Class RGroebnerBaseSeq<C extends RegularRingElem<C>>

java.lang.Object

edu.jas.gb.GroebnerBaseAbstract<C>

edu.jas.gbufd.RGroebnerBaseSeq<C>

Type Parameters:

C - coefficient type

All Implemented Interfaces:

GroebnerBase<C>, Serializable

Direct Known Subclasses:

RGroebnerBasePseudoSeq

public class RGroebnerBaseSeq<C extends RegularRingElem<C>>
extends GroebnerBaseAbstract<C>

Regular ring Groebner Base sequential algorithm. Implements R-Groebner bases and GB test.

Author:

Heinz Kredel

See Also:

• Serialized Form

Field Summary

Fields

Modifier and Type	Field	Description
protected RReduction<C>	rred	Reduction engine.

Fields inherited from class GroebnerBaseAbstract

blas, red, strategy

Constructor Summary

Constructors

Constructor	Description
RGroebnerBaseSeq()	Constructor.
RGroebnerBaseSeq(RReduction<C> rred)	Constructor.

Method Summary

Modifier and Type	Method	Description
List<GenPolynomial<C>>	GB(int modv, List<GenPolynomial<C>> F)	R-Groebner base using pairlist class.
boolean	isGB(int modv, List<GenPolynomial<C>> F)	R-Groebner base test.
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, 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

rred

protected RReduction<C extends RegularRingElem<C>> rred

Reduction engine.

Constructor Details

RGroebnerBaseSeq

public RGroebnerBaseSeq()

Constructor.

RGroebnerBaseSeq

public RGroebnerBaseSeq(RReduction<C> rred)

Constructor.

Parameters:

rred - R-Reduction engine

Method Details

isGB

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

R-Groebner base test.

Specified by:

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

Overrides:

isGB in class GroebnerBaseAbstract<C extends RegularRingElem<C>>

Parameters:

modv - module variable number.

F - polynomial list.

Returns:

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

GB

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

R-Groebner base using pairlist class.

Parameters:

modv - module variable number.

F - polynomial list.

Returns:

GB(F) a R-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 RegularRingElem<C>>

Overrides:

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

Parameters:

Gp - a Groebner base.

Returns:

a reduced Groebner base of Gp.