The GAP 4 package 'simpcomp' ============================ About ===== simpcomp is a GAP package for working with simplicial complexes. It allows the computation of many properties of simplicial complexes (such as the f-, g- and h-vecors, the face lattice, the automorphism group, (co-)homology with explicit basis computation, intersection form, etc.) and provides the user with functions to compute new complexes from old (simplex links and stars, connected sums, cartesian products, handle additions, bistellar flips, etc.). Furthermore, it comes with an extensive library of known triangulations of manifolds and provides the user with the possibility to create own complex libraries. simpcomp caches computed properties of a simplicial complex, thus avoiding unnecessary computations, internally handles the vertex labeling of the complexes and insures the consistency of a simplicial complex throughout all operations. simpcomp relies on the GAP package homology for its homology computation, but also provides the user with an own (co-)homology algorithm in case the packacke homology is not available. For automorphism group computation the GAP package GRAPE is used, which in turn uses the program nauty by Brendan McKay. An internal automorphism group calculation algorithm in used as fallback if the GRAPE package is not available. License ======= simpcomp is free software. The code is released under the GPL version 2 or later (at your preference). For the text of the GPL see the file COPYING in the simpcomp directory or http://www.gnu.org/licenses/. Dependencies ============ * GAP (>=4.4) * Depending on GAP packages: GAPDoc (>= 0.9999), part of the core GAP system. * Strongly suggested other packages: Homology (>= 1.4.2), GRAPE (>= 4.2) Download and installation ========================= 0. Download simpcomp 1. Install the GAP system, version 4.4 or higher. 2. (recommended) Install the GAP-packages Homology, version 1.4.2 or higher and GRAPE, version 4.2 or higher. 3. Download one of the simpcomp archives .zip, .tar.gz, .zoo 4. Unpack the archive to the directory GAPROOT/pkg/. 5. From within GAP, run "SCRunTest();" or "ReadPackage("simpcomp","tst/testshort.gap");" for a quick test, run "ReadPackage("simpcomp","tst/testall.gap");" for an extensive test. Changes ======= 31/01/2013 - Version 1.6.1: Minor update. - Fixed minor bug in SCChiralMap and SCRegularMap. - Updated deployment system. 22/01/2013 - Version 1.6.0: Major update. - Added functions SCHeegaardSplitting, SCHeegaardSplittingSmallGenus and SCIsHeegaardSplitting to handle Heegaard splittings. - Added infinte series of d-tori SCSeriesTorus. - Added infinte series of lens spaces SCSeriesLensSpace. - Fixed bug in SCLibDelete. - Recalculated examples of documentation. - Fixed inconsistency in SCsFromGroupExt (non-strongly connected 2-pseudomanifolds are now all computed). - Added external code for bistellar flips. - Fixed bug in SCOrientation. - Added function SCSeriesBrehmKuehnelTorus. - Fixed minor bug in SCCartesianProduct (typo in description of topological type). - Added classification of cyclic combinatorial 3-mflds up to 22 vertices. - Added K3-surface K3_17 with standard PL-structure to the library. - Fixed bug in SCIntersectionFormSignature. - Revised documentation. - Added SCSurface, generates a surface of prescribed orientability and genus. - Added SCDifferenceCycles (analogue of SCGenerators for cyclic combinatorial manifolds). - Added census of highly symmetric surfaces. This includes the functions: SCNrRegularTorus, SCNrChiralTori, SCRegularTorus, SCChiralTori, SCSeriesSymmetricTorus, SCRegularMap, SCChiralMap, SCRegularMaps and SCChiralMaps. - Fixed dependencies on external UNIX programs to avoid problems with simpcomp running under Windows. - Added further combinatorial 3-manifolds with transitive cyclic symmetry. In particular, added functions SCSeriesHomologySphere, SCSeriesConnectedSum, SCSeriesSeifertFibredSpace and extended SCSeriesLensSpace. - New deployment system for full support of Google Code Git repository. 23/11/2011 - Version 1.5.4: GAP 4.5 release: required GAP-version is now 4.5 - Updated references to other packages 28/10/2011 - Version 1.5.3: Tiny update - Replaced test file in PackageInfo.g 27/10/2011 - Version 1.5.2: Minor update - Fixed bug in function SCNumFacesOp - Fixed bug in function SCsFromGroupExt - Removed unnecessary .git subdirectory from package archive 27/10/2011 - Version 1.5.2: Minor update - Fixed bug in function SCNumFacesOp - Fixed bug in function SCsFromGroupExt - Removed unnecessary .git subdirectory from package archive 16/08/2011 - Version 1.5.1: Minor update - Added the GAP package ''io'' to the list of ''NeededOtherPackages''. - Fixed bug in function SCMove (thanks to Paul VanKoughnett for reporting!), bistellar move was performed on argument, too. - Fixed bug in shelling code (thanks to Samuel Kolins for reporting!), shelling intersection was not checked for pureness. - Extended SCExportJavaView to work with higher-dimensional complexes. For complexes of dim > 2, the 2-skeleton is exported now. - Added new series of triangulations of certain Hamiltonian subcomplexes of the cross polytope in arbitrary dimension: SCSeriesBid. 01/06/2011 - Version 1.5.0: Major update. Reworked most parts of package. - Completely rewritten type system, simpcomp is now compliant to the standard GAP object format. Introduced new object type SCPolyhedralComplex, from which both SCSimplicialComplex and SCNormalSurface are derived. - Changed naming of .-operator for simpcomp objects -- now there exist short and long versions of method names. - SCFaces and operator [] for polyhedral complex are now synonyms for SCSkel. - Vertex labels must now be elements with a total ordering. - Changed behaviour of operator = for SCSimplicialComplex: complexes are now only equal if and only if they have the same facet lists in standard labelling 1..n (used to include combinatorial isomorphy). - Fixed bug in SCRelabel... functions. As a side-effect, function SCSortComplex was deprecated and is now gone. - Fixed serveral small bugs in the classification functions for transitive manifolds with the prefix SCs... -- now all manifolds should be found. - Heavily reworked SCsFromGroup...-functions, should be much faster now. - Added and changed a lot of new functionality reagarding infinite series of triangulations, function prefix SCSeries... - Changed file format to binary one. Note that SCSave/SCLoad now use the binary format. If you want to continue using XML, use SCSaveXML/SCLoadXML. The package falls back to old format where neccessary. - Fixed bugs in SCDetermineTopologicalType and SCSpanningTree reported by Jack Schmidt (thank you!). In some cases, the spanning tree was not computed correctly. SCDetermineTopological did not work correctly with user libraries. - SCIsInKd now only checks one link if the complex has a transitive automorphism group. - Fixed polymake export/import SCExportPolymake/SCImportPolymake. - Fixed small bug in SCAutmorphismGroupInternal. - Changed the way the documentation is generated (using GAPDoc) -- the examples should now always be up to date and in sync with the code. - Changed package tests. Got rid of testshort.gap and testall.gap, the only function you need from now on is SCRunTest(). - Added interface to GAP package "homalg" by Mohamed Barakat -- the package can now be used for homology-related computations. In particular, simpcomp can now calculate homology groups with arbitrary coefficients using homalg. 17/08/2010 - Version 1.3.3: Minor bug-fix - Adjusted test files to accommodate some changes made in the versions 1.3.1 and 1.3.2 12/08/2010 - Version 1.3.2: Minor bug-fix - Fixed dependencies on other packages 05/08/2010 - Version 1.3.1: Minor bug-fix - Fixed minor issues with undeclared local variables - Fixed wrong output format of SCAutomorphismGroupInternal 26/05/2010 - Version 1.3.0: Major update. New functions, updated library and bug fixes. - simpcomp has learned to generate all triangulations with k-transitive automorphism groups given a prescribed dimension and vertex number. See the function prefix SCsFromGroup. - Expanded the library to also contain pseudomanifolds -- the library now contains ca. 650 manifolds and ca. 7000 pseudomanifolds, it indexes the properties IsManifold and IsPM and supports them in property-based searches. - SCExportLatexTable now uses SCFacets instead of SCFacetsEx and thus respects vertex labelings. Take care not to choose to wild labels though, these are not checked for latex compatibility during the export. - Changed naming scheme of automorphism groups -- StructureDescription is only called if the group cannot be found in GAPs group libraries out of speed considerations. - Fixed small error in SCIntFunc.ReadPermGroup resulting in an error when trying to load complexes with trivial automorphism groups 30/04/2010 - Version 1.2.73: Midsize update. simpcomp now has a mascot! - Added support for polyhedral Morse functions, prefix: SCMorse..., including a (naive) test for tightness of a triangulation (SCIsTight). - Minor updates of the complex library. 07/04/2010 - Version 1.1.43 - IMPORTANT FIX: fixed incorrect calculation of g-vectors (last entry was missing) and updated library accordingly - Added SCDehnSommervilleCheck and SCDehnSommervilleMatrix - Added SCFVectorBdCyclicPolytope and SCBdCyclicPolytope - Removed cyclic polytopes from library (see above) - Added SCIsFlag to check whether a complex is flag - Added SCRandomize to support randomizing of complexes via bistellar moves - Again modified f-vector routine; should be faster now - SCFromGenerators now saves the automorphism group to the complex - Fixed small error in SCSortComplex 14/01/2010 - Version 1.1.21 - Improved performance of f-vector calculation (does not need face lattice any more) 26/11/2009 - Version 1.1.9 - Fixed loading errors of package when package `homology' is not loaded - Added support for normal surfaces, along with additional documentation - Complexes in library updated 16/11/2009 - Version 1.0.440 - Updated file and directory attributes to comply with GAP standard. - Added function SCIntersectionFormSignature. Thanks to Michael Eisermann for helpful comments on calculating signatures of matrices without the need of calculating eigenvalues. 11/11/2009 - Version 1.0.435 - Updated Documentation - Updated GRAPE availability test to reliably work with GRAPE 4.3 26/10/2009 - Version 1.0.403 - Minor compatibility fixes in this release - Fixed some error messages on undefined global variables during loading of simpcomp when the packages `homology' and/or `GRAPE' are not present - Fallback to functions of `homology' package are now handled correctly - Added extended testing functionality and SCRunTest 13/10/2009 - Version 1.0.389 - Initial version Roadmap ======= The following features are planned to be supported in future versions of simpcomp: * Further extension of the library Flexibilization of bistellar flip interface Bugs ==== We have thorougly tested simpcomp on errors. If you none the less encouter errors or inconsistencies when working with simpcomp, please contact the authors. Contact ======= Felix Effenberger, effenberger@mathematik.uni-stuttgart.de and Jonathan Spreer, spreer@mathematik.uni-stuttgart.de Address: University of Stuttgart Department of Mathematics Institute of Geometry and Topology D-70550 Stuttgart, Germany