Theorems · Theorem · commutative algebra

MvPowerSeries.coeff_eq_zero_of_lt_weightedOrder

∀ {σ : Type u_1} {R : Type u_2} [inst : Semiring R] (w : σ → ℕ) {f : MvPowerSeries σ R} {d : σ →₀ ℕ},
  ↑((Finsupp.weight w) d) < MvPowerSeries.weightedOrder w f → (MvPowerSeries.coeff d) f = 0

The nth coefficient of a formal power series is 0 if n is strictly smaller than the order of the power series.

Defined in

Mathlib.RingTheory.MvPowerSeries.Order

Cited by

14 results in Mathlib

Foundations

Depth 84 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

Semiring