homogenizeLM — Mathlib

English

The factorial multiple of hasseDeriv k equals the k-fold iterate of derivative (dup).

Русский

Факториальная кратность умножения на hasseDeriv_k равна k-кратной итерации производной (dup).

LaTeX

$$$k! \cdot \mathrm{hasseDeriv}_k = \operatorname{derivative}^{\,k}$$$

Lean4

/-- `homogenize` as a bundled linear map. -/
@[simps]
noncomputable def homogenizeLM (n : ℕ) : R[X] →ₗ[R] MvPolynomial (Fin 2) R
    where
  toFun p := homogenize p n
  map_add' := (homogenize_add · · n)
  map_smul' := (homogenize_smul · · n)

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