div — Mathlib

English

The divisor q in Weierstrass division is the limit of the inductively constructed sequence: div = PowerSeries.mk(i ↦ (H.divCoeff f i).1).

Русский

Делитель Вейершстра определяется как предел последовательности q_k: div = PowerSeries.mk(i ↦ (H.divCoeff f i).1).

LaTeX

$$$ \\text{div} = \\mathrm{PowerSeries.mk} \\big( i \\mapsto (H.\\divCoeff f i).1 \\big). $$$

Lean4

/-- The limit `q` of the
inductively constructed sequence `qₖ` in the proof of Weierstrass division. -/
noncomputable def div [IsPrecomplete I A] : A⟦X⟧ :=
  PowerSeries.mk fun i ↦ (H.divCoeff f i).1

Похожие утверждения