Lazard.h

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#pragma once
 
#include "McCallum.h"
#include "utils.h"
 
namespace smtrat {
namespace cad {
namespace projection {
 
/**
 * Contains the implementation of Lazards projection operator as specified in @cite Lauard1994.
 */
namespace lazard {
 
/**
 * Implements the part of Lazards projection operator from @cite Lazard1994 that deals with a single polynomial `p`:
 * \f$ \{ leading_coeff(p), trailing_coeff(p), discriminant(p) \} \f$
 */
template<typename Poly, typename Callback>
void single(const Poly& p, carl::Variable variable, Callback&& cb) {
    SMTRAT_LOG_DEBUG("smtrat.cad.projection", "Lazard_single(" << p << ")");
    returnPoly(projection::discriminant(variable, p), cb);
    returnPoly(projection::normalize(carl::to_univariate_polynomial(p.lcoeff(), variable)), cb);
    returnPoly(projection::normalize(carl::to_univariate_polynomial(p.tcoeff(), variable)), cb);
}
 
/**
 * Implements the part of Lazard projection operator from @cite Lazard1994 that deals with two polynomials `p` and `q` which is just the respective part of McCallums projection operator mccallum::paired.
 */
template<typename Poly, typename Callback>
void paired(const Poly& p, const UPoly& q, carl::Variable variable, Callback&& cb) {
    SMTRAT_LOG_DEBUG("smtrat.cad.projection", "Lazard_paired(" << p << ", " << q << ") -> McCallum_paired");
    mccallum::paired(p, q, variable, std::forward<Callback>(cb));
}
 
} // namespace lazard
} // namespace projection
} // namespace cad
} // namespace smtrat