edu.jas.gb
Class GroebnerBaseAbstract<C extends RingElem<C>>

java.lang.Object
  edu.jas.gb.GroebnerBaseAbstract<C>

Type Parameters:

C - coefficient type

All Implemented Interfaces:

GroebnerBase<C>, java.io.Serializable

Direct Known Subclasses:

DGroebnerBaseSeq, GBProxy, GroebnerBaseDistributed, GroebnerBaseDistributedHybrid, GroebnerBaseParallel, GroebnerBasePartial, GroebnerBasePseudoRecSeq, GroebnerBasePseudoSeq, GroebnerBaseSeq, GroebnerBaseSeqPairDistributed, GroebnerBaseSeqPairParallel, GroebnerBaseSeqPairSeq, RGroebnerBaseSeq

public abstract class GroebnerBaseAbstract<C extends RingElem<C>>
extends java.lang.Object
implements GroebnerBase<C>

Groebner Bases abstract class. Implements common Groebner bases and GB test methods.

Author:

Heinz Kredel

See Also:

Serialized Form

Field Summary

BasicLinAlg<GenPolynomial<C>>	blas linear algebra engine.
Reduction<C>	red Reduction engine.
PairList<C>	strategy Strategy for pair selection.

Constructor Summary

GroebnerBaseAbstract()
Constructor.

GroebnerBaseAbstract(Reduction<C> red)
Constructor.

GroebnerBaseAbstract(Reduction<C> red, PairList<C> pl)
Constructor.

Method Summary

int	cancel() Cancel ThreadPool.
int	commonZeroTest(java.util.List<GenPolynomial<C>> F) Common zero test.
ExtendedGB<C>	extGB(int modv, java.util.List<GenPolynomial<C>> F) Extended Groebner base using critical pair class.
ExtendedGB<C>	extGB(java.util.List<GenPolynomial<C>> F) Extended Groebner base using critical pair class.
java.util.List<GenPolynomial<C>>	GB(java.util.List<GenPolynomial<C>> F) Groebner base using pairlist class.
boolean	isGB(int modv, java.util.List<GenPolynomial<C>> F) Groebner base test.
boolean	isGB(java.util.List<GenPolynomial<C>> F) Groebner base test.
boolean	isReductionMatrix(ExtendedGB<C> exgb) Test if reduction matrix.
boolean	isReductionMatrix(java.util.List<GenPolynomial<C>> F, java.util.List<GenPolynomial<C>> G, java.util.List<java.util.List<GenPolynomial<C>>> Mf, java.util.List<java.util.List<GenPolynomial<C>>> Mg) Test if reduction matrix.
ExtendedGB<C>	minimalExtendedGB(int flen, java.util.List<GenPolynomial<C>> Gp, java.util.List<java.util.List<GenPolynomial<C>>> M) Minimal extended groebner basis.
java.util.List<GenPolynomial<C>>	minimalGB(java.util.List<GenPolynomial<C>> Gp) Minimal ordered Groebner basis.
java.util.List<java.util.List<GenPolynomial<C>>>	normalizeMatrix(int flen, java.util.List<java.util.List<GenPolynomial<C>>> M) Normalize M.
void	terminate() Cleanup and terminate ThreadPool.

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Methods inherited from interface edu.jas.gb.GroebnerBase

GB

Field Detail

red

public final Reduction<C extends RingElem<C>> red

Reduction engine.

strategy

public final PairList<C extends RingElem<C>> strategy

Strategy for pair selection.

blas

public final BasicLinAlg<GenPolynomial<C extends RingElem<C>>> blas

linear algebra engine.

Constructor Detail

GroebnerBaseAbstract

public GroebnerBaseAbstract()

Constructor.

GroebnerBaseAbstract

public GroebnerBaseAbstract(Reduction<C> red)

Constructor.

Parameters:

red - Reduction engine

GroebnerBaseAbstract

public GroebnerBaseAbstract(Reduction<C> red,
                            PairList<C> pl)

Constructor.

Parameters:

red - Reduction engine

pl - pair selection strategy

Method Detail

isGB

public boolean isGB(java.util.List<GenPolynomial<C>> F)

Groebner base test.

Specified by:

isGB in interface GroebnerBase<C extends RingElem<C>>

Parameters:

F - polynomial list.

Returns:

true, if F is a Groebner base, else false.

isGB

public boolean isGB(int modv,
                    java.util.List<GenPolynomial<C>> F)

Groebner base test.

Specified by:

isGB in interface GroebnerBase<C extends RingElem<C>>

Parameters:

modv - module variable number.

F - polynomial list.

Returns:

true, if F is a Groebner base, else false.

commonZeroTest

public int commonZeroTest(java.util.List<GenPolynomial<C>> F)

Common zero test.

Parameters:

F - polynomial list.

Returns:

-1, 0 or 1 if dimension(ideal(F)) &eq; -1, 0 or ≥ 1.

GB

public java.util.List<GenPolynomial<C>> GB(java.util.List<GenPolynomial<C>> F)

Groebner base using pairlist class.

Specified by:

GB in interface GroebnerBase<C extends RingElem<C>>

Parameters:

F - polynomial list.

Returns:

GB(F) a Groebner base of F.

extGB

public ExtendedGB<C> extGB(java.util.List<GenPolynomial<C>> F)

Extended Groebner base using critical pair class.

Specified by:

extGB in interface GroebnerBase<C extends RingElem<C>>

Parameters:

F - polynomial list.

Returns:

a container for a Groebner base G of F together with back-and-forth transformations.

extGB

public ExtendedGB<C> extGB(int modv,
                           java.util.List<GenPolynomial<C>> F)

Extended Groebner base using critical pair class.

Specified by:

extGB in interface GroebnerBase<C extends RingElem<C>>

Parameters:

modv - module variable number.

F - polynomial list.

Returns:

a container for a Groebner base G of F together with back-and-forth transformations.

minimalGB

public java.util.List<GenPolynomial<C>> minimalGB(java.util.List<GenPolynomial<C>> Gp)

Minimal ordered Groebner basis.

Specified by:

minimalGB in interface GroebnerBase<C extends RingElem<C>>

Parameters:

Gp - a Groebner base.

Returns:

a reduced Groebner base of Gp.

isReductionMatrix

public boolean isReductionMatrix(ExtendedGB<C> exgb)

Test if reduction matrix.

Specified by:

isReductionMatrix in interface GroebnerBase<C extends RingElem<C>>

Parameters:

exgb - an ExtendedGB container.

Returns:

true, if exgb contains a reduction matrix, else false.

isReductionMatrix

public boolean isReductionMatrix(java.util.List<GenPolynomial<C>> F,
                                 java.util.List<GenPolynomial<C>> G,
                                 java.util.List<java.util.List<GenPolynomial<C>>> Mf,
                                 java.util.List<java.util.List<GenPolynomial<C>>> Mg)

Test if reduction matrix.

Specified by:

isReductionMatrix in interface GroebnerBase<C extends RingElem<C>>

Parameters:

F - a polynomial list.

G - a Groebner base.

Mf - a possible reduction matrix.

Mg - a possible reduction matrix.

Returns:

true, if Mg and Mf are reduction matrices, else false.

normalizeMatrix

public java.util.List<java.util.List<GenPolynomial<C>>> normalizeMatrix(int flen,
                                                                        java.util.List<java.util.List<GenPolynomial<C>>> M)

Normalize M. Make all rows the same size and make certain column elements zero.

Parameters:

M - a reduction matrix.

Returns:

normalized M.

minimalExtendedGB

public ExtendedGB<C> minimalExtendedGB(int flen,
                                       java.util.List<GenPolynomial<C>> Gp,
                                       java.util.List<java.util.List<GenPolynomial<C>>> M)

Minimal extended groebner basis.

Parameters:

Gp - a Groebner base.

M - a reduction matrix, is modified.

Returns:

a (partially) reduced Groebner base of Gp in a container.

terminate

public void terminate()

Cleanup and terminate ThreadPool.

cancel

public int cancel()

Cancel ThreadPool.