Class OrderedSyzPairlist<C extends RingElem<C>>

java.lang.Object

edu.jas.gb.OrderedPairlist<C>

edu.jas.gb.OrderedSyzPairlist<C>

All Implemented Interfaces:

PairList<C>, Serializable

public class OrderedSyzPairlist<C extends RingElem<C>>
extends OrderedPairlist<C>

Pair list management. For the Buchberger algorithm following the syzygy criterions by Gebauer & Möller. Implemented using GenPolynomial, TreeMap and BitSet.

Author:

Heinz Kredel

See Also:

• Serialized Form

Field Summary

Fields inherited from class OrderedPairlist

moduleVars, oneInGB, P, pairlist, putCount, red, reduction, remCount, ring, useCriterion4

Constructor Summary

Constructors

Constructor	Description
OrderedSyzPairlist()	Constructor.
OrderedSyzPairlist(int m, GenPolynomialRing<C> r)	Constructor.
OrderedSyzPairlist(GenPolynomialRing<C> r)	Constructor.

Method Summary

Modifier and Type	Method	Description
PairList<C>	create(int m, GenPolynomialRing<C> r)	Create a new PairList.
PairList<C>	create(GenPolynomialRing<C> r)	Create a new PairList.
boolean	criterion3(int i, int j, ExpVector eij)	GB criterium 3.
int	put(GenPolynomial<C> p)	Put one Polynomial to the pairlist and reduction matrix.
Pair<C>	removeNext()	Remove the next required pair from the pairlist and reduction matrix.

Methods inherited from class OrderedPairlist

getList, getRing, hasNext, put, putCount, putOne, putOne, remCount, setList, size, toString

Methods inherited from class Object

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

Constructor Details

OrderedSyzPairlist

public OrderedSyzPairlist()

Constructor.

OrderedSyzPairlist

public OrderedSyzPairlist(GenPolynomialRing<C> r)

Constructor.

Parameters:

r - polynomial factory.

OrderedSyzPairlist

public OrderedSyzPairlist(int m,
 GenPolynomialRing<C> r)

Constructor.

Parameters:

m - number of module variables.

r - polynomial factory.

Method Details

create

public PairList<C> create(GenPolynomialRing<C> r)

Create a new PairList.

Specified by:

create in interface PairList<C extends RingElem<C>>

Overrides:

create in class OrderedPairlist<C extends RingElem<C>>

Parameters:

r - polynomial ring.

create

public PairList<C> create(int m,
 GenPolynomialRing<C> r)

Create a new PairList.

Specified by:

create in interface PairList<C extends RingElem<C>>

Overrides:

create in class OrderedPairlist<C extends RingElem<C>>

Parameters:

m - number of module variables.

r - polynomial ring.

put

public int put(GenPolynomial<C> p)

Put one Polynomial to the pairlist and reduction matrix. Removes all unnecessary pairs identified by the syzygy criterion and criterion 4.

Specified by:

put in interface PairList<C extends RingElem<C>>

Overrides:

put in class OrderedPairlist<C extends RingElem<C>>

Parameters:

p - polynomial.

Returns:

the index of the added polynomial.

removeNext

public Pair<C> removeNext()

Remove the next required pair from the pairlist and reduction matrix. Apply the criterions 3 and 4 to see if the S-polynomial is required.

Specified by:

removeNext in interface PairList<C extends RingElem<C>>

Overrides:

removeNext in class OrderedPairlist<C extends RingElem<C>>

Returns:

the next pair if one exists, otherwise null.

criterion3

public boolean criterion3(int i,
 int j,
 ExpVector eij)

GB criterium 3.

Specified by:

criterion3 in interface PairList<C extends RingElem<C>>

Overrides:

criterion3 in class OrderedPairlist<C extends RingElem<C>>

Returns:

true if the S-polynomial(i,j) is required.