Package edu.jas.gb

Class WordReductionSeq<C extends RingElem<C>>

java.lang.Object

edu.jas.gb.WordReductionAbstract<C>

edu.jas.gb.WordReductionSeq<C>

Type Parameters:

C - coefficient type

All Implemented Interfaces:

WordReduction<C>, java.io.Serializable

public class WordReductionSeq<C extends RingElem<C>>
extends WordReductionAbstract<C>

Polynomial word reduction sequential use algorithm. Implements normalform.

Author:

Heinz Kredel

See Also:

Serialized Form

Constructor Summary

Constructors

Constructor	Description
WordReductionSeq()	Constructor.

Method Summary

Modifier and Type	Method	Description
GenWordPolynomial<C>	leftNormalform(java.util.List<GenWordPolynomial<C>> Pp, GenWordPolynomial<C> Ap)	Left normalform with recording.
GenWordPolynomial<C>	leftNormalform(java.util.List<GenWordPolynomial<C>> lrow, java.util.List<GenWordPolynomial<C>> Pp, GenWordPolynomial<C> Ap)	Left normalform with recording.
GenWordPolynomial<C>	normalform(java.util.List<GenWordPolynomial<C>> Pp, GenWordPolynomial<C> Ap)	Normalform.
GenWordPolynomial<C>	normalform(java.util.List<GenWordPolynomial<C>> lrow, java.util.List<GenWordPolynomial<C>> rrow, java.util.List<GenWordPolynomial<C>> Pp, GenWordPolynomial<C> Ap)	Normalform with left and right recording.
GenWordPolynomial<C>	rightNormalform(java.util.List<GenWordPolynomial<C>> Pp, GenWordPolynomial<C> Ap)	Right normalform with recording.
GenWordPolynomial<C>	rightNormalform(java.util.List<GenWordPolynomial<C>> rrow, java.util.List<GenWordPolynomial<C>> Pp, GenWordPolynomial<C> Ap)	Right normalform with recording.

Methods inherited from class edu.jas.gb.WordReductionAbstract

irreducibleSet, isNormalform, isNormalform, isReducible, isReductionNF, isTopReducible, normalform, SPolynomial, SPolynomial, SPolynomials

Methods inherited from class java.lang.Object

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

Constructor Detail

WordReductionSeq

public WordReductionSeq()

Constructor.

Method Detail

normalform

public GenWordPolynomial<C> normalform(java.util.List<GenWordPolynomial<C>> Pp,
                                       GenWordPolynomial<C> Ap)

Normalform.

Parameters:

Ap - polynomial.

Pp - polynomial list.

Returns:

nf(Ap) with respect to Pp.

normalform

public GenWordPolynomial<C> normalform(java.util.List<GenWordPolynomial<C>> lrow,
                                       java.util.List<GenWordPolynomial<C>> rrow,
                                       java.util.List<GenWordPolynomial<C>> Pp,
                                       GenWordPolynomial<C> Ap)

Normalform with left and right recording.

Parameters:

lrow - left recording matrix, is modified.

rrow - right recording matrix, is modified.

Pp - a polynomial list for reduction.

Ap - a polynomial.

Returns:

nf(Pp,Ap), the normal form of Ap wrt. Pp.

leftNormalform

public GenWordPolynomial<C> leftNormalform(java.util.List<GenWordPolynomial<C>> Pp,
                                           GenWordPolynomial<C> Ap)

Left normalform with recording.

Parameters:

Pp - a polynomial list for reduction.

Ap - a polynomial.

Returns:

nf(Pp,Ap), the left normal form of Ap wrt. Pp.

leftNormalform

public GenWordPolynomial<C> leftNormalform(java.util.List<GenWordPolynomial<C>> lrow,
                                           java.util.List<GenWordPolynomial<C>> Pp,
                                           GenWordPolynomial<C> Ap)

Left normalform with recording.

Parameters:

lrow - left recording matrix, is modified.

Pp - a polynomial list for reduction.

Ap - a polynomial.

Returns:

nf(Pp,Ap), the left normal form of Ap wrt. Pp.

rightNormalform

public GenWordPolynomial<C> rightNormalform(java.util.List<GenWordPolynomial<C>> Pp,
                                            GenWordPolynomial<C> Ap)

Right normalform with recording.

Parameters:

Pp - a polynomial list for reduction.

Ap - a polynomial.

Returns:

nf(Pp,Ap), the right normal form of Ap wrt. Pp.

rightNormalform

public GenWordPolynomial<C> rightNormalform(java.util.List<GenWordPolynomial<C>> rrow,
                                            java.util.List<GenWordPolynomial<C>> Pp,
                                            GenWordPolynomial<C> Ap)

Right normalform with recording.

Parameters:

rrow - right recording matrix, is modified.

Pp - a polynomial list for reduction.

Ap - a polynomial.

Returns:

nf(Pp,Ap), the right normal form of Ap wrt. Pp.