(**************************************************
**             polynome.mli                     ***
**        Formal polynome module                ***
**      POUSSARD PA    march 2000               ***
**************************************************)

open Input_util
open Algebra
open Format

(* it is both a subtype of Euclidian_Ring and Vectorial Space *)
module type Polynomial  =
sig
  include Vectorial_Space
    
  type stathm = int (* type of polynome stathm that is it's degree ! *)
		  
  type init = (int -> scalar -> unit ) -> unit		

  val one : elem
  val t_of_int : int -> elem
  val ( ** ) : elem -> elem -> elem
      
  val degree : elem -> stathm
  val stathm : elem -> stathm
  val less  : stathm -> stathm -> bool
      
  val ( // ) : elem -> elem -> elem (* div quotient *)
  val (mod)   : elem -> elem -> elem (* div remainder *)
  val div_mod : elem -> elem -> elem * elem (* fst : // ,snd : mod *) 

  val derive : elem -> elem (* derivate *)
  val int  : elem -> elem (* intergrate *)
      
  val vcreate: init -> int -> elem (* creation function. works like
				    Vector.vcreate *)
  val monome : scalar -> int ->elem (* elem = t*x^(int) *)
  val copy : elem -> elem (* copy in new struct *)
      
  val vget : elem -> int -> scalar
      (* raise Invalid_argument if int < 0 *)
  val vput :  elem -> int -> scalar -> unit
      (* raise Invalid_argument if int < 0 or int > degree *)
end

(* it is both a subtype of Euclidian_Ring and Banach *)
module type Normed_Polynomial =
sig
  include Banach

  type stathm = int (* type of polynome stathm that is it's degree ! *)
		  
  type init = (int -> scalar -> unit ) -> unit		
      (*ring struct*)
  val one : elem
  val t_of_int : int -> elem
  val ( ** ) : elem -> elem -> elem
      
  val degree : elem -> stathm
  val stathm : elem -> stathm
  val less  : stathm -> stathm -> bool
      
  val ( // ) : elem -> elem -> elem (* div quotient *)
  val (mod)   : elem -> elem -> elem (* div remainder *)
  val div_mod : elem -> elem -> elem * elem (* fst : // ,snd : mod *) 

  val derive : elem -> elem (* derivate *)
  val int  : elem -> elem (* intergrate *)
      
  val vcreate: init -> int -> elem (* creation function. works like
				    Vector.vcreate *)
  val monome : scalar -> int ->elem (* elem = t*x^(int) *)
  val copy : elem -> elem (* copy in new struct *)
      
  val vget : elem -> int -> scalar
      (* raise Invalid_argument if int < 0 *)
  val vput :  elem -> int -> scalar -> unit
      (* raise Invalid_argument if int < 0 or int > degree *)
end

  
module Make (R0:Field) : Polynomial
  with type scalar = R0.elem 
  and type stathm = int 

module Make_Normed(R0:Normed_Field) : Normed_Polynomial
  with type scalar = R0.elem 
  and type stathm = int 
  and type norm = R0.norm