proposition: Lemma sgp_right_scale c p x : sgp_right (c *: p) x = sgr c * sgp_right p x.
proof: Proof. have [->|c0] := eqVneq c 0; first by rewrite scale0r sgr0 mul0r sgp_right0. by rewrite -mul_polyC sgp_right_mul sgp_rightNroot ?hornerC ?rootC ?c0. Qed.
imports: mathcomp.ssreflect.ssreflect mathcomp(ssrfun ssrbool eqtype ssrnat seq choice fintype) mathcomp(bigop order ssralg poly polydiv ssrnum zmodp) mathcomp(polyorder path interval ssrint)