Class GroebnerBasePseudoSeq<C extends GcdRingElem<C>>

java.lang.Object

edu.jas.gb.GroebnerBaseAbstract<C>

edu.jas.gbufd.GroebnerBasePseudoSeq<C>

Type Parameters:

C - coefficient type

All Implemented Interfaces:

GroebnerBase<C>, Serializable

public class GroebnerBasePseudoSeq<C extends GcdRingElem<C>>
extends GroebnerBaseAbstract<C>

Groebner Base with pseudo reduction sequential algorithm. Implements coefficient fraction free Groebner bases. Coefficients can for example be integers or (commutative) univariate polynomials.

Author:

Heinz Kredel

See Also:

• GBAlgorithmBuilder
• GBFactory
• Serialized Form

Field Summary

Fields

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

Fields inherited from class GroebnerBaseAbstract

blas, strategy

Constructor Summary

Constructors

Constructor	Description
GroebnerBasePseudoSeq(PseudoReduction<C> red, RingFactory<C> rf, PairList<C> pl)	Constructor.
GroebnerBasePseudoSeq(RingFactory<C> rf)	Constructor.
GroebnerBasePseudoSeq(RingFactory<C> rf, PairList<C> pl)	Constructor.

Method Summary

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

Methods inherited from class GroebnerBaseAbstract

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

Methods inherited from class Object

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

Field Details

engine

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

Greatest common divisor engine for coefficient content and primitive parts.

red

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

Pseudo reduction engine.

cofac

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

Coefficient ring factory.

Constructor Details

GroebnerBasePseudoSeq

public GroebnerBasePseudoSeq(RingFactory<C> rf)

Constructor.

Parameters:

rf - coefficient ring factory.

GroebnerBasePseudoSeq

public GroebnerBasePseudoSeq(RingFactory<C> rf,
 PairList<C> pl)

Constructor.

Parameters:

rf - coefficient ring factory.

pl - pair selection strategy

GroebnerBasePseudoSeq

public GroebnerBasePseudoSeq(PseudoReduction<C> red,
 RingFactory<C> rf,
 PairList<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 Details

GB

public List<GenPolynomial<C>> GB(int modv,
 List<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 List<GenPolynomial<C>> minimalGB(List<GenPolynomial<C>> Gp)

Minimal ordered Groebner basis.

Specified by:

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

Overrides:

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

Parameters:

Gp - a Groebner base.

Returns:

a reduced Groebner base of Gp.