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/******************************************************************************
* Top contributors (to current version):
* Gereon Kremer, Aina Niemetz
*
* This file is part of the cvc5 project.
*
* Copyright (c) 2009-2021 by the authors listed in the file AUTHORS
* in the top-level source directory and their institutional affiliations.
* All rights reserved. See the file COPYING in the top-level source
* directory for licensing information.
* ****************************************************************************
*
* Utilities for converting to and from LibPoly objects.
*/
#ifndef CVC5__THEORY__ARITH__NL__POLY_CONVERSION_H
#define CVC5__THEORY__ARITH__NL__POLY_CONVERSION_H
#include "cvc4_private.h"
#ifdef CVC5_POLY_IMP
#include <poly/polyxx.h>
#include <cstddef>
#include <map>
#include <utility>
#include "expr/node.h"
#include "util/real_algebraic_number.h"
namespace cvc5 {
namespace theory {
namespace arith {
class BoundInference;
namespace nl {
/** Bijective mapping between CVC4 variables and poly variables. */
struct VariableMapper
{
/** A mapping from CVC4 variables to poly variables. */
std::map<cvc5::Node, poly::Variable> mVarCVCpoly;
/** A mapping from poly variables to CVC4 variables. */
std::map<poly::Variable, cvc5::Node> mVarpolyCVC;
/** Retrieves the according poly variable. */
poly::Variable operator()(const cvc5::Node& n);
/** Retrieves the according CVC4 variable. */
cvc5::Node operator()(const poly::Variable& n);
};
/** Convert a poly univariate polynomial to a cvc5::Node. */
cvc5::Node as_cvc_upolynomial(const poly::UPolynomial& p,
const cvc5::Node& var);
/** Convert a cvc5::Node to a poly univariate polynomial. */
poly::UPolynomial as_poly_upolynomial(const cvc5::Node& n,
const cvc5::Node& var);
/**
* Constructs a polynomial from the given node.
*
* While a Node may contain rationals, a Polynomial does not.
* We therefore also store the denominator of the returned polynomial and
* use it to construct the integer polynomial recursively.
* Once the polynomial has been fully constructed, we can oftentimes ignore the
* denominator (except for its sign, which is always positive, though).
* This is the case if we are solely interested in the roots of the polynomials
* (like in the context of CAD). If we need the actual polynomial (for example
* in the context of ICP) the second overload provides the denominator in the
* third argument.
*/
poly::Polynomial as_poly_polynomial(const cvc5::Node& n, VariableMapper& vm);
poly::Polynomial as_poly_polynomial(const cvc5::Node& n,
VariableMapper& vm,
poly::Rational& denominator);
/**
* Constructs a node from the given polynomial.
*
* This methods does the straight-forward conversion from a polynomial into Node
* representation, using the given variable mapper.
* The resulting node is not minimized in any form (it may contain spurious
* multiplications with one or use NONLINEAR_MULT where regular MULT may be
* sufficient), so it may be sensible to rewrite it afterwards.
*/
cvc5::Node as_cvc_polynomial(const poly::Polynomial& p, VariableMapper& vm);
/**
* Constructs a constraints (a polynomial and a sign condition) from the given
* node.
*/
std::pair<poly::Polynomial, poly::SignCondition> as_poly_constraint(
Node n, VariableMapper& vm);
/**
* Transforms a real algebraic number to a node suitable for putting it into a
* model. The resulting node can be either a constant (suitable for
* addCheckModelSubstitution) or a witness term (suitable for
* addCheckModelWitness).
*/
Node ran_to_node(const RealAlgebraicNumber& ran, const Node& ran_variable);
Node ran_to_node(const poly::AlgebraicNumber& an, const Node& ran_variable);
/**
* Transforms a poly::Value to a node.
* The resulting node can be either a constant or a witness term.
*/
Node value_to_node(const poly::Value& v, const Node& ran_variable);
/**
* Constructs a lemma that excludes a given interval from the feasible values of
* a variable. Conceptually, the resulting lemma has the form
* (OR
* (<= var interval.lower)
* (<= interval.upper var)
* )
* This method honors the interval bound types (open or closed), but also deals
* with real algebraic endpoints. If allowNonlinearLemma is false, real
* algebraic endpoints are reflected by coarse (numeric) approximations and thus
* may lead to lemmas that are weaker than they could be. Also, lemma creation
* may fail altogether.
* If allowNonlinearLemma is true, it tries to construct better lemmas (based on
* the sign of the defining polynomial of the real algebraic number). These
* lemmas are nonlinear, though, and may thus be expensive to use in the
* subsequent solving process.
*/
Node excluding_interval_to_lemma(const Node& variable,
const poly::Interval& interval,
bool allowNonlinearLemma);
/**
* Transforms a node to a poly::AlgebraicNumber.
* Expects a node of the following form:
* (AND
* (= (polynomial in __z) 0)
* (< CONST __z)
* (< __z CONST)
* )
*/
poly::AlgebraicNumber node_to_poly_ran(const Node& n, const Node& ran_variable);
/** Transforms a node to a RealAlgebraicNumber by calling node_to_poly_ran. */
RealAlgebraicNumber node_to_ran(const Node& n, const Node& ran_variable);
/**
* Transforms a node to a poly::Value.
*/
poly::Value node_to_value(const Node& n, const Node& ran_variable);
/**
* Give a rough estimate of the bitsize of the representation of `v`.
* It can be used as a rough measure of the size of complexity of a value, for
* example to avoid divergence or disallow huge lemmas.
*/
std::size_t bitsize(const poly::Value& v);
poly::IntervalAssignment getBounds(VariableMapper& vm, const BoundInference& bi);
} // namespace nl
} // namespace arith
} // namespace theory
} // namespace cvc5
#endif
#endif
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