pull request successfully merged into master. Build succeeded: |
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…satz (#20495) This is a formalization of Alon's Combinatorial Nullstellensatz. Meanwhile, prove several results * a multivariate polynomial that vanishes on a too large product set vanishes identically Probably, this file should belong to the `RingTheory.MvPolynomial` hierarchy.
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This is a formalization of Alon's Combinatorial Nullstellensatz.
Meanwhile, prove several results
Probably, this file should belong to the
RingTheory.MvPolynomialhierarchy.