edu.jas.gb

Class WordGroebnerBaseAbstract<C extends RingElem<C>>

java.lang.Object

edu.jas.gb.WordGroebnerBaseAbstract<C>

Type Parameters:

C - coefficient type

All Implemented Interfaces:

WordGroebnerBase<C>, java.io.Serializable

Direct Known Subclasses:

WordGroebnerBasePseudoRecSeq, WordGroebnerBasePseudoSeq, WordGroebnerBaseSeq

public abstract class WordGroebnerBaseAbstract<C extends RingElem<C>>
extends java.lang.Object
implements WordGroebnerBase<C>

Non-commutative Groebner Bases abstract class. Implements common Groebner bases and GB test methods.

Author:

Heinz Kredel

See Also:

Serialized Form

Field Summary

Fields

Modifier and Type	Field and Description
WordReduction<C>	red Reduction engine.
WordPairList<C>	strategy Strategy for pair selection.

Constructor Summary

Constructors

Constructor and Description
WordGroebnerBaseAbstract() Constructor.
WordGroebnerBaseAbstract(WordReduction<C> red) Constructor.
WordGroebnerBaseAbstract(WordReduction<C> red, WordPairList<C> pl) Constructor.

Method Summary

Modifier and Type	Method and Description
int	cancel() Cancel ThreadPool.
int	commonZeroTest(java.util.List<GenWordPolynomial<C>> F) Common zero test, test if univariate leading words exist for all variables.
abstract java.util.List<GenWordPolynomial<C>>	GB(java.util.List<GenWordPolynomial<C>> F) Groebner base using pairlist class.
boolean	isGB(java.util.List<GenWordPolynomial<C>> F) Word Groebner base test.
boolean	isMinimalGB(java.util.List<GenWordPolynomial<C>> Gp) Test for minimal ordered Groebner basis.
java.util.List<GenWordPolynomial<C>>	minimalGB(java.util.List<GenWordPolynomial<C>> Gp) Minimal ordered Groebner basis.
java.util.List<GenWordPolynomial<C>>	normalizeZerosOnes(java.util.List<GenWordPolynomial<C>> A) Normalize polynomial list.
void	terminate() Cleanup and terminate ThreadPool.
java.lang.String	toString() Get the String representation with GB engines.
java.util.List<java.lang.Long>	univariateDegrees(java.util.List<GenWordPolynomial<C>> A) Univariate head term degrees.

Methods inherited from class java.lang.Object

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

Field Detail

red

public final WordReduction<C extends RingElem<C>> red

Reduction engine.

strategy

public final WordPairList<C extends RingElem<C>> strategy

Strategy for pair selection.

Constructor Detail

WordGroebnerBaseAbstract

public WordGroebnerBaseAbstract()

Constructor.

WordGroebnerBaseAbstract

public WordGroebnerBaseAbstract(WordReduction<C> red)

Constructor.

Parameters:

red - Word Reduction engine

WordGroebnerBaseAbstract

public WordGroebnerBaseAbstract(WordReduction<C> red,
                                WordPairList<C> pl)

Constructor.

Parameters:

red - Word Reduction engine

pl - Word pair selection strategy

Method Detail

toString

public java.lang.String toString()

Get the String representation with GB engines.

Overrides:

toString in class java.lang.Object

See Also:

Object.toString()

normalizeZerosOnes

public java.util.List<GenWordPolynomial<C>> normalizeZerosOnes(java.util.List<GenWordPolynomial<C>> A)

Normalize polynomial list.

Parameters:

A - list of polynomials.

Returns:

list of polynomials with zeros removed and ones/units reduced.

commonZeroTest

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

Common zero test, test if univariate leading words exist for all variables.

Parameters:

F - polynomial list.

Returns:

-1, 0 or 1 if "dimension"(ideal(F)) &eq; -1, 0 or ≥ 1.

univariateDegrees

public java.util.List<java.lang.Long> univariateDegrees(java.util.List<GenWordPolynomial<C>> A)

Univariate head term degrees.

Parameters:

A - list of polynomials.

Returns:

a list of the degrees of univariate head terms.

isGB

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

Word Groebner base test.

Specified by:

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

Parameters:

F - Word polynomial list.

Returns:

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

GB

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

Groebner base using pairlist class.

Specified by:

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

Parameters:

F - polynomial list.

Returns:

GB(F) a Groebner base of F.

minimalGB

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

Minimal ordered Groebner basis.

Specified by:

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

Parameters:

Gp - a Groebner base.

Returns:

a reduced Groebner base of Gp.

isMinimalGB

public boolean isMinimalGB(java.util.List<GenWordPolynomial<C>> Gp)

Test for minimal ordered Groebner basis.

Parameters:

Gp - an ideal base.

Returns:

true, if Gp is a reduced minimal Groebner base.

terminate

public void terminate()

Cleanup and terminate ThreadPool.

cancel

public int cancel()

Cancel ThreadPool.