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>>, 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.

See Also:

• GBAlgorithmBuilder
• GBFactory
• Serialized Form

Field Summary

Fields

Modifier and Type	Field	Description
protected final GenPolynomialRing<C>	cofac	Coefficient ring factory.
private static final boolean	debug
protected final GreatestCommonDivisorAbstract<C>	engine	Greatest common divisor engine for coefficient content and primitive parts.
private static final org.apache.logging.log4j.Logger	logger
protected final SolvablePseudoReduction<GenPolynomial<C>>	sred	Pseudo reduction engine.
protected final SolvablePseudoReduction<C>	sredRec	Pseudo reduction engine.

Fields inherited from class 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
boolean	isLeftGBidem(int modv, List<GenSolvablePolynomial<GenPolynomial<C>>> F)	Left Groebner base idempotence test.
boolean	isLeftGBsimple(int modv, List<GenSolvablePolynomial<GenPolynomial<C>>> F)	Left Groebner base test.
boolean	isTwosidedGB(int modv, List<GenSolvablePolynomial<GenPolynomial<C>>> Fp)	Twosided Groebner base test.
List<GenSolvablePolynomial<GenPolynomial<C>>>	leftGB(int modv, List<GenSolvablePolynomial<GenPolynomial<C>>> F)	Left Groebner base using pairlist class.
List<GenSolvablePolynomial<GenPolynomial<C>>>	leftMinimalGB(List<GenSolvablePolynomial<GenPolynomial<C>>> Gp)	Minimal ordered Solvable Groebner basis.
List<GenSolvablePolynomial<GenPolynomial<C>>>	twosidedGB(int modv, List<GenSolvablePolynomial<GenPolynomial<C>>> Fp)	Twosided Solvable Groebner base using pairlist class.

Methods inherited from class SolvableGroebnerBaseAbstract

cancel, commonZeroTest, constructUnivariate, constructUnivariate, extLeftGB, extLeftGB, extRightGB, extRightGB, 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 Object

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

Field Details

logger

private static final org.apache.logging.log4j.Logger logger

debug

private static final boolean debug

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 Details

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 Details

leftGB

public List<GenSolvablePolynomial<GenPolynomial<C>>> leftGB(int modv,
 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 List<GenSolvablePolynomial<GenPolynomial<C>>> leftMinimalGB(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 List<GenSolvablePolynomial<GenPolynomial<C>>> twosidedGB(int modv,
 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,
 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,
 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,
 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.