Package edu.jas.gb
Class GroebnerBaseSigSeqIter<C extends RingElem<C>>
- java.lang.Object
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- edu.jas.gb.GroebnerBaseAbstract<C>
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- edu.jas.gb.GroebnerBaseSigSeqIter<C>
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- Type Parameters:
C
- coefficient type
- All Implemented Interfaces:
GroebnerBase<C>
,java.io.Serializable
- Direct Known Subclasses:
GroebnerBaseArriSigSeqIter
,GroebnerBaseF5zSigSeqIter
,GroebnerBaseGGVSigSeqIter
public class GroebnerBaseSigSeqIter<C extends RingElem<C>> extends GroebnerBaseAbstract<C>
Groebner Base signature based sequential iterative algorithm. Implements Groebner bases after the paper "Signature-based Algorithms to Compute Gröbner Bases" by Christian Eder and John Perry, ISSAC 2011. Compare the jython+JAS code in examples/basic_sigbased_gb.py. Originally the Python+Sage code is from http://www.math.usm.edu/perry/Research/basic_sigbased_gb.py- Author:
- Heinz Kredel
- See Also:
GBAlgorithmBuilder
,GBFactory
,GroebnerBaseGGVSigSeqIter
,GroebnerBaseArriSigSeqIter
,GroebnerBaseF5zSigSeqIter
, Serialized Form
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Field Summary
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Fields inherited from class edu.jas.gb.GroebnerBaseAbstract
blas, red, strategy
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Constructor Summary
Constructors Constructor Description GroebnerBaseSigSeqIter()
Constructor.GroebnerBaseSigSeqIter(SigReductionSeq<C> red)
Constructor.
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Method Summary
All Methods Instance Methods Concrete Methods Modifier and Type Method Description java.util.List<GenPolynomial<C>>
GB(int modv, java.util.List<GenPolynomial<C>> F)
Groebner base signature iterative algorithm.java.util.List<GenPolynomial<C>>
GB(int modv, java.util.List<GenPolynomial<C>> G, GenPolynomial<C> f)
Groebner base iterated.-
Methods inherited from class edu.jas.gb.GroebnerBaseAbstract
cancel, commonZeroTest, constructUnivariate, extGB, extGB, GB, GB, GB, isGB, isGB, isGB, isGB, isGB, isGB, isGBidem, isGBsimple, isMinimalGB, isMinReductionMatrix, isMinReductionMatrix, isReductionMatrix, isReductionMatrix, minimalExtendedGB, minimalGB, normalizeMatrix, normalizeZerosOnes, terminate, toString, univariateDegrees
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Constructor Detail
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GroebnerBaseSigSeqIter
public GroebnerBaseSigSeqIter()
Constructor.
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GroebnerBaseSigSeqIter
public GroebnerBaseSigSeqIter(SigReductionSeq<C> red)
Constructor.- Parameters:
red
- Reduction engine
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Method Detail
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GB
public java.util.List<GenPolynomial<C>> GB(int modv, java.util.List<GenPolynomial<C>> F)
Groebner base signature iterative algorithm.- Parameters:
modv
- module variable number.F
- polynomial list.- Returns:
- GB(F) a Groebner base of F.
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GB
public java.util.List<GenPolynomial<C>> GB(int modv, java.util.List<GenPolynomial<C>> G, GenPolynomial<C> f)
Groebner base iterated.- Parameters:
modv
- module variable number.G
- polynomial list of a Groebner base.f
- polynomial.- Returns:
- GB(G,f) a Groebner base of G+(f).
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