edu.jas.gbufd

Class GroebnerBasePseudoRecSeq<C extends GcdRingElem<C>>

java.lang.Object

edu.jas.gb.GroebnerBaseAbstract<GenPolynomial<C>>

edu.jas.gbufd.GroebnerBasePseudoRecSeq<C>

Type Parameters:

C - base coefficient type

All Implemented Interfaces:

GroebnerBase<GenPolynomial<C>>, java.io.Serializable

public class GroebnerBasePseudoRecSeq<C extends GcdRingElem<C>>
extends GroebnerBaseAbstract<GenPolynomial<C>>

Groebner Base with pseudo reduction sequential algorithm for integral function coefficients. Implements polynomial fraction free coefficients Groebner bases. Coefficients can for example be (commutative) multivariate polynomials.

Author:

Heinz Kredel

See Also:

GBAlgorithmBuilder, GBFactory, Serialized Form

Field Summary

Fields

Modifier and Type	Field and Description
protected RingFactory<C>	baseCofac Base coefficient ring factory.
protected RingFactory<GenPolynomial<C>>	cofac Coefficient ring factory.
protected GreatestCommonDivisorAbstract<C>	engine Greatest common divisor engine for coefficient content and primitive parts.
protected PseudoReduction<GenPolynomial<C>>	red Pseudo reduction engine.
protected PseudoReduction<C>	redRec Pseudo reduction engine.

Fields inherited from class edu.jas.gb.GroebnerBaseAbstract

blas, strategy

Constructor Summary

Constructors

Constructor and Description
GroebnerBasePseudoRecSeq(PseudoReduction<GenPolynomial<C>> red, RingFactory<GenPolynomial<C>> rf, PairList<GenPolynomial<C>> pl) Constructor.
GroebnerBasePseudoRecSeq(RingFactory<GenPolynomial<C>> rf) Constructor.
GroebnerBasePseudoRecSeq(RingFactory<GenPolynomial<C>> rf, PairList<GenPolynomial<C>> pl) Constructor.

Method Summary

Modifier and Type	Method and Description
java.util.List<GenPolynomial<GenPolynomial<C>>>	GB(int modv, java.util.List<GenPolynomial<GenPolynomial<C>>> F) Groebner base using pairlist class.
boolean	isGBsimple(int modv, java.util.List<GenPolynomial<GenPolynomial<C>>> F) Groebner base simple test.
java.util.List<GenPolynomial<GenPolynomial<C>>>	minimalGB(java.util.List<GenPolynomial<GenPolynomial<C>>> Gp) Minimal ordered Groebner basis.

Methods inherited from class edu.jas.gb.GroebnerBaseAbstract

cancel, commonZeroTest, constructUnivariate, extGB, extGB, GB, GB, isGB, isGB, isGB, isGB, isGB, isGBidem, isMinimalGB, isReductionMatrix, isReductionMatrix, minimalExtendedGB, normalizeMatrix, normalizeZerosOnes, terminate, toString, univariateDegrees

Methods inherited from class java.lang.Object

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

Field Detail

engine

protected final GreatestCommonDivisorAbstract<C extends GcdRingElem<C>> engine

Greatest common divisor engine for coefficient content and primitive parts.

redRec

protected final PseudoReduction<C extends GcdRingElem<C>> redRec

Pseudo reduction engine.

red

protected final PseudoReduction<GenPolynomial<C extends GcdRingElem<C>>> red

Pseudo reduction engine.

cofac

protected final RingFactory<GenPolynomial<C extends GcdRingElem<C>>> cofac

Coefficient ring factory.

baseCofac

protected final RingFactory<C extends GcdRingElem<C>> baseCofac

Base coefficient ring factory.

Constructor Detail

GroebnerBasePseudoRecSeq

public GroebnerBasePseudoRecSeq(RingFactory<GenPolynomial<C>> rf)

Constructor.

Parameters:

rf - coefficient ring factory.

GroebnerBasePseudoRecSeq

public GroebnerBasePseudoRecSeq(RingFactory<GenPolynomial<C>> rf,
                                PairList<GenPolynomial<C>> pl)

Constructor.

Parameters:

rf - coefficient ring factory.

pl - pair selection strategy

GroebnerBasePseudoRecSeq

public GroebnerBasePseudoRecSeq(PseudoReduction<GenPolynomial<C>> red,
                                RingFactory<GenPolynomial<C>> rf,
                                PairList<GenPolynomial<C>> pl)

Constructor.

Parameters:

red - pseudo reduction engine. Note: red must be an instance of PseudoReductionSeq.

rf - coefficient ring factory.

pl - pair selection strategy

Method Detail

GB

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

Groebner base using pairlist class.

Parameters:

modv - module variable number.

F - polynomial list.

Returns:

GB(F) a Groebner base of F.

minimalGB

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

Minimal ordered Groebner basis.

Specified by:

minimalGB in interface GroebnerBase<GenPolynomial<C extends GcdRingElem<C>>>

Overrides:

minimalGB in class GroebnerBaseAbstract<GenPolynomial<C extends GcdRingElem<C>>>

Parameters:

Gp - a Groebner base.

Returns:

a reduced Groebner base of Gp.

isGBsimple

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

Groebner base simple test.

Overrides:

isGBsimple in class GroebnerBaseAbstract<GenPolynomial<C extends GcdRingElem<C>>>

Parameters:

modv - module variable number.

F - recursive polynomial list.

Returns:

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