Package edu.jas.gbufd

Class SyzygySeq<C extends GcdRingElem<C>>

java.lang.Object

edu.jas.gbufd.SyzygyAbstract<C>

edu.jas.gbufd.SyzygySeq<C>

Type Parameters:

C - coefficient type

All Implemented Interfaces:

Syzygy<C>, java.io.Serializable

public class SyzygySeq<C extends GcdRingElem<C>>
extends SyzygyAbstract<C>

SyzygySeq class. Implements Syzygy computations and tests.

Author:

Heinz Kredel

See Also:

Serialized Form

Field Summary

Fields

Modifier and Type	Field	Description
protected GroebnerBaseAbstract<C>	bb	Groebner base engine.

Fields inherited from class edu.jas.gbufd.SyzygyAbstract

blas, red

Constructor Summary

Constructors

Constructor	Description
SyzygySeq(RingFactory<C> cf)	Constructor.

Method Summary

Modifier and Type	Method	Description
java.util.List<edu.jas.gbufd.ResPart<C>>	resolution(ModuleList<C> M)	Resolution of a module.
java.util.List	resolution(PolynomialList<C> F)	Resolution of a polynomial list.
java.util.List<edu.jas.gbufd.ResPart<C>>	resolutionArbitrary(ModuleList<C> M)	Resolution of a module.
java.util.List	resolutionArbitrary(PolynomialList<C> F)	Resolution of a polynomial list.
java.util.List<java.util.List<GenPolynomial<C>>>	zeroRelationsArbitrary(int modv, java.util.List<GenPolynomial<C>> F)	Syzygy module from arbitrary base.

Methods inherited from class edu.jas.gbufd.SyzygyAbstract

isZeroRelation, isZeroRelation, zeroRelations, zeroRelations, zeroRelations, zeroRelations, zeroRelationsArbitrary, zeroRelationsArbitrary

Methods inherited from class java.lang.Object

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

Field Detail

bb

protected GroebnerBaseAbstract<C extends GcdRingElem<C>> bb

Groebner base engine.

Constructor Detail

SyzygySeq

public SyzygySeq(RingFactory<C> cf)

Constructor.

Parameters:

cf - coefficient ring.

Method Detail

resolution

public java.util.List<edu.jas.gbufd.ResPart<C>> resolution(ModuleList<C> M)

Resolution of a module. Only with direct GBs.

Parameters:

M - a module list of a Groebner basis.

Returns:

a resolution of M.

resolution

public java.util.List resolution(PolynomialList<C> F)

Resolution of a polynomial list. Only with direct GBs.

Parameters:

F - a polynomial list of a Groebner basis.

Returns:

a resolution of F.

resolutionArbitrary

public java.util.List resolutionArbitrary(PolynomialList<C> F)

Resolution of a polynomial list.

Parameters:

F - a polynomial list of an arbitrary basis.

Returns:

a resolution of F.

resolutionArbitrary

public java.util.List<edu.jas.gbufd.ResPart<C>> resolutionArbitrary(ModuleList<C> M)

Resolution of a module.

Parameters:

M - a module list of an arbitrary basis.

Returns:

a resolution of M.

zeroRelationsArbitrary

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

Syzygy module from arbitrary base.

Parameters:

modv - number of module variables.

F - a polynomial list.

Returns:

syz(F), a basis for the module of syzygies for F.