(************************************************************************)
(*         *   The Coq Proof Assistant / The Coq Development Team       *)
(*  v      *         Copyright INRIA, CNRS and contributors             *)
(* <O___,, * (see version control and CREDITS file for authors & dates) *)
(*   \VV/  **************************************************************)
(*    //   *    This file is distributed under the terms of the         *)
(*         *     GNU Lesser General Public License Version 2.1          *)
(*         *     (see LICENSE file for the text of the license)         *)
(************************************************************************)

module IMap : CSig.MapS with type key = int

type proof

module Fourier : sig
  val find_point : Polynomial.cstr list -> (Vect.t, proof) Util.union
  val optimise : Vect.t -> Polynomial.cstr list -> Itv.interval option
end

val pp_proof : out_channel -> proof -> unit

module Proof : sig
  val mk_proof :
    Polynomial.cstr list -> proof -> (Vect.t * Polynomial.cstr) list

  val add_op : Polynomial.op -> Polynomial.op -> Polynomial.op
end

exception TimeOut