Package edu.jas.gbufd

Interface SolvableSyzygy<C extends RingElem<C>>

Type Parameters:

C - coefficient type

All Superinterfaces:

java.io.Serializable

All Known Implementing Classes:

SolvableSyzygyAbstract, SolvableSyzygySeq

public interface SolvableSyzygy<C extends RingElem<C>>
extends java.io.Serializable

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

Author:

Heinz Kredel

Method Summary

Modifier and Type	Method	Description
boolean	isLeftOreCond(GenSolvablePolynomial<C> a, GenSolvablePolynomial<C> b, GenSolvablePolynomial<C>[] oc)	Test left Ore condition.
boolean	isLeftZeroRelation(ModuleList<C> Z, ModuleList<C> F)	Test if left sysygy of modules
boolean	isLeftZeroRelation(java.util.List<java.util.List<GenSolvablePolynomial<C>>> Z, java.util.List<GenSolvablePolynomial<C>> F)	Test if left syzygy.
boolean	isRightOreCond(GenSolvablePolynomial<C> a, GenSolvablePolynomial<C> b, GenSolvablePolynomial<C>[] oc)	Test right Ore condition.
boolean	isRightZeroRelation(ModuleList<C> Z, ModuleList<C> F)	Test if right sysygy of modules
boolean	isRightZeroRelation(java.util.List<java.util.List<GenSolvablePolynomial<C>>> Z, java.util.List<GenSolvablePolynomial<C>> F)	Test if right syzygy.
GenSolvablePolynomial<C>[]	leftOreCond(GenSolvablePolynomial<C> a, GenSolvablePolynomial<C> b)	Left Ore condition.
java.util.List<java.util.List<GenSolvablePolynomial<C>>>	leftZeroRelations(int modv, 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>>>	leftZeroRelations(java.util.List<GenSolvablePolynomial<C>> F)	Left syzygy for left 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.
ModuleList<C>	leftZeroRelationsArbitrary(ModuleList<C> M)	Left syzygy for arbitrary left module base.
java.util.List<java.util.List<GenSolvablePolynomial<C>>>	leftZeroRelationsArbitrary(java.util.List<GenSolvablePolynomial<C>> F)	Left syzygy module from arbitrary base.
java.util.List<edu.jas.gbufd.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.gbufd.SolvResPart<C>>	resolutionArbitrary(ModuleList<C> M)	Resolution of a module.
java.util.List	resolutionArbitrary(PolynomialList<C> F)	Resolution of a polynomial list.
GenSolvablePolynomial<C>[]	rightOreCond(GenSolvablePolynomial<C> a, GenSolvablePolynomial<C> b)	Right Ore condition.
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.gbufd.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.gbufd.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.

isLeftOreCond

boolean isLeftOreCond(GenSolvablePolynomial<C> a,
                      GenSolvablePolynomial<C> b,
                      GenSolvablePolynomial<C>[] oc)

Test left Ore condition.

Parameters:

a - solvable polynomial

b - solvable polynomial

oc - = [p,q] two solvable polynomials

Returns:

true if p*a = q*b, else false

isRightOreCond

boolean isRightOreCond(GenSolvablePolynomial<C> a,
                       GenSolvablePolynomial<C> b,
                       GenSolvablePolynomial<C>[] oc)

Test right Ore condition.

Parameters:

a - solvable polynomial

b - solvable polynomial

oc - = [p,q] two solvable polynomials

Returns:

true if a*p = b*q, else false

leftOreCond

GenSolvablePolynomial<C>[] leftOreCond(GenSolvablePolynomial<C> a,
                                       GenSolvablePolynomial<C> b)

Left Ore condition. Generators for the left Ore condition of two solvable polynomials.

Parameters:

a - solvable polynomial

b - solvable polynomial

Returns:

[p,q] with p*a = q*b

rightOreCond

GenSolvablePolynomial<C>[] rightOreCond(GenSolvablePolynomial<C> a,
                                        GenSolvablePolynomial<C> b)

Right Ore condition. Generators for the right Ore condition of two solvable polynomials.

Parameters:

a - solvable polynomial

b - solvable polynomial

Returns:

[p,q] with a*p = b*q