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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 *)
(************************************************************************)
type vname = string;;
type term =
| Zero
| Const of Num.num
| Var of vname
| Inv of term
| Opp of term
| Add of (term * term)
| Sub of (term * term)
| Mul of (term * term)
| Div of (term * term)
| Pow of (term * int)
type positivstellensatz =
Axiom_eq of int
| Axiom_le of int
| Axiom_lt of int
| Rational_eq of Num.num
| Rational_le of Num.num
| Rational_lt of Num.num
| Square of term
| Monoid of int list
| Eqmul of term * positivstellensatz
| Sum of positivstellensatz * positivstellensatz
| Product of positivstellensatz * positivstellensatz
type poly
val poly_isconst : poly -> bool
val poly_neg : poly -> poly
val poly_mul : poly -> poly -> poly
val poly_pow : poly -> int -> poly
val poly_const : Num.num -> poly
val poly_of_term : term -> poly
val term_of_poly : poly -> term
val term_of_sos : positivstellensatz * (Num.num * poly) list ->
positivstellensatz
val string_of_poly : poly -> string
exception TooDeep
val deepen_until : int -> (int -> 'a) -> int -> 'a
val real_positivnullstellensatz_general : bool -> int -> poly list ->
(poly * positivstellensatz) list ->
poly -> poly list * (positivstellensatz * (Num.num * poly) list) list
val sumofsquares : poly -> Num.num * ( Num.num * poly) list
|
