Package edu.jas.gb
Interface SigReduction<C extends RingElem<C>>
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- 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
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Method Summary
All Methods Instance Methods Abstract Methods Modifier and Type Method 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.
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Method Detail
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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.
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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.
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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.
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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.
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