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, GroebnerBaseDistributed, GroebnerBaseDistributedEC, GroebnerBaseDistributedHybrid, GroebnerBaseDistributedHybridEC, GroebnerBaseFGLM, GroebnerBaseParallel, GroebnerBasePartial, GroebnerBasePseudoParallel, GroebnerBasePseudoRecSeq, GroebnerBasePseudoSeq, GroebnerBaseRational, GroebnerBaseSeq, GroebnerBaseSeqPairDistributed, GroebnerBaseSeqPairParallel, GroebnerBaseSeqPairSeq, GroebnerBaseSeqQuotient, 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.

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.
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	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.
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

equals, 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()

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.

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.