edu.jas.gb
Interface GroebnerBase<C extends RingElem<C>>

Type Parameters:

C - coefficient type

All Superinterfaces:

java.io.Serializable

All Known Implementing Classes:

DGroebnerBaseSeq, EGroebnerBaseSeq, GBProxy, GroebnerBaseAbstract, GroebnerBaseDistributed, GroebnerBaseDistributedHybrid, GroebnerBaseParallel, GroebnerBasePartial, GroebnerBasePseudoRecSeq, GroebnerBasePseudoSeq, GroebnerBaseSeq, GroebnerBaseSeqPairDistributed, GroebnerBaseSeqPairParallel, GroebnerBaseSeqPairSeq, RGroebnerBasePseudoSeq, RGroebnerBaseSeq

public interface GroebnerBase<C extends RingElem<C>>
extends java.io.Serializable

Groebner Bases interface. Defines methods for Groebner bases and GB test.

Author:

Heinz Kredel

Method Summary

ExtendedGB<C>	extGB(int modv, java.util.List<GenPolynomial<C>> F) Extended Groebner base using critical pair class.
ExtendedGB<C>	extGB(java.util.List<GenPolynomial<C>> F) Extended Groebner base using critical pair class.
java.util.List<GenPolynomial<C>>	GB(int modv, java.util.List<GenPolynomial<C>> F) Groebner base using pairlist class.
java.util.List<GenPolynomial<C>>	GB(java.util.List<GenPolynomial<C>> F) Groebner base using pairlist class.
boolean	isGB(int modv, java.util.List<GenPolynomial<C>> F) Groebner base test.
boolean	isGB(java.util.List<GenPolynomial<C>> F) Groebner base test.
boolean	isReductionMatrix(ExtendedGB<C> exgb) Test if reduction matrix.
boolean	isReductionMatrix(java.util.List<GenPolynomial<C>> F, java.util.List<GenPolynomial<C>> G, java.util.List<java.util.List<GenPolynomial<C>>> Mf, java.util.List<java.util.List<GenPolynomial<C>>> Mg) Test if reduction matrix.
java.util.List<GenPolynomial<C>>	minimalGB(java.util.List<GenPolynomial<C>> Gp) Minimal ordered groebner basis.

Method Detail

isGB

boolean isGB(java.util.List<GenPolynomial<C>> F)

Groebner base test.

Parameters:

F - polynomial list.

Returns:

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

isGB

boolean isGB(int modv,
             java.util.List<GenPolynomial<C>> F)

Groebner base test.

Parameters:

modv - module variable number.

F - polynomial list.

Returns:

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

GB

java.util.List<GenPolynomial<C>> GB(java.util.List<GenPolynomial<C>> F)

Groebner base using pairlist class.

Parameters:

F - polynomial list.

Returns:

GB(F) a Groebner base of F.

GB

java.util.List<GenPolynomial<C>> GB(int modv,
                                    java.util.List<GenPolynomial<C>> F)

Groebner base using pairlist class.

Parameters:

modv - module variable number.

F - polynomial list.

Returns:

GB(F) a Groebner base of F.

extGB

ExtendedGB<C> extGB(java.util.List<GenPolynomial<C>> F)

Extended Groebner base using critical pair class.

Parameters:

F - polynomial list.

Returns:

a container for a Groebner base G of F together with back-and-forth transformations.

extGB

ExtendedGB<C> extGB(int modv,
                    java.util.List<GenPolynomial<C>> F)

Extended Groebner base using critical pair class.

Parameters:

modv - module variable number.

F - polynomial list.

Returns:

a container for a Groebner base G of F together with back-and-forth transformations.

minimalGB

java.util.List<GenPolynomial<C>> minimalGB(java.util.List<GenPolynomial<C>> Gp)

Minimal ordered groebner basis.

Parameters:

Gp - a Groebner base.

Returns:

a reduced Groebner base of Gp.

isReductionMatrix

boolean isReductionMatrix(ExtendedGB<C> exgb)

Test if reduction matrix.

Parameters:

exgb - an ExtendedGB container.

Returns:

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

isReductionMatrix

boolean isReductionMatrix(java.util.List<GenPolynomial<C>> F,
                          java.util.List<GenPolynomial<C>> G,
                          java.util.List<java.util.List<GenPolynomial<C>>> Mf,
                          java.util.List<java.util.List<GenPolynomial<C>>> Mg)

Test if reduction matrix.

Parameters:

F - a polynomial list.

G - a Groebner base.

Mf - a possible reduction matrix.

Mg - a possible reduction matrix.

Returns:

true, if Mg and Mf are reduction matrices, else false.