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/********************* */
/*! \file projections.cpp
** \verbatim
** Top contributors (to current version):
** Gereon Kremer
** This file is part of the CVC4 project.
** Copyright (c) 2009-2020 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.\endverbatim
**
** This file is part of the CVC4 project.
** Copyright (c) 2009-2020 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.\endverbatim
**
** \brief Implements utilities for CAD projection operators.
**
** Implements utilities for CAD projection operators.
**/
#include "projections.h"
#ifdef CVC4_POLY_IMP
namespace CVC4 {
namespace theory {
namespace arith {
namespace nl {
namespace cad {
using namespace poly;
void reduce_projection_polynomials(std::vector<Polynomial>& polys)
{
std::sort(polys.begin(), polys.end());
auto it = std::unique(polys.begin(), polys.end());
polys.erase(it, polys.end());
}
void add_polynomial(std::vector<Polynomial>& polys, const Polynomial& poly)
{
for (const auto& p : square_free_factors(poly))
{
if (is_constant(p)) continue;
polys.emplace_back(p);
}
}
void add_polynomials(std::vector<Polynomial>& polys,
const std::vector<Polynomial>& p)
{
for (const auto& q : p) add_polynomial(polys, q);
}
void make_finest_square_free_basis(std::vector<Polynomial>& polys)
{
for (std::size_t i = 0, n = polys.size(); i < n; ++i)
{
for (std::size_t j = i + 1; j < n; ++j)
{
Polynomial g = gcd(polys[i], polys[j]);
if (!is_constant(g))
{
polys[i] = div(polys[i], g);
polys[j] = div(polys[j], g);
polys.emplace_back(g);
}
}
}
auto it = std::remove_if(polys.begin(), polys.end(), [](const Polynomial& p) {
return is_constant(p);
});
polys.erase(it, polys.end());
reduce_projection_polynomials(polys);
}
void make_finest_square_free_basis(std::vector<poly::Polynomial>& lhs,
std::vector<poly::Polynomial>& rhs)
{
for (std::size_t i = 0, ln = lhs.size(); i < ln; ++i)
{
for (std::size_t j = 0, rn = rhs.size(); j < rn; ++j)
{
if (lhs[i] == rhs[j]) continue;
Polynomial g = gcd(lhs[i], rhs[j]);
if (!is_constant(g))
{
lhs[i] = div(lhs[i], g);
rhs[j] = div(rhs[j], g);
lhs.emplace_back(g);
rhs.emplace_back(g);
}
}
}
reduce_projection_polynomials(lhs);
reduce_projection_polynomials(rhs);
}
std::vector<Polynomial> projection_mccallum(
const std::vector<Polynomial>& polys)
{
std::vector<Polynomial> res;
for (const auto& p : polys)
{
for (const auto& coeff : coefficients(p))
{
add_polynomial(res, coeff);
}
add_polynomial(res, discriminant(p));
}
for (std::size_t i = 0, n = polys.size(); i < n; ++i)
{
for (std::size_t j = i + 1; j < n; ++j)
{
add_polynomial(res, resultant(polys[i], polys[j]));
}
}
reduce_projection_polynomials(res);
return res;
}
} // namespace cad
} // namespace nl
} // namespace arith
} // namespace theory
} // namespace CVC4
#endif
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