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+(************************************************************************)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
+(* \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 Itv : sig
+
+ type interval = Num.num option * Num.num option
+ val range : interval -> Num.num option
+ val smaller_itv : interval -> interval -> bool
+
+end
+
+module IMap : CSig.MapS with type key = int
+
+type proof
+
+module Fourier : sig
+
+ val find_point : Polynomial.cstr_compat list ->
+ ((IMap.key * Num.num) list, proof) Util.union
+
+ val optimise : Polynomial.Vect.t ->
+ Polynomial.cstr_compat list ->
+ Itv.interval option
+
+end
+
+val pp_proof : out_channel -> proof -> unit
+
+module Proof : sig
+
+ val mk_proof : Polynomial.cstr_compat list ->
+ proof -> (Polynomial.Vect.t * Polynomial.cstr_compat) list
+
+ val add_op : Polynomial.op -> Polynomial.op -> Polynomial.op
+
+end
+
+val max_nb_cstr : int ref
+
+val eval_op : Polynomial.op -> Num.num -> Num.num -> bool
+
+exception TimeOut