Class SyzygyAbstract<C extends GcdRingElem<C>>

java.lang.Object

edu.jas.gbufd.SyzygyAbstract<C>

Type Parameters:

C - coefficient type

All Implemented Interfaces:

Syzygy<C>, Serializable

Direct Known Subclasses:

SyzygySeq

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

SyzygyAbstract class. Implements Syzygy computations and tests.

See Also:

• Serialized Form

Field Summary

Fields

Modifier and Type	Field	Description
protected BasicLinAlg<GenPolynomial<C>>	blas	Linear algebra engine.
private static final boolean	debug
private static final org.apache.logging.log4j.Logger	logger
protected Reduction<C>	red	Reduction engine.

Constructor Summary

Constructors

Constructor	Description
SyzygyAbstract()	Constructor.

Method Summary

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

Methods inherited from class Object

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

Methods inherited from interface Syzygy

resolution, resolution, resolutionArbitrary, resolutionArbitrary, zeroRelationsArbitrary

Field Details

logger

private static final org.apache.logging.log4j.Logger logger

debug

private static final boolean debug

red

protected Reduction<C extends GcdRingElem<C>> red

Reduction engine.

blas

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

Linear algebra engine.

Constructor Details

SyzygyAbstract

public SyzygyAbstract()

Constructor.

Method Details

zeroRelations

public List<List<GenPolynomial<C>>> zeroRelations(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 List<List<GenPolynomial<C>>> zeroRelations(int modv,
 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 List<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(List<List<GenPolynomial<C>>> Z,
 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 List<List<GenPolynomial<C>>> zeroRelationsArbitrary(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.