Theorems · Theorem · commutative algebra

MvPolynomial.weightedHomogeneousComponent_of_mem

∀ {R : Type u_1} {M : Type u_2} [inst : CommSemiring R] {σ : Type u_3} [inst_1 : AddCommMonoid M] {w : σ → M}
  [inst_2 : DecidableEq M] {m n : M} {p : MvPolynomial σ R},
  p ∈ MvPolynomial.weightedHomogeneousSubmodule R w n →
    (MvPolynomial.weightedHomogeneousComponent w m) p = if m = n then p else 0

The weighted homogeneous components of a weighted homogeneous polynomial.

Defined in

Mathlib.RingTheory.MvPolynomial.WeightedHomogeneous

Cited by

2 results in Mathlib

Foundations

Depth 87 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommSemiringAddCommMonoidDecidableEq