DixonSolver< Ring, Field, RandomPrime, MethodTraits > Class Template Reference

Interface for the different specialization of p-adic lifting based solvers. More...

#include <rational-solver.h>

Public Member Functions
template<class IMatrix, class Vector1, class Vector2>
SolverReturnStatus	solve (Vector1 &num, Integer &den, const IMatrix &A, const Vector2 &b, const bool side, int maxPrimes=5) const
	Solve a linear system Ax=b over quotient field of a ring giving a random solution if the system is singular and consistent, giving the unique solution if the system is non-singular.
template<class IMatrix, class Vector1, class Vector2>
SolverReturnStatus	solveNonsingular (Vector1 &num, Integer &den, const IMatrix &A, const Vector2 &b, int maxPrimes=5) const
	Solve a nonsingular linear system Ax=b over quotient field of a ring, giving the unique solution of the system.
template<class IMatrix, class Vector1, class Vector2>
SolverReturnStatus	solveSingular (Vector1 &num, Integer &den, const IMatrix &A, const Vector2 &b, int maxPrimes=5) const
	brief Solve a singular linear system Ax=b over quotient field of a ring, giving a random solution if the system is singular and consistent.

Detailed Description

template<class Ring, class Field, class RandomPrime, class MethodTraits = Method::DenseElimination>
class LinBox::DixonSolver< Ring, Field, RandomPrime, MethodTraits >

Interface for the different specialization of p-adic lifting based solvers.

The following type are abstract in the implementation and can be change during the instanciation of the class:

• Ring: ring over which entries are defined
• Field: finite field for p-adic lifting
• RandomPrime: generator of random primes
• MethodTraits: type of subalgorithm to use in p-adic lifting (default is Method::DenseElimination)

Examples

examples/dixonsolve.C.

Member Function Documentation

solve()

template<class Ring, class Field, class RandomPrime, class MethodTraits = Method::DenseElimination>

template<class IMatrix, class Vector1, class Vector2>

SolverReturnStatus solve	(	Vector1 &	num,
		Integer &	den,
		const IMatrix &	A,
		const Vector2 &	b,
		const bool	side,
		int	maxPrimes = 5 ) const

Solve a linear system Ax=b over quotient field of a ring giving a random solution if the system is singular and consistent, giving the unique solution if the system is non-singular.

Parameters

num	Vector of numerators of the solution
den	The common denominator. 1/den * num is the rational solution of Ax=b.
A	Matrix of linear system
b	Right-hand side of system
maxPrimes	maximum number of moduli to try
side

Returns

status of solution

Examples

examples/dixonsolve.C.

solveNonsingular()

template<class Ring, class Field, class RandomPrime, class MethodTraits = Method::DenseElimination>

template<class IMatrix, class Vector1, class Vector2>

SolverReturnStatus solveNonsingular	(	Vector1 &	num,
		Integer &	den,
		const IMatrix &	A,
		const Vector2 &	b,
		int	maxPrimes = 5 ) const

Solve a nonsingular linear system Ax=b over quotient field of a ring, giving the unique solution of the system.

Parameters

num	Vector of numerators of the solution
den	The common denominator. 1/den * num is the rational solution of Ax=b.
A	Matrix of linear system
b	Right-hand side of system
maxPrimes	maximum number of moduli to try

Returns

status of solution

Examples

examples/dixonsolve.C.

solveSingular()

template<class Ring, class Field, class RandomPrime, class MethodTraits = Method::DenseElimination>

template<class IMatrix, class Vector1, class Vector2>

SolverReturnStatus solveSingular	(	Vector1 &	num,
		Integer &	den,
		const IMatrix &	A,
		const Vector2 &	b,
		int	maxPrimes = 5 ) const

brief Solve a singular linear system Ax=b over quotient field of a ring, giving a random solution if the system is singular and consistent.

Parameters

num	Vector of numerators of the solution
den	The common denominator. 1/den * num is the rational solution of Ax=b.
A	Matrix of linear system
b	Right-hand side of system
maxPrimes	maximum number of moduli to try

Returns

status of solution

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

• rational-solver.h