(** * Basic polynomials *)
(** ** Constant polynomial  - [pcst ar a] is the constant polynomial with [ar] variables and equal to the constant [a]. *)
Definition pcst (ar a:nat) : pol :=
(ar, [(a,nil)]).

(* Specifications: *)
Lemma parity_pcst ar a :
parity (pcst ar a) = ar.
Lemma pscalar_mon_correct : forall n m l,
peval_mon (pscalar_mon n m) l = n * peval_mon m l.
Lemma pscalar_correct : forall n p l,
peval (pscalar n p) l = n * peval p l.