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, GBOptimized, GBProxy, GroebnerBaseDistributedEC, GroebnerBaseDistributedHybridEC, GroebnerBaseFGLM, GroebnerBaseParallel, GroebnerBaseParIter, GroebnerBasePartial, GroebnerBasePseudoParallel, GroebnerBasePseudoRecParallel, GroebnerBasePseudoRecSeq, GroebnerBasePseudoSeq, GroebnerBaseQuotient, GroebnerBaseRational, GroebnerBaseSeq, GroebnerBaseSeqIter, GroebnerBaseSeqPairDistributed, GroebnerBaseSeqPairParallel, GroebnerBaseSeqPairSeq, GroebnerBaseSigSeqIter, GroebnerBaseWalk, 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:

GBAlgorithmBuilder, GBFactory, Serialized Form

Field Summary

Fields

Modifier and Type	Field and Description
BasicLinAlg<GenPolynomial<C>>	blas linear algebra engine.
Reduction<C>	red Reduction engine.
PairList<C>	strategy Strategy for pair selection.

Constructor Summary

Constructors

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

Method Summary

Modifier and Type	Method and Description
int	cancel() Cancel ThreadPool.
int	commonZeroTest(java.util.List<GenPolynomial<C>> F) Common zero test.
GenPolynomial<C>	constructUnivariate(int i, java.util.List<GenPolynomial<C>> G) Construct univariate polynomial of minimal degree in variable i of a zero dimensional ideal(G).
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.
ModuleList<C>	GB(ModuleList<C> M) GB.
ModuleList<C>	GB(ModuleList<C> M, boolean top) GB.
boolean	isGB(int modv, java.util.List<GenPolynomial<C>> F) Groebner base test.
boolean	isGB(int modv, java.util.List<GenPolynomial<C>> F, boolean b) Groebner base test.
boolean	isGB(java.util.List<GenPolynomial<C>> F) Groebner base test.
boolean	isGB(java.util.List<GenPolynomial<C>> F, boolean b) Groebner base test.
boolean	isGB(ModuleList<C> M) isGB.
boolean	isGB(ModuleList<C> M, boolean top) isGB.
boolean	isGBidem(int modv, java.util.List<GenPolynomial<C>> F) Groebner base idempotence test.
boolean	isGBsimple(int modv, java.util.List<GenPolynomial<C>> F) Groebner base simple test.
boolean	isMinimalGB(java.util.List<GenPolynomial<C>> Gp) Test for minimal ordered Groebner basis.
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.
java.util.List<GenPolynomial<C>>	normalizeZerosOnes(java.util.List<GenPolynomial<C>> A) Normalize polynomial list.
void	terminate() Cleanup and terminate ThreadPool.
java.lang.String	toString() Get the String representation with GB engines.
java.util.List<java.lang.Long>	univariateDegrees(java.util.List<GenPolynomial<C>> A) Univariate head term degrees.

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, 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(PairList<C> pl)

Constructor.

Parameters:

pl - pair selection strategy

GroebnerBaseAbstract

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

Constructor.

Parameters:

red - Reduction engine

pl - pair selection strategy

Method Detail

toString

public java.lang.String toString()

Get the String representation with GB engines.

Overrides:

toString in class java.lang.Object

See Also:

Object.toString()

normalizeZerosOnes

public java.util.List<GenPolynomial<C>> normalizeZerosOnes(java.util.List<GenPolynomial<C>> A)

Normalize polynomial list.

Parameters:

A - list of polynomials.

Returns:

list of polynomials with zeros removed and ones/units reduced.

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.

isGB

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

Groebner base test.

Parameters:

F - polynomial list.

b - true for simple test, false for GB test.

Returns:

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

isGB

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

Groebner base test.

Parameters:

modv - module variable number.

F - polynomial list.

b - true for simple test, false for GB test.

Returns:

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

isGBsimple

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

Groebner base simple test.

Parameters:

modv - module variable number.

F - polynomial list.

Returns:

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

isGBidem

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

Groebner base idempotence test.

Parameters:

modv - module variable number.

F - polynomial list.

Returns:

true, if F is equal to GB(F), 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.

isGB

public boolean isGB(ModuleList<C> M)

isGB.

Specified by:

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

Parameters:

M - a module basis.

Returns:

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

isGB

public boolean isGB(ModuleList<C> M,
                    boolean top)

isGB.

Parameters:

M - a module basis.

top - true for TOP term order, false for POT term order.

Returns:

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

GB

public ModuleList<C> GB(ModuleList<C> M)

GB.

Specified by:

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

Parameters:

M - a module basis.

Returns:

GB(M), a Groebner base of M.

GB

public ModuleList<C> GB(ModuleList<C> M,
                        boolean top)

GB.

Parameters:

M - a module basis.

top - true for TOP term order, false for POT term order.

Returns:

GB(M), a Groebner base of M wrt. TOP or POT.

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.

isMinimalGB

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

Test for minimal ordered Groebner basis.

Parameters:

Gp - an ideal base.

Returns:

true, if Gp is a reduced minimal Groebner base.

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.

univariateDegrees

public java.util.List<java.lang.Long> univariateDegrees(java.util.List<GenPolynomial<C>> A)

Univariate head term degrees.

Parameters:

A - list of polynomials.

Returns:

a list of the degrees of univariate head terms.

constructUnivariate

public GenPolynomial<C> constructUnivariate(int i,
                                            java.util.List<GenPolynomial<C>> G)

Construct univariate polynomial of minimal degree in variable i of a zero dimensional ideal(G).

Parameters:

i - variable index.

G - list of polynomials, a monic reduced Gröbner base of a zero dimensional ideal.

Returns:

univariate polynomial of minimal degree in variable i in ideal(G)

terminate

public void terminate()

Cleanup and terminate ThreadPool.

cancel

public int cancel()

Cancel ThreadPool.