Package edu.jas.gb
Class WordGroebnerBaseAbstract<C extends RingElem<C>>
- java.lang.Object
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- edu.jas.gb.WordGroebnerBaseAbstract<C>
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- Type Parameters:
C
- coefficient type
- All Implemented Interfaces:
WordGroebnerBase<C>
,java.io.Serializable
- Direct Known Subclasses:
WordGroebnerBasePseudoRecSeq
,WordGroebnerBasePseudoSeq
,WordGroebnerBaseSeq
public abstract class WordGroebnerBaseAbstract<C extends RingElem<C>> extends java.lang.Object implements WordGroebnerBase<C>
Non-commutative Groebner Bases abstract class. Implements common Groebner bases and GB test methods.- Author:
- Heinz Kredel
- See Also:
- Serialized Form
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Field Summary
Fields Modifier and Type Field Description WordReduction<C>
red
Reduction engine.WordPairList<C>
strategy
Strategy for pair selection.
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Constructor Summary
Constructors Constructor Description WordGroebnerBaseAbstract()
Constructor.WordGroebnerBaseAbstract(WordReduction<C> red)
Constructor.WordGroebnerBaseAbstract(WordReduction<C> red, WordPairList<C> pl)
Constructor.
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Method Summary
All Methods Instance Methods Abstract Methods Concrete Methods Modifier and Type Method Description int
cancel()
Cancel ThreadPool.int
commonZeroTest(java.util.List<GenWordPolynomial<C>> F)
Common zero test, test if univariate leading words exist for all variables.abstract java.util.List<GenWordPolynomial<C>>
GB(java.util.List<GenWordPolynomial<C>> F)
Groebner base using pairlist class.boolean
isGB(java.util.List<GenWordPolynomial<C>> F)
Word Groebner base test.boolean
isMinimalGB(java.util.List<GenWordPolynomial<C>> Gp)
Test for minimal ordered Groebner basis.java.util.List<GenWordPolynomial<C>>
minimalGB(java.util.List<GenWordPolynomial<C>> Gp)
Minimal ordered Groebner basis.java.util.List<GenWordPolynomial<C>>
normalizeZerosOnes(java.util.List<GenWordPolynomial<C>> A)
Normalize polynomial list.void
terminate()
Cleanup and terminate ThreadPool.java.lang.String
toString()
Get the String representation with GB engines.java.util.List<java.lang.Long>
univariateDegrees(java.util.List<GenWordPolynomial<C>> A)
Univariate head term degrees.
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Field Detail
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red
public final WordReduction<C extends RingElem<C>> red
Reduction engine.
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strategy
public final WordPairList<C extends RingElem<C>> strategy
Strategy for pair selection.
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Constructor Detail
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WordGroebnerBaseAbstract
public WordGroebnerBaseAbstract()
Constructor.
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WordGroebnerBaseAbstract
public WordGroebnerBaseAbstract(WordReduction<C> red)
Constructor.- Parameters:
red
- Word Reduction engine
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WordGroebnerBaseAbstract
public WordGroebnerBaseAbstract(WordReduction<C> red, WordPairList<C> pl)
Constructor.- Parameters:
red
- Word Reduction enginepl
- Word pair selection strategy
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Method Detail
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toString
public java.lang.String toString()
Get the String representation with GB engines.- Overrides:
toString
in classjava.lang.Object
- See Also:
Object.toString()
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normalizeZerosOnes
public java.util.List<GenWordPolynomial<C>> normalizeZerosOnes(java.util.List<GenWordPolynomial<C>> A)
Normalize polynomial list.- Parameters:
A
- list of polynomials.- Returns:
- list of polynomials with zeros removed and ones/units reduced.
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commonZeroTest
public int commonZeroTest(java.util.List<GenWordPolynomial<C>> F)
Common zero test, test if univariate leading words exist for all variables.- Parameters:
F
- polynomial list.- Returns:
- -1, 0 or 1 if "dimension"(ideal(F)) &eq; -1, 0 or ≥ 1.
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univariateDegrees
public java.util.List<java.lang.Long> univariateDegrees(java.util.List<GenWordPolynomial<C>> A)
Univariate head term degrees.- Parameters:
A
- list of polynomials.- Returns:
- a list of the degrees of univariate head terms.
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isGB
public boolean isGB(java.util.List<GenWordPolynomial<C>> F)
Word Groebner base test.- Specified by:
isGB
in interfaceWordGroebnerBase<C extends RingElem<C>>
- Parameters:
F
- Word polynomial list.- Returns:
- true, if F is a Groebner base, else false.
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GB
public abstract java.util.List<GenWordPolynomial<C>> GB(java.util.List<GenWordPolynomial<C>> F)
Groebner base using pairlist class.- Specified by:
GB
in interfaceWordGroebnerBase<C extends RingElem<C>>
- Parameters:
F
- polynomial list.- Returns:
- GB(F) a Groebner base of F.
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minimalGB
public java.util.List<GenWordPolynomial<C>> minimalGB(java.util.List<GenWordPolynomial<C>> Gp)
Minimal ordered Groebner basis.- Specified by:
minimalGB
in interfaceWordGroebnerBase<C extends RingElem<C>>
- Parameters:
Gp
- a Groebner base.- Returns:
- a reduced Groebner base of Gp.
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isMinimalGB
public boolean isMinimalGB(java.util.List<GenWordPolynomial<C>> Gp)
Test for minimal ordered Groebner basis.- Parameters:
Gp
- an ideal base.- Returns:
- true, if Gp is a reduced minimal Groebner base.
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terminate
public void terminate()
Cleanup and terminate ThreadPool.
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cancel
public int cancel()
Cancel ThreadPool.
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