edu.jas.gbmod

Class SolvableSyzygyAbstract<C extends RingElem<C>>

java.lang.Object

edu.jas.gbmod.SolvableSyzygyAbstract<C>

Type Parameters:

C - coefficient type

All Implemented Interfaces:

SolvableSyzygy<C>

public class SolvableSyzygyAbstract<C extends RingElem<C>>
extends java.lang.Object
implements SolvableSyzygy<C>

Syzygy class for solvable polynomials. Implements Syzygy computations and tests.

Author:

Heinz Kredel

Field Summary

Fields

Modifier and Type	Field and Description
protected BasicLinAlg<GenPolynomial<C>>	blas Linear algebra engine.
protected Reduction<C>	red Reduction engine.
protected SolvableReduction<C>	sred Solvable reduction engine.

Constructor Summary

Constructors

Constructor and Description
SolvableSyzygyAbstract() Constructor.

Method Summary

Methods

Modifier and Type	Method and Description
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.

Methods inherited from class java.lang.Object

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

Field Detail

sred

protected SolvableReduction<C extends RingElem<C>> sred

Solvable reduction engine.

red

protected Reduction<C extends RingElem<C>> red

Reduction engine.

blas

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

Linear algebra engine.

Constructor Detail

SolvableSyzygyAbstract

public SolvableSyzygyAbstract()

Constructor.

Method Detail

leftZeroRelations

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

Left syzygy for left Groebner base.

Specified by:

leftZeroRelations in interface SolvableSyzygy<C extends RingElem<C>>

Parameters:

F - a Groebner base.

Returns:

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

leftZeroRelations

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

Left syzygy for left Groebner base.

Specified by:

leftZeroRelations in interface SolvableSyzygy<C extends RingElem<C>>

Parameters:

modv - number of module variables.

F - a Groebner base.

Returns:

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

leftZeroRelations

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

Left syzygy for left module Groebner base.

Specified by:

leftZeroRelations in interface SolvableSyzygy<C extends RingElem<C>>

Parameters:

M - a Groebner base.

Returns:

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

isLeftZeroRelation

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

Test if left syzygy.

Specified by:

isLeftZeroRelation in interface SolvableSyzygy<C extends RingElem<C>>

Parameters:

Z - list of sysygies.

F - a polynomial list.

Returns:

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

isRightZeroRelation

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

Test if right syzygy.

Specified by:

isRightZeroRelation in interface SolvableSyzygy<C extends RingElem<C>>

Parameters:

Z - list of sysygies.

F - a polynomial list.

Returns:

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

isLeftZeroRelation

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

Test if left sysygy of modules

Specified by:

isLeftZeroRelation in interface SolvableSyzygy<C extends RingElem<C>>

Parameters:

Z - list of sysygies.

F - a module list.

Returns:

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

isRightZeroRelation

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

Test if right sysygy of modules

Specified by:

isRightZeroRelation in interface SolvableSyzygy<C extends RingElem<C>>

Parameters:

Z - list of sysygies.

F - a module list.

Returns:

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

resolution

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

Resolution of a module. Only with direct GBs.

Specified by:

resolution in interface SolvableSyzygy<C extends RingElem<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 SolvableSyzygy<C extends RingElem<C>>

Parameters:

F - a polynomial list of a Groebner basis.

Returns:

a resolution of F.

resolutionArbitrary

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

Resolution of a module.

Specified by:

resolutionArbitrary in interface SolvableSyzygy<C extends RingElem<C>>

Parameters:

M - a module list of an arbitrary basis.

Returns:

a resolution of M.

resolutionArbitrary

public java.util.List resolutionArbitrary(PolynomialList<C> F)

Resolution of a polynomial list.

Specified by:

resolutionArbitrary in interface SolvableSyzygy<C extends RingElem<C>>

Parameters:

F - a polynomial list of an arbitrary basis.

Returns:

a resolution of F.

leftZeroRelationsArbitrary

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

Left syzygy module from arbitrary base.

Specified by:

leftZeroRelationsArbitrary in interface SolvableSyzygy<C extends RingElem<C>>

Parameters:

F - a solvable polynomial list.

Returns:

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

leftZeroRelationsArbitrary

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

Left syzygy module from arbitrary base.

Specified by:

leftZeroRelationsArbitrary in interface SolvableSyzygy<C extends RingElem<C>>

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

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

Left syzygy for arbitrary left module base.

Specified by:

leftZeroRelationsArbitrary in interface SolvableSyzygy<C extends RingElem<C>>

Parameters:

M - an arbitrary base.

Returns:

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

rightZeroRelationsArbitrary

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

Right syzygy module from arbitrary base.

Specified by:

rightZeroRelationsArbitrary in interface SolvableSyzygy<C extends RingElem<C>>

Parameters:

F - a solvable polynomial list.

Returns:

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

rightZeroRelationsArbitrary

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

Right syzygy module from arbitrary base.

Specified by:

rightZeroRelationsArbitrary in interface SolvableSyzygy<C extends RingElem<C>>

Parameters:

modv - number of module variables.

F - a solvable polynomial list.

Returns:

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