Package edu.jas.gb

Class SolvableGroebnerBaseSeq<C extends RingElem<C>>

java.lang.Object

edu.jas.gb.SolvableGroebnerBaseAbstract<C>

edu.jas.gb.SolvableGroebnerBaseSeq<C>

Type Parameters:

C - coefficient type

All Implemented Interfaces:

SolvableGroebnerBase<C>, java.io.Serializable

public class SolvableGroebnerBaseSeq<C extends RingElem<C>>
extends SolvableGroebnerBaseAbstract<C>

Solvable Groebner bases sequential algorithms. Implements common left, right and twosided Groebner bases and left, right and twosided GB tests.

Author:

Heinz Kredel

See Also:

Serialized Form

Field Summary

Fields inherited from class edu.jas.gb.SolvableGroebnerBaseAbstract

blas, cbb, red, sred, strategy

Constructor Summary

Constructors

Constructor	Description
SolvableGroebnerBaseSeq()	Constructor.
SolvableGroebnerBaseSeq(PairList<C> pl)	Constructor.
SolvableGroebnerBaseSeq(SolvableReduction<C> sred)	Constructor.
SolvableGroebnerBaseSeq(SolvableReduction<C> sred, PairList<C> pl)	Constructor.

Method Summary

Modifier and Type	Method	Description
SolvableExtendedGB<C>	extLeftGB(int modv, java.util.List<GenSolvablePolynomial<C>> F)	Solvable Extended Groebner base using critical pair class.
boolean	isLeftReductionMatrix(SolvableExtendedGB<C> exgb)	Test if M is a left reduction matrix.
java.util.List<GenSolvablePolynomial<C>>	leftGB(int modv, java.util.List<GenSolvablePolynomial<C>> F)	Left Groebner base using pairlist class.
SolvableExtendedGB<C>	minimalSolvableExtendedGB(int flen, java.util.List<GenSolvablePolynomial<C>> Gp, java.util.List<java.util.List<GenSolvablePolynomial<C>>> M)	Minimal solvable extended groebner basis.
java.util.List<java.util.List<GenSolvablePolynomial<C>>>	normalizeMatrix(int flen, java.util.List<java.util.List<GenSolvablePolynomial<C>>> M)	Normalize M.
java.util.List<GenSolvablePolynomial<C>>	rightGB(int modv, java.util.List<GenSolvablePolynomial<C>> F)	Right Groebner base via right reduction using pairlist class.
java.util.List<GenSolvablePolynomial<C>>	twosidedGB(int modv, java.util.List<GenSolvablePolynomial<C>> Fp)	Twosided Groebner base using pairlist class.

Methods inherited from class edu.jas.gb.SolvableGroebnerBaseAbstract

cancel, commonZeroTest, constructUnivariate, constructUnivariate, extLeftGB, extRightGB, extRightGB, isLeftGB, isLeftGB, isLeftGB, isLeftGB, isLeftGB, isLeftGB, isLeftGBidem, isLeftGBsimple, isLeftReductionMatrix, isRightGB, isRightGB, isRightGB, isRightGB, isRightGBidem, isRightGBidem, isTwosidedGB, isTwosidedGB, isTwosidedGB, isTwosidedGB, isTwosidedGBidem, isTwosidedGBidem, leftGB, leftGB, leftGB, leftMinimalGB, normalizeZerosOnes, 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

Constructor Detail

SolvableGroebnerBaseSeq

public SolvableGroebnerBaseSeq()

Constructor.

SolvableGroebnerBaseSeq

public SolvableGroebnerBaseSeq(SolvableReduction<C> sred)

Constructor.

Parameters:

sred - Solvable reduction engine

SolvableGroebnerBaseSeq

public SolvableGroebnerBaseSeq(PairList<C> pl)

Constructor.

Parameters:

pl - pair selection strategy

SolvableGroebnerBaseSeq

public SolvableGroebnerBaseSeq(SolvableReduction<C> sred,
                               PairList<C> pl)

Constructor.

Parameters:

sred - Solvable reduction engine

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 - number of module variables.

F - solvable polynomial list.

Returns:

leftGB(F) a left Groebner base of F.

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 RingElem<C>>

Overrides:

extLeftGB in class SolvableGroebnerBaseAbstract<C extends RingElem<C>>

Parameters:

modv - module variable number.

F - solvable polynomial list.

Returns:

a container for an extended left Groebner base of F.

twosidedGB

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

Twosided Groebner base using pairlist class.

Parameters:

modv - number of module variables.

Fp - solvable polynomial list.

Returns:

tsGB(Fp) a twosided Groebner base of Fp.

normalizeMatrix

public java.util.List<java.util.List<GenSolvablePolynomial<C>>> normalizeMatrix(int flen,
                                                                                java.util.List<java.util.List<GenSolvablePolynomial<C>>> M)

Normalize M. Make all rows the same size and make certain column elements zero.

Parameters:

M - a reduction matrix.

Returns:

normalized M.

isLeftReductionMatrix

public boolean isLeftReductionMatrix(SolvableExtendedGB<C> exgb)

Test if M is a left reduction matrix.

Specified by:

isLeftReductionMatrix in interface SolvableGroebnerBase<C extends RingElem<C>>

Overrides:

isLeftReductionMatrix in class SolvableGroebnerBaseAbstract<C extends RingElem<C>>

Parameters:

exgb - an SolvableExtendedGB container.

Returns:

true, if exgb contains a left reduction matrix, else false.

minimalSolvableExtendedGB

public SolvableExtendedGB<C> minimalSolvableExtendedGB(int flen,
                                                       java.util.List<GenSolvablePolynomial<C>> Gp,
                                                       java.util.List<java.util.List<GenSolvablePolynomial<C>>> M)

Minimal solvable extended groebner basis.

Parameters:

Gp - a left Groebner base.

M - a left reduction matrix, is modified.

Returns:

a (partially) reduced left Groebner base of Gp in a container.

rightGB

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

Right Groebner base via right reduction using pairlist class. Overrides rightGB() via opposite ring.

Specified by:

rightGB in interface SolvableGroebnerBase<C extends RingElem<C>>

Overrides:

rightGB in class SolvableGroebnerBaseAbstract<C extends RingElem<C>>

Parameters:

modv - number of module variables.

F - solvable polynomial list.

Returns:

rightGB(F) a right Groebner base of F.