Package edu.jas.gbufd
Class SolvableSyzygySeq<C extends GcdRingElem<C>>
java.lang.Object
edu.jas.gbufd.SolvableSyzygyAbstract<C>
edu.jas.gbufd.SolvableSyzygySeq<C>
- Type Parameters:
C
- coefficient type
- All Implemented Interfaces:
SolvableSyzygy<C>
,Serializable
Syzygy sequential class for solvable polynomials. Implements Syzygy
computations and tests with Groebner bases.
- See Also:
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Field Summary
FieldsModifier and TypeFieldDescriptionprivate static boolean
private static final boolean
private static final org.apache.logging.log4j.Logger
protected SolvableGroebnerBase
<C> Groebner basis engine.Fields inherited from class edu.jas.gbufd.SolvableSyzygyAbstract
blas, red, sred
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Constructor Summary
Constructors -
Method Summary
Modifier and TypeMethodDescriptionLeft Ore condition.Left simplifier.leftZeroRelationsArbitrary
(int modv, List<GenSolvablePolynomial<C>> F) Left syzygy module from arbitrary base.List
<SolvResPart<C>> resolution
(ModuleList<C> M) Resolution of a module.Resolution of a polynomial list.List
<SolvResPart<C>> Resolution of a module.Resolution of a polynomial list.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 Details
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logger
private static final org.apache.logging.log4j.Logger logger -
debug
private static final boolean debug -
assertEnabled
private static boolean assertEnabled -
sbb
Groebner basis engine.
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Constructor Details
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SolvableSyzygySeq
Constructor.- Parameters:
cf
- coefficient ring.
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Method Details
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resolution
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
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
Resolution of a module.- Parameters:
M
- a module list of an arbitrary basis.- Returns:
- a resolution of M.
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resolutionArbitrary
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 List<List<GenSolvablePolynomial<C>>> leftZeroRelationsArbitrary(int modv, 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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