Package edu.jas.gb

Class SolvableReductionAbstract<C extends RingElem<C>>

java.lang.Object

edu.jas.gb.SolvableReductionAbstract<C>

Type Parameters:

C - coefficient type

All Implemented Interfaces:

SolvableReduction<C>, java.io.Serializable

Direct Known Subclasses:

SolvablePseudoReductionSeq, SolvableReductionPar, SolvableReductionSeq

public abstract class SolvableReductionAbstract<C extends RingElem<C>>
extends java.lang.Object
implements SolvableReduction<C>

Solvable polynomial Reduction abstract class. Implements common left, right S-Polynomial, left normalform and left irreducible set.

Author:

Heinz Kredel

See Also:

Serialized Form

Constructor Summary

Constructors

Constructor	Description
SolvableReductionAbstract()	Constructor.

Method Summary

Modifier and Type	Method	Description
boolean	isLeftReductionNF(java.util.List<GenSolvablePolynomial<C>> row, java.util.List<GenSolvablePolynomial<C>> Pp, GenSolvablePolynomial<C> Ap, GenSolvablePolynomial<C> Np)	Is reduction of normal form.
boolean	isNormalform(java.util.List<GenSolvablePolynomial<C>> Pp, GenSolvablePolynomial<C> Ap)	Is in Normalform.
boolean	isReducible(java.util.List<GenSolvablePolynomial<C>> Pp, GenSolvablePolynomial<C> Ap)	Is reducible.
boolean	isRightReductionNF(java.util.List<GenSolvablePolynomial<C>> row, java.util.List<GenSolvablePolynomial<C>> Pp, GenSolvablePolynomial<C> Ap, GenSolvablePolynomial<C> Np)	Is right reduction of normal form.
boolean	isTopReducible(java.util.List<GenSolvablePolynomial<C>> P, GenSolvablePolynomial<C> A)	Is top reducible.
java.util.List<GenSolvablePolynomial<C>>	leftIrreducibleSet(java.util.List<GenSolvablePolynomial<C>> Pp)	Left irreducible set.
ModuleList<C>	leftNormalform(ModuleList<C> Pp, ModuleList<C> Ap)	Module left normalform set.
ModuleList<C>	leftNormalform(ModuleList<C> Pp, ModuleList<C> Ap, boolean top)	Module left normalform set.
java.util.List<GenSolvablePolynomial<C>>	leftNormalform(java.util.List<GenSolvablePolynomial<C>> Pp, java.util.List<GenSolvablePolynomial<C>> Ap)	Left Normalform Set.
GenSolvablePolynomial<C>	leftSPolynomial(GenSolvablePolynomial<C> Ap, GenSolvablePolynomial<C> Bp)	Left S-Polynomial.
GenSolvablePolynomial<C>	leftSPolynomial(java.util.List<GenSolvablePolynomial<C>> S, int i, GenSolvablePolynomial<C> Ap, int j, GenSolvablePolynomial<C> Bp)	S-Polynomial with recording.
GenSolvablePolynomial<C>	normalform(java.util.List<GenSolvablePolynomial<C>> Pp, GenSolvablePolynomial<C> Ap)	Two-sided Normalform.
GenSolvablePolynomial<C>	rightSPolynomial(GenSolvablePolynomial<C> Ap, GenSolvablePolynomial<C> Bp)	Right S-Polynomial.

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

leftNormalform, leftNormalform, rightNormalform, rightNormalform

Constructor Detail

SolvableReductionAbstract

public SolvableReductionAbstract()

Constructor.

Method Detail

leftSPolynomial

public GenSolvablePolynomial<C> leftSPolynomial(GenSolvablePolynomial<C> Ap,
                                                GenSolvablePolynomial<C> Bp)

Left S-Polynomial.

Specified by:

leftSPolynomial in interface SolvableReduction<C extends RingElem<C>>

Parameters:

Ap - solvable polynomial.

Bp - solvable polynomial.

Returns:

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

leftSPolynomial

public GenSolvablePolynomial<C> leftSPolynomial(java.util.List<GenSolvablePolynomial<C>> S,
                                                int i,
                                                GenSolvablePolynomial<C> Ap,
                                                int j,
                                                GenSolvablePolynomial<C> Bp)

S-Polynomial with recording.

Specified by:

leftSPolynomial in interface SolvableReduction<C extends RingElem<C>>

Parameters:

S - recording matrix, is modified.

i - index of Ap in basis list.

Ap - a polynomial.

j - index of Bp in basis list.

Bp - a polynomial.

Returns:

leftSpol(Ap, Bp), the left S-Polynomial for Ap and Bp.

leftNormalform

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

Left Normalform Set.

Specified by:

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

Parameters:

Ap - solvable polynomial list.

Pp - solvable polynomial list.

Returns:

list of left-nf(a) with respect to Pp for all a in Ap.

leftNormalform

public ModuleList<C> leftNormalform(ModuleList<C> Pp,
                                    ModuleList<C> Ap)

Module left normalform set.

Parameters:

Ap - module list.

Pp - module list.

Returns:

list of left-nf(a) with respect to Pp for all a in Ap.

leftNormalform

public ModuleList<C> leftNormalform(ModuleList<C> Pp,
                                    ModuleList<C> Ap,
                                    boolean top)

Module left normalform set.

Parameters:

Ap - module list.

Pp - module list.

top - true for TOP term order, false for POT term order.

Returns:

list of left-nf(a) with respect to Pp for all a in Ap.

leftIrreducibleSet

public java.util.List<GenSolvablePolynomial<C>> leftIrreducibleSet(java.util.List<GenSolvablePolynomial<C>> Pp)

Left irreducible set.

Specified by:

leftIrreducibleSet in interface SolvableReduction<C extends RingElem<C>>

Parameters:

Pp - solvable polynomial list.

Returns:

a list P of solvable polynomials which are in normalform wrt. P.

isLeftReductionNF

public boolean isLeftReductionNF(java.util.List<GenSolvablePolynomial<C>> row,
                                 java.util.List<GenSolvablePolynomial<C>> Pp,
                                 GenSolvablePolynomial<C> Ap,
                                 GenSolvablePolynomial<C> Np)

Is reduction of normal form.

Specified by:

isLeftReductionNF in interface SolvableReduction<C extends RingElem<C>>

Parameters:

row - recording matrix.

Pp - a solvable polynomial list for reduction.

Ap - a solvable polynomial.

Np - nf(Pp,Ap), a left normal form of Ap wrt. Pp.

Returns:

true, if Np + sum( row[i]*Pp[i] ) == Ap, else false.

rightSPolynomial

public GenSolvablePolynomial<C> rightSPolynomial(GenSolvablePolynomial<C> Ap,
                                                 GenSolvablePolynomial<C> Bp)

Right S-Polynomial.

Specified by:

rightSPolynomial in interface SolvableReduction<C extends RingElem<C>>

Parameters:

Ap - solvable polynomial.

Bp - solvable polynomial.

Returns:

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

isTopReducible

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

Is top reducible. Is left right symmetric.

Specified by:

isTopReducible in interface SolvableReduction<C extends RingElem<C>>

Parameters:

A - solvable polynomial.

P - solvable polynomial list.

Returns:

true if A is top reducible with respect to P.

isReducible

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

Is reducible. Is left right symmetric.

Specified by:

isReducible in interface SolvableReduction<C extends RingElem<C>>

Parameters:

Ap - solvable polynomial.

Pp - solvable polynomial list.

Returns:

true if Ap is reducible with respect to Pp.

isNormalform

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

Is in Normalform. Is left right symmetric.

Specified by:

isNormalform in interface SolvableReduction<C extends RingElem<C>>

Parameters:

Ap - polynomial.

Pp - polynomial list.

Returns:

true if Ap is in normalform with respect to Pp.

isRightReductionNF

public boolean isRightReductionNF(java.util.List<GenSolvablePolynomial<C>> row,
                                  java.util.List<GenSolvablePolynomial<C>> Pp,
                                  GenSolvablePolynomial<C> Ap,
                                  GenSolvablePolynomial<C> Np)

Is right reduction of normal form.

Specified by:

isRightReductionNF in interface SolvableReduction<C extends RingElem<C>>

Parameters:

row - recording matrix.

Pp - a solvable polynomial list for reduction.

Ap - a solvable polynomial.

Np - nf(Pp,Ap), a left normal form of Ap wrt. Pp.

Returns:

true, if Np + sum( Pp[i]*row[i] ) == Ap, else false.

normalform

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

Two-sided Normalform.

Specified by:

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

Parameters:

Ap - solvable polynomial.

Pp - solvable polynomial list.

Returns:

two-sided-nf(Ap) with respect to Pp.