edu.jas.gb

Class ReductionSeq<C extends RingElem<C>>

java.lang.Object

edu.jas.gb.ReductionAbstract<C>

edu.jas.gb.ReductionSeq<C>

Type Parameters:

C - coefficient type

All Implemented Interfaces:

Reduction<C>, java.io.Serializable

public class ReductionSeq<C extends RingElem<C>>
extends ReductionAbstract<C>

Polynomial reduction sequential use algorithm. Implements normalform.

Author:

Heinz Kredel

See Also:

Serialized Form

Constructor Summary

Constructors

Constructor and Description
ReductionSeq() Constructor.

Method Summary

Modifier and Type	Method and Description
GenPolynomial<C>	normalform(java.util.List<GenPolynomial<C>> Pp, GenPolynomial<C> Ap) Normalform.
GenPolynomial<C>	normalform(java.util.List<GenPolynomial<C>> row, java.util.List<GenPolynomial<C>> Pp, GenPolynomial<C> Ap) Normalform with recording.
GenPolynomial<C>	normalformMarked(java.util.List<Monomial<C>> Mp, java.util.List<GenPolynomial<C>> Pp, GenPolynomial<C> Ap) Normalform with respect to marked head terms.

Methods inherited from class edu.jas.gb.ReductionAbstract

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

Methods inherited from class java.lang.Object

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

Constructor Detail

ReductionSeq

public ReductionSeq()

Constructor.

Method Detail

normalform

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

Normalform.

Parameters:

Ap - polynomial.

Pp - polynomial list.

Returns:

nf(Ap) with respect to Pp.

normalformMarked

public GenPolynomial<C> normalformMarked(java.util.List<Monomial<C>> Mp,
                                         java.util.List<GenPolynomial<C>> Pp,
                                         GenPolynomial<C> Ap)

Normalform with respect to marked head terms.

Overrides:

normalformMarked in class ReductionAbstract<C extends RingElem<C>>

Parameters:

Mp - leading monomial list.

Pp - polynomial list.

Ap - polynomial.

Returns:

nf(Ap) with respect to Mp+Pp.

normalform

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

Normalform with recording.

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.