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.- Author:
- Heinz Kredel
- See Also:
- Serialized Form
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Field Summary
Fields Modifier and Type Field Description protected DReduction<C>
dred
Reduction engine.-
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, 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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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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