proposition: Fact scale_polyE a p : scale_poly a p = a%:P * p.
proof: Proof. apply/polyP=> n; rewrite unlock coef_poly coefCM. 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)