edu.jas.gbufd

Interface CharacteristicSet<C extends GcdRingElem<C>>

Type Parameters:

C - coefficient type

All Superinterfaces:

java.io.Serializable

All Known Implementing Classes:

CharacteristicSetSimple, CharacteristicSetWu

public interface CharacteristicSet<C extends GcdRingElem<C>>
extends java.io.Serializable

Characteristic Set interface. Defines methods for Characteristic Sets and tests.

Author:

Heinz Kredel

Method Summary

Modifier and Type	Method and Description
java.util.List<GenPolynomial<C>>	characteristicSet(java.util.List<GenPolynomial<C>> A) Characteristic set.
GenPolynomial<C>	characteristicSetReduction(java.util.List<GenPolynomial<C>> A, GenPolynomial<C> P) Characteristic set reduction.
boolean	isCharacteristicSet(java.util.List<GenPolynomial<C>> A) Characteristic set test.

Method Detail

characteristicSet

java.util.List<GenPolynomial<C>> characteristicSet(java.util.List<GenPolynomial<C>> A)

Characteristic set. According to the implementing algorithm (simple, Wu, etc).

Parameters:

A - list of generic polynomials.

Returns:

charSet(A) with at most one polynomial per main variable.

isCharacteristicSet

boolean isCharacteristicSet(java.util.List<GenPolynomial<C>> A)

Characteristic set test.

Parameters:

A - list of generic polynomials.

Returns:

true, if A is (at least a simple) characteristic set, else false.

characteristicSetReduction

GenPolynomial<C> characteristicSetReduction(java.util.List<GenPolynomial<C>> A,
                                            GenPolynomial<C> P)

Characteristic set reduction. Pseudo remainder wrt. the main variable. With further pseudo reduction of the leading coefficient depending on the implementing algorithm.

Parameters:

P - generic polynomial.

A - list of generic polynomials as characteristic set.

Returns:

characteristicSetRemainder(A,P) or characteristicSetReductionCoeff(A,characteristicSetRemainder(A,P)) depending on the algorithm.