homogenize_map — Mathlib

English

The homogenization commutes with polynomial maps: homogenize (p.map f) n = MvPolynomial.map f (homogenize p n).

Русский

Гомогенизация сохраняет отображение полиномов: homogenize (p.map f) n = MvPolynomial.map f (homogenize p n).

LaTeX

$$$\mathrm{homogenize}(p.map f)\, n = \mathrm{MvPolynomial.map} f\big( \mathrm{homogenize}(p,n) \big)$$$

Lean4

theorem homogenize_map {S : Type*} [CommSemiring S] (f : R →+* S) (p : R[X]) (n : ℕ) :
    homogenize (p.map f) n = MvPolynomial.map f (homogenize p n) := by simp [homogenize]

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