Package edu.jas.gbufd
Class SolvableSyzygySeq<C extends GcdRingElem<C>>
- java.lang.Object
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- edu.jas.gbufd.SolvableSyzygyAbstract<C>
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- edu.jas.gbufd.SolvableSyzygySeq<C>
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- Type Parameters:
C
- coefficient type
- All Implemented Interfaces:
SolvableSyzygy<C>
,java.io.Serializable
public class SolvableSyzygySeq<C extends GcdRingElem<C>> extends SolvableSyzygyAbstract<C>
Syzygy sequential class for solvable polynomials. Implements Syzygy computations and tests with Groebner bases.- Author:
- Heinz Kredel
- See Also:
- Serialized Form
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Field Summary
Fields Modifier and Type Field Description protected SolvableGroebnerBase<C>
sbb
Groebner basis engine.-
Fields inherited from class edu.jas.gbufd.SolvableSyzygyAbstract
blas, red, sred
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Constructor Summary
Constructors Constructor Description SolvableSyzygySeq(RingFactory<C> cf)
Constructor.
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Method Summary
All Methods Instance Methods Concrete Methods Modifier and Type Method Description GenSolvablePolynomial<C>[]
leftOreCond(GenSolvablePolynomial<C> a, GenSolvablePolynomial<C> b)
Left Ore condition.GenSolvablePolynomial<C>[]
leftSimplifier(GenSolvablePolynomial<C> a, GenSolvablePolynomial<C> b)
Left simplifier.java.util.List<java.util.List<GenSolvablePolynomial<C>>>
leftZeroRelationsArbitrary(int modv, java.util.List<GenSolvablePolynomial<C>> F)
Left syzygy module from arbitrary base.java.util.List<edu.jas.gbufd.SolvResPart<C>>
resolution(ModuleList<C> M)
Resolution of a module.java.util.List
resolution(PolynomialList<C> F)
Resolution of a polynomial list.java.util.List<edu.jas.gbufd.SolvResPart<C>>
resolutionArbitrary(ModuleList<C> M)
Resolution of a module.java.util.List
resolutionArbitrary(PolynomialList<C> F)
Resolution of a polynomial list.GenSolvablePolynomial<C>[]
rightOreCond(GenSolvablePolynomial<C> a, GenSolvablePolynomial<C> b)
Right Ore condition.-
Methods inherited from class edu.jas.gbufd.SolvableSyzygyAbstract
compare, isLeftOreCond, isLeftOreCond, isLeftZeroRelation, isLeftZeroRelation, isRightOreCond, isRightOreCond, isRightZeroRelation, isRightZeroRelation, leftZeroRelations, leftZeroRelations, leftZeroRelations, leftZeroRelationsArbitrary, leftZeroRelationsArbitrary, rightZeroRelations, rightZeroRelations, rightZeroRelations, rightZeroRelationsArbitrary, rightZeroRelationsArbitrary, rightZeroRelationsArbitrary
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Field Detail
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sbb
protected SolvableGroebnerBase<C extends GcdRingElem<C>> sbb
Groebner basis engine.
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Constructor Detail
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SolvableSyzygySeq
public SolvableSyzygySeq(RingFactory<C> cf)
Constructor.- Parameters:
cf
- coefficient ring.
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Method Detail
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resolution
public java.util.List<edu.jas.gbufd.SolvResPart<C>> resolution(ModuleList<C> M)
Resolution of a module. Only with direct GBs.- Parameters:
M
- a module list of a Groebner basis.- Returns:
- a resolution of M.
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resolution
public java.util.List resolution(PolynomialList<C> F)
Resolution of a polynomial list. Only with direct GBs.- Parameters:
F
- a polynomial list of a Groebner basis.- Returns:
- a resolution of F.
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resolutionArbitrary
public java.util.List<edu.jas.gbufd.SolvResPart<C>> resolutionArbitrary(ModuleList<C> M)
Resolution of a module.- Parameters:
M
- a module list of an arbitrary basis.- Returns:
- a resolution of M.
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resolutionArbitrary
public java.util.List resolutionArbitrary(PolynomialList<C> F)
Resolution of a polynomial list.- Parameters:
F
- a polynomial list of an arbitrary basis.- Returns:
- a resolution of F.
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leftZeroRelationsArbitrary
public java.util.List<java.util.List<GenSolvablePolynomial<C>>> leftZeroRelationsArbitrary(int modv, java.util.List<GenSolvablePolynomial<C>> F)
Left syzygy module from arbitrary base.- Parameters:
modv
- number of module variables.F
- a solvable polynomial list.- Returns:
- syz(F), a basis for the module of left syzygies for F.
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leftOreCond
public GenSolvablePolynomial<C>[] leftOreCond(GenSolvablePolynomial<C> a, GenSolvablePolynomial<C> b)
Left Ore condition. Generators for the left Ore condition of two solvable polynomials.- Parameters:
a
- solvable polynomialb
- solvable polynomial- Returns:
- [p,q] with p*a = q*b
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rightOreCond
public GenSolvablePolynomial<C>[] rightOreCond(GenSolvablePolynomial<C> a, GenSolvablePolynomial<C> b)
Right Ore condition. Generators for the right Ore condition of two solvable polynomials.- Parameters:
a
- solvable polynomialb
- solvable polynomial- Returns:
- [p,q] with a*p = b*q
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leftSimplifier
public GenSolvablePolynomial<C>[] leftSimplifier(GenSolvablePolynomial<C> a, GenSolvablePolynomial<C> b)
Left simplifier. Method of Apel & Lassner (1987).- Specified by:
leftSimplifier
in classSolvableSyzygyAbstract<C extends GcdRingElem<C>>
- Parameters:
a
- solvable polynomialb
- solvable polynomial- Returns:
- [p,q] with a/b = p/q and q is minimal and monic
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