Class DGroebnerBaseSeq<C extends RingElem<C>>

java.lang.Object

edu.jas.gb.GroebnerBaseAbstract<C>

edu.jas.gb.DGroebnerBaseSeq<C>

Type Parameters:

C - coefficient type

All Implemented Interfaces:

GroebnerBase<C>, Serializable

Direct Known Subclasses:

EGroebnerBaseSeq

public class DGroebnerBaseSeq<C extends RingElem<C>>
extends GroebnerBaseAbstract<C>

D-Groebner Base sequential algorithm. Implements D-Groebner bases and GB test. Note: Minimal reduced GBs are not unique. see BWK, section 10.1.

Author:

Heinz Kredel

See Also:

• Serialized Form

Field Summary

Fields

Modifier and Type	Field	Description
protected DReduction<C>	dred	Reduction engine.

Fields inherited from class GroebnerBaseAbstract

blas, red, strategy

Constructor Summary

Constructors

Constructor	Description
DGroebnerBaseSeq()	Constructor.
DGroebnerBaseSeq(DReduction<C> dred)	Constructor.

Method Summary

Modifier and Type	Method	Description
ExtendedGB<C>	extGB(int modv, List<GenPolynomial<C>> F)	Extended Groebner base using pairlist class.
List<GenPolynomial<C>>	GB(int modv, List<GenPolynomial<C>> F)	D-Groebner base using pairlist class.
GenPolynomial<C>	inverse(GenPolynomial<C> h, List<GenPolynomial<C>> F)	Inverse for element modulo ideal.
boolean	isGB(int modv, List<GenPolynomial<C>> F)	D-Groebner base test.
ExtendedGB<C>	minimalExtendedGB(int flen, List<GenPolynomial<C>> Gp, List<List<GenPolynomial<C>>> M)	Minimal extended groebner basis.

Methods inherited from class GroebnerBaseAbstract

cancel, commonZeroTest, constructUnivariate, extGB, GB, GB, GB, isGB, isGB, isGB, isGB, isGB, isGBidem, isGBsimple, isMinimalGB, isMinReductionMatrix, isMinReductionMatrix, isReductionMatrix, isReductionMatrix, minimalGB, normalizeMatrix, normalizeZerosOnes, terminate, toString, univariateDegrees

Methods inherited from class Object

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

Field Details

dred

protected DReduction<C extends RingElem<C>> dred

Reduction engine.

Constructor Details

DGroebnerBaseSeq

public DGroebnerBaseSeq()

Constructor.

DGroebnerBaseSeq

public DGroebnerBaseSeq(DReduction<C> dred)

Constructor.

Parameters:

dred - D-Reduction engine

Method Details

isGB

public boolean isGB(int modv,
 List<GenPolynomial<C>> F)

D-Groebner base test.

Specified by:

isGB in interface GroebnerBase<C extends RingElem<C>>

Overrides:

isGB in class GroebnerBaseAbstract<C extends RingElem<C>>

Parameters:

modv - module variable number.

F - polynomial list.

Returns:

true, if F is a D-Groebner base, else false.

GB

public List<GenPolynomial<C>> GB(int modv,
 List<GenPolynomial<C>> F)

D-Groebner base using pairlist class.

Parameters:

modv - module variable number.

F - polynomial list.

Returns:

GB(F) a D-Groebner base of F.

extGB

public ExtendedGB<C> extGB(int modv,
 List<GenPolynomial<C>> F)

Extended Groebner base using pairlist class.

Specified by:

extGB in interface GroebnerBase<C extends RingElem<C>>

Overrides:

extGB in class GroebnerBaseAbstract<C extends RingElem<C>>

Parameters:

modv - module variable number.

F - polynomial list.

Returns:

a container for an extended Groebner base of F.

minimalExtendedGB

public ExtendedGB<C> minimalExtendedGB(int flen,
 List<GenPolynomial<C>> Gp,
 List<List<GenPolynomial<C>>> M)

Minimal extended groebner basis.

Overrides:

minimalExtendedGB in class GroebnerBaseAbstract<C extends RingElem<C>>

Parameters:

flen - length of rows.

Gp - a Groebner base.

M - a reduction matrix.

Returns:

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

inverse

public GenPolynomial<C> inverse(GenPolynomial<C> h,
 List<GenPolynomial<C>> F)

Inverse for element modulo ideal.

Parameters:

h - polynomial

F - polynomial list

Returns:

inverse of h with respect to ideal(F), if defined