Package edu.jas.gb
Class DGroebnerBaseSeq<C extends RingElem<C>>
java.lang.Object
edu.jas.gb.GroebnerBaseAbstract<C>
edu.jas.gb.DGroebnerBaseSeq<C>
- Type Parameters:
C
- coefficient type
- All Implemented Interfaces:
GroebnerBase<C>
,Serializable
- Direct Known Subclasses:
EGroebnerBaseSeq
D-Groebner Base sequential algorithm. Implements D-Groebner bases and GB
test. Note: Minimal reduced GBs are not unique. see BWK, section 10.1.
- See Also:
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Field Summary
FieldsModifier and TypeFieldDescriptionprivate static final boolean
protected DReduction
<C> Reduction engine.private static final org.apache.logging.log4j.Logger
Fields inherited from class edu.jas.gb.GroebnerBaseAbstract
blas, red, strategy
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Constructor Summary
Constructors -
Method Summary
Modifier and TypeMethodDescriptionextGB
(int modv, List<GenPolynomial<C>> F) Extended Groebner base using pairlist class.GB
(int modv, List<GenPolynomial<C>> F) D-Groebner base using pairlist class.inverse
(GenPolynomial<C> h, List<GenPolynomial<C>> F) Inverse for element modulo ideal.boolean
isGB
(int modv, List<GenPolynomial<C>> F) D-Groebner base test.minimalExtendedGB
(int flen, List<GenPolynomial<C>> Gp, List<List<GenPolynomial<C>>> M) Minimal extended groebner basis.Methods inherited from class edu.jas.gb.GroebnerBaseAbstract
cancel, commonZeroTest, constructUnivariate, criterion3, extGB, GB, GB, GB, isGB, isGB, isGB, isGB, isGB, isGBidem, isGBsimple, isMinimalGB, isMinReductionMatrix, isMinReductionMatrix, isReductionMatrix, isReductionMatrix, minimalGB, normalizeMatrix, normalizeZerosOnes, terminate, toString, univariateDegrees
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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 -
dred
Reduction engine.
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Constructor Details
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DGroebnerBaseSeq
public DGroebnerBaseSeq()Constructor. -
DGroebnerBaseSeq
Constructor.- Parameters:
dred
- D-Reduction engine
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Method Details
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isGB
D-Groebner base test.- Specified by:
isGB
in interfaceGroebnerBase<C extends RingElem<C>>
- Overrides:
isGB
in classGroebnerBaseAbstract<C extends RingElem<C>>
- Parameters:
modv
- module variable number.F
- polynomial list.- Returns:
- true, if F is a D-Groebner base, else false.
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GB
D-Groebner base using pairlist class.- Parameters:
modv
- module variable number.F
- polynomial list.- Returns:
- GB(F) a D-Groebner base of F.
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extGB
Extended Groebner base using pairlist class.- Specified by:
extGB
in interfaceGroebnerBase<C extends RingElem<C>>
- Overrides:
extGB
in classGroebnerBaseAbstract<C extends RingElem<C>>
- Parameters:
modv
- module variable number.F
- polynomial list.- Returns:
- a container for an extended Groebner base of F.
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minimalExtendedGB
public ExtendedGB<C> minimalExtendedGB(int flen, List<GenPolynomial<C>> Gp, List<List<GenPolynomial<C>>> M) Minimal extended groebner basis.- Overrides:
minimalExtendedGB
in classGroebnerBaseAbstract<C extends RingElem<C>>
- Parameters:
flen
- length of rows.Gp
- a Groebner base.M
- a reduction matrix.- Returns:
- a (partially) reduced Groebner base of Gp in a (fake) container.
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inverse
Inverse for element modulo ideal.- Parameters:
h
- polynomialF
- polynomial list- Returns:
- inverse of h with respect to ideal(F), if defined
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