proposition: Lemma coefZ a p i : (a *: p)`_i = a * p`_i.
proof: Proof. rewrite -[*:%R]/scale_poly unlock coef_poly. by case: leqP => // le_p_n; rewrite nth_default ?mulr0. Qed.
imports: HB(structures) mathcomp(ssreflect ssrbool ssrfun eqtype ssrnat seq choice) mathcomp(fintype bigop finset tuple) mathcomp(div ssralg countalg binomial)