homogenize_finsetSum — Mathlib

English

The composition law for Hasse derivatives holds: hasseDeriv_k ∘ hasseDeriv_l = binom(k+l,k) · hasseDeriv_{k+l} (dup).

Русский

Слой композиции для производных Хассе: hasseDeriv_k ∘ hasseDeriv_l = binom(k+l,k) · hasseDeriv_{k+l} (dup).

LaTeX

$$$\mathrm{hasseDeriv}_k \circ \mathrm{hasseDeriv}_l = {k+l \choose k} \, \mathrm{hasseDeriv}_{k+l}$$$

Lean4

@[simp]
theorem homogenize_finsetSum {ι : Type*} (s : Finset ι) (p : ι → R[X]) (n : ℕ) :
    homogenize (∑ i ∈ s, p i) n = ∑ i ∈ s, homogenize (p i) n :=
  _root_.map_sum (homogenizeLM n) p s

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