Package edu.jas.gb
Class EReductionSeq<C extends RingElem<C>>
java.lang.Object
edu.jas.gb.ReductionAbstract<C>
edu.jas.gb.DReductionSeq<C>
edu.jas.gb.EReductionSeq<C>
- Type Parameters:
C
- coefficient type
- All Implemented Interfaces:
DReduction<C>
,EReduction<C>
,Reduction<C>
,Serializable
Polynomial E-Reduction sequential use algorithm. Implements normalform.
- See Also:
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Field Summary
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Constructor Summary
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Method Summary
Modifier and TypeMethodDescriptionirreducibleSet
(List<GenPolynomial<C>> Pp) Irreducible set.boolean
isNormalform
(List<GenPolynomial<C>> Pp, GenPolynomial<C> Ap) Is in Normalform.boolean
isTopReducible
(List<GenPolynomial<C>> P, GenPolynomial<C> A) Is top reducible.normalform
(List<GenPolynomial<C>> Pp, GenPolynomial<C> Ap) Normalform using e-reduction.normalform
(List<GenPolynomial<C>> row, List<GenPolynomial<C>> Pp, GenPolynomial<C> Ap) Normalform with recording.Methods inherited from class edu.jas.gb.DReductionSeq
criterion4, criterion4, GPolynomial, GPolynomial, SPolynomial, SPolynomial
Methods inherited from class edu.jas.gb.ReductionAbstract
criterion4, isNormalform, isReducible, isReductionNF, moduleCriterion, moduleCriterion, normalform, normalform, normalform, normalformMarked
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.DReduction
GPolynomial, GPolynomial
Methods inherited from interface edu.jas.gb.Reduction
criterion4, criterion4, criterion4, isNormalform, isReducible, isReductionNF, moduleCriterion, moduleCriterion, normalform, SPolynomial, SPolynomial
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Field Details
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logger
private static final org.apache.logging.log4j.Logger logger
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Constructor Details
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EReductionSeq
public EReductionSeq()Constructor.
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Method Details
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isTopReducible
Is top reducible.- Specified by:
isTopReducible
in interfaceReduction<C extends RingElem<C>>
- Overrides:
isTopReducible
in classDReductionSeq<C extends RingElem<C>>
- Parameters:
P
- polynomial list.A
- polynomial.- Returns:
- true if A is top reducible with respect to P.
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isNormalform
Is in Normalform.- Specified by:
isNormalform
in interfaceReduction<C extends RingElem<C>>
- Overrides:
isNormalform
in classDReductionSeq<C extends RingElem<C>>
- Parameters:
Pp
- polynomial list.Ap
- polynomial.- Returns:
- true if Ap is in normalform with respect to Pp.
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normalform
Normalform using e-reduction.- Specified by:
normalform
in interfaceReduction<C extends RingElem<C>>
- Overrides:
normalform
in classDReductionSeq<C extends RingElem<C>>
- Parameters:
Pp
- polynomial list.Ap
- polynomial.- Returns:
- e-nf(Ap) with respect to Pp.
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normalform
public GenPolynomial<C> normalform(List<GenPolynomial<C>> row, List<GenPolynomial<C>> Pp, GenPolynomial<C> Ap) Normalform with recording.- Specified by:
normalform
in interfaceReduction<C extends RingElem<C>>
- Overrides:
normalform
in classDReductionSeq<C extends RingElem<C>>
- Parameters:
row
- recording matrix, is modified.Pp
- a polynomial list for reduction.Ap
- a polynomial.- Returns:
- nf(Pp,Ap), the normal form of Ap wrt. Pp.
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irreducibleSet
Irreducible set.- Specified by:
irreducibleSet
in interfaceReduction<C extends RingElem<C>>
- Overrides:
irreducibleSet
in classDReductionSeq<C extends RingElem<C>>
- Parameters:
Pp
- polynomial list.- Returns:
- a list P of polynomials which are in normalform wrt. P.
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