Package edu.jas.gbufd

Class SolvablePseudoReductionSeq<C extends GcdRingElem<C>>

java.lang.Object

edu.jas.gb.SolvableReductionAbstract<C>

edu.jas.gbufd.SolvablePseudoReductionSeq<C>

Type Parameters:

C - coefficient type

All Implemented Interfaces:

SolvableReduction<C>, SolvablePseudoReduction<C>, java.io.Serializable

public class SolvablePseudoReductionSeq<C extends GcdRingElem<C>>
extends SolvableReductionAbstract<C>
implements SolvablePseudoReduction<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	Description
SolvablePseudoReductionSeq()	Constructor.

Method Summary

Modifier and Type	Method	Description
GenSolvablePolynomial<C>	leftNormalform(java.util.List<GenSolvablePolynomial<C>> Pp, GenSolvablePolynomial<C> Ap)	Left normalform.
GenSolvablePolynomial<C>	leftNormalform(java.util.List<GenSolvablePolynomial<C>> row, java.util.List<GenSolvablePolynomial<C>> Pp, GenSolvablePolynomial<C> Ap)	Left normalform with recording.
PseudoReductionEntry<C>	leftNormalformFactor(java.util.List<GenSolvablePolynomial<C>> Pp, GenSolvablePolynomial<C> Ap)	Left normalform with factor.
GenSolvablePolynomial<GenPolynomial<C>>	leftNormalformRecursive(java.util.List<GenSolvablePolynomial<GenPolynomial<C>>> Pp, GenSolvablePolynomial<GenPolynomial<C>> Ap)	Left normalform recursive.
GenSolvablePolynomial<C>	rightNormalform(java.util.List<GenSolvablePolynomial<C>> Pp, GenSolvablePolynomial<C> Ap)	Right normalform.
GenSolvablePolynomial<C>	rightNormalform(java.util.List<GenSolvablePolynomial<C>> row, java.util.List<GenSolvablePolynomial<C>> Pp, GenSolvablePolynomial<C> Ap)	Right normalform with recording.
PseudoReductionEntry<C>	rightNormalformFactor(java.util.List<GenSolvablePolynomial<C>> Pp, GenSolvablePolynomial<C> Ap)	Right normalform with multiplication factor.
GenSolvablePolynomial<GenPolynomial<C>>	rightNormalformRecursive(java.util.List<GenSolvablePolynomial<GenPolynomial<C>>> Pp, GenSolvablePolynomial<GenPolynomial<C>> Ap)	Right normalform recursive.

Methods inherited from class edu.jas.gb.SolvableReductionAbstract

isLeftReductionNF, isNormalform, isReducible, isRightReductionNF, isTopReducible, leftIrreducibleSet, leftNormalform, leftNormalform, leftNormalform, leftSPolynomial, leftSPolynomial, normalform, rightSPolynomial, rightSPolynomial

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.SolvableReduction

isLeftReductionNF, isNormalform, isReducible, isRightReductionNF, isTopReducible, leftIrreducibleSet, leftNormalform, leftSPolynomial, leftSPolynomial, normalform, rightSPolynomial

Constructor Detail

SolvablePseudoReductionSeq

public SolvablePseudoReductionSeq()

Constructor.

Method Detail

leftNormalform

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

Left normalform.

Specified by:

leftNormalform in interface SolvableReduction<C extends GcdRingElem<C>>

Parameters:

Ap - polynomial.

Pp - polynomial list.

Returns:

nf(Ap) with respect to Pp.

leftNormalformRecursive

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

Left normalform recursive.

Specified by:

leftNormalformRecursive in interface SolvablePseudoReduction<C extends GcdRingElem<C>>

Parameters:

Ap - recursive polynomial.

Pp - recursive polynomial list.

Returns:

nf(Ap) with respect to Pp.

leftNormalform

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

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

Specified by:

leftNormalform in interface SolvableReduction<C extends GcdRingElem<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.

leftNormalformFactor

public PseudoReductionEntry<C> leftNormalformFactor(java.util.List<GenSolvablePolynomial<C>> Pp,
                                                    GenSolvablePolynomial<C> Ap)

Left normalform with factor.

Specified by:

leftNormalformFactor in interface SolvablePseudoReduction<C extends GcdRingElem<C>>

Parameters:

Pp - polynomial list.

Ap - polynomial.

Returns:

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

rightNormalform

public GenSolvablePolynomial<C> rightNormalform(java.util.List<GenSolvablePolynomial<C>> Pp,
                                                GenSolvablePolynomial<C> Ap)

Right normalform.

Specified by:

rightNormalform in interface SolvableReduction<C extends GcdRingElem<C>>

Parameters:

Ap - polynomial.

Pp - polynomial list.

Returns:

nf(Ap) with respect to Pp.

rightNormalformRecursive

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

Right normalform recursive.

Specified by:

rightNormalformRecursive in interface SolvablePseudoReduction<C extends GcdRingElem<C>>

Parameters:

Ap - recursive polynomial.

Pp - recursive polynomial list.

Returns:

nf(Ap) with respect to Pp.

rightNormalform

public GenSolvablePolynomial<C> rightNormalform(java.util.List<GenSolvablePolynomial<C>> row,
                                                java.util.List<GenSolvablePolynomial<C>> Pp,
                                                GenSolvablePolynomial<C> Ap)

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

Specified by:

rightNormalform in interface SolvableReduction<C extends GcdRingElem<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.

rightNormalformFactor

public PseudoReductionEntry<C> rightNormalformFactor(java.util.List<GenSolvablePolynomial<C>> Pp,
                                                     GenSolvablePolynomial<C> Ap)

Right normalform with multiplication factor.

Specified by:

rightNormalformFactor in interface SolvablePseudoReduction<C extends GcdRingElem<C>>

Parameters:

Pp - polynomial list.

Ap - polynomial.

Returns:

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