edu.jas.gbufd

Class SolvableGroebnerBasePseudoSeq<C extends GcdRingElem<C>>

java.lang.Object

edu.jas.gb.SolvableGroebnerBaseAbstract<C>

edu.jas.gbufd.SolvableGroebnerBasePseudoSeq<C>

Type Parameters:

C - coefficient type

All Implemented Interfaces:

SolvableGroebnerBase<C>, java.io.Serializable

public class SolvableGroebnerBasePseudoSeq<C extends GcdRingElem<C>>
extends SolvableGroebnerBaseAbstract<C>

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

Author:

Heinz Kredel

See Also:

GBAlgorithmBuilder, GBFactory, Serialized Form

Field Summary

Fields

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

Fields inherited from class edu.jas.gb.SolvableGroebnerBaseAbstract

blas, cbb, red, strategy

Constructor Summary

Constructors

Constructor and Description
SolvableGroebnerBasePseudoSeq(RingFactory<C> rf) Constructor.
SolvableGroebnerBasePseudoSeq(RingFactory<C> rf, PairList<C> pl) Constructor.
SolvableGroebnerBasePseudoSeq(SolvablePseudoReduction<C> red, RingFactory<C> rf, PairList<C> pl) Constructor.

Method Summary

Modifier and Type	Method and Description
SolvableExtendedGB<C>	extLeftGB(int modv, java.util.List<GenSolvablePolynomial<C>> F) Solvable Extended Groebner base using critical pair class.
java.util.List<GenSolvablePolynomial<C>>	leftGB(int modv, java.util.List<GenSolvablePolynomial<C>> F) Left Groebner base using pairlist class.
java.util.List<GenSolvablePolynomial<C>>	leftMinimalGB(java.util.List<GenSolvablePolynomial<C>> Gp) Minimal ordered Solvable Groebner basis.
java.util.List<GenSolvablePolynomial<C>>	twosidedGB(int modv, java.util.List<GenSolvablePolynomial<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, isLeftGBidem, isLeftGBsimple, isLeftReductionMatrix, isLeftReductionMatrix, isRightGB, isRightGB, isRightGB, isRightGBidem, isRightGBidem, isTwosidedGB, isTwosidedGB, isTwosidedGB, isTwosidedGBidem, isTwosidedGBidem, leftGB, leftGB, normalizeZerosOnes, rightGB, rightGB, rightGB, rightMinimalGB, terminate, 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.

sred

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

Pseudo reduction engine.

cofac

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

Coefficient ring factory.

Constructor Detail

SolvableGroebnerBasePseudoSeq

public SolvableGroebnerBasePseudoSeq(RingFactory<C> rf)

Constructor.

Parameters:

rf - coefficient ring factory.

SolvableGroebnerBasePseudoSeq

public SolvableGroebnerBasePseudoSeq(RingFactory<C> rf,
                                     PairList<C> pl)

Constructor.

Parameters:

rf - coefficient ring factory.

pl - pair selection strategy

SolvableGroebnerBasePseudoSeq

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

Constructor.

Parameters:

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

rf - coefficient ring factory.

pl - pair selection strategy

Method Detail

leftGB

public java.util.List<GenSolvablePolynomial<C>> leftGB(int modv,
                                                       java.util.List<GenSolvablePolynomial<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<C>> leftMinimalGB(java.util.List<GenSolvablePolynomial<C>> Gp)

Minimal ordered Solvable Groebner basis.

Specified by:

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

Overrides:

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

Parameters:

Gp - a Solvable Groebner base.

Returns:

a reduced Solvable Groebner base of Gp.

twosidedGB

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

extLeftGB

public SolvableExtendedGB<C> extLeftGB(int modv,
                                       java.util.List<GenSolvablePolynomial<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<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;