Theorems · Theorem · commutative algebra
MvPolynomial.mem_coeffs_iff
∀ {R : Type u} {σ : Type u_1} [inst : CommSemiring R] {p : MvPolynomial σ R} {c : R},
c ∈ p.coeffs ↔ ∃ n ∈ p.support, c = MvPolynomial.coeff n p- Defined in
- Mathlib.Algebra.MvPolynomial.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 75 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommSemiring
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Finsetstatement and proof · cited by 13,712
- CommSemiringstatement and proof · cited by 10,911
- Finsuppstatement and proof · cited by 5,255
- MvPolynomialstatement and proof · cited by 2,140
- MvPolynomial.coeffstatement and proof · cited by 315
- MvPolynomial.supportstatement and proof · cited by 220
- Classical.decEqproof · cited by 134
- Finset.mem_imageproof · cited by 105
- MvPolynomial.coeffsstatement · cited by 24
Cited by1
Results whose statement or proof uses this declaration.
- MvPolynomial.zero_notMem_coeffsproof · cited by 0