edu.jas.application
Class CReductionSeq<C extends GcdRingElem<C>>

java.lang.Object
  edu.jas.application.CReductionSeq<C>

Type Parameters:

C - coefficient type

public class CReductionSeq<C extends GcdRingElem<C>>
extends java.lang.Object

Polynomial parametric ring reduction sequential use algorithm. Implements normalform, condition construction and polynomial determination.

Author:

Heinz Kredel

Field Summary

protected RingFactory<C>	cofac Polynomial coefficient ring factory.
protected GreatestCommonDivisor<C>	engine Greatest common divisor engine.
protected boolean	top Flag if top-reduction only should be used.

Constructor Summary

CReductionSeq(RingFactory<C> rf)
Constructor.

Method Summary

java.util.List<Condition<C>>	caseDistinction(Condition<C> cond, GenPolynomial<GenPolynomial<C>> A) Case distinction conditions of parametric polynomial list.
java.util.List<Condition<C>>	caseDistinction(java.util.List<Condition<C>> cd, GenPolynomial<GenPolynomial<C>> A) Case distinction conditions of parametric polynomial list.
java.util.List<Condition<C>>	caseDistinction(java.util.List<GenPolynomial<GenPolynomial<C>>> L) Case distinction conditions of parametric polynomial list.
java.util.List<ColoredSystem<C>>	determine(java.util.List<Condition<C>> cd, java.util.List<GenPolynomial<GenPolynomial<C>>> H) Determine polynomial list.
java.util.List<ColoredSystem<C>>	determine(java.util.List<GenPolynomial<GenPolynomial<C>>> H) Determine polynomial list.
boolean	isNormalform(java.util.List<ColorPolynomial<C>> Pp) Is in Normalform.
boolean	isNormalform(java.util.List<ColorPolynomial<C>> Pp, ColorPolynomial<C> Ap) Is in Normalform.
boolean	isReducible(java.util.List<ColorPolynomial<C>> Pp, ColorPolynomial<C> Ap) Is reducible.
boolean	isTopReducible(java.util.List<ColorPolynomial<C>> P, ColorPolynomial<C> A) Is top reducible.
ColorPolynomial<C>	normalform(Condition<C> cond, java.util.List<ColorPolynomial<C>> Pp, ColorPolynomial<C> Ap) Normalform.
ColorPolynomial<C>	SPolynomial(ColorPolynomial<C> Ap, ColorPolynomial<C> Bp) S-Polynomial.

Methods inherited from class java.lang.Object

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

Field Detail

engine

protected final GreatestCommonDivisor<C extends GcdRingElem<C>> engine

Greatest common divisor engine.

cofac

protected final RingFactory<C extends GcdRingElem<C>> cofac

Polynomial coefficient ring factory.

top

protected boolean top

Flag if top-reduction only should be used.

Constructor Detail

CReductionSeq

public CReductionSeq(RingFactory<C> rf)

Constructor.

Parameters:

rf - coefficient factory.

Method Detail

SPolynomial

public ColorPolynomial<C> SPolynomial(ColorPolynomial<C> Ap,
                                      ColorPolynomial<C> Bp)

S-Polynomial.

Parameters:

Ap - polynomial.

Bp - polynomial.

Returns:

spol(Ap,Bp) the S-polynomial of Ap and Bp.

isTopReducible

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

Is top reducible.

Parameters:

A - polynomial.

P - polynomial list.

Returns:

true if A is top reducible with respect to P.

isReducible

public boolean isReducible(java.util.List<ColorPolynomial<C>> Pp,
                           ColorPolynomial<C> Ap)

Is reducible.

Parameters:

Ap - polynomial.

Pp - polynomial list.

Returns:

true if Ap is reducible with respect to Pp.

isNormalform

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

Is in Normalform.

Parameters:

Ap - polynomial.

Pp - polynomial list.

Returns:

true if Ap is in normalform with respect to Pp.

isNormalform

public boolean isNormalform(java.util.List<ColorPolynomial<C>> Pp)

Is in Normalform.

Parameters:

Pp - polynomial list.

Returns:

true if each Ap in Pp is in normalform with respect to Pp\{Ap}.

normalform

public ColorPolynomial<C> normalform(Condition<C> cond,
                                     java.util.List<ColorPolynomial<C>> Pp,
                                     ColorPolynomial<C> Ap)

Normalform.

Parameters:

Ap - polynomial.

Pp - polynomial list.

cond - condition for these polynomials.

Returns:

nf(Ap) with respect to Pp.

caseDistinction

public java.util.List<Condition<C>> caseDistinction(java.util.List<GenPolynomial<GenPolynomial<C>>> L)

Case distinction conditions of parametric polynomial list. The returned condition determines the polynomial list.

Parameters:

L - list of parametric polynomials.

Returns:

list of conditions as case distinction.

caseDistinction

public java.util.List<Condition<C>> caseDistinction(java.util.List<Condition<C>> cd,
                                                    GenPolynomial<GenPolynomial<C>> A)

Case distinction conditions of parametric polynomial list.

Parameters:

cd - a list of conditions.

A - a parametric polynomial.

Returns:

list of conditions as case distinction extending the conditions in cd.

caseDistinction

public java.util.List<Condition<C>> caseDistinction(Condition<C> cond,
                                                    GenPolynomial<GenPolynomial<C>> A)

Case distinction conditions of parametric polynomial list.

Parameters:

A - a parametric polynomial.

cond - a condition.

Returns:

list of case distinction conditions.

determine

public java.util.List<ColoredSystem<C>> determine(java.util.List<GenPolynomial<GenPolynomial<C>>> H)

Determine polynomial list.

Parameters:

H - polynomial list.

Returns:

new determined list of colored systems.

determine

public java.util.List<ColoredSystem<C>> determine(java.util.List<Condition<C>> cd,
                                                  java.util.List<GenPolynomial<GenPolynomial<C>>> H)

Determine polynomial list.

Parameters:

H - polynomial list.

cd - case distiction, a condition list.

Returns:

new determined list of colored systems.