Theorems · Theorem · commutative algebra

MvPolynomial.coeff_weightedHomogeneousComponent

∀ {R : Type u_1} {M : Type u_2} [inst : CommSemiring R] {σ : Type u_3} [inst_1 : AddCommMonoid M] {w : σ → M} (n : M)
  (φ : MvPolynomial σ R) [inst_2 : DecidableEq M] (d : σ →₀ ℕ),
  MvPolynomial.coeff d ((MvPolynomial.weightedHomogeneousComponent w n) φ) =
    if (Finsupp.weight w) d = n then MvPolynomial.coeff d φ else 0

Defined in

Mathlib.RingTheory.MvPolynomial.WeightedHomogeneous

Cited by

8 results in Mathlib

Foundations

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

Assumes

CommSemiringAddCommMonoidDecidableEq