proposition: Lemma poly_numfield_eqp (p : {poly rat}) : p != 0 -> p ^^ in_alg _ %= \prod_(x <- numfield_roots p) ('X - x%:P).
proof: Proof. by move=> p_neq0; rewrite /numfield_roots; case: eqP => //= ?; case: sig2_eqW. Qed.
imports: HB(structures) mathcomp(all_ssreflect all_fingroup all_algebra) mathcomp(all_solvable all_field polyrcf) Abel(various classic_ext map_gal algR) Abel(char0 cyclotomic_ext real_closed_ext)