Package edu.jas.gb
Class DReductionSeq<C extends RingElem<C>>
java.lang.Object
edu.jas.gb.ReductionAbstract<C>
edu.jas.gb.DReductionSeq<C>
- Type Parameters:
C
- coefficient type
- All Implemented Interfaces:
DReduction<C>
,Reduction<C>
,Serializable
- Direct Known Subclasses:
EReductionSeq
public class DReductionSeq<C extends RingElem<C>>
extends ReductionAbstract<C>
implements DReduction<C>
Polynomial D-Reduction sequential use algorithm. Implements normalform.
- See Also:
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Field Summary
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Constructor Summary
Constructors -
Method Summary
Modifier and TypeMethodDescriptionboolean
criterion4
(GenPolynomial<C> A, GenPolynomial<C> B) GB criterium 4.boolean
criterion4
(GenPolynomial<C> A, GenPolynomial<C> B, ExpVector e) GB criterium 4.GPolynomial
(GenPolynomial<C> Ap, GenPolynomial<C> Bp) G-Polynomial.GPolynomial
(List<GenPolynomial<C>> row, int i, GenPolynomial<C> Ap, int j, GenPolynomial<C> Bp) G-Polynomial with recording.irreducibleSet
(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 d-reduction.normalform
(List<GenPolynomial<C>> row, List<GenPolynomial<C>> Pp, GenPolynomial<C> Ap) Normalform with recording.SPolynomial
(GenPolynomial<C> Ap, GenPolynomial<C> Bp) S-Polynomial.SPolynomial
(List<GenPolynomial<C>> row, int i, GenPolynomial<C> Ap, int j, GenPolynomial<C> Bp) S-Polynomial with recording.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.Reduction
criterion4, isNormalform, isReducible, isReductionNF, moduleCriterion, moduleCriterion, normalform
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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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DReductionSeq
public DReductionSeq()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 classReductionAbstract<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 classReductionAbstract<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 d-reduction.- Specified by:
normalform
in interfaceReduction<C extends RingElem<C>>
- Parameters:
Pp
- polynomial list.Ap
- polynomial.- Returns:
- d-nf(Ap) with respect to Pp.
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SPolynomial
S-Polynomial.- Specified by:
SPolynomial
in interfaceReduction<C extends RingElem<C>>
- Overrides:
SPolynomial
in classReductionAbstract<C extends RingElem<C>>
- Parameters:
Ap
- polynomial.Bp
- polynomial.- Returns:
- spol(Ap,Bp) the S-polynomial of Ap and Bp.
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GPolynomial
G-Polynomial.- Specified by:
GPolynomial
in interfaceDReduction<C extends RingElem<C>>
- Parameters:
Ap
- polynomial.Bp
- polynomial.- Returns:
- gpol(Ap,Bp) the g-polynomial of Ap and Bp.
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SPolynomial
public GenPolynomial<C> SPolynomial(List<GenPolynomial<C>> row, int i, GenPolynomial<C> Ap, int j, GenPolynomial<C> Bp) S-Polynomial with recording.- Specified by:
SPolynomial
in interfaceReduction<C extends RingElem<C>>
- Overrides:
SPolynomial
in classReductionAbstract<C extends RingElem<C>>
- Parameters:
row
- recording vector, is modified.i
- index of Ap in basis list.Ap
- a polynomial.j
- index of Bp in basis list.Bp
- a polynomial.- Returns:
- spol(Ap, Bp), the s-Polynomial for Ap and Bp.
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GPolynomial
public GenPolynomial<C> GPolynomial(List<GenPolynomial<C>> row, int i, GenPolynomial<C> Ap, int j, GenPolynomial<C> Bp) G-Polynomial with recording.- Specified by:
GPolynomial
in interfaceDReduction<C extends RingElem<C>>
- Parameters:
row
- recording matrix, is modified.i
- index of Ap in basis list.Ap
- a polynomial.j
- index of Bp in basis list.Bp
- a polynomial.- Returns:
- gpol(Ap, Bp), the g-Polynomial for Ap and Bp.
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criterion4
GB criterium 4. Use only for commutative polynomial rings. This version works also for d-Groebner bases.- Specified by:
criterion4
in interfaceReduction<C extends RingElem<C>>
- Overrides:
criterion4
in classReductionAbstract<C extends RingElem<C>>
- Parameters:
A
- polynomial.B
- polynomial.e
- = lcm(ht(A),ht(B))- Returns:
- true if the S-polynomial(i,j) is required, else false.
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criterion4
GB criterium 4. Use only for commutative polynomial rings. This version works also for d-Groebner bases.- Specified by:
criterion4
in interfaceReduction<C extends RingElem<C>>
- Overrides:
criterion4
in classReductionAbstract<C extends RingElem<C>>
- Parameters:
A
- polynomial.B
- polynomial.- Returns:
- true if the S-polynomial(i,j) is required, else false.
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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>>
- 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 classReductionAbstract<C extends RingElem<C>>
- Parameters:
Pp
- polynomial list.- Returns:
- a list P of polynomials which are in normalform wrt. P.
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