DiophantineSolver< QSolver > Class Template Reference

DiophantineSolver<QSolver> creates a diophantine solver using a QSolver to generate rational solutions. More...

#include <diophantine-solver.h>

Collaboration diagram for DiophantineSolver< QSolver >:

Public Member Functions
	DiophantineSolver (QSolver &rs)
	Constructor from a rationalSolver. More...
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)
	Solve a linear system Ax=b over quotient field of a ring. More...
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 random solution of the general linear system Ax=b over quotient field of a ring. More...
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)
	Find a solution of the linear system Ax=b whose denominator (when written as an integer vector over a single denom) is minimal. More...

Detailed Description

template<class QSolver>
class LinBox::DiophantineSolver< QSolver >

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.

Constructor & Destructor Documentation

DiophantineSolver()

DiophantineSolver ( QSolver &  rs )

inline

Constructor from a rationalSolver.

Parameters

rs	a rationalSolver

Member Function Documentation

solve()

SolverReturnStatus solve	(	Vector1 &	x,
		Integer &	den,
		const IMatrix &	A,
		const Vector2 &	b,
		const int	maxPrimes = DEFAULT_MAXPRIMES,
		const SolverLevel	level = SL_DEFAULT
	)

Solve a linear system Ax=b over quotient field of a ring.

Parameters

A	Matrix of linear system
x	Vector in which to store solution
b	Right-hand side of system
maxPrimes	maximum number of moduli to try
level	level of certification to be used
den

Returns

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)

randomSolve()

SolverReturnStatus randomSolve	(	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.

Parameters

A	Matrix of linear system
x	Vector in which to store solution
b	Right-hand side of system
maxPrimes	maximum number of moduli to try
level	level of certification to be used
den

Returns

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)

diophantineSolve()

SolverReturnStatus diophantineSolve	(	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.

Parameters

A	Matrix of linear system
x	Vector in which to store solution
b	Right-hand side of system
maxPrimes	maximum number of moduli to try
level	level of certification to be used
den

Returns

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)

status of solution - OK, FAILED, SINGULAR, INCONSISTENT, BAD_PRECONDITIONER

---

The documentation for this class was generated from the following files:

• diophantine-solver.h
• diophantine-solver.inl