Theorems · Theorem · commutative algebra

MvPolynomial.weightedTotalDegree_eq_zero_iff

∀ {R : Type u_1} {M : Type u_2} [inst : CommSemiring R] {σ : Type u_3} [inst_1 : AddCommMonoid M]
  [inst_2 : LinearOrder M] [inst_3 : OrderBot M] [CanonicallyOrderedAdd M] {w : σ → M},
  MvPolynomial.NonTorsionWeight w →
    ∀ (p : MvPolynomial σ R), MvPolynomial.weightedTotalDegree w p = 0 ↔ ∀ m ∈ p.support, ∀ (x : σ), m x = 0

If w is a nontorsion weight function, then a multivariate polynomial has weighted total degree zero if and only if for every m ∈ p.support and x : σ, m x = 0.

Defined in

Mathlib.RingTheory.MvPolynomial.WeightedHomogeneous

Cited by

1 results in Mathlib

Foundations

Depth 82 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommSemiringAddCommMonoidLinearOrderOrderBotCanonicallyOrderedAdd