Package edu.jas.gbufd

Class RPseudoReductionSeq<C extends RegularRingElem<C>>

java.lang.Object

edu.jas.gb.ReductionAbstract<C>

edu.jas.gbufd.RReductionSeq<C>

edu.jas.gbufd.RPseudoReductionSeq<C>

Type Parameters:

C - coefficient type

All Implemented Interfaces:

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

public class RPseudoReductionSeq<C extends RegularRingElem<C>>
extends RReductionSeq<C>
implements RPseudoReduction<C>

Polynomial regular ring pseudo reduction sequential use algorithm. Implements fraction free normalform algorithm.

Author:

Heinz Kredel

See Also:

Serialized Form

Constructor Summary

Constructors

Constructor	Description
RPseudoReductionSeq()	Constructor.

Method Summary

Modifier and Type	Method	Description
GenPolynomial<C>	normalform(java.util.List<GenPolynomial<C>> Pp, GenPolynomial<C> Ap)	Normalform using r-reduction.
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 using r-reduction.
GenPolynomial<GenPolynomial<C>>	normalformRecursive(java.util.List<GenPolynomial<GenPolynomial<C>>> Pp, GenPolynomial<GenPolynomial<C>> Ap)	Normalform recursive.

Methods inherited from class edu.jas.gbufd.RReductionSeq

booleanClosure, booleanClosure, booleanRemainder, criterion4, criterion4, irreducibleSet, isBooleanClosed, isBooleanClosed, isNormalform, isReducedBooleanClosed, isStrongTopReducible, isTopReducible, reducedBooleanClosure, reducedBooleanClosure

Methods inherited from class edu.jas.gb.ReductionAbstract

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

Methods inherited from interface edu.jas.gbufd.RReduction

booleanClosure, booleanRemainder, isBooleanClosed, isBooleanClosed, isStrongTopReducible, reducedBooleanClosure, reducedBooleanClosure

Constructor Detail

RPseudoReductionSeq

public RPseudoReductionSeq()

Constructor.

Method Detail

normalform

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

Normalform using r-reduction.

Specified by:

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

Overrides:

normalform in class RReductionSeq<C extends RegularRingElem<C>>

Parameters:

Ap - polynomial.

Pp - polynomial list.

Returns:

r-nf(Ap) with respect to Pp.

normalformFactor

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

Normalform using r-reduction.

Specified by:

normalformFactor in interface PseudoReduction<C extends RegularRingElem<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 RegularRingElem<C>>

Overrides:

normalform in class RReductionSeq<C extends RegularRingElem<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 RegularRingElem<C>>

Parameters:

Ap - recursive polynomial.

Pp - recursive polynomial list.

Returns:

nf(Ap) with respect to Pp.