Package edu.jas.gbufd

Class WordGroebnerBasePseudoSeq<C extends GcdRingElem<C>>

java.lang.Object

edu.jas.gb.WordGroebnerBaseAbstract<C>

edu.jas.gbufd.WordGroebnerBasePseudoSeq<C>

Type Parameters:

C - coefficient type

All Implemented Interfaces:

WordGroebnerBase<C>, java.io.Serializable

public class WordGroebnerBasePseudoSeq<C extends GcdRingElem<C>>
extends WordGroebnerBaseAbstract<C>

Non-commutative word Groebner Base sequential algorithm. Implements Groebner bases and GB test. Coefficients can for example be integers or (commutative) univariate polynomials.

Author:

Heinz Kredel

See Also:

Serialized Form

Field Summary

Fields

Modifier and Type	Field	Description
protected RingFactory<C>	cofac	Coefficient ring factory.

Fields inherited from class edu.jas.gb.WordGroebnerBaseAbstract

red, strategy

Constructor Summary

Constructors

Constructor	Description
WordGroebnerBasePseudoSeq(RingFactory<C> rf)	Constructor.
WordGroebnerBasePseudoSeq(RingFactory<C> rf, WordPseudoReductionSeq<C> red)	Constructor.
WordGroebnerBasePseudoSeq(RingFactory<C> rf, WordPseudoReductionSeq<C> red, WordPairList<C> pl)	Constructor.

Method Summary

Modifier and Type	Method	Description
C	baseContent(GenWordPolynomial<C> P)	GenWordPolynomial base coefficient content.
GenWordPolynomial<C>	basePrimitivePart(GenWordPolynomial<C> P)	GenWordPolynomial base coefficient primitive part.
java.util.List<GenWordPolynomial<C>>	basePrimitivePart(java.util.List<GenWordPolynomial<C>> F)	List of GenWordPolynomial base coefficient primitive part.
java.util.List<GenWordPolynomial<C>>	GB(java.util.List<GenWordPolynomial<C>> F)	Word Groebner base using word pairlist class.

Methods inherited from class edu.jas.gb.WordGroebnerBaseAbstract

cancel, commonZeroTest, isGB, isMinimalGB, minimalGB, normalizeZerosOnes, terminate, toString, univariateDegrees

Methods inherited from class java.lang.Object

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

Field Detail

cofac

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

Coefficient ring factory.

Constructor Detail

WordGroebnerBasePseudoSeq

public WordGroebnerBasePseudoSeq(RingFactory<C> rf)

Constructor.

Parameters:

rf - coefficient ring factory.

WordGroebnerBasePseudoSeq

public WordGroebnerBasePseudoSeq(RingFactory<C> rf,
                                 WordPseudoReductionSeq<C> red)

Constructor.

Parameters:

rf - coefficient ring factory.

red - Reduction engine

WordGroebnerBasePseudoSeq

public WordGroebnerBasePseudoSeq(RingFactory<C> rf,
                                 WordPseudoReductionSeq<C> red,
                                 WordPairList<C> pl)

Constructor.

Parameters:

rf - coefficient ring factory.

red - Reduction engine

pl - pair selection strategy

Method Detail

GB

public java.util.List<GenWordPolynomial<C>> GB(java.util.List<GenWordPolynomial<C>> F)

Word Groebner base using word pairlist class.

Specified by:

GB in interface WordGroebnerBase<C extends GcdRingElem<C>>

Specified by:

GB in class WordGroebnerBaseAbstract<C extends GcdRingElem<C>>

Parameters:

F - word polynomial list.

Returns:

GB(F) a finite non-commutative Groebner base of F, if it exists.

baseContent

public C baseContent(GenWordPolynomial<C> P)

GenWordPolynomial base coefficient content.

Parameters:

P - GenWordPolynomial.

Returns:

cont(P).

basePrimitivePart

public GenWordPolynomial<C> basePrimitivePart(GenWordPolynomial<C> P)

GenWordPolynomial base coefficient primitive part.

Parameters:

P - GenWordPolynomial.

Returns:

pp(P).

basePrimitivePart

public java.util.List<GenWordPolynomial<C>> basePrimitivePart(java.util.List<GenWordPolynomial<C>> F)

List of GenWordPolynomial base coefficient primitive part.

Parameters:

F - list of GenWordPolynomials.

Returns:

pp(F).