Package edu.jas.gbufd

Class WordGroebnerBasePseudoRecSeq<C extends GcdRingElem<C>>

java.lang.Object

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

edu.jas.gbufd.WordGroebnerBasePseudoRecSeq<C>

Type Parameters:

C - coefficient type

All Implemented Interfaces:

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

public class WordGroebnerBasePseudoRecSeq<C extends GcdRingElem<C>>
extends WordGroebnerBaseAbstract<GenPolynomial<C>>

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

Author:

Heinz Kredel

See Also:

Serialized Form

Field Summary

Fields

Modifier and Type	Field	Description
protected GenPolynomialRing<C>	cofac	Coefficient ring factory.
protected GreatestCommonDivisorAbstract<C>	engine	Greatest common divisor engine for coefficient content and primitive parts.
protected WordPseudoReduction<GenPolynomial<C>>	red	Reduction engine.
protected WordPseudoReduction<C>	redRec	Reduction engine.

Fields inherited from class edu.jas.gb.WordGroebnerBaseAbstract

strategy

Constructor Summary

Constructors

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

Method Summary

Modifier and Type	Method	Description
java.util.List<GenWordPolynomial<GenPolynomial<C>>>	GB(java.util.List<GenWordPolynomial<GenPolynomial<C>>> F)	Word Groebner base using word pairlist class.
boolean	isGB(java.util.List<GenWordPolynomial<GenPolynomial<C>>> F)	Wird Groebner base simple test.
java.util.List<GenWordPolynomial<GenPolynomial<C>>>	minimalGB(java.util.List<GenWordPolynomial<GenPolynomial<C>>> Gp)	Minimal ordered Groebner basis.
GenPolynomial<C>	recursiveContent(GenWordPolynomial<GenPolynomial<C>> P)	GenWordPolynomial recursive coefficient content.
GenWordPolynomial<GenPolynomial<C>>	recursivePrimitivePart(GenWordPolynomial<GenPolynomial<C>> P)	GenWordPolynomial recursive coefficient primitive part.
java.util.List<GenWordPolynomial<GenPolynomial<C>>>	recursivePrimitivePart(java.util.List<GenWordPolynomial<GenPolynomial<C>>> F)	List of GenWordPolynomial recursive coefficient primitive part.

Methods inherited from class edu.jas.gb.WordGroebnerBaseAbstract

cancel, commonZeroTest, isMinimalGB, 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 WordPseudoReduction<C extends GcdRingElem<C>> redRec

Reduction engine.

red

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

Reduction engine.

cofac

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

Coefficient ring factory.

Constructor Detail

WordGroebnerBasePseudoRecSeq

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

Constructor.

Parameters:

rf - coefficient ring factory.

WordGroebnerBasePseudoRecSeq

public WordGroebnerBasePseudoRecSeq(RingFactory<GenPolynomial<C>> rf,
                                    WordPseudoReductionSeq<GenPolynomial<C>> red)

Constructor.

Parameters:

rf - coefficient ring factory.

red - Reduction engine

WordGroebnerBasePseudoRecSeq

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

Constructor.

Parameters:

rf - coefficient ring factory.

red - Reduction engine

pl - pair selection strategy

Method Detail

GB

public java.util.List<GenWordPolynomial<GenPolynomial<C>>> GB(java.util.List<GenWordPolynomial<GenPolynomial<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<GenPolynomial<C extends GcdRingElem<C>>>

Parameters:

F - word polynomial list.

Returns:

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

minimalGB

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

Minimal ordered Groebner basis.

Specified by:

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

Overrides:

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

Parameters:

Gp - a Groebner base.

Returns:

a reduced Groebner base of Gp.

isGB

public boolean isGB(java.util.List<GenWordPolynomial<GenPolynomial<C>>> F)

Wird Groebner base simple test.

Specified by:

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

Overrides:

isGB in class WordGroebnerBaseAbstract<GenPolynomial<C extends GcdRingElem<C>>>

Parameters:

F - recursive polynomial list.

Returns:

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

recursiveContent

public GenPolynomial<C> recursiveContent(GenWordPolynomial<GenPolynomial<C>> P)

GenWordPolynomial recursive coefficient content.

Parameters:

P - recursive GenWordPolynomial.

Returns:

cont(P).

recursivePrimitivePart

public GenWordPolynomial<GenPolynomial<C>> recursivePrimitivePart(GenWordPolynomial<GenPolynomial<C>> P)

GenWordPolynomial recursive coefficient primitive part.

Parameters:

P - recursive GenWordPolynomial.

Returns:

pp(P).

recursivePrimitivePart

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

List of GenWordPolynomial recursive coefficient primitive part.

Parameters:

F - list of recursive GenWordPolynomials.

Returns:

pp(F).