proposition: Lemma map_Qnum_poly (nu : {rmorphism algC -> algC}) p : p \in polyOver 1%VS -> map_poly (nu \o QnC) p = (map_poly QnC p).
proof: Proof. move=> Qp; apply/polyP=> i; rewrite /= !coef_map /=. have /vlineP[a ->]: p`_i \in 1%VS by apply: polyOverP. by rewrite alg_num_field !fmorph_rat. Qed.
imports: HB(structures) mathcomp(ssreflect ssrbool ssrfun eqtype ssrnat seq path) mathcomp(div choice fintype tuple finfun bigop prime) mathcomp(ssralg poly polydiv ssrnum ssrint archimedean rat) mathcomp(finalg zmodp matrix mxalgebra mxpoly vector intdiv) mathcomp(falgebra fieldext separable galois algC cyclotomic)