Package edu.jas.gb
Interface GroebnerBase<C extends RingElem<C>>
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- Type Parameters:
C
- coefficient type
- All Superinterfaces:
java.io.Serializable
- All Known Implementing Classes:
DGroebnerBaseSeq
,EGroebnerBaseSeq
,GBOptimized
,GBProxy
,GroebnerBaseAbstract
,GroebnerBaseArriSigSeqIter
,GroebnerBaseDistributedEC
,GroebnerBaseDistributedHybridEC
,GroebnerBaseF5zSigSeqIter
,GroebnerBaseFGLM
,GroebnerBaseGGVSigSeqIter
,GroebnerBaseParallel
,GroebnerBaseParIter
,GroebnerBasePartial
,GroebnerBasePseudoParallel
,GroebnerBasePseudoRecParallel
,GroebnerBasePseudoRecSeq
,GroebnerBasePseudoSeq
,GroebnerBaseQuotient
,GroebnerBaseRational
,GroebnerBaseSeq
,GroebnerBaseSeqIter
,GroebnerBaseSeqPairDistributed
,GroebnerBaseSeqPairParallel
,GroebnerBaseSeqPairSeq
,GroebnerBaseSigSeqIter
,GroebnerBaseWalk
,RGroebnerBasePseudoSeq
,RGroebnerBaseSeq
public interface GroebnerBase<C extends RingElem<C>> extends java.io.Serializable
Groebner Bases interface. Defines methods for Groebner bases and GB test.- Author:
- Heinz Kredel
- See Also:
GBAlgorithmBuilder
,GBFactory
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Method Summary
All Methods Instance Methods Abstract Methods Modifier and Type Method Description ExtendedGB<C>
extGB(int modv, java.util.List<GenPolynomial<C>> F)
Extended Groebner base using critical pair class.ExtendedGB<C>
extGB(java.util.List<GenPolynomial<C>> F)
Extended Groebner base using critical pair class.java.util.List<GenPolynomial<C>>
GB(int modv, java.util.List<GenPolynomial<C>> F)
Groebner base using pairlist class.ModuleList<C>
GB(ModuleList<C> M)
GB.java.util.List<GenPolynomial<C>>
GB(java.util.List<GenPolynomial<C>> F)
Groebner base using pairlist class.boolean
isGB(int modv, java.util.List<GenPolynomial<C>> F)
Groebner base test.boolean
isGB(ModuleList<C> M)
isGB.boolean
isGB(java.util.List<GenPolynomial<C>> F)
Groebner base test.boolean
isReductionMatrix(ExtendedGB<C> exgb)
Test if reduction matrix.boolean
isReductionMatrix(java.util.List<GenPolynomial<C>> F, java.util.List<GenPolynomial<C>> G, java.util.List<java.util.List<GenPolynomial<C>>> Mf, java.util.List<java.util.List<GenPolynomial<C>>> Mg)
Test if reduction matrix.java.util.List<GenPolynomial<C>>
minimalGB(java.util.List<GenPolynomial<C>> Gp)
Minimal ordered groebner basis.
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Method Detail
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isGB
boolean isGB(java.util.List<GenPolynomial<C>> F)
Groebner base test.- Parameters:
F
- polynomial list.- Returns:
- true, if F is a Groebner base, else false.
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isGB
boolean isGB(int modv, java.util.List<GenPolynomial<C>> F)
Groebner base test.- Parameters:
modv
- module variable number.F
- polynomial list.- Returns:
- true, if F is a Groebner base, else false.
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GB
java.util.List<GenPolynomial<C>> GB(java.util.List<GenPolynomial<C>> F)
Groebner base using pairlist class.- Parameters:
F
- polynomial list.- Returns:
- GB(F) a Groebner base of F.
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GB
java.util.List<GenPolynomial<C>> GB(int modv, java.util.List<GenPolynomial<C>> F)
Groebner base using pairlist class.- Parameters:
modv
- module variable number.F
- polynomial list.- Returns:
- GB(F) a Groebner base of F.
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isGB
boolean isGB(ModuleList<C> M)
isGB.- Parameters:
M
- a module basis.- Returns:
- true, if M is a Groebner base, else false.
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GB
ModuleList<C> GB(ModuleList<C> M)
GB.- Parameters:
M
- a module basis.- Returns:
- GB(M), a Groebner base of M.
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extGB
ExtendedGB<C> extGB(java.util.List<GenPolynomial<C>> F)
Extended Groebner base using critical pair class.- Parameters:
F
- polynomial list.- Returns:
- a container for a Groebner base G of F together with back-and-forth transformations.
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extGB
ExtendedGB<C> extGB(int modv, java.util.List<GenPolynomial<C>> F)
Extended Groebner base using critical pair class.- Parameters:
modv
- module variable number.F
- polynomial list.- Returns:
- a container for a Groebner base G of F together with back-and-forth transformations.
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minimalGB
java.util.List<GenPolynomial<C>> minimalGB(java.util.List<GenPolynomial<C>> Gp)
Minimal ordered groebner basis.- Parameters:
Gp
- a Groebner base.- Returns:
- a reduced Groebner base of Gp.
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isReductionMatrix
boolean isReductionMatrix(ExtendedGB<C> exgb)
Test if reduction matrix.- Parameters:
exgb
- an ExtendedGB container.- Returns:
- true, if exgb contains a reduction matrix, else false.
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isReductionMatrix
boolean isReductionMatrix(java.util.List<GenPolynomial<C>> F, java.util.List<GenPolynomial<C>> G, java.util.List<java.util.List<GenPolynomial<C>>> Mf, java.util.List<java.util.List<GenPolynomial<C>>> Mg)
Test if reduction matrix.- Parameters:
F
- a polynomial list.G
- a Groebner base.Mf
- a possible reduction matrix.Mg
- a possible reduction matrix.- Returns:
- true, if Mg and Mf are reduction matrices, else false.
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