edu.jas.gb

Interface SigReduction<C extends RingElem<C>>

Type Parameters:

C - coefficient type

All Superinterfaces:

java.io.Serializable

All Known Implementing Classes:

SigReductionSeq

public interface SigReduction<C extends RingElem<C>>
extends java.io.Serializable

Polynomial SigReduction interface. Defines S-Polynomial, normalform with respect to signatures.

Author:

Heinz Kredel

Method Summary

Modifier and Type	Method and Description
boolean	isSigNormalform(java.util.List<SigPoly<C>> F, java.util.List<SigPoly<C>> G, SigPoly<C> A) Is in Normalform.
boolean	isSigReducible(java.util.List<SigPoly<C>> F, java.util.List<SigPoly<C>> G, SigPoly<C> A) Is top reducible.
SigPoly<C>	sigNormalform(java.util.List<GenPolynomial<C>> F, java.util.List<SigPoly<C>> G, SigPoly<C> A) Normalform.
GenPolynomial<C>	SPolynomial(SigPoly<C> Ap, SigPoly<C> Bp) S-Polynomial.

Method Detail

SPolynomial

GenPolynomial<C> SPolynomial(SigPoly<C> Ap,
                             SigPoly<C> Bp)

S-Polynomial.

Parameters:

Ap - polynomial.

Bp - polynomial.

Returns:

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

isSigReducible

boolean isSigReducible(java.util.List<SigPoly<C>> F,
                       java.util.List<SigPoly<C>> G,
                       SigPoly<C> A)

Is top reducible. Condition is lt(B) | lt(A) for some B in F or G.

Parameters:

A - polynomial.

F - polynomial list.

G - polynomial list.

Returns:

true if A is top reducible with respect to P.

isSigNormalform

boolean isSigNormalform(java.util.List<SigPoly<C>> F,
                        java.util.List<SigPoly<C>> G,
                        SigPoly<C> A)

Is in Normalform.

Parameters:

A - polynomial.

F - polynomial list.

G - polynomial list.

Returns:

true if A is in normalform with respect to F and G.

sigNormalform

SigPoly<C> sigNormalform(java.util.List<GenPolynomial<C>> F,
                         java.util.List<SigPoly<C>> G,
                         SigPoly<C> A)

Normalform.

Parameters:

A - polynomial.

F - polynomial list.

G - polynomial list.

Returns:

nf(A) with respect to F and G.