Class GroebnerBaseGGVSigSeqIter<C extends RingElem<C>>

java.lang.Object

edu.jas.gb.GroebnerBaseAbstract<C>

edu.jas.gb.GroebnerBaseSigSeqIter<C>

edu.jas.gb.GroebnerBaseGGVSigSeqIter<C>

Type Parameters:

C - coefficient type

All Implemented Interfaces:

GroebnerBase<C>, Serializable

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

Groebner Base GGV signature based sequential iterative algorithm. Implements Groebner bases.

See Also:

• GBAlgorithmBuilder
• GBFactory
• Serialized Form

Field Summary

Fields

Modifier and Type	Field	Description
private static final org.apache.logging.log4j.Logger	logger

Fields inherited from class GroebnerBaseSigSeqIter

sred

Fields inherited from class GroebnerBaseAbstract

blas, red, strategy

Constructor Summary

Constructors

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

Method Summary

Modifier and Type	Method	Description
(package private) List<ExpVector>	initializeSyz(List<GenPolynomial<C>> F, List<SigPoly<C>> G)	Initializes syzygy list.
(package private) List<SigPair<C>>	pruneP(List<SigPair<C>> P, List<ExpVector> syz)	Prune total pair list P.
(package private) List<SigPair<C>>	pruneS(List<SigPair<C>> S, List<ExpVector> syz, List<SigPoly<C>> done, List<SigPoly<C>> G)	Prune pair list of degree d.
(package private) GenPolynomial<C>	SPolynomial(SigPoly<C> A, SigPoly<C> B)	S-Polynomial.
(package private) void	updateSyz(List<ExpVector> syz, SigPoly<C> r)	Update syzygy list.

Methods inherited from class GroebnerBaseSigSeqIter

GB, GB, newPair, newPair, sigNormalform, SPolynomial, SPolynomialFactors

Methods inherited from class GroebnerBaseAbstract

cancel, commonZeroTest, constructUnivariate, criterion3, 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

Field Details

logger

private static final org.apache.logging.log4j.Logger logger

Constructor Details

GroebnerBaseGGVSigSeqIter

public GroebnerBaseGGVSigSeqIter()

Constructor.

GroebnerBaseGGVSigSeqIter

public GroebnerBaseGGVSigSeqIter(SigReductionSeq<C> red)

Constructor.

Parameters:

red - Reduction engine

Method Details

SPolynomial

GenPolynomial<C> SPolynomial(SigPoly<C> A,
 SigPoly<C> B)

S-Polynomial.

Overrides:

SPolynomial in class GroebnerBaseSigSeqIter<C extends RingElem<C>>

Parameters:

A - polynomial.

B - polynomial.

Returns:

spol(A,B) the S-polynomial of A and B.

pruneP

List<SigPair<C>> pruneP(List<SigPair<C>> P,
 List<ExpVector> syz)

Prune total pair list P.

Overrides:

pruneP in class GroebnerBaseSigSeqIter<C extends RingElem<C>>

Parameters:

P - pair list.

syz - list of exponent vectors representing syzygies.

Returns:

updated pair list.

pruneS

List<SigPair<C>> pruneS(List<SigPair<C>> S,
 List<ExpVector> syz,
 List<SigPoly<C>> done,
 List<SigPoly<C>> G)

Prune pair list of degree d.

Overrides:

pruneS in class GroebnerBaseSigSeqIter<C extends RingElem<C>>

Parameters:

S - pair list.

syz - list of exponent vectors representing syzygies.

done - list of treated polynomials.

G - polynomial with signature list.

Returns:

updated pair list.

initializeSyz

List<ExpVector> initializeSyz(List<GenPolynomial<C>> F,
 List<SigPoly<C>> G)

Initializes syzygy list.

Overrides:

initializeSyz in class GroebnerBaseSigSeqIter<C extends RingElem<C>>

Parameters:

F - polynomial list.

G - polynomial with signature list.

Returns:

list of exponent vectors representing syzygies.

updateSyz

void updateSyz(List<ExpVector> syz,
 SigPoly<C> r)

Update syzygy list.

Overrides:

updateSyz in class GroebnerBaseSigSeqIter<C extends RingElem<C>>

Parameters:

syz - list of exponent vectors representing syzygies.

r - polynomial. Note: szy is modified to represent updated list of exponent vectors.