Package edu.jas.gbufd
Class WordGroebnerBasePseudoRecSeq<C extends GcdRingElem<C>>
- Type Parameters:
C
- coefficient type
- All Implemented Interfaces:
WordGroebnerBase<GenPolynomial<C>>
,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.
- See Also:
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Field Summary
FieldsModifier and TypeFieldDescriptionprotected final GenPolynomialRing
<C> Coefficient ring factory.private static final boolean
protected final GreatestCommonDivisorAbstract
<C> Greatest common divisor engine for coefficient content and primitive parts.private static final org.apache.logging.log4j.Logger
protected final WordPseudoReduction
<GenPolynomial<C>> Reduction engine.protected final WordPseudoReduction
<C> Reduction engine.Fields inherited from class edu.jas.gb.WordGroebnerBaseAbstract
strategy
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Constructor Summary
ConstructorsConstructorDescriptionConstructor.WordGroebnerBasePseudoRecSeq
(RingFactory<GenPolynomial<C>> rf, WordPseudoReductionSeq<GenPolynomial<C>> red) Constructor.WordGroebnerBasePseudoRecSeq
(RingFactory<GenPolynomial<C>> rf, WordPseudoReductionSeq<GenPolynomial<C>> red, WordPairList<GenPolynomial<C>> pl) Constructor. -
Method Summary
Modifier and TypeMethodDescriptionGB
(List<GenWordPolynomial<GenPolynomial<C>>> F) Word Groebner base using word pairlist class.boolean
isGB
(List<GenWordPolynomial<GenPolynomial<C>>> F) Wird Groebner base simple test.minimalGB
(List<GenWordPolynomial<GenPolynomial<C>>> Gp) Minimal ordered Groebner basis.GenWordPolynomial recursive coefficient content.GenWordPolynomial recursive coefficient primitive part.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 Details
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logger
private static final org.apache.logging.log4j.Logger logger -
debug
private static final boolean debug -
engine
Greatest common divisor engine for coefficient content and primitive parts. -
redRec
Reduction engine. -
red
Reduction engine. -
cofac
Coefficient ring factory.
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Constructor Details
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WordGroebnerBasePseudoRecSeq
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 Details
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GB
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 List<GenWordPolynomial<GenPolynomial<C>>> minimalGB(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
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
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 List<GenWordPolynomial<GenPolynomial<C>>> recursivePrimitivePart(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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