Package edu.jas.gb
Class DReductionSeq<C extends RingElem<C>>
- java.lang.Object
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- edu.jas.gb.ReductionAbstract<C>
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- edu.jas.gb.DReductionSeq<C>
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- Type Parameters:
C
- coefficient type
- All Implemented Interfaces:
DReduction<C>
,Reduction<C>
,java.io.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.- Author:
- Heinz Kredel
- See Also:
- Serialized Form
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Constructor Summary
Constructors Constructor Description DReductionSeq()
Constructor.
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Method Summary
All Methods Instance Methods Concrete Methods Modifier and Type Method Description boolean
criterion4(GenPolynomial<C> A, GenPolynomial<C> B)
GB criterium 4.boolean
criterion4(GenPolynomial<C> A, GenPolynomial<C> B, ExpVector e)
GB criterium 4.GenPolynomial<C>
GPolynomial(GenPolynomial<C> Ap, GenPolynomial<C> Bp)
G-Polynomial.GenPolynomial<C>
GPolynomial(java.util.List<GenPolynomial<C>> row, int i, GenPolynomial<C> Ap, int j, GenPolynomial<C> Bp)
G-Polynomial with recording.java.util.List<GenPolynomial<C>>
irreducibleSet(java.util.List<GenPolynomial<C>> Pp)
Irreducible set.boolean
isNormalform(java.util.List<GenPolynomial<C>> Pp, GenPolynomial<C> Ap)
Is in Normalform.boolean
isTopReducible(java.util.List<GenPolynomial<C>> P, GenPolynomial<C> A)
Is top reducible.GenPolynomial<C>
normalform(java.util.List<GenPolynomial<C>> Pp, GenPolynomial<C> Ap)
Normalform using d-reduction.GenPolynomial<C>
normalform(java.util.List<GenPolynomial<C>> row, java.util.List<GenPolynomial<C>> Pp, GenPolynomial<C> Ap)
Normalform with recording.GenPolynomial<C>
SPolynomial(GenPolynomial<C> Ap, GenPolynomial<C> Bp)
S-Polynomial.GenPolynomial<C>
SPolynomial(java.util.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
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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, isNormalform, isReducible, isReductionNF, moduleCriterion, moduleCriterion, normalform
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Constructor Detail
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DReductionSeq
public DReductionSeq()
Constructor.
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Method Detail
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isTopReducible
public boolean isTopReducible(java.util.List<GenPolynomial<C>> P, GenPolynomial<C> A)
Is top reducible.- Specified by:
isTopReducible
in interfaceReduction<C extends RingElem<C>>
- Overrides:
isTopReducible
in classReductionAbstract<C extends RingElem<C>>
- Parameters:
A
- polynomial.P
- polynomial list.- Returns:
- true if A is top reducible with respect to P.
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isNormalform
public boolean isNormalform(java.util.List<GenPolynomial<C>> Pp, GenPolynomial<C> Ap)
Is in Normalform.- Specified by:
isNormalform
in interfaceReduction<C extends RingElem<C>>
- Overrides:
isNormalform
in classReductionAbstract<C extends RingElem<C>>
- Parameters:
Ap
- polynomial.Pp
- polynomial list.- Returns:
- true if Ap is in normalform with respect to Pp.
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normalform
public GenPolynomial<C> normalform(java.util.List<GenPolynomial<C>> Pp, GenPolynomial<C> Ap)
Normalform using d-reduction.- Specified by:
normalform
in interfaceReduction<C extends RingElem<C>>
- Parameters:
Ap
- polynomial.Pp
- polynomial list.- Returns:
- d-nf(Ap) with respect to Pp.
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SPolynomial
public GenPolynomial<C> SPolynomial(GenPolynomial<C> Ap, GenPolynomial<C> Bp)
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
public GenPolynomial<C> GPolynomial(GenPolynomial<C> Ap, GenPolynomial<C> Bp)
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(java.util.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(java.util.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
public boolean criterion4(GenPolynomial<C> A, GenPolynomial<C> B, ExpVector e)
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
public boolean criterion4(GenPolynomial<C> A, GenPolynomial<C> B)
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(java.util.List<GenPolynomial<C>> row, java.util.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
public java.util.List<GenPolynomial<C>> irreducibleSet(java.util.List<GenPolynomial<C>> Pp)
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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