Theorems · Theorem · commutative algebra

MvPolynomial.isWeightedHomogeneous_zero_iff_weightedTotalDegree_eq_zero

∀ {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} {p : MvPolynomial σ R},
  MvPolynomial.IsWeightedHomogeneous w p 0 ↔ MvPolynomial.weightedTotalDegree w p = 0

A multivariate polynomial is weighted homogeneous of weighted degree zero if and only if its weighted total degree is equal to zero.

Defined in

Mathlib.RingTheory.MvPolynomial.WeightedHomogeneous

Cited by

2 results in Mathlib

Foundations

Depth 81 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommSemiringAddCommMonoidLinearOrderOrderBotCanonicallyOrderedAdd