Theorems · Theorem · commutative algebra

PowerSeries.coeff_subst_X_pow

∀ {R : Type u_2} [inst : CommRing R] {S : Type u_4} [inst_1 : CommRing S] [inst_2 : Algebra R S] {k : ℕ},
  k ≠ 0 →
    ∀ (f : PowerSeries R) (n : ℕ),
      (PowerSeries.coeff n) (PowerSeries.subst (PowerSeries.X ^ k) f) =
        if k ∣ n then (algebraMap R S) ((PowerSeries.coeff (n / k)) f) else 0

Defined in

Mathlib.RingTheory.PowerSeries.Substitution

Cited by

2 results in Mathlib

Foundations

Depth 111 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingCommRingAlgebra