Package edu.jas.gbufd

Class SolvableGroebnerBasePseudoRecSeq<C extends GcdRingElem<C>>

java.lang.Object

edu.jas.gb.SolvableGroebnerBaseAbstract<GenPolynomial<C>>

edu.jas.gbufd.SolvableGroebnerBasePseudoRecSeq<C>

Type Parameters:

C - coefficient type

All Implemented Interfaces:

SolvableGroebnerBase<GenPolynomial<C>>, java.io.Serializable

public class SolvableGroebnerBasePseudoRecSeq<C extends GcdRingElem<C>>
extends SolvableGroebnerBaseAbstract<GenPolynomial<C>>

Solvable Groebner Base with pseudo reduction sequential algorithm. Implements coefficient fraction free Groebner bases. Coefficients can for example be (commutative) multivariate polynomials.

Author:

Heinz Kredel

See Also:

GBAlgorithmBuilder, GBFactory, Serialized Form

Field Summary

Fields

Modifier and Type	Field	Description
protected GenPolynomialRing<C>	cofac	Coefficient ring factory.
protected GreatestCommonDivisorAbstract<C>	engine	Greatest common divisor engine for coefficient content and primitive parts.
protected SolvablePseudoReduction<GenPolynomial<C>>	sred	Pseudo reduction engine.
protected SolvablePseudoReduction<C>	sredRec	Pseudo reduction engine.

Fields inherited from class edu.jas.gb.SolvableGroebnerBaseAbstract

blas, cbb, red, strategy

Constructor Summary

Constructors

Constructor	Description
SolvableGroebnerBasePseudoRecSeq(RingFactory<GenPolynomial<C>> rf)	Constructor.
SolvableGroebnerBasePseudoRecSeq(RingFactory<GenPolynomial<C>> rf, PairList<GenPolynomial<C>> pl)	Constructor.
SolvableGroebnerBasePseudoRecSeq(RingFactory<GenPolynomial<C>> rf, SolvablePseudoReduction<C> red)	Constructor.
SolvableGroebnerBasePseudoRecSeq(RingFactory<GenPolynomial<C>> rf, SolvablePseudoReduction<C> red, PairList<GenPolynomial<C>> pl)	Constructor.

Method Summary

Modifier and Type	Method	Description
SolvableExtendedGB<GenPolynomial<C>>	extLeftGB(int modv, java.util.List<GenSolvablePolynomial<GenPolynomial<C>>> F)	Solvable Extended Groebner base using critical pair class.
boolean	isLeftGBidem(int modv, java.util.List<GenSolvablePolynomial<GenPolynomial<C>>> F)	Left Groebner base idempotence test.
boolean	isLeftGBsimple(int modv, java.util.List<GenSolvablePolynomial<GenPolynomial<C>>> F)	Left Groebner base test.
boolean	isTwosidedGB(int modv, java.util.List<GenSolvablePolynomial<GenPolynomial<C>>> Fp)	Twosided Groebner base test.
java.util.List<GenSolvablePolynomial<GenPolynomial<C>>>	leftGB(int modv, java.util.List<GenSolvablePolynomial<GenPolynomial<C>>> F)	Left Groebner base using pairlist class.
java.util.List<GenSolvablePolynomial<GenPolynomial<C>>>	leftMinimalGB(java.util.List<GenSolvablePolynomial<GenPolynomial<C>>> Gp)	Minimal ordered Solvable Groebner basis.
java.util.List<GenSolvablePolynomial<GenPolynomial<C>>>	twosidedGB(int modv, java.util.List<GenSolvablePolynomial<GenPolynomial<C>>> Fp)	Twosided Solvable Groebner base using pairlist class.

Methods inherited from class edu.jas.gb.SolvableGroebnerBaseAbstract

cancel, commonZeroTest, constructUnivariate, constructUnivariate, extLeftGB, isLeftGB, isLeftGB, isLeftGB, isLeftGB, isLeftGB, isLeftGB, isLeftReductionMatrix, isLeftReductionMatrix, isRightGB, isRightGB, isRightGB, isRightGB, isRightGBidem, isRightGBidem, isTwosidedGB, isTwosidedGB, isTwosidedGB, isTwosidedGBidem, isTwosidedGBidem, leftGB, leftGB, leftGB, normalizeZerosOnes, rightGB, rightGB, rightGB, rightMinimalGB, terminate, twosidedGB, twosidedGB, twosidedGB, univariateDegrees

Methods inherited from class java.lang.Object

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

Field Detail

engine

protected final GreatestCommonDivisorAbstract<C extends GcdRingElem<C>> engine

Greatest common divisor engine for coefficient content and primitive parts.

sredRec

protected final SolvablePseudoReduction<C extends GcdRingElem<C>> sredRec

Pseudo reduction engine.

sred

protected final SolvablePseudoReduction<GenPolynomial<C extends GcdRingElem<C>>> sred

Pseudo reduction engine.

cofac

protected final GenPolynomialRing<C extends GcdRingElem<C>> cofac

Coefficient ring factory.

Constructor Detail

SolvableGroebnerBasePseudoRecSeq

public SolvableGroebnerBasePseudoRecSeq(RingFactory<GenPolynomial<C>> rf)

Constructor.

Parameters:

rf - coefficient ring factory.

SolvableGroebnerBasePseudoRecSeq

public SolvableGroebnerBasePseudoRecSeq(RingFactory<GenPolynomial<C>> rf,
                                        PairList<GenPolynomial<C>> pl)

Constructor.

Parameters:

rf - coefficient ring factory.

pl - pair selection strategy

SolvableGroebnerBasePseudoRecSeq

public SolvableGroebnerBasePseudoRecSeq(RingFactory<GenPolynomial<C>> rf,
                                        SolvablePseudoReduction<C> red)

Constructor.

Parameters:

rf - coefficient ring factory.

red - pseudo reduction engine. Note: red must be an instance of PseudoReductionSeq.

SolvableGroebnerBasePseudoRecSeq

public SolvableGroebnerBasePseudoRecSeq(RingFactory<GenPolynomial<C>> rf,
                                        SolvablePseudoReduction<C> red,
                                        PairList<GenPolynomial<C>> pl)

Constructor.

Parameters:

rf - coefficient ring factory.

red - pseudo reduction engine. Note: red must be an instance of PseudoReductionSeq.

pl - pair selection strategy

Method Detail

leftGB

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

Left Groebner base using pairlist class.

Parameters:

modv - module variable number.

F - polynomial list.

Returns:

GB(F) a Groebner base of F.

leftMinimalGB

public java.util.List<GenSolvablePolynomial<GenPolynomial<C>>> leftMinimalGB(java.util.List<GenSolvablePolynomial<GenPolynomial<C>>> Gp)

Minimal ordered Solvable Groebner basis.

Specified by:

leftMinimalGB in interface SolvableGroebnerBase<C extends GcdRingElem<C>>

Overrides:

leftMinimalGB in class SolvableGroebnerBaseAbstract<GenPolynomial<C extends GcdRingElem<C>>>

Parameters:

Gp - a Solvable Groebner base.

Returns:

a reduced Solvable Groebner base of Gp.

twosidedGB

public java.util.List<GenSolvablePolynomial<GenPolynomial<C>>> twosidedGB(int modv,
                                                                          java.util.List<GenSolvablePolynomial<GenPolynomial<C>>> Fp)

Twosided Solvable Groebner base using pairlist class.

Parameters:

modv - number of module variables.

Fp - solvable polynomial list.

Returns:

tsGB(Fp) a twosided Groebner base of Fp.

isLeftGBsimple

public boolean isLeftGBsimple(int modv,
                              java.util.List<GenSolvablePolynomial<GenPolynomial<C>>> F)

Left Groebner base test.

Overrides:

isLeftGBsimple in class SolvableGroebnerBaseAbstract<GenPolynomial<C extends GcdRingElem<C>>>

Parameters:

modv - number of module variables.

F - solvable polynomial list.

Returns:

true, if F is a left Groebner base, else false.

isLeftGBidem

public boolean isLeftGBidem(int modv,
                            java.util.List<GenSolvablePolynomial<GenPolynomial<C>>> F)

Left Groebner base idempotence test.

Overrides:

isLeftGBidem in class SolvableGroebnerBaseAbstract<GenPolynomial<C extends GcdRingElem<C>>>

Parameters:

modv - module variable number.

F - solvable polynomial list.

Returns:

true, if F is equal to GB(F), else false.

isTwosidedGB

public boolean isTwosidedGB(int modv,
                            java.util.List<GenSolvablePolynomial<GenPolynomial<C>>> Fp)

Twosided Groebner base test.

Specified by:

isTwosidedGB in interface SolvableGroebnerBase<C extends GcdRingElem<C>>

Overrides:

isTwosidedGB in class SolvableGroebnerBaseAbstract<GenPolynomial<C extends GcdRingElem<C>>>

Parameters:

modv - number of module variables.

Fp - solvable polynomial list.

Returns:

true, if Fp is a two-sided Groebner base, else false.

extLeftGB

public SolvableExtendedGB<GenPolynomial<C>> extLeftGB(int modv,
                                                      java.util.List<GenSolvablePolynomial<GenPolynomial<C>>> F)

Solvable Extended Groebner base using critical pair class.

Specified by:

extLeftGB in interface SolvableGroebnerBase<C extends GcdRingElem<C>>

Overrides:

extLeftGB in class SolvableGroebnerBaseAbstract<GenPolynomial<C extends GcdRingElem<C>>>

Parameters:

modv - module variable number.

F - solvable polynomial list.

Returns:

a container for an extended left Groebner base of F. Note: not implemented;