edu.jas.ps

Class StandardBaseSeq<C extends RingElem<C>>

java.lang.Object

edu.jas.ps.StandardBaseSeq<C>

Type Parameters:

C - coefficient type

public class StandardBaseSeq<C extends RingElem<C>>
extends java.lang.Object

Standard Base sequential algorithm. Implements Standard bases and GB test. Note: Currently the term order is fixed to the order defined by the iterator over exponent vectors ExpVectorIterator.

Author:

Heinz Kredel

Field Summary

Fields

Modifier and Type	Field and Description
ReductionSeq<C>	red Reduction engine.

Constructor Summary

Constructors

Constructor and Description
StandardBaseSeq() Constructor.
StandardBaseSeq(ReductionSeq<C> red) Constructor.

Method Summary

Modifier and Type	Method and Description
boolean	isSTD(int modv, java.util.List<MultiVarPowerSeries<C>> F) Standard base test.
boolean	isSTD(java.util.List<MultiVarPowerSeries<C>> F) Standard base test.
java.util.List<MultiVarPowerSeries<C>>	minimalSTD(java.util.List<MultiVarPowerSeries<C>> Gp) Minimal ordered Standard basis.
java.util.List<MultiVarPowerSeries<C>>	normalizeZerosOnes(java.util.List<MultiVarPowerSeries<C>> A) Normalize power series list.
java.util.List<MultiVarPowerSeries<C>>	STD(int modv, java.util.List<MultiVarPowerSeries<C>> F) Standard base using pairlist class.
java.util.List<MultiVarPowerSeries<C>>	STD(java.util.List<MultiVarPowerSeries<C>> F) Standard base using pairlist class.

Methods inherited from class java.lang.Object

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

Field Detail

red

public final ReductionSeq<C extends RingElem<C>> red

Reduction engine.

Constructor Detail

StandardBaseSeq

public StandardBaseSeq()

Constructor.

StandardBaseSeq

public StandardBaseSeq(ReductionSeq<C> red)

Constructor.

Parameters:

red - Reduction engine

Method Detail

normalizeZerosOnes

public java.util.List<MultiVarPowerSeries<C>> normalizeZerosOnes(java.util.List<MultiVarPowerSeries<C>> A)

Normalize power series list.

Parameters:

A - list of power series.

Returns:

list of power series with zeros removed and ones/units reduced.

isSTD

public boolean isSTD(java.util.List<MultiVarPowerSeries<C>> F)

Standard base test.

Parameters:

F - power series list.

Returns:

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

isSTD

public boolean isSTD(int modv,
                     java.util.List<MultiVarPowerSeries<C>> F)

Standard base test.

Parameters:

modv - module variable number.

F - power series list.

Returns:

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

STD

public java.util.List<MultiVarPowerSeries<C>> STD(java.util.List<MultiVarPowerSeries<C>> F)

Standard base using pairlist class.

Parameters:

F - power series list.

Returns:

STD(F) a Standard base of F.

STD

public java.util.List<MultiVarPowerSeries<C>> STD(int modv,
                                                  java.util.List<MultiVarPowerSeries<C>> F)

Standard base using pairlist class.

Parameters:

modv - module variable number.

F - power series list.

Returns:

STD(F) a Standard base of F.

minimalSTD

public java.util.List<MultiVarPowerSeries<C>> minimalSTD(java.util.List<MultiVarPowerSeries<C>> Gp)

Minimal ordered Standard basis.

Parameters:

Gp - a Standard base.

Returns:

a minimal Standard base of Gp, not auto reduced.