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

Type Parameters:

C - coefficient type

All Known Implementing Classes:

SolvableSyzygyAbstract

public interface SolvableSyzygy<C extends RingElem<C>>

Syzygy interface for solvable polynomials. Defines syzygy computations and tests.

Author:

Heinz Kredel

Method Summary

boolean	isLeftZeroRelation(java.util.List<java.util.List<GenSolvablePolynomial<C>>> Z, java.util.List<GenSolvablePolynomial<C>> F) Test if left syzygy.
boolean	isLeftZeroRelation(ModuleList<C> Z, ModuleList<C> F) Test if left sysygy of modules
boolean	isRightZeroRelation(java.util.List<java.util.List<GenSolvablePolynomial<C>>> Z, java.util.List<GenSolvablePolynomial<C>> F) Test if right syzygy.
boolean	isRightZeroRelation(ModuleList<C> Z, ModuleList<C> F) Test if right sysygy of modules
java.util.List<java.util.List<GenSolvablePolynomial<C>>>	leftZeroRelations(int modv, java.util.List<GenSolvablePolynomial<C>> F) Left syzygy for left Groebner base.
java.util.List<java.util.List<GenSolvablePolynomial<C>>>	leftZeroRelations(java.util.List<GenSolvablePolynomial<C>> F) Left syzygy for left Groebner base.
ModuleList<C>	leftZeroRelations(ModuleList<C> M) Left syzygy for left module Groebner base.
java.util.List<java.util.List<GenSolvablePolynomial<C>>>	leftZeroRelationsArbitrary(int modv, java.util.List<GenSolvablePolynomial<C>> F) Left syzygy module from arbitrary base.
java.util.List<java.util.List<GenSolvablePolynomial<C>>>	leftZeroRelationsArbitrary(java.util.List<GenSolvablePolynomial<C>> F) Left syzygy module from arbitrary base.
ModuleList<C>	leftZeroRelationsArbitrary(ModuleList<C> M) Left syzygy for arbitrary left module base.
java.util.List<edu.jas.gbmod.SolvResPart<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.SolvResPart<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<GenSolvablePolynomial<C>>>	rightZeroRelationsArbitrary(int modv, java.util.List<GenSolvablePolynomial<C>> F) Right syzygy module from arbitrary base.
java.util.List<java.util.List<GenSolvablePolynomial<C>>>	rightZeroRelationsArbitrary(java.util.List<GenSolvablePolynomial<C>> F) Right syzygy module from arbitrary base.

Method Detail

leftZeroRelations

java.util.List<java.util.List<GenSolvablePolynomial<C>>> leftZeroRelations(java.util.List<GenSolvablePolynomial<C>> F)

Left syzygy for left Groebner base.

Parameters:

F - a Groebner base.

Returns:

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

leftZeroRelations

java.util.List<java.util.List<GenSolvablePolynomial<C>>> leftZeroRelations(int modv,
                                                                           java.util.List<GenSolvablePolynomial<C>> F)

Left syzygy for left Groebner base.

Parameters:

modv - number of module variables.

F - a Groebner base.

Returns:

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

leftZeroRelations

ModuleList<C> leftZeroRelations(ModuleList<C> M)

Left syzygy for left module Groebner base.

Parameters:

M - a Groebner base.

Returns:

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

isLeftZeroRelation

boolean isLeftZeroRelation(java.util.List<java.util.List<GenSolvablePolynomial<C>>> Z,
                           java.util.List<GenSolvablePolynomial<C>> F)

Test if left syzygy.

Parameters:

Z - list of sysygies.

F - a polynomial list.

Returns:

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

isRightZeroRelation

boolean isRightZeroRelation(java.util.List<java.util.List<GenSolvablePolynomial<C>>> Z,
                            java.util.List<GenSolvablePolynomial<C>> F)

Test if right syzygy.

Parameters:

Z - list of sysygies.

F - a polynomial list.

Returns:

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

isLeftZeroRelation

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

Test if left sysygy of modules

Parameters:

Z - list of sysygies.

F - a module list.

Returns:

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

isRightZeroRelation

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

Test if right sysygy of modules

Parameters:

Z - list of sysygies.

F - a module list.

Returns:

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

resolution

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

Resolution of a module.

Parameters:

M - a module list of an arbitrary basis.

Returns:

a resolution of M.

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.

leftZeroRelationsArbitrary

java.util.List<java.util.List<GenSolvablePolynomial<C>>> leftZeroRelationsArbitrary(java.util.List<GenSolvablePolynomial<C>> F)

Left syzygy module from arbitrary base.

Parameters:

F - a solvable polynomial list.

Returns:

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

leftZeroRelationsArbitrary

java.util.List<java.util.List<GenSolvablePolynomial<C>>> leftZeroRelationsArbitrary(int modv,
                                                                                    java.util.List<GenSolvablePolynomial<C>> F)

Left syzygy module from arbitrary base.

Parameters:

modv - number of module variables.

F - a solvable polynomial list.

Returns:

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

leftZeroRelationsArbitrary

ModuleList<C> leftZeroRelationsArbitrary(ModuleList<C> M)

Left syzygy for arbitrary left module base.

Parameters:

M - an arbitrary base.

Returns:

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

rightZeroRelationsArbitrary

java.util.List<java.util.List<GenSolvablePolynomial<C>>> rightZeroRelationsArbitrary(java.util.List<GenSolvablePolynomial<C>> F)

Right syzygy module from arbitrary base.

Parameters:

F - a solvable polynomial list.

Returns:

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

rightZeroRelationsArbitrary

java.util.List<java.util.List<GenSolvablePolynomial<C>>> rightZeroRelationsArbitrary(int modv,
                                                                                     java.util.List<GenSolvablePolynomial<C>> F)

Right syzygy module from arbitrary base.

Parameters:

modv - number of module variables.

F - a solvable polynomial list.

Returns:

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