Theorems · Theorem · commutative algebra
MvPolynomial.ext_iff
∀ {R : Type u} {σ : Type u_1} [inst : CommSemiring R] {p q : MvPolynomial σ R},
p = q ↔ ∀ (m : σ →₀ ℕ), MvPolynomial.coeff m p = MvPolynomial.coeff m q- Defined in
- Mathlib.Algebra.MvPolynomial.Basic
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 61 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.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- 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.extproof · cited by 61
Cited by4
Results whose statement or proof uses this declaration.
- MvPolynomial.ker_mapproof · cited by 3
- MvPolynomial.monomial_dvd_monomialproof · cited by 2
- MvPolynomial.C_dvd_iff_map_hom_eq_zeroproof · cited by 1
- MvPolynomial.eq_zero_iffproof · cited by 1