(* $Id: ringFieldSig.mli,v 1.13 2008/01/30 19:45:10 averell Exp $ *)
(**
  Signatures for modules representing algebraic rings and fields.

  @author Florent Hivert
*)


module type RING = sig
  type t
    (** The type of the elements of the ring. *)
  val zero   : t
    (** The zero of the ring. *)
  val one    : t
    (** The one of the ring. *)
  val of_int : int -> t
    (** The multiple of the one of the ring. *)
  val is_zero : t -> bool
    (** Test fo zero element. *)
  val ( =/ ) : t -> t -> bool
    (** The equality of two elements of the ring. *)
  val ( +/ ) : t -> t -> t
    (** The sum of two elements of the ring. *)
  val ( -/ ) : t -> t -> t
    (** The difference of two elements of the ring. *)
  val negate : t -> t
    (** The negation of a element of the ring. *)
  val ( */ ) : t -> t -> t
    (** The product of two elements of the ring. *)
  val pow    : t -> int -> t
    (** The power of an element of the ring by a [int]. *)
  val print  : t -> unit
    (** Pretty print an element of the ring. *)
end

module type POLY = 
sig
  type coeffRing

  include RING   

  (* convert from ring and from/to ring list *)
  val of_R     : coeffRing -> t
  val of_Rlist : coeffRing list -> t
  val to_Rlist : t -> coeffRing list

  (* the X polynomial *)
  val x        : t
  val multX    : t -> t
  val multXn   : t -> int -> t
  val monome   : coeffRing -> int -> t
  val degree   : t -> int
  val multCoeff : t -> coeffRing -> t
  val coeff    : t -> int -> coeffRing
  val lcoeff   : t -> coeffRing
  val eval     : t -> coeffRing -> coeffRing
end