edu.jas.gbufd

Class PseudoReductionPar<C extends RingElem<C>>

java.lang.Object

edu.jas.gb.ReductionAbstract<C>

edu.jas.gbufd.PseudoReductionPar<C>

Type Parameters:

C - coefficient type

All Implemented Interfaces:

Reduction<C>, PseudoReduction<C>, java.io.Serializable

public class PseudoReductionPar<C extends RingElem<C>>
extends ReductionAbstract<C>
implements PseudoReduction<C>

Polynomial pseudo reduction sequential use algorithm. Coefficients of polynomials must not be from a field, i.e. the fraction free reduction is implemented. Implements normalform.

Author:

Heinz Kredel

See Also:

Serialized Form

Constructor Summary

Constructors

Constructor and Description
PseudoReductionPar() 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.
PseudoReductionEntry<C>	normalformFactor(java.util.List<GenPolynomial<C>> Pp, GenPolynomial<C> Ap) Normalform.
GenPolynomial<GenPolynomial<C>>	normalformRecursive(java.util.List<GenPolynomial<GenPolynomial<C>>> Pp, GenPolynomial<GenPolynomial<C>> Ap) Normalform recursive.

Methods inherited from class edu.jas.gb.ReductionAbstract

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

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.Reduction

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

Constructor Detail

PseudoReductionPar

public PseudoReductionPar()

Constructor.

Method Detail

normalform

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

Normalform.

Specified by:

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

Parameters:

Ap - polynomial.

Pp - polynomial list.

Returns:

nf(Ap) with respect to Pp.

normalformFactor

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

Normalform.

Specified by:

normalformFactor in interface PseudoReduction<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.

normalform

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

Normalform with recording. Note: Only meaningful if all divisions are exact. Compute first the multiplication factor m with normalform(Pp,Ap,m), then call this method with normalform(row,Pp,m*Ap).

Specified by:

normalform in interface Reduction<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.

normalformRecursive

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

Normalform recursive.

Specified by:

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

Parameters:

Ap - recursive polynomial.

Pp - recursive polynomial list.

Returns:

nf(Ap) with respect to Pp.