Package edu.jas.gbufd
Class RPseudoReductionSeq<C extends RegularRingElem<C>>
- java.lang.Object
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- edu.jas.gb.ReductionAbstract<C>
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- edu.jas.gbufd.RReductionSeq<C>
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- edu.jas.gbufd.RPseudoReductionSeq<C>
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- Type Parameters:
C
- coefficient type
- All Implemented Interfaces:
Reduction<C>
,PseudoReduction<C>
,RPseudoReduction<C>
,RReduction<C>
,java.io.Serializable
public class RPseudoReductionSeq<C extends RegularRingElem<C>> extends RReductionSeq<C> implements RPseudoReduction<C>
Polynomial regular ring pseudo reduction sequential use algorithm. Implements fraction free normalform algorithm.- Author:
- Heinz Kredel
- See Also:
- Serialized Form
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Constructor Summary
Constructors Constructor Description RPseudoReductionSeq()
Constructor.
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Method Summary
All Methods Instance Methods Concrete Methods Modifier and Type Method Description GenPolynomial<C>
normalform(java.util.List<GenPolynomial<C>> Pp, GenPolynomial<C> Ap)
Normalform using r-reduction.GenPolynomial<C>
normalform(java.util.List<GenPolynomial<C>> row, java.util.List<GenPolynomial<C>> Pp, GenPolynomial<C> Ap)
Normalform with recording.PseudoReductionEntry<C>
normalformFactor(java.util.List<GenPolynomial<C>> Pp, GenPolynomial<C> Ap)
Normalform using r-reduction.GenPolynomial<GenPolynomial<C>>
normalformRecursive(java.util.List<GenPolynomial<GenPolynomial<C>>> Pp, GenPolynomial<GenPolynomial<C>> Ap)
Normalform recursive.-
Methods inherited from class edu.jas.gbufd.RReductionSeq
booleanClosure, booleanClosure, booleanRemainder, criterion4, criterion4, irreducibleSet, isBooleanClosed, isBooleanClosed, isNormalform, isReducedBooleanClosed, isStrongTopReducible, isTopReducible, reducedBooleanClosure, reducedBooleanClosure
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Methods inherited from class edu.jas.gb.ReductionAbstract
criterion4, isNormalform, isReducible, isReductionNF, moduleCriterion, moduleCriterion, normalform, normalform, normalform, normalformMarked, SPolynomial, SPolynomial
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Methods inherited from class java.lang.Object
clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait
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Methods inherited from interface edu.jas.gb.Reduction
criterion4, criterion4, criterion4, irreducibleSet, isNormalform, isNormalform, isReducible, isReductionNF, isTopReducible, moduleCriterion, moduleCriterion, normalform, SPolynomial, SPolynomial
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Methods inherited from interface edu.jas.gbufd.RReduction
booleanClosure, booleanRemainder, isBooleanClosed, isBooleanClosed, isStrongTopReducible, reducedBooleanClosure, reducedBooleanClosure
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Constructor Detail
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RPseudoReductionSeq
public RPseudoReductionSeq()
Constructor.
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Method Detail
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normalform
public GenPolynomial<C> normalform(java.util.List<GenPolynomial<C>> Pp, GenPolynomial<C> Ap)
Normalform using r-reduction.- Specified by:
normalform
in interfaceReduction<C extends RegularRingElem<C>>
- Overrides:
normalform
in classRReductionSeq<C extends RegularRingElem<C>>
- Parameters:
Ap
- polynomial.Pp
- polynomial list.- Returns:
- r-nf(Ap) with respect to Pp.
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normalformFactor
public PseudoReductionEntry<C> normalformFactor(java.util.List<GenPolynomial<C>> Pp, GenPolynomial<C> Ap)
Normalform using r-reduction.- Specified by:
normalformFactor
in interfacePseudoReduction<C extends RegularRingElem<C>>
- Parameters:
Pp
- polynomial list.Ap
- polynomial.- Returns:
- ( nf(Ap), mf ) with respect to Pp and mf as multiplication factor for Ap.
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normalform
public GenPolynomial<C> normalform(java.util.List<GenPolynomial<C>> row, java.util.List<GenPolynomial<C>> Pp, GenPolynomial<C> Ap)
Normalform with recording. Note: Only meaningful if all divisions are exact. Compute first the multiplication factorm
withnormalform(Pp,Ap,m)
, then call this method withnormalform(row,Pp,m*Ap)
.- Specified by:
normalform
in interfaceReduction<C extends RegularRingElem<C>>
- Overrides:
normalform
in classRReductionSeq<C extends RegularRingElem<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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normalformRecursive
public GenPolynomial<GenPolynomial<C>> normalformRecursive(java.util.List<GenPolynomial<GenPolynomial<C>>> Pp, GenPolynomial<GenPolynomial<C>> Ap)
Normalform recursive.- Specified by:
normalformRecursive
in interfacePseudoReduction<C extends RegularRingElem<C>>
- Parameters:
Ap
- recursive polynomial.Pp
- recursive polynomial list.- Returns:
- nf(Ap) with respect to Pp.
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