edu.jas.gbufd

Class SyzygyAbstract<C extends GcdRingElem<C>>

java.lang.Object

edu.jas.gbufd.SyzygyAbstract<C>

Type Parameters:

C - coefficient type

All Implemented Interfaces:

Syzygy<C>, java.io.Serializable

Direct Known Subclasses:

SyzygySeq

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

SyzygyAbstract class. Implements Syzygy computations and tests.

Author:

Heinz Kredel

See Also:

Serialized Form

Field Summary

Fields

Modifier and Type	Field and Description
protected BasicLinAlg<GenPolynomial<C>>	blas Linear algebra engine.
protected Reduction<C>	red Reduction engine.

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<java.util.List<GenPolynomial<C>>>	zeroRelations(int modv, GenVector<GenPolynomial<C>> v) Syzygy module from Groebner base. v must be a 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(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

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

Methods inherited from interface edu.jas.gbufd.Syzygy

resolution, resolution, resolutionArbitrary, resolutionArbitrary, zeroRelationsArbitrary

Field Detail

red

protected Reduction<C extends GcdRingElem<C>> red

Reduction engine.

blas

protected BasicLinAlg<GenPolynomial<C extends GcdRingElem<C>>> blas

Linear algebra engine.

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.

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 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.