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>, 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 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.
List<GenPolynomial<C>>	convGroebnerToLex(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
List<GenPolynomial<C>>	GB(int modv, List<GenPolynomial<C>> F)	Groebner base using FGLM algorithm.
GenPolynomial<C>	lMinterm(List<GenPolynomial<C>> G, GenPolynomial<C> t)	Algorithm lMinterm: MINTERM algorithm for inverse lexicographical term order.
List<GenPolynomial<C>>	redTerms(List<GenPolynomial<C>> groebnerBasis)	Compute the residues to given polynomial list.
void	terminate()	Cleanup and terminate ThreadPool.
String	toString()	Get the String representation with GB engine.

Methods inherited from class 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 Object

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

Constructor Details

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 Details

toString

public String toString()

Get the String representation with GB engine.

Overrides:

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

See Also:

• Object.toString()

GB

public List<GenPolynomial<C>> GB(int modv,
 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 List<GenPolynomial<C>> convGroebnerToLex(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(List<GenPolynomial<C>> G,
 GenPolynomial<C> t)

Algorithm lMinterm: MINTERM algorithm for inverse lexicographical term order.

Parameters:

G - Groebner basis

t - Term

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 List<GenPolynomial<C>> redTerms(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>>