proposition: Lemma poly_take_drop n p : take_poly n p + drop_poly n p * 'X^n = p.
proof: Proof. apply/polyP => i; rewrite coefD coefMXn coef_take_poly coef_drop_poly. by case: ltnP => ni; rewrite ?addr0 ?add0r//= subnK. Qed.
imports: HB(structures) mathcomp(ssreflect ssrbool ssrfun eqtype ssrnat seq choice) mathcomp(fintype bigop finset tuple) mathcomp(div ssralg countalg binomial)