/usr/include/linbox/algorithms/diophantine-solver.h is in liblinbox-dev 1.1.6~rc0-4.1.
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/* linbox/algorithms/diophantine-solver.h
* Copyright (C) 2004 David Pritchard
*
* Written by David Pritchard <daveagp@mit.edu>
*
* This library 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 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., 59 Temple Place - Suite 330,
* Boston, MA 02111-1307, USA.
*/
#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 {
const char* solverReturnString[]
= {"OK", "FAILED", "SINGULAR", "INCONSISTENT", "BAD_PRECONDITIONER", "BAD_PRIME"};
/**
* \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 _R;
Integer _rone;
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), _R(rs.getRing()), lastCertificate(_R, 0) {
_R.init(_rone, 1);
};
/** Solve a linear system 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
*
* @return status of solution. if (return != SS_FAILED), and (level >= SL_LASVEGAS), solution is guaranteed correct.
* SS_FAILED - all primes used were bad
* SS_OK - solution found.
* SS_INCONSISTENT - system appreared inconsistent. certificate is in lastCertificate if (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 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
*
* @return status of solution. if (return != SS_FAILED), and (level >= SL_LASVEGAS), solution is guaranteed correct.
* SS_FAILED - all primes used were bad
* SS_OK - solution found.
* SS_INCONSISTENT - system appreared inconsistent. certificate is in lastCertificate if (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 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
*
* @return status of solution. if (return != SS_FAILED) and (level >= SL_LASVEGAS), solution is guaranteed correct
* if (return == SS_OK) and (level >= SL_LASVEGAS), solution is guaranteed minimal.
* SS_FAILED - all primes used were bad
* SS_OK - solution found. certificate of minimality is in lastCertificate if (level >= SL_CERTIFIED)
* SS_INCONSISTENT - system appreared inconsistent. certificate of inconsistency is in lastCertificate if (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>
#endif
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