edu.jas.gbmod
Interface Syzygy<C extends RingElem<C>>

Type Parameters:

C - coefficient type

All Known Implementing Classes:

SyzygyAbstract

public interface Syzygy<C extends RingElem<C>>

Syzygy interface. Defines Syzygy computations and tests.

Author:

Heinz Kredel

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.
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.

Method Detail

zeroRelations

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.

Parameters:

F - a Groebner base.

Returns:

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

zeroRelations

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.

Parameters:

modv - number of module variables.

F - a Groebner base.

Returns:

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

zeroRelations

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.

Parameters:

modv - number of module variables.

v - a Groebner base.

Returns:

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

zeroRelations

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

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

Parameters:

M - a module Groebner base.

Returns:

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

isZeroRelation

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

Test if sysygy.

Parameters:

Z - list of sysygies.

F - a polynomial list.

Returns:

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

isZeroRelation

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

Test if sysygy of modules.

Parameters:

Z - list of sysygies.

F - a module list.

Returns:

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

resolution

java.util.List<edu.jas.gbmod.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

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

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

java.util.List<edu.jas.gbmod.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

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

Syzygy module from arbitrary base.

Parameters:

F - a polynomial list.

Returns:

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

zeroRelationsArbitrary

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.

zeroRelationsArbitrary

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

Syzygy module from arbitrary module base.

Parameters:

M - an arbitrary module base.

Returns:

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