Package edu.jas.gbufd
Class WordGroebnerBasePseudoRecSeq<C extends GcdRingElem<C>>
- java.lang.Object
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- edu.jas.gb.WordGroebnerBaseAbstract<GenPolynomial<C>>
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- edu.jas.gbufd.WordGroebnerBasePseudoRecSeq<C>
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- Type Parameters:
C
- coefficient type
- All Implemented Interfaces:
WordGroebnerBase<GenPolynomial<C>>
,java.io.Serializable
public class WordGroebnerBasePseudoRecSeq<C extends GcdRingElem<C>> extends WordGroebnerBaseAbstract<GenPolynomial<C>>
Non-commutative word Groebner Base sequential algorithm. Implements Groebner bases and GB test. Coefficients can for example be (commutative) multivariate polynomials.- Author:
- Heinz Kredel
- See Also:
- Serialized Form
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Field Summary
Fields Modifier and Type Field Description protected GenPolynomialRing<C>
cofac
Coefficient ring factory.protected GreatestCommonDivisorAbstract<C>
engine
Greatest common divisor engine for coefficient content and primitive parts.protected WordPseudoReduction<GenPolynomial<C>>
red
Reduction engine.protected WordPseudoReduction<C>
redRec
Reduction engine.-
Fields inherited from class edu.jas.gb.WordGroebnerBaseAbstract
strategy
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Constructor Summary
Constructors Constructor Description WordGroebnerBasePseudoRecSeq(RingFactory<GenPolynomial<C>> rf)
Constructor.WordGroebnerBasePseudoRecSeq(RingFactory<GenPolynomial<C>> rf, WordPseudoReductionSeq<GenPolynomial<C>> red)
Constructor.WordGroebnerBasePseudoRecSeq(RingFactory<GenPolynomial<C>> rf, WordPseudoReductionSeq<GenPolynomial<C>> red, WordPairList<GenPolynomial<C>> pl)
Constructor.
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Method Summary
All Methods Instance Methods Concrete Methods Modifier and Type Method Description java.util.List<GenWordPolynomial<GenPolynomial<C>>>
GB(java.util.List<GenWordPolynomial<GenPolynomial<C>>> F)
Word Groebner base using word pairlist class.boolean
isGB(java.util.List<GenWordPolynomial<GenPolynomial<C>>> F)
Wird Groebner base simple test.java.util.List<GenWordPolynomial<GenPolynomial<C>>>
minimalGB(java.util.List<GenWordPolynomial<GenPolynomial<C>>> Gp)
Minimal ordered Groebner basis.GenPolynomial<C>
recursiveContent(GenWordPolynomial<GenPolynomial<C>> P)
GenWordPolynomial recursive coefficient content.GenWordPolynomial<GenPolynomial<C>>
recursivePrimitivePart(GenWordPolynomial<GenPolynomial<C>> P)
GenWordPolynomial recursive coefficient primitive part.java.util.List<GenWordPolynomial<GenPolynomial<C>>>
recursivePrimitivePart(java.util.List<GenWordPolynomial<GenPolynomial<C>>> F)
List of GenWordPolynomial recursive coefficient primitive part.-
Methods inherited from class edu.jas.gb.WordGroebnerBaseAbstract
cancel, commonZeroTest, isMinimalGB, normalizeZerosOnes, terminate, toString, univariateDegrees
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Field Detail
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engine
protected final GreatestCommonDivisorAbstract<C extends GcdRingElem<C>> engine
Greatest common divisor engine for coefficient content and primitive parts.
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redRec
protected final WordPseudoReduction<C extends GcdRingElem<C>> redRec
Reduction engine.
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red
protected final WordPseudoReduction<GenPolynomial<C extends GcdRingElem<C>>> red
Reduction engine.
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cofac
protected final GenPolynomialRing<C extends GcdRingElem<C>> cofac
Coefficient ring factory.
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Constructor Detail
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WordGroebnerBasePseudoRecSeq
public WordGroebnerBasePseudoRecSeq(RingFactory<GenPolynomial<C>> rf)
Constructor.- Parameters:
rf
- coefficient ring factory.
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WordGroebnerBasePseudoRecSeq
public WordGroebnerBasePseudoRecSeq(RingFactory<GenPolynomial<C>> rf, WordPseudoReductionSeq<GenPolynomial<C>> red)
Constructor.- Parameters:
rf
- coefficient ring factory.red
- Reduction engine
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WordGroebnerBasePseudoRecSeq
public WordGroebnerBasePseudoRecSeq(RingFactory<GenPolynomial<C>> rf, WordPseudoReductionSeq<GenPolynomial<C>> red, WordPairList<GenPolynomial<C>> pl)
Constructor.- Parameters:
rf
- coefficient ring factory.red
- Reduction enginepl
- pair selection strategy
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Method Detail
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GB
public java.util.List<GenWordPolynomial<GenPolynomial<C>>> GB(java.util.List<GenWordPolynomial<GenPolynomial<C>>> F)
Word Groebner base using word pairlist class.- Specified by:
GB
in interfaceWordGroebnerBase<C extends GcdRingElem<C>>
- Specified by:
GB
in classWordGroebnerBaseAbstract<GenPolynomial<C extends GcdRingElem<C>>>
- Parameters:
F
- word polynomial list.- Returns:
- GB(F) a finite non-commutative Groebner base of F, if it exists.
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minimalGB
public java.util.List<GenWordPolynomial<GenPolynomial<C>>> minimalGB(java.util.List<GenWordPolynomial<GenPolynomial<C>>> Gp)
Minimal ordered Groebner basis.- Specified by:
minimalGB
in interfaceWordGroebnerBase<C extends GcdRingElem<C>>
- Overrides:
minimalGB
in classWordGroebnerBaseAbstract<GenPolynomial<C extends GcdRingElem<C>>>
- Parameters:
Gp
- a Groebner base.- Returns:
- a reduced Groebner base of Gp.
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isGB
public boolean isGB(java.util.List<GenWordPolynomial<GenPolynomial<C>>> F)
Wird Groebner base simple test.- Specified by:
isGB
in interfaceWordGroebnerBase<C extends GcdRingElem<C>>
- Overrides:
isGB
in classWordGroebnerBaseAbstract<GenPolynomial<C extends GcdRingElem<C>>>
- Parameters:
F
- recursive polynomial list.- Returns:
- true, if F is a Groebner base, else false.
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recursiveContent
public GenPolynomial<C> recursiveContent(GenWordPolynomial<GenPolynomial<C>> P)
GenWordPolynomial recursive coefficient content.- Parameters:
P
- recursive GenWordPolynomial.- Returns:
- cont(P).
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recursivePrimitivePart
public GenWordPolynomial<GenPolynomial<C>> recursivePrimitivePart(GenWordPolynomial<GenPolynomial<C>> P)
GenWordPolynomial recursive coefficient primitive part.- Parameters:
P
- recursive GenWordPolynomial.- Returns:
- pp(P).
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recursivePrimitivePart
public java.util.List<GenWordPolynomial<GenPolynomial<C>>> recursivePrimitivePart(java.util.List<GenWordPolynomial<GenPolynomial<C>>> F)
List of GenWordPolynomial recursive coefficient primitive part.- Parameters:
F
- list of recursive GenWordPolynomials.- Returns:
- pp(F).
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