Class GroebnerBaseSigSeqIter<C extends RingElem<C>>

java.lang.Object

edu.jas.gb.GroebnerBaseAbstract<C>

edu.jas.gb.GroebnerBaseSigSeqIter<C>

Type Parameters:

C - coefficient type

All Implemented Interfaces:

GroebnerBase<C>, Serializable

Direct Known Subclasses:

GroebnerBaseArriSigSeqIter, GroebnerBaseF5zSigSeqIter, GroebnerBaseGGVSigSeqIter

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

Groebner Base signature based sequential iterative algorithm. Implements Groebner bases after the paper "Signature-based Algorithms to Compute Gröbner Bases" by Christian Eder and John Perry, ISSAC 2011. Compare the jython+JAS code in examples/basic_sigbased_gb.py. Originally the Python+Sage code is from http://www.math.usm.edu/perry/Research/basic_sigbased_gb.py

Author:

Heinz Kredel

See Also:

• GBAlgorithmBuilder
• GBFactory
• GroebnerBaseGGVSigSeqIter
• GroebnerBaseArriSigSeqIter
• GroebnerBaseF5zSigSeqIter
• Serialized Form

Field Summary

Fields inherited from class GroebnerBaseAbstract

blas, red, strategy

Constructor Summary

Constructors

Constructor	Description
GroebnerBaseSigSeqIter()	Constructor.
GroebnerBaseSigSeqIter(SigReductionSeq<C> red)	Constructor.

Method Summary

Modifier and Type	Method	Description
List<GenPolynomial<C>>	GB(int modv, List<GenPolynomial<C>> F)	Groebner base signature iterative algorithm.
List<GenPolynomial<C>>	GB(int modv, List<GenPolynomial<C>> G, GenPolynomial<C> f)	Groebner base iterated.

Methods inherited from class GroebnerBaseAbstract

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

Methods inherited from class Object

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

Constructor Details

GroebnerBaseSigSeqIter

public GroebnerBaseSigSeqIter()

Constructor.

GroebnerBaseSigSeqIter

public GroebnerBaseSigSeqIter(SigReductionSeq<C> red)

Constructor.

Parameters:

red - Reduction engine

Method Details

GB

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

Groebner base signature iterative algorithm.

Parameters:

modv - module variable number.

F - polynomial list.

Returns:

GB(F) a Groebner base of F.

GB

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

Groebner base iterated.

Parameters:

modv - module variable number.

G - polynomial list of a Groebner base.

f - polynomial.

Returns:

GB(G,f) a Groebner base of G+(f).