Theorems · Theorem · commutative algebra
MvPolynomial.support_expand
∀ {σ : Type u_1} {R : Type u_3} [inst : CommSemiring R] {p : ℕ} (φ : MvPolynomial σ R) [inst_1 : DecidableEq σ],
p ≠ 0 → ((MvPolynomial.expand p) φ).support = Finset.image (fun x => p • x) φ.support- Defined in
- Mathlib.Algebra.MvPolynomial.Expand
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 100 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommSemiringDecidableEq
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Finsetstatement · cited by 13,712
- CommSemiringstatement and proof · cited by 10,911
- Finsuppstatement and proof · cited by 5,255
- AlgHomstatement · cited by 3,236
- MvPolynomialstatement and proof · cited by 2,140
- Finset.imagestatement · cited by 910
- LE.le.antisymmproof · cited by 507
- MvPolynomial.supportstatement · cited by 220
- MvPolynomial.expandstatement · cited by 44
- MvPolynomial.coeff_expand_smulproof · cited by 6
- MvPolynomial.support_expand_subsetproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- MvPolynomial.totalDegree_expandproof · cited by 0