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>

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

SyzygyAbstract class. Implements Syzygy computations and tests.

Author:

Heinz Kredel

Field Summary

protected BasicLinAlg<GenPolynomial<C>>	blas Linear algebra engine.
protected Reduction<C>	red Reduction engine.

Constructor Summary

SyzygyAbstract()
Constructor.

Method Summary

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. 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(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

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

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.

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.