Package edu.jas.application
Class CReductionSeq<C extends GcdRingElem<C>>
- java.lang.Object
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- edu.jas.application.CReductionSeq<C>
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- Type Parameters:
C
- coefficient type
- All Implemented Interfaces:
java.io.Serializable
public class CReductionSeq<C extends GcdRingElem<C>> extends java.lang.Object implements java.io.Serializable
Polynomial parametric ring reduction sequential use algorithm. Implements normalform, condition construction and polynomial determination.- Author:
- Heinz Kredel
- See Also:
- Serialized Form
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Field Summary
Fields Modifier and Type Field Description protected RingFactory<C>
cofac
Polynomial coefficient ring factory.protected GreatestCommonDivisor<C>
engine
Greatest common divisor engine.protected boolean
top
Flag if top-reduction only should be used.
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Constructor Summary
Constructors Constructor Description CReductionSeq(RingFactory<C> rf)
Constructor.
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Method Summary
All Methods Instance Methods Concrete Methods Modifier and Type Method Description java.util.List<Condition<C>>
caseDistinction(Condition<C> cond, GenPolynomial<GenPolynomial<C>> A)
Case distinction conditions of parametric polynomial list.java.util.List<Condition<C>>
caseDistinction(java.util.List<Condition<C>> cd, GenPolynomial<GenPolynomial<C>> A)
Case distinction conditions of parametric polynomial list.java.util.List<Condition<C>>
caseDistinction(java.util.List<GenPolynomial<GenPolynomial<C>>> L)
Case distinction conditions of parametric polynomial list.java.util.List<ColoredSystem<C>>
determine(java.util.List<Condition<C>> cd, java.util.List<GenPolynomial<GenPolynomial<C>>> H)
Determine polynomial list.java.util.List<ColoredSystem<C>>
determine(java.util.List<GenPolynomial<GenPolynomial<C>>> H)
Determine polynomial list.boolean
isNormalform(java.util.List<ColorPolynomial<C>> Pp)
Is in Normalform.boolean
isNormalform(java.util.List<ColorPolynomial<C>> Pp, ColorPolynomial<C> Ap)
Is in Normalform.boolean
isReducible(java.util.List<ColorPolynomial<C>> Pp, ColorPolynomial<C> Ap)
Is reducible.boolean
isTopReducible(java.util.List<ColorPolynomial<C>> P, ColorPolynomial<C> A)
Is top reducible.ColorPolynomial<C>
normalform(Condition<C> cond, java.util.List<ColorPolynomial<C>> Pp, ColorPolynomial<C> Ap)
Normalform.ColorPolynomial<C>
SPolynomial(ColorPolynomial<C> Ap, ColorPolynomial<C> Bp)
S-Polynomial.
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Field Detail
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engine
protected final GreatestCommonDivisor<C extends GcdRingElem<C>> engine
Greatest common divisor engine.
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cofac
protected final RingFactory<C extends GcdRingElem<C>> cofac
Polynomial coefficient ring factory.
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top
protected boolean top
Flag if top-reduction only should be used.
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Constructor Detail
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CReductionSeq
public CReductionSeq(RingFactory<C> rf)
Constructor.- Parameters:
rf
- coefficient factory.
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Method Detail
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SPolynomial
public ColorPolynomial<C> SPolynomial(ColorPolynomial<C> Ap, ColorPolynomial<C> Bp)
S-Polynomial.- Parameters:
Ap
- polynomial.Bp
- polynomial.- Returns:
- spol(Ap,Bp) the S-polynomial of Ap and Bp.
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isTopReducible
public boolean isTopReducible(java.util.List<ColorPolynomial<C>> P, ColorPolynomial<C> A)
Is top reducible.- Parameters:
A
- polynomial.P
- polynomial list.- Returns:
- true if A is top reducible with respect to P.
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isReducible
public boolean isReducible(java.util.List<ColorPolynomial<C>> Pp, ColorPolynomial<C> Ap)
Is reducible.- Parameters:
Ap
- polynomial.Pp
- polynomial list.- Returns:
- true if Ap is reducible with respect to Pp.
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isNormalform
public boolean isNormalform(java.util.List<ColorPolynomial<C>> Pp, ColorPolynomial<C> Ap)
Is in Normalform.- Parameters:
Ap
- polynomial.Pp
- polynomial list.- Returns:
- true if Ap is in normalform with respect to Pp.
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isNormalform
public boolean isNormalform(java.util.List<ColorPolynomial<C>> Pp)
Is in Normalform.- Parameters:
Pp
- polynomial list.- Returns:
- true if each Ap in Pp is in normalform with respect to Pp\{Ap}.
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normalform
public ColorPolynomial<C> normalform(Condition<C> cond, java.util.List<ColorPolynomial<C>> Pp, ColorPolynomial<C> Ap)
Normalform.- Parameters:
Ap
- polynomial.Pp
- polynomial list.cond
- condition for these polynomials.- Returns:
- nf(Ap) with respect to Pp.
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caseDistinction
public java.util.List<Condition<C>> caseDistinction(java.util.List<GenPolynomial<GenPolynomial<C>>> L)
Case distinction conditions of parametric polynomial list. The returned condition determines the polynomial list.- Parameters:
L
- list of parametric polynomials.- Returns:
- list of conditions as case distinction.
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caseDistinction
public java.util.List<Condition<C>> caseDistinction(java.util.List<Condition<C>> cd, GenPolynomial<GenPolynomial<C>> A)
Case distinction conditions of parametric polynomial list.- Parameters:
cd
- a list of conditions.A
- a parametric polynomial.- Returns:
- list of conditions as case distinction extending the conditions in cd.
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caseDistinction
public java.util.List<Condition<C>> caseDistinction(Condition<C> cond, GenPolynomial<GenPolynomial<C>> A)
Case distinction conditions of parametric polynomial list.- Parameters:
A
- a parametric polynomial.cond
- a condition.- Returns:
- list of case distinction conditions.
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determine
public java.util.List<ColoredSystem<C>> determine(java.util.List<GenPolynomial<GenPolynomial<C>>> H)
Determine polynomial list.- Parameters:
H
- polynomial list.- Returns:
- new determined list of colored systems.
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determine
public java.util.List<ColoredSystem<C>> determine(java.util.List<Condition<C>> cd, java.util.List<GenPolynomial<GenPolynomial<C>>> H)
Determine polynomial list.- Parameters:
H
- polynomial list.cd
- case distinction, a condition list.- Returns:
- new determined list of colored systems.
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