homogenize_add — Mathlib

English

Homogenization commutes with finite sums: homogenize (sum over i in s of p i) equals sum over i in s of homogenize (p i).

Русский

Гомогенизация сохраняет сумму по конечному множеству: homogenize (∑ p_i) = ∑ homogenize (p_i).

LaTeX

$$$\mathrm{homogenize}(\sum_{i\in s} p_i) = \sum_{i\in s} \mathrm{homogenize}(p_i)$$$

Lean4

@[simp]
theorem homogenize_add (p q : R[X]) (n : ℕ) : homogenize (p + q) n = homogenize p n + homogenize q n := by
  simp [homogenize, Finset.sum_add_distrib]

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