Theorems · Theorem · commutative algebra

MvPolynomial.sum_weightedHomogeneousComponent

∀ {R : Type u_1} {M : Type u_2} [inst : CommSemiring R] {σ : Type u_3} [inst_1 : AddCommMonoid M] (w : σ → M)
  (φ : MvPolynomial σ R), ∑ᶠ (m : M), (MvPolynomial.weightedHomogeneousComponent w m) φ = φ

Every polynomial is the sum of its weighted homogeneous components.

Defined in

Mathlib.RingTheory.MvPolynomial.WeightedHomogeneous

Cited by

1 results in Mathlib

Foundations

Depth 85 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommSemiringAddCommMonoid