Theorems · Theorem · commutative algebra

MvPolynomial.IsWeightedHomogeneous.coeff_eq_zero

∀ {R : Type u_1} {M : Type u_2} [inst : CommSemiring R] {σ : Type u_3} [inst_1 : AddCommMonoid M] {φ : MvPolynomial σ R}
  {n : M} {w : σ → M},
  MvPolynomial.IsWeightedHomogeneous w φ n → ∀ (d : σ →₀ ℕ), (Finsupp.weight w) d ≠ n → MvPolynomial.coeff d φ = 0

The weighted degree of a weighted homogeneous polynomial controls its support.

Defined in

Mathlib.RingTheory.MvPolynomial.WeightedHomogeneous

Cited by

1 results in Mathlib

Foundations

Depth 80 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommSemiringAddCommMonoid