/usr/include/linbox/algorithms/diophantine-solver.h is in liblinbox-dev 1.4.2-3.
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* Copyright (C) 2004 David Pritchard
*
* Written by David Pritchard <daveagp@mit.edu>
*
* ========LICENCE========
* This file is part of the library LinBox.
*
* LinBox is free software: you can redistribute it and/or modify
* it under the terms of the GNU Lesser General Public
* License as published by the Free Software Foundation; either
* version 2.1 of the License, or (at your option) any later version.
*
* This library is distributed in the hope that it will be useful,
* but WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
* Lesser General Public License for more details.
*
* You should have received a copy of the GNU Lesser General Public
* License along with this library; if not, write to the Free Software
* Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA
* ========LICENCE========
*/
#ifndef __LINBOX_diophantine_solver_H
#define __LINBOX_diophantine_solver_H
#include "linbox/algorithms/rational-solver.h"
#include "linbox/solutions/methods.h"
#include "linbox/blackbox/archetype.h"
#include "linbox/blackbox/lambda-sparse.h"
#include "linbox/blackbox/compose.h"
namespace LinBox
{
extern const char* solverReturnString[6] ;
/**
* \brief DiophantineSolver<QSolver> creates a diophantine solver using a QSolver to generate rational solutions
* Methods solve, randomSolve just expose functions from underlying rational solver.
* Method diophantineSolve creates a solution with minimal denominator, and can also create
* a certificate of minimality (described in 'Certified Dense Linear System Solving' by Mulders+Storjohann)
* which will be left in the public field lastCertificate.
*/
template<class QSolver>
class DiophantineSolver {
protected:
typedef typename QSolver::RingType Ring;
typedef typename Ring::Element Integer;
QSolver& _rationalSolver;
Ring _ring;
public:
// information for last diophantine solve
mutable int numSolutionsNeeded;
mutable int numFailedCallsToSolver;
mutable int numRevelantSolutions;
VectorFraction<Ring> lastCertificate;
/*! Constructor from a rationalSolver
* @param rs a rationalSolver
*/
DiophantineSolver (QSolver& rs) :
_rationalSolver(rs), _ring(rs.getRing())
,numSolutionsNeeded(0),numFailedCallsToSolver(0),numRevelantSolutions (0)
, lastCertificate(_ring, 0)
{ }
/** Solve a linear system \c Ax=b over quotient field of a ring.
*
* @param A Matrix of linear system
* @param x Vector in which to store solution
* @param b Right-hand side of system
* @param maxPrimes maximum number of moduli to try
* @param level level of certification to be used
* @param den
*
* @return status of solution. if \c (return != SS_FAILED), and \c (level >= SL_LASVEGAS), solution is guaranteed correct.
* \c SS_FAILED - all primes used were bad
* \c SS_OK - solution found.
* \c SS_INCONSISTENT - system appreared inconsistent. certificate is in \p lastCertificate if \c (level >= SL_CERTIFIED)
*/
template<class IMatrix, class Vector1, class Vector2>
SolverReturnStatus solve(Vector1& x, Integer& den, const IMatrix& A, const Vector2& b, const int maxPrimes = DEFAULT_MAXPRIMES,
const SolverLevel level = SL_DEFAULT);
/** Find a random solution of the general linear system \c Ax=b over quotient field of a ring.
*
* @param A Matrix of linear system
* @param x Vector in which to store solution
* @param b Right-hand side of system
* @param maxPrimes maximum number of moduli to try
* @param level level of certification to be used
* @param den
*
* @return status of solution. if \c (return != SS_FAILED), and \c (level >= SL_LASVEGAS), solution is guaranteed correct.
* \c SS_FAILED - all primes used were bad
* \c SS_OK - solution found.
* \c SS_INCONSISTENT - system appreared inconsistent. certificate is in \p lastCertificate if \c (level >= SL_CERTIFIED)
*/
template<class IMatrix, class Vector1, class Vector2>
SolverReturnStatus randomSolve(Vector1& x, Integer& den, const IMatrix& A, const Vector2& b, const int maxPrimes = DEFAULT_MAXPRIMES,
const SolverLevel level = SL_DEFAULT);
/**
* Find a solution of the linear system \c Ax=b whose denominator (when written as an integer vector over a single denom) is minimal.
*
* @param A Matrix of linear system
* @param x Vector in which to store solution
* @param b Right-hand side of system
* @param maxPrimes maximum number of moduli to try
* @param level level of certification to be used
* @param den
*
* @return status of solution. if \c (return != SS_FAILED) and \c (level >= SL_LASVEGAS), solution is guaranteed correct
* if \c (return == SS_OK) and \c (level >= SL_LASVEGAS), solution is guaranteed minimal.
* \c SS_FAILED - all primes used were bad
* \c SS_OK - solution found. certificate of minimality is in lastCertificate if \c (level >= SL_CERTIFIED)
* \c SS_INCONSISTENT - system appreared inconsistent. certificate of inconsistency is in \p lastCertificate if \c (level >= SL_CERTIFIED)
*
* @return status of solution - OK, FAILED, SINGULAR, INCONSISTENT, BAD_PRECONDITIONER
*/
template<class IMatrix, class Vector1, class Vector2>
SolverReturnStatus diophantineSolve(Vector1& x, Integer& den, const IMatrix& A, const Vector2& b, const int maxPrimes = DEFAULT_MAXPRIMES,
const SolverLevel level = SL_DEFAULT);
};
}
#include "linbox/algorithms/diophantine-solver.inl"
#ifdef LinBoxSrcOnly
#include "linbox/algorithms/diophantine-solver.C"
#endif
#endif //__LINBOX_diophantine_solver_H
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