Package edu.jas.gbufd

Class GroebnerBaseFGLM<C extends GcdRingElem<C>>

java.lang.Object

edu.jas.gb.GroebnerBaseAbstract<C>

edu.jas.gbufd.GroebnerBaseFGLM<C>

Type Parameters:

C - coefficient type

All Implemented Interfaces:

GroebnerBase<C>, java.io.Serializable

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

Groebner Base sequential FGLM algorithm. Implements Groebner base computation via FGLM algorithm.

Author:

Jan Suess

See Also:

GBAlgorithmBuilder, GBFactory, Serialized Form

Field Summary

Fields inherited from class edu.jas.gb.GroebnerBaseAbstract

blas, red, strategy

Constructor Summary

Constructors

Constructor	Description
GroebnerBaseFGLM()	Constructor.
GroebnerBaseFGLM(GroebnerBaseAbstract<C> gb)	Constructor.
GroebnerBaseFGLM(Reduction<C> red)	Constructor.
GroebnerBaseFGLM(Reduction<C> red, PairList<C> pl)	Constructor.
GroebnerBaseFGLM(Reduction<C> red, PairList<C> pl, GroebnerBaseAbstract<C> gb)	Constructor.

Method Summary

Modifier and Type	Method	Description
int	cancel()	Cancel ThreadPool.
java.util.List<GenPolynomial<C>>	convGroebnerToLex(java.util.List<GenPolynomial<C>> groebnerBasis)	Algorithm CONVGROEBNER: Converts Groebner bases w.r.t. total degree termorder into Groebner base w.r.t to inverse lexicographical term order
java.util.List<GenPolynomial<C>>	GB(int modv, java.util.List<GenPolynomial<C>> F)	Groebner base using FGLM algorithm.
GenPolynomial<C>	lMinterm(java.util.List<GenPolynomial<C>> G, GenPolynomial<C> t)	Algorithm lMinterm: MINTERM algorithm for inverse lexicographical term order.
java.util.List<GenPolynomial<C>>	redTerms(java.util.List<GenPolynomial<C>> groebnerBasis)	Compute the residues to given polynomial list.
void	terminate()	Cleanup and terminate ThreadPool.
java.lang.String	toString()	Get the String representation with GB engine.

Methods inherited from class edu.jas.gb.GroebnerBaseAbstract

commonZeroTest, constructUnivariate, extGB, extGB, GB, GB, GB, isGB, isGB, isGB, isGB, isGB, isGB, isGBidem, isGBsimple, isMinimalGB, isMinReductionMatrix, isMinReductionMatrix, isReductionMatrix, isReductionMatrix, minimalExtendedGB, minimalGB, normalizeMatrix, normalizeZerosOnes, univariateDegrees

Methods inherited from class java.lang.Object

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

Constructor Detail

GroebnerBaseFGLM

public GroebnerBaseFGLM()

Constructor.

GroebnerBaseFGLM

public GroebnerBaseFGLM(Reduction<C> red)

Constructor.

Parameters:

red - Reduction engine

GroebnerBaseFGLM

public GroebnerBaseFGLM(Reduction<C> red,
                        PairList<C> pl)

Constructor.

Parameters:

red - Reduction engine

pl - pair selection strategy

GroebnerBaseFGLM

public GroebnerBaseFGLM(Reduction<C> red,
                        PairList<C> pl,
                        GroebnerBaseAbstract<C> gb)

Constructor.

Parameters:

red - Reduction engine

pl - pair selection strategy

gb - backing GB algorithm.

GroebnerBaseFGLM

public GroebnerBaseFGLM(GroebnerBaseAbstract<C> gb)

Constructor.

Parameters:

gb - backing GB algorithm.

Method Detail

toString

public java.lang.String toString()

Get the String representation with GB engine.

Overrides:

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

See Also:

Object.toString()

GB

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

Groebner base using FGLM algorithm.

Parameters:

modv - module variable number.

F - polynomial list.

Returns:

GB(F) a inv lex term order Groebner base of F.

convGroebnerToLex

public java.util.List<GenPolynomial<C>> convGroebnerToLex(java.util.List<GenPolynomial<C>> groebnerBasis)

Algorithm CONVGROEBNER: Converts Groebner bases w.r.t. total degree termorder into Groebner base w.r.t to inverse lexicographical term order

Returns:

Groebner base w.r.t to inverse lexicographical term order

lMinterm

public GenPolynomial<C> lMinterm(java.util.List<GenPolynomial<C>> G,
                                 GenPolynomial<C> t)

Algorithm lMinterm: MINTERM algorithm for inverse lexicographical term order.

Parameters:

t - Term

G - Groebner basis

Returns:

Term that specifies condition (D) or null (Condition (D) in "A computational approach to commutative algebra", Becker, Weispfenning, Kredel 1993, p. 427)

redTerms

public java.util.List<GenPolynomial<C>> redTerms(java.util.List<GenPolynomial<C>> groebnerBasis)

Compute the residues to given polynomial list.

Returns:

List of reduced terms

terminate

public void terminate()

Cleanup and terminate ThreadPool.

Overrides:

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

cancel

public int cancel()

Cancel ThreadPool.

Overrides:

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