edu.jas.gbufd

Class SolvableSyzygySeq<C extends GcdRingElem<C>>

java.lang.Object

edu.jas.gbufd.SolvableSyzygyAbstract<C>

edu.jas.gbufd.SolvableSyzygySeq<C>

Type Parameters:

C - coefficient type

All Implemented Interfaces:

SolvableSyzygy<C>, java.io.Serializable

public class SolvableSyzygySeq<C extends GcdRingElem<C>>
extends SolvableSyzygyAbstract<C>

Syzygy sequential class for solvable polynomials. Implements Syzygy computations and tests with Groebner bases.

Author:

Heinz Kredel

See Also:

Serialized Form

Field Summary

Fields

Modifier and Type	Field and Description
protected SolvableGroebnerBase<C>	sbb Groebner basis engine.

Fields inherited from class edu.jas.gbufd.SolvableSyzygyAbstract

blas, red, sred

Constructor Summary

Constructors

Constructor and Description
SolvableSyzygySeq(RingFactory<C> cf) Constructor.

Method Summary

Modifier and Type	Method and Description
GenSolvablePolynomial<C>[]	leftOreCond(GenSolvablePolynomial<C> a, GenSolvablePolynomial<C> b) Left Ore condition.
GenSolvablePolynomial<C>[]	leftSimplifier(GenSolvablePolynomial<C> a, GenSolvablePolynomial<C> b) Left simplifier.
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<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.

Methods inherited from class edu.jas.gbufd.SolvableSyzygyAbstract

compare, isLeftOreCond, isLeftZeroRelation, isLeftZeroRelation, isRightOreCond, isRightZeroRelation, isRightZeroRelation, leftZeroRelations, leftZeroRelations, leftZeroRelations, leftZeroRelationsArbitrary, leftZeroRelationsArbitrary, rightZeroRelations, rightZeroRelations, rightZeroRelations, rightZeroRelationsArbitrary, rightZeroRelationsArbitrary, rightZeroRelationsArbitrary

Methods inherited from class java.lang.Object

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

Field Detail

sbb

protected SolvableGroebnerBase<C extends GcdRingElem<C>> sbb

Groebner basis engine.

Constructor Detail

SolvableSyzygySeq

public SolvableSyzygySeq(RingFactory<C> cf)

Constructor.

Parameters:

cf - coefficient ring.

Method Detail

resolution

public 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

public 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

public 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

public 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

public 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.

leftOreCond

public 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

public 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

leftSimplifier

public GenSolvablePolynomial<C>[] leftSimplifier(GenSolvablePolynomial<C> a,
                                                 GenSolvablePolynomial<C> b)

Left simplifier. Method of Apel & Lassner (1987).

Specified by:

leftSimplifier in class SolvableSyzygyAbstract<C extends GcdRingElem<C>>

Parameters:

a - solvable polynomial

b - solvable polynomial

Returns:

[p,q] with a/b = p/q and q is minimal and monic