linbox
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DiophantineSolver<QSolver> creates a diophantine solver using a QSolver to generate rational solutions. More...
#include <diophantine-solver.h>
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... | |
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.
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inline |
Constructor from a rationalSolver.
rs | a rationalSolver |
SolverReturnStatus solve | ( | Vector1 & | x, |
Integer & | den, | ||
const IMatrix & | A, | ||
const Vector2 & | b, | ||
const int | maxPrimes = DEFAULT_MAXPRIMES , |
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const SolverLevel | level = SL_DEFAULT |
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) |
Solve a linear system Ax=b
over quotient field of a ring.
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 |
(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) 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.
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 |
(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) 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.
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 |
(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)