Package edu.jas.gbufd

Class WordPseudoReductionSeq<C extends RingElem<C>>

java.lang.Object

edu.jas.gb.WordReductionAbstract<C>

edu.jas.gbufd.WordPseudoReductionSeq<C>

Type Parameters:

C - coefficient type

All Implemented Interfaces:

WordReduction<C>, WordPseudoReduction<C>, java.io.Serializable

public class WordPseudoReductionSeq<C extends RingElem<C>>
extends WordReductionAbstract<C>
implements WordPseudoReduction<C>

Polynomial word reduction sequential use algorithm. Implements normalform.

Author:

Heinz Kredel

See Also:

Serialized Form

Constructor Summary

Constructors

Constructor	Description
WordPseudoReductionSeq()	Constructor.

Method Summary

Modifier and Type	Method	Description
GenWordPolynomial<C>	leftNormalform(java.util.List<GenWordPolynomial<C>> Pp, GenWordPolynomial<C> Ap)	Normalform with left recording.
GenWordPolynomial<C>	leftNormalform(java.util.List<GenWordPolynomial<C>> lrow, java.util.List<GenWordPolynomial<C>> Pp, GenWordPolynomial<C> Ap)	Normalform with left 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.
WordPseudoReductionEntry<C>	normalformFactor(java.util.List<GenWordPolynomial<C>> Pp, GenWordPolynomial<C> Ap)	Normalform with multiplication factor.
GenWordPolynomial<GenPolynomial<C>>	normalformRecursive(java.util.List<GenWordPolynomial<GenPolynomial<C>>> Pp, GenWordPolynomial<GenPolynomial<C>> Ap)	Normalform with polynomial coefficients.
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

Methods inherited from interface edu.jas.gb.WordReduction

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

Constructor Detail

WordPseudoReductionSeq

public WordPseudoReductionSeq()

Constructor.

Method Detail

normalform

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

Normalform.

Specified by:

normalform in interface WordReduction<C extends RingElem<C>>

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.

Specified by:

normalform in interface WordReduction<C extends RingElem<C>>

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.

normalformFactor

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

Normalform with multiplication factor.

Specified by:

normalformFactor in interface WordPseudoReduction<C extends RingElem<C>>

Parameters:

Pp - polynomial list.

Ap - polynomial.

Returns:

( nf(Ap), mf ) with respect to Pp and mf as multiplication factor for Ap.

normalformRecursive

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

Normalform with polynomial coefficients.

Specified by:

normalformRecursive in interface WordPseudoReduction<C extends RingElem<C>>

Parameters:

Ap - polynomial.

Pp - polynomial list.

Returns:

nf(Ap) with respect to Pp.

leftNormalform

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

Description copied from interface: WordReduction

Normalform with left recording.

Specified by:

leftNormalform in interface WordReduction<C extends RingElem<C>>

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)

Description copied from interface: WordReduction

Normalform with left recording.

Specified by:

leftNormalform in interface WordReduction<C extends RingElem<C>>

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)

Description copied from interface: WordReduction

Right normalform with recording.

Specified by:

rightNormalform in interface WordReduction<C extends RingElem<C>>

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)

Description copied from interface: WordReduction

Right normalform with recording.

Specified by:

rightNormalform in interface WordReduction<C extends RingElem<C>>

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.