Package edu.jas.gb
Groebner bases package.
This package contains classes for polynomial and solvable polynomial
reduction, Groebner bases and ideal arithmetic as well as thread
parallel and distributed versions of Buchbergers algorithm,
e.g. ReductionSeq
, GroebnerBaseAbstract
,
GroebnerBaseSeq
, GroebnerBaseParallel
and
GroebnerBaseDistributed
. Moreover there are Groebner
bases in polynomial rings over principal ideal domains and Euclidean
domains, so called D- and E-Groebner bases, see
DGroebnerBaseSeq
and EGroebnerBaseSeq
.
The latest additions include free non-commutative polynomial
reduction, S-polynomials and two-sided Groebner bases, see
WordReductionSeq
and WordGroebnerBaseSeq
.
Heinz Kredel
Last modified: Fri Sep 21 21:46:36 CEST 2012
$Id$
-
Interface Summary Interface Description DReduction<C extends RingElem<C>> Polynomial D Reduction interface.EReduction<C extends RingElem<C>> Polynomial E-Reduction interface.GroebnerBase<C extends RingElem<C>> Groebner Bases interface.PairList<C extends RingElem<C>> Pair list management interface.Reduction<C extends RingElem<C>> Polynomial Reduction interface.SigReduction<C extends RingElem<C>> Polynomial SigReduction interface.SolvableGroebnerBase<C extends RingElem<C>> Solvable Groebner Bases interface.SolvableReduction<C extends RingElem<C>> Solvable polynomial Reduction interface.WordGroebnerBase<C extends RingElem<C>> Non-commutative Groebner Bases interface for GenWordPolynomials.WordPairList<C extends RingElem<C>> WordPair list management interface.WordReduction<C extends RingElem<C>> Polynomial WordReduction interface. -
Class Summary Class Description AbstractPair<C extends RingElem<C>> Serializable abstract subclass to hold pairs of polynomials.CriticalPair<C extends RingElem<C>> Serializable subclass to hold critical pairs of polynomials.CriticalPairComparator<C extends RingElem<C>> Comparator for critical pairs of polynomials.CriticalPairList<C extends RingElem<C>> Critical pair list management.Cyclic Class to produce a system of equations defined as Cyclic.DGroebnerBaseSeq<C extends RingElem<C>> D-Groebner Base sequential algorithm.DReductionSeq<C extends RingElem<C>> Polynomial D-Reduction sequential use algorithm.EGroebnerBaseSeq<C extends RingElem<C>> E-Groebner Base sequential algorithm.EReductionSeq<C extends RingElem<C>> Polynomial E-Reduction sequential use algorithm.ExtendedGB<C extends RingElem<C>> Container for a GB and transformation matrices.GBClientSP<C extends RingElem<C>> Objects of this class are to be send to a ExecutableServer.GBDistSP<C extends RingElem<C>> Deprecated. use RunGB or RunSGB for standalone executionGBExerClient<C extends RingElem<C>> Objects of this class are to be send to a ExecutableServer.GBHybridExerClient<C extends RingElem<C>> Objects of this class are to be send to a ExecutableServer.GBOptimized<C extends GcdRingElem<C>> Groebner bases via optimized variable and term order.GBProxy<C extends GcdRingElem<C>> Groebner bases parallel proxy.GBSPTransportMess Distributed GB transport message.GBSPTransportMessEnd Distributed GB transport message for termination.GBSPTransportMessPair<C extends RingElem<C>> Distributed GB transport message for pairs.GBSPTransportMessPairIndex Distributed GB transport message for index pairs.GBSPTransportMessPoly<C extends RingElem<C>> Distributed GB transport message for polynomial.GBSPTransportMessReq Distributed GB transport message for requests.GBTransportMess Distributed GB transport message.GBTransportMessEnd Distributed GB transport message for termination.GBTransportMessPair<C extends RingElem<C>> Distributed GB transport message for pairs.GBTransportMessPairIndex Distributed GB transport message for index pairs.GBTransportMessPoly<C extends RingElem<C>> Distributed GB transport message for polynomial.GBTransportMessReq Distributed GB transport message for requests.GroebnerBaseAbstract<C extends RingElem<C>> Groebner Bases abstract class.GroebnerBaseArriSigSeqIter<C extends RingElem<C>> Groebner Base Arri signature based sequential iterative algorithm.GroebnerBaseDistributedEC<C extends RingElem<C>> Groebner Base distributed algorithm.GroebnerBaseDistributedHybridEC<C extends RingElem<C>> Groebner Base distributed hybrid algorithm.GroebnerBaseF5zSigSeqIter<C extends RingElem<C>> Groebner Base F5z signature based sequential iterative algorithm.GroebnerBaseGGVSigSeqIter<C extends RingElem<C>> Groebner Base GGV signature based sequential iterative algorithm.GroebnerBaseParallel<C extends RingElem<C>> Groebner Base parallel algorithm.GroebnerBaseParIter<C extends RingElem<C>> Groebner Base parallel iterative algorithm.GroebnerBaseSeq<C extends RingElem<C>> Groebner Base sequential algorithm.GroebnerBaseSeqIter<C extends RingElem<C>> Groebner Base sequential iterative algorithm.GroebnerBaseSeqPairDistributed<C extends RingElem<C>> Deprecated. no direct alternativeGroebnerBaseSeqPairParallel<C extends RingElem<C>> Groebner Base parallel algorithm.GroebnerBaseSeqPairSeq<C extends RingElem<C>> Groebner Base sequential algorithm.GroebnerBaseSigSeqIter<C extends RingElem<C>> Groebner Base signature based sequential iterative algorithm.HybridReducerClientEC<C extends RingElem<C>> Distributed clients reducing worker threads.HybridReducerReceiverEC<C extends RingElem<C>> Distributed server receiving worker thread.HybridReducerServerEC<C extends RingElem<C>> Distributed server reducing worker proxy threads.Katsura Class to produce a system of equations as defined by Katsura.LeftSolvableReducer<C extends RingElem<C>> Reducing left worker threads.LeftSolvableReducerSeqPair<C extends RingElem<C>> Reducing left worker threads.MiReducer<C extends RingElem<C>> Reducing worker threads for minimal GB.MiReducerClient<C extends RingElem<C>> Distributed clients reducing worker threads for minimal GB.MiReducerClientEC<C extends RingElem<C>> Distributed clients reducing worker threads for minimal GB.MiReducerClientSeqPair<C extends RingElem<C>> Distributed clients reducing worker threads for minimal GB.MiReducerIter<C extends RingElem<C>> Reducing worker threads for minimal GB.MiReducerSeqPair<C extends RingElem<C>> Reducing worker threads for minimal GB.MiReducerServer<C extends RingElem<C>> Distributed server reducing worker threads for minimal GB Not jet distributed but threaded.MiReducerServerEC<C extends RingElem<C>> Distributed server reducing worker threads for minimal GB Not jet distributed but threaded.MiReducerServerSeqPair<C extends RingElem<C>> Distributed server reducing worker threads for minimal GB Not jet distributed but threaded.OrderedDPairlist<C extends RingElem<C>> Pair list management for d-Groebner bases.OrderedMinPairlist<C extends RingElem<C>> Pair list management.OrderedPairlist<C extends RingElem<C>> Pair list management.OrderedSyzPairlist<C extends RingElem<C>> Pair list management.OrderedWordPairlist<C extends RingElem<C>> Pair list management of word polynomials.Pair<C extends RingElem<C>> Serializable subclass to hold pairs of polynomials.Reducer<C extends RingElem<C>> Reducing worker threads.ReducerClientEC<C extends RingElem<C>> Distributed clients reducing worker threads.ReducerClientSeqPair<C extends RingElem<C>> Distributed clients reducing worker threads.ReducerIter<C extends RingElem<C>> Reducing worker threads.ReducerSeqPair<C extends RingElem<C>> Reducing worker threads.ReducerServerEC<C extends RingElem<C>> Distributed server reducing worker threads.ReducerServerSeqPair<C extends RingElem<C>> Distributed server reducing worker threads.ReductionAbstract<C extends RingElem<C>> Polynomial Reduction abstract class.ReductionPar<C extends RingElem<C>> Polynomial reduction parallel usable algorithm.ReductionSeq<C extends RingElem<C>> Polynomial reduction sequential use algorithm.SGBProxy<C extends GcdRingElem<C>> Groebner bases parallel proxy.SigPair<C extends RingElem<C>> Serializable subclass to hold pairs of polynomials.SigPoly<C extends RingElem<C>> Container for a polynomial and its signature.SigReductionSeq<C extends RingElem<C>> Polynomial SigReduction class.SolvableExtendedGB<C extends RingElem<C>> Container for a GB and transformation matrices.SolvableGroebnerBaseAbstract<C extends RingElem<C>> Solvable Groebner Bases abstract class.SolvableGroebnerBaseParallel<C extends RingElem<C>> Solvable Groebner Base parallel algorithm.SolvableGroebnerBaseSeq<C extends RingElem<C>> Solvable Groebner bases sequential algorithms.SolvableGroebnerBaseSeqPairParallel<C extends RingElem<C>> Solvable Groebner Base parallel algorithm.SolvableMiReducer<C extends RingElem<C>> Reducing worker threads for minimal GB.SolvableMiReducerSeqPair<C extends RingElem<C>> Reducing worker threads for minimal GB.SolvableReductionAbstract<C extends RingElem<C>> Solvable polynomial Reduction abstract class.SolvableReductionPar<C extends RingElem<C>> Solvable polynomial Reduction parallel usable algorithm.SolvableReductionSeq<C extends RingElem<C>> Solvable polynomial Reduction algorithm.TwosidedSolvableReducer<C extends RingElem<C>> Reducing twosided worker threads.TwosidedSolvableReducerSeqPair<C extends RingElem<C>> Reducing twosided worker threads.WordGroebnerBaseAbstract<C extends RingElem<C>> Non-commutative Groebner Bases abstract class.WordGroebnerBaseSeq<C extends RingElem<C>> Non-commutative word Groebner Base sequential algorithm.WordPair<C extends RingElem<C>> Serializable subclass to hold pairs of word polynomials.WordReductionAbstract<C extends RingElem<C>> Polynomial word reduction abstract class.WordReductionSeq<C extends RingElem<C>> Polynomial word reduction sequential use algorithm.