Package edu.jas.gb
Class SigReductionSeq<C extends RingElem<C>>
java.lang.Object
edu.jas.gb.SigReductionSeq<C>
- Type Parameters:
C
- coefficient type
- All Implemented Interfaces:
SigReduction<C>
,Serializable
Polynomial SigReduction class. Implements common S-Polynomial, normalform
with respect to signatures.
- See Also:
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Field Summary
FieldsModifier and TypeFieldDescriptionprivate static final org.apache.logging.log4j.Logger
(package private) final ReductionAbstract
<C> -
Constructor Summary
Constructors -
Method Summary
Modifier and TypeMethodDescriptionboolean
Is in top normalform.boolean
Is top reducible.boolean
Is sigma redundant.boolean
Is sigma redundant, alternative algorithm.minDegSubset
(List<SigPair<C>> F) Select signature polynomials of minimal degree and non minimal degree.long
minimalSigDegree
(List<SigPair<C>> F) Minimal degree of signatures.Select polynomials.Select signatures.sigNormalform
(List<GenPolynomial<C>> F, List<SigPoly<C>> G, SigPoly<C> A) Top normalform.sigSemiNormalform
(List<GenPolynomial<C>> F, List<SigPoly<C>> G, SigPoly<C> A) Top semi-complete normalform.Sort signature polynomials according to the degree its signatures.SPolynomial
(SigPoly<C> A, SigPoly<C> B) S-Polynomial.SPolynomialExpVectorFactors
(SigPoly<C> A, SigPoly<C> B) S-Polynomial factors.GenPolynomial<C>[]
SPolynomialFactors
(SigPoly<C> A, SigPoly<C> B) S-Polynomial polynomial factors.SPolynomialHalf
(SigPoly<C> A, SigPoly<C> B) S-Polynomial half.
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Field Details
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logger
private static final org.apache.logging.log4j.Logger logger -
red
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Constructor Details
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SigReductionSeq
public SigReductionSeq()Constructor.
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Method Details
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SPolynomial
S-Polynomial.- Specified by:
SPolynomial
in interfaceSigReduction<C extends RingElem<C>>
- Parameters:
A
- polynomial.B
- polynomial.- Returns:
- spol(A,B) the S-polynomial of A and B.
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SPolynomialExpVectorFactors
S-Polynomial factors.- Parameters:
A
- monic polynomial.B
- monic polynomial.- Returns:
- exponent vectors [e,f] such that spol(A,B) = e*a - f*B.
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SPolynomialHalf
S-Polynomial half.- Parameters:
A
- monic polynomial.B
- monic polynomial.- Returns:
- e*A "half" of an S-polynomial such that spol(A,B) = e*A - f*B.
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SPolynomialFactors
S-Polynomial polynomial factors.- Parameters:
A
- monic polynomial.B
- monic polynomial.- Returns:
- polynomials [e,f] such that spol(A,B) = e*a - f*B.
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isSigReducible
Is top reducible. Condition is lt(B) | lt(A) for some B in F or G.- Specified by:
isSigReducible
in interfaceSigReduction<C extends RingElem<C>>
- Parameters:
F
- polynomial list.G
- polynomial list.A
- polynomial.- Returns:
- true if A is top reducible with respect to F and G.
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isSigNormalform
Is in top normalform.- Specified by:
isSigNormalform
in interfaceSigReduction<C extends RingElem<C>>
- Parameters:
F
- polynomial list.G
- polynomial list.A
- polynomial.- Returns:
- true if A is in top normalform with respect to F and G.
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isSigRedundant
Is sigma redundant.- Parameters:
G
- polynomial list.A
- polynomial.- Returns:
- true if A is sigma redundant with respect to G.
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isSigRedundantAlt
Is sigma redundant, alternative algorithm.- Parameters:
G
- polynomial list.A
- polynomial.- Returns:
- true if A is sigma redundant per alternative algorithm with respect to G.
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sigNormalform
Top normalform.- Specified by:
sigNormalform
in interfaceSigReduction<C extends RingElem<C>>
- Parameters:
F
- polynomial list.G
- polynomial list.A
- polynomial.- Returns:
- nf(A) with respect to F and G.
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sigSemiNormalform
Top semi-complete normalform.- Parameters:
F
- polynomial list.G
- polynomial list.A
- polynomial.- Returns:
- nf(A) with respect to F and G.
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polys
Select polynomials.- Parameters:
F
- list of signature polynomials.- Returns:
- the polynomials in F.
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sigmas
Select signatures.- Parameters:
F
- list of signature polynomials.- Returns:
- the signatures in F.
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minimalSigDegree
Minimal degree of signatures.- Parameters:
F
- list of signature polynomials.- Returns:
- the minimal degree of the signatures in F.
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minDegSubset
Select signature polynomials of minimal degree and non minimal degree.- Parameters:
F
- list of signature polynomials.- Returns:
- [m,p] where m is the list of signature polynomials of F of minimal degree and p contains the rest of the signature polynomials with non minimal degree.
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sortSigma
Sort signature polynomials according to the degree its signatures.- Parameters:
F
- list of signature polynomials.- Returns:
- list of signature polynomials sorted by degree of sigma.
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