edu.jas.ring
Class GroebnerBaseSeqPairSeq<C extends RingElem<C>>

java.lang.Object
  edu.jas.ring.GroebnerBaseAbstract<C>
      edu.jas.ring.GroebnerBaseSeqPairSeq<C>

All Implemented Interfaces:

GroebnerBase<C>, java.io.Serializable

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

Groebner Base sequential algorithm. Implements Groebner bases and GB test. Uses sequential pair list class.

Author:

Heinz Kredel

See Also:

Serialized Form

Field Summary

Fields inherited from class edu.jas.ring.GroebnerBaseAbstract

red

Constructor Summary

GroebnerBaseSeqPairSeq()
Constructor.

GroebnerBaseSeqPairSeq(Reduction<C> red)
Constructor.

Method Summary

ExtendedGB<C>	extGB(int modv, 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.
ExtendedGB<C>	minimalExtendedGB(int flen, java.util.List<GenPolynomial<C>> Gp, java.util.List<java.util.List<GenPolynomial<C>>> M) Minimal extended groebner basis.
java.util.List<java.util.List<GenPolynomial<C>>>	normalizeMatrix(int flen, java.util.List<java.util.List<GenPolynomial<C>>> M) Normalize M.

Methods inherited from class edu.jas.ring.GroebnerBaseAbstract

extGB, GB, isGB, isGB, isReductionMatrix, isReductionMatrix, minimalGB

Methods inherited from class java.lang.Object

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

Constructor Detail

GroebnerBaseSeqPairSeq

public GroebnerBaseSeqPairSeq()

Constructor.

GroebnerBaseSeqPairSeq

public GroebnerBaseSeqPairSeq(Reduction<C> red)

Constructor.

Parameters:

red - Reduction engine

Method Detail

GB

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

Groebner base using pairlist class.

Type parameter:

C coefficient type.

Parameters:

modv - module variable number.

F - polynomial list.

Returns:

GB(F) a Groebner base of F.

extGB

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

Extended Groebner base using critical pair class.

Specified by:

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

Overrides:

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

Type parameter:

C coefficient type.

Parameters:

modv - module variable number.

F - polynomial list.

Returns:

a container for an extended Groebner base of F.

normalizeMatrix

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

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

Type parameter:

C coefficient type.

Parameters:

M - a reduction matrix.

Returns:

normalized M.

minimalExtendedGB

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

Minimal extended groebner basis.

Type parameter:

C coefficient type.

Parameters:

Gp - a Groebner base.

M - a reduction matrix, is modified.

Returns:

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