proposition: Lemma scale_poly_eq (p q : {poly R}) (a : R) : (a != 0) -> (p == q) = (p \scale a == q \scale a).
proof: Proof. move=> Ha. by rewrite /scaleX_poly -(subr_eq0 p q) -(@comp_poly2_eq0 _ (p - q) ('X * a%:P)) ?size_XmulC // rmorphB subr_eq add0r. Qed.
imports: mathcomp(all_ssreflect) mathcomp(ssralg poly polydiv polyorder ssrnum zmodp) mathcomp(polyrcf qe_rcf_th complex) poly_normal pol