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|
(************************************************************************)
(* v * The Coq Proof Assistant / The Coq Development Team *)
(* <O___,, * CNRS-Ecole Polytechnique-INRIA Futurs-Universite Paris Sud *)
(* \VV/ **************************************************************)
(* // * This file is distributed under the terms of the *)
(* * GNU Lesser General Public License Version 2.1 *)
(************************************************************************)
(* Building recursive polynom operations from a type of coefficients *)
module type Coef = sig
type t
val equal : t -> t -> bool
val lt : t -> t -> bool
val le : t -> t -> bool
val abs : t -> t
val plus : t -> t -> t
val mult : t -> t -> t
val sub : t -> t -> t
val opp : t -> t
val div : t -> t -> t
val modulo : t -> t -> t
val puis : t -> int -> t
val pgcd : t -> t -> t
val hash : t -> int
val of_num : Num.num -> t
val to_string : t -> string
end
module type S = sig
type coef
type variable = int
type t = Pint of coef | Prec of variable * t array
val of_num : Num.num -> t
val x : variable -> t
val monome : variable -> int -> t
val is_constantP : t -> bool
val is_zero : t -> bool
val max_var_pol : t -> variable
val max_var_pol2 : t -> variable
val max_var : t array -> variable
val equal : t -> t -> bool
val norm : t -> t
val deg : variable -> t -> int
val deg_total : t -> int
val copyP : t -> t
val coef : variable -> int -> t -> t
val plusP : t -> t -> t
val content : t -> coef
val div_int : t -> coef -> t
val vire_contenu : t -> t
val vars : t -> variable list
val int_of_Pint : t -> coef
val multx : int -> variable -> t -> t
val multP : t -> t -> t
val deriv : variable -> t -> t
val oppP : t -> t
val moinsP : t -> t -> t
val puisP : t -> int -> t
val ( @@ ) : t -> t -> t
val ( -- ) : t -> t -> t
val ( ^^ ) : t -> int -> t
val coefDom : variable -> t -> t
val coefConst : variable -> t -> t
val remP : variable -> t -> t
val coef_int_tete : t -> coef
val normc : t -> t
val coef_constant : t -> coef
val univ : bool ref
val string_of_var : int -> string
val nsP : int ref
val to_string : t -> string
val printP : t -> unit
val print_tpoly : t array -> unit
val print_lpoly : t list -> unit
val quo_rem_pol : t -> t -> variable -> t * t
val div_pol : t -> t -> variable -> t
val divP : t -> t -> t
val div_pol_rat : t -> t -> bool
val pseudo_div : t -> t -> variable -> t * t * int * t
val pgcdP : t -> t -> t
val pgcd_pol : t -> t -> variable -> t
val content_pol : t -> variable -> t
val pgcd_coef_pol : t -> t -> variable -> t
val pgcd_pol_rec : t -> t -> variable -> t
val gcd_sub_res : t -> t -> variable -> t
val gcd_sub_res_rec : t -> t -> t -> t -> int -> variable -> t
val lazard_power : t -> t -> int -> variable -> t
val sans_carre : t -> variable -> t
val facteurs : t -> variable -> t list
val facteurs_impairs : t -> variable -> t list
val hcontentP : (string, t) Hashtbl.t
val prcontentP : unit -> unit
val contentP : t * variable -> t
val hash : t -> int
module Hashpol : Hashtbl.S with type key=t
val memoP : string -> 'a Hashpol.t -> (t -> 'a) -> t -> 'a
val hfactorise : t list list Hashpol.t
val prfactorise : unit -> unit
val factorise : t -> t list list
val facteurs2 : t -> t list
val pol_de_factorisation : t list list -> t
val set_of_array_facteurs : t list array -> t list
val factorise_tableauP2 :
t array -> t list array -> t array * (t * int list) array
val factorise_tableauP : t array -> t array * (t * int list) array
val is_positif : t -> bool
val is_negatif : t -> bool
val pseudo_euclide :
t list -> t -> t -> variable ->
t * t * int * t * t * (t * int) list * (t * int) list
val implique_non_nul : t list -> t -> bool
val ajoute_non_nul : t -> t list -> t list
end
module Make (C:Coef) : S with type coef = C.t
|
