p-adic lifting for linear system solutions.
[linbox/algorithms]

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Detailed Description

interface for solving linear system by p-adic lifting technique over the quotient field of a ring. i.e. solution over the rational for an integer linear system.

Headers

#include<linbox/algorithms/rational-solver.h>

References

See the following reference for details on this algorithm:

• Robert T. Moenck and John H. Carter: Approximate algorithms to derive exact solutions to system of linear equations. In Proc. EUROSAM'79, volume 72 of Lectures Note in Computer Science, pages 65-72, Berlin-Heidelberger-New York, 1979. Springer-Verlag.

• John D. Dixon: Exact Solution of linear equations using p-adic expansions. Numerische Mathematik, volume 40, pages 137-141, 1982.

Data Structures
class	RationalSolver
	interface for the different specialization of p-adic lifting based solvers. More...
Enumerations
enum	LinBox::SolverReturnStatus {   LinBox::SS_OK, LinBox::SS_FAILED, LinBox::SS_SINGULAR, LinBox::SS_INCONSISTENT,   LinBox::SS_BAD_PRECONDITIONER }
	define the different return status of the p-adic based solver's computation. More...
enum	LinBox::SolverLevel { LinBox::SL_MONTECARLO, LinBox::SL_LASVEGAS, LinBox::SL_CERTIFIED }
	define the different strategy which can be used in the p-adic based solver. More...

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Enumeration Type Documentation

enum SolverReturnStatus

define the different return status of the p-adic based solver's computation. Enumeration values: SS_OK  SS_FAILED  SS_SINGULAR  SS_INCONSISTENT  SS_BAD_PRECONDITIONER

enum SolverLevel

define the different strategy which can be used in the p-adic based solver. used to determine what level of solving should be done: Monte Carlo: Try to solve if possible, but result is not guaranteed. In any case a 0 denominator should not be returned. Las Vegas : Result should be guaranteed correct. Certified : Additionally, provide certificates that the result returned is correct. if the return value is SS_INCONSISTENT, this means lastCertificate satisfies lC.A = 0, lC.b != 0 if diophantine solving was called and the return value is SS_OK, this means lastCertificate satisfies den(lC.A) = 1, den(lC.b) = den(answer) Enumeration values: SL_MONTECARLO  SL_LASVEGAS  SL_CERTIFIED

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