edu.jas.gbmod

Class SyzygyAbstract<C extends GcdRingElem<C>>

java.lang.Object

edu.jas.gbmod.SyzygyAbstract<C>

Type Parameters:

C - coefficient type

All Implemented Interfaces:

Syzygy<C>, java.io.Serializable

public class SyzygyAbstract<C extends GcdRingElem<C>>
extends java.lang.Object
implements Syzygy<C>

SyzygyAbstract class. Implements Syzygy computations and tests.

See Also:

Serialized Form

Constructor Summary

Constructors

Constructor and Description
SyzygyAbstract() Constructor.

Method Summary

Modifier and Type	Method and Description
boolean	isZeroRelation(java.util.List<java.util.List<GenPolynomial<C>>> Z, java.util.List<GenPolynomial<C>> F) Test if sysygy.
boolean	isZeroRelation(ModuleList<C> Z, ModuleList<C> F) Test if sysygy of modules.
java.util.List<edu.jas.gbmod.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.gbmod.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>>>	zeroRelations(int modv, GenVector<GenPolynomial<C>> v) Syzygy module from Groebner base.
java.util.List<java.util.List<GenPolynomial<C>>>	zeroRelations(int modv, java.util.List<GenPolynomial<C>> F) Syzygy module from Groebner base.
java.util.List<java.util.List<GenPolynomial<C>>>	zeroRelations(java.util.List<GenPolynomial<C>> F) Syzygy module from Groebner base.
ModuleList<C>	zeroRelations(ModuleList<C> M) Syzygy module from module Groebner base.
java.util.List<java.util.List<GenPolynomial<C>>>	zeroRelationsArbitrary(int modv, java.util.List<GenPolynomial<C>> F) Syzygy module from arbitrary base.
java.util.List<java.util.List<GenPolynomial<C>>>	zeroRelationsArbitrary(java.util.List<GenPolynomial<C>> F) Syzygy module from arbitrary base.
ModuleList<C>	zeroRelationsArbitrary(ModuleList<C> M) Syzygy module from arbitrary module base.

Methods inherited from class java.lang.Object

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

Constructor Detail

SyzygyAbstract

public SyzygyAbstract()

Constructor.

Method Detail

zeroRelations

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

Syzygy module from Groebner base. F must be a Groebner base.

Specified by:

zeroRelations in interface Syzygy<C extends GcdRingElem<C>>

Parameters:

F - a Groebner base.

Returns:

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

zeroRelations

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

Syzygy module from Groebner base. F must be a Groebner base.

Specified by:

zeroRelations in interface Syzygy<C extends GcdRingElem<C>>

Parameters:

modv - number of module variables.

F - a Groebner base.

Returns:

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

zeroRelations

public java.util.List<java.util.List<GenPolynomial<C>>> zeroRelations(int modv,
                                                                      GenVector<GenPolynomial<C>> v)

Syzygy module from Groebner base. v must be a Groebner base.

Specified by:

zeroRelations in interface Syzygy<C extends GcdRingElem<C>>

Parameters:

modv - number of module variables.

v - a Groebner base.

Returns:

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

zeroRelations

public ModuleList<C> zeroRelations(ModuleList<C> M)

Syzygy module from module Groebner base. M must be a module Groebner base.

Specified by:

zeroRelations in interface Syzygy<C extends GcdRingElem<C>>

Parameters:

M - a module Groebner base.

Returns:

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

isZeroRelation

public boolean isZeroRelation(java.util.List<java.util.List<GenPolynomial<C>>> Z,
                              java.util.List<GenPolynomial<C>> F)

Test if sysygy.

Specified by:

isZeroRelation in interface Syzygy<C extends GcdRingElem<C>>

Parameters:

Z - list of sysygies.

F - a polynomial list.

Returns:

true, if Z is a list of syzygies for F, else false.

isZeroRelation

public boolean isZeroRelation(ModuleList<C> Z,
                              ModuleList<C> F)

Test if sysygy of modules.

Specified by:

isZeroRelation in interface Syzygy<C extends GcdRingElem<C>>

Parameters:

Z - list of sysygies.

F - a module list.

Returns:

true, if Z is a list of syzygies for F, else false.

resolution

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

Resolution of a module. Only with direct GBs.

Specified by:

resolution in interface Syzygy<C extends GcdRingElem<C>>

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.

Specified by:

resolution in interface Syzygy<C extends GcdRingElem<C>>

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.

Specified by:

resolutionArbitrary in interface Syzygy<C extends GcdRingElem<C>>

Parameters:

F - a polynomial list of an arbitrary basis.

Returns:

a resolution of F.

resolutionArbitrary

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

Resolution of a module.

Specified by:

resolutionArbitrary in interface Syzygy<C extends GcdRingElem<C>>

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(java.util.List<GenPolynomial<C>> F)

Syzygy module from arbitrary base.

Specified by:

zeroRelationsArbitrary in interface Syzygy<C extends GcdRingElem<C>>

Parameters:

F - a polynomial list.

Returns:

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

zeroRelationsArbitrary

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

Syzygy module from arbitrary base.

Specified by:

zeroRelationsArbitrary in interface Syzygy<C extends GcdRingElem<C>>

Parameters:

modv - number of module variables.

F - a polynomial list.

Returns:

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

zeroRelationsArbitrary

public ModuleList<C> zeroRelationsArbitrary(ModuleList<C> M)

Syzygy module from arbitrary module base.

Specified by:

zeroRelationsArbitrary in interface Syzygy<C extends GcdRingElem<C>>

Parameters:

M - an arbitrary module base.

Returns:

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