substAlgHom_coe — Mathlib

English

Substituting a into a monomial a monomial form gives a product expression: substAlgHom ha (monomial e r) = algebraMap(r) · (e.prod (a s)^n).

Русский

Подстановка в мономиал даёт произведение: substAlgHom ha (monomial e r) = algebraMap(r) · (e.prod (a s)^n).

LaTeX

$$$\\operatorname{substAlgHom ha} (\\mathrm{monomial} \\ e\\ r) = (\\mathrm{algebraMap}\\ R (\\mathrm{MvPowerSeries}_{\\tau S}))\\ r \\,*\, \\biggl(e.prod \\ h \\mapsto (a\\, h)^n\\biggr)$$$

Lean4

theorem substAlgHom_coe (ha : HasSubst a) (p : MvPolynomial σ R) : substAlgHom (R := R) ha p = MvPolynomial.aeval a p :=
  by simp [substAlgHom]

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