(** ** Power of a polynomial

  - [ppower p n] is the polynomial [p] to the power [n].
*)

Fixpoint ppower (p:pol)(n:nat) : pol :=
  match n with
  | 0 => pcst (fst p) 1
  | S n' => pmult p (ppower p n')
  end.

(* Specifications: *)
Lemma parity_ppower p n : parity (ppower p n) = parity p.
Lemma pWF_ppower p n : pWF p -> pWF (ppower p n).
Lemma ppower_correct p n l : peval (ppower p n) l = power (peval p l) n.