algebraMap_hahnSeries_injective — Mathlib

English

The inverse isomorphism toMvPowerSeries preserves coefficients: the n-th coefficient of (toMvPowerSeries)^{-1}(f) equals the n-th coefficient of f.

Русский

Обратное отображение toMvPowerSeries сохраняет коэффициенты: n-й коэффициент (toMvPowerSeries)^{-1}(f) равен n-м коэффициенту f.

LaTeX

$$$\\operatorname{coeff}_{n}(\\mathrm{toMvPowerSeries}^{-1}(f))=\\operatorname{MvPowerSeries}.\\mathrm{coeff}_{n}(f)$$$

Lean4

theorem _root_.Polynomial.algebraMap_hahnSeries_injective : Function.Injective (algebraMap R[X] (HahnSeries Γ R)) :=
  ofPowerSeries_injective.comp (Polynomial.coe_injective R)

Похожие утверждения