Package edu.jas.gb

Class EReductionSeq<C extends RingElem<C>>

java.lang.Object

edu.jas.gb.ReductionAbstract<C>

edu.jas.gb.DReductionSeq<C>

edu.jas.gb.EReductionSeq<C>

Type Parameters:

C - coefficient type

All Implemented Interfaces:

DReduction<C>, EReduction<C>, Reduction<C>, java.io.Serializable

public class EReductionSeq<C extends RingElem<C>>
extends DReductionSeq<C>
implements EReduction<C>

Polynomial E-Reduction sequential use algorithm. Implements normalform.

Author:

Heinz Kredel

See Also:

Serialized Form

Constructor Summary

Constructors

Constructor	Description
EReductionSeq()	Constructor.

Method Summary

Modifier and Type	Method	Description
java.util.List<GenPolynomial<C>>	irreducibleSet(java.util.List<GenPolynomial<C>> Pp)	Irreducible set.
boolean	isNormalform(java.util.List<GenPolynomial<C>> Pp, GenPolynomial<C> Ap)	Is in Normalform.
boolean	isTopReducible(java.util.List<GenPolynomial<C>> P, GenPolynomial<C> A)	Is top reducible.
GenPolynomial<C>	normalform(java.util.List<GenPolynomial<C>> Pp, GenPolynomial<C> Ap)	Normalform using e-reduction.
GenPolynomial<C>	normalform(java.util.List<GenPolynomial<C>> row, java.util.List<GenPolynomial<C>> Pp, GenPolynomial<C> Ap)	Normalform with recording.

Methods inherited from class edu.jas.gb.DReductionSeq

criterion4, criterion4, GPolynomial, GPolynomial, SPolynomial, SPolynomial

Methods inherited from class edu.jas.gb.ReductionAbstract

criterion4, isNormalform, isReducible, isReductionNF, moduleCriterion, moduleCriterion, normalform, normalform, normalform, normalformMarked

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.DReduction

GPolynomial, GPolynomial

Methods inherited from interface edu.jas.gb.Reduction

criterion4, criterion4, criterion4, isNormalform, isReducible, isReductionNF, moduleCriterion, moduleCriterion, normalform, SPolynomial, SPolynomial

Constructor Detail

EReductionSeq

public EReductionSeq()

Constructor.

Method Detail

isTopReducible

public boolean isTopReducible(java.util.List<GenPolynomial<C>> P,
                              GenPolynomial<C> A)

Is top reducible.

Specified by:

isTopReducible in interface Reduction<C extends RingElem<C>>

Overrides:

isTopReducible in class DReductionSeq<C extends RingElem<C>>

Parameters:

A - polynomial.

P - polynomial list.

Returns:

true if A is top reducible with respect to P.

isNormalform

public boolean isNormalform(java.util.List<GenPolynomial<C>> Pp,
                            GenPolynomial<C> Ap)

Is in Normalform.

Specified by:

isNormalform in interface Reduction<C extends RingElem<C>>

Overrides:

isNormalform in class DReductionSeq<C extends RingElem<C>>

Parameters:

Ap - polynomial.

Pp - polynomial list.

Returns:

true if Ap is in normalform with respect to Pp.

normalform

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

Normalform using e-reduction.

Specified by:

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

Overrides:

normalform in class DReductionSeq<C extends RingElem<C>>

Parameters:

Ap - polynomial.

Pp - polynomial list.

Returns:

e-nf(Ap) with respect to Pp.

normalform

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

Normalform with recording.

Specified by:

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

Overrides:

normalform in class DReductionSeq<C extends RingElem<C>>

Parameters:

row - recording matrix, is modified.

Pp - a polynomial list for reduction.

Ap - a polynomial.

Returns:

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

irreducibleSet

public java.util.List<GenPolynomial<C>> irreducibleSet(java.util.List<GenPolynomial<C>> Pp)

Irreducible set.

Specified by:

irreducibleSet in interface Reduction<C extends RingElem<C>>

Overrides:

irreducibleSet in class DReductionSeq<C extends RingElem<C>>

Parameters:

Pp - polynomial list.

Returns:

a list P of polynomials which are in normalform wrt. P.