Package edu.jas.gb
Class DGroebnerBaseSeq<C extends RingElem<C>>
- java.lang.Object
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- edu.jas.gb.GroebnerBaseAbstract<C>
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- edu.jas.gb.DGroebnerBaseSeq<C>
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- Type Parameters:
C
- coefficient type
- All Implemented Interfaces:
GroebnerBase<C>
,java.io.Serializable
- Direct Known Subclasses:
EGroebnerBaseSeq
public class DGroebnerBaseSeq<C extends RingElem<C>> extends GroebnerBaseAbstract<C>
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:
- Serialized Form
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Field Summary
Fields Modifier and Type Field Description private static boolean
debug
protected DReduction<C>
dred
Reduction engine.private static org.apache.logging.log4j.Logger
logger
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Fields inherited from class edu.jas.gb.GroebnerBaseAbstract
blas, red, strategy
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Constructor Summary
Constructors Constructor Description DGroebnerBaseSeq()
Constructor.DGroebnerBaseSeq(DReduction<C> dred)
Constructor.
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Method Summary
All Methods Instance Methods Concrete Methods Modifier and Type Method Description ExtendedGB<C>
extGB(int modv, java.util.List<GenPolynomial<C>> F)
Extended Groebner base using pairlist class.java.util.List<GenPolynomial<C>>
GB(int modv, java.util.List<GenPolynomial<C>> F)
D-Groebner base using pairlist class.GenPolynomial<C>
inverse(GenPolynomial<C> h, java.util.List<GenPolynomial<C>> F)
Inverse for element modulo ideal.boolean
isGB(int modv, java.util.List<GenPolynomial<C>> F)
D-Groebner base test.ExtendedGB<C>
minimalExtendedGB(int flen, java.util.List<GenPolynomial<C>> Gp, java.util.List<java.util.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 Detail
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logger
private static final org.apache.logging.log4j.Logger logger
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debug
private static final boolean debug
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dred
protected DReduction<C extends RingElem<C>> dred
Reduction engine.
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Constructor Detail
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DGroebnerBaseSeq
public DGroebnerBaseSeq()
Constructor.
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DGroebnerBaseSeq
public DGroebnerBaseSeq(DReduction<C> dred)
Constructor.- Parameters:
dred
- D-Reduction engine
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Method Detail
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isGB
public boolean isGB(int modv, java.util.List<GenPolynomial<C>> F)
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
public java.util.List<GenPolynomial<C>> GB(int modv, java.util.List<GenPolynomial<C>> F)
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
public ExtendedGB<C> extGB(int modv, java.util.List<GenPolynomial<C>> F)
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, java.util.List<GenPolynomial<C>> Gp, java.util.List<java.util.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
public GenPolynomial<C> inverse(GenPolynomial<C> h, java.util.List<GenPolynomial<C>> F)
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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