(** ** Scalar multiplication of a polynomial

  - [pscalar n p] is the polynomial [p] where all coefficients have been multiplied by [n].
*)

Definition pscalar_mon (n:nat)(m:mon) : mon :=
  (n * fst m, snd m).Definition pscalar (n:nat)(p:pol) : pol :=
  (fst p, map (pscalar_mon n) (snd p)).

Lemma pscalar_mon_correct : forall n m l, peval_mon (pscalar_mon n m) l = n * peval_mon m l.