(* Build a polynomial directly from a list of coefficients. *)
Definition Poly := foldr cons_poly 0%:P.

(* Specifications: *)
Lemma PolyK c s : last c s != 0 -> Poly s = s :> seq R.
Lemma polyseqK p : Poly p = p.
Lemma coef_Poly s i : (Poly s)`_i = s`_i.
Definition poly_expanded_def n E := Poly (mkseq E n).