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<div class="ChapSects"><a href="chap6.html#X82BDBFFC81D080D1">6 <span class="Heading">Functions and operations for <code class="code">SCSimplicialComplex</code></span></a>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap6.html#X7A93E4B08536E2C8">6.1 <span class="Heading">Creating an <code class="code">SCSimplicialComplex</code> object from a facet list</span></a>
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<span class="ContSS"><br /><span class="nocss"> </span><a href="chap6.html#X7B5A874584FF34A7">6.1-1 SCFromFacets</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap6.html#X7B5470FD7E2320DE">6.1-2 SC</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap6.html#X827D29DD79A82CFA">6.1-3 SCFromDifferenceCycles</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap6.html#X804A0B1F85B333C2">6.1-4 SCFromGenerators</a></span>
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<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap6.html#X867E1FF580230E20">6.2 <span class="Heading">Isomorphism signatures</span></a>
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<span class="ContSS"><br /><span class="nocss"> </span><a href="chap6.html#X7E95E36680C188C4">6.2-1 SCExportToString</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap6.html#X80098C5F7B80A621">6.2-2 SCExportIsoSig</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap6.html#X7E915DA7821DD513">6.2-3 SCFromIsoSig</a></span>
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<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap6.html#X79072405786FEA0B">6.3 <span class="Heading">Generating some standard triangulations</span></a>
</span>
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<span class="ContSS"><br /><span class="nocss"> </span><a href="chap6.html#X7E04DD807AF33B78">6.3-1 SCBdCyclicPolytope</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap6.html#X839F3BD37DBA3F3C">6.3-2 SCBdSimplex</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap6.html#X856E48967BBFCF0E">6.3-3 SCEmpty</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap6.html#X7A23532F7A8A3988">6.3-4 SCSimplex</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap6.html#X8664A90879248282">6.3-5 SCSeriesTorus</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap6.html#X87C67A0087F645C1">6.3-6 SCSurface</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap6.html#X831315CD80BA3654">6.3-7 SCFVectorBdCrossPolytope</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap6.html#X7C010361858F0214">6.3-8 SCFVectorBdCyclicPolytope</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap6.html#X7C3E0F7687AC966E">6.3-9 SCFVectorBdSimplex</a></span>
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<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap6.html#X814FE0267D7C54A9">6.4 <span class="Heading">Generating infinite series of transitive triangulations</span></a>
</span>
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<span class="ContSS"><br /><span class="nocss"> </span><a href="chap6.html#X7EA6421A8156EBDF">6.4-1 SCSeriesAGL</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap6.html#X85E6FD6D84FF762B">6.4-2 SCSeriesBrehmKuehnelTorus</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap6.html#X786AD599875BD006">6.4-3 SCSeriesBdHandleBody</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap6.html#X8787A3A4788E950C">6.4-4 SCSeriesBid</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap6.html#X7C0223DF83CC961B">6.4-5 SCSeriesC2n</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap6.html#X7E2927DA7F60D957">6.4-6 SCSeriesConnectedSum</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap6.html#X7D1CEF9F86D3AE66">6.4-7 SCSeriesCSTSurface</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap6.html#X7C56D2B7858A80C7">6.4-8 SCSeriesD2n</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap6.html#X7CCBF8F487036415">6.4-9 SCSeriesHandleBody</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap6.html#X8519C1B678C101BF">6.4-10 SCSeriesHomologySphere</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap6.html#X78DA125479E1D77F">6.4-11 SCSeriesK</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap6.html#X7B8300428516DAD8">6.4-12 SCSeriesKu</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap6.html#X813C5B0E7FA7C1A3">6.4-13 SCSeriesL</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap6.html#X7EAC6828812A241A">6.4-14 SCSeriesLe</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap6.html#X8280ED8280FF9218">6.4-15 SCSeriesLensSpace</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap6.html#X7DDC1B127F21CFA4">6.4-16 SCSeriesPrimeTorus</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap6.html#X7CC3944D7E2F6458">6.4-17 SCSeriesSeifertFibredSpace</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap6.html#X7B71BC8B7D74AFD5">6.4-18 SCSeriesS2xS2</a></span>
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<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap6.html#X7899878881EA47F8">6.5 <span class="Heading">A census of regular and chiral maps</span></a>
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<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap6.html#X867D2AFC79B11405">6.5-1 SCChiralMap</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap6.html#X85BB97CB8240E59B">6.5-2 SCChiralMaps</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap6.html#X7B362D25784E7217">6.5-3 SCChiralTori</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap6.html#X7AB15983833FCA6B">6.5-4 SCNrChiralTori</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap6.html#X87180AD07F799C5A">6.5-5 SCNrRegularTorus</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap6.html#X83D0946E7E2C4163">6.5-6 SCRegularMap</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap6.html#X7F75F5E183CC097E">6.5-7 SCRegularMaps</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap6.html#X79B6F47187668CDF">6.5-8 SCRegularTorus</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap6.html#X87CE08247BE77E44">6.5-9 SCSeriesSymmetricTorus</a></span>
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<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap6.html#X7F4308DB7C3699D1">6.6 <span class="Heading">Generating new complexes from old</span></a>
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<span class="ContSS"><br /><span class="nocss"> </span><a href="chap6.html#X8255A2F97A7432F9">6.6-1 SCCartesianPower</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap6.html#X859DA29B83BDE35E">6.6-2 SCCartesianProduct</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap6.html#X82C9F57780C0B7F8">6.6-3 SCConnectedComponents</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap6.html#X7C63CDF28162C755">6.6-4 SCConnectedProduct</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap6.html#X81338CE18195607C">6.6-5 SCConnectedSum</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap6.html#X78B843417D63B408">6.6-6 SCConnectedSumMinus</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap6.html#X84F3487182AB102A">6.6-7 SCDifferenceCycleCompress</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap6.html#X8510B6CF85070A28">6.6-8 SCDifferenceCycleExpand</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap6.html#X8278E1157A318C32">6.6-9 SCStronglyConnectedComponents</a></span>
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<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap6.html#X87C1C49987E75A9C">6.7 <span class="Heading">Simplicial complexes from transitive permutation groups</span></a>
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<span class="ContSS"><br /><span class="nocss"> </span><a href="chap6.html#X7C1592677A76A3E5">6.7-1 SCsFromGroupExt</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap6.html#X7A04D77085D9BE4E">6.7-2 SCsFromGroupByTransitivity</a></span>
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<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap6.html#X81FDA1407B1E96C9">6.8 <span class="Heading">The classification of cyclic combinatorial 3-manifolds</span></a>
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<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap6.html#X805BBDF58568614F">6.8-1 SCNrCyclic3Mflds</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap6.html#X84477B9E7CAEED7B">6.8-2 SCCyclic3MfldTopTypes</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap6.html#X781256E37DA1B69F">6.8-3 SCCyclic3Mfld</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap6.html#X8490744E81DA45BF">6.8-4 SCCyclic3MfldByType</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap6.html#X86F8AED6843FCD65">6.8-5 SCCyclic3MfldListOfGivenType</a></span>
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<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap6.html#X81CE90127800B91A">6.9 <span class="Heading">Computing properties of simplicial complexes</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap6.html#X7B69B327809F67A0">6.9-1 SCAltshulerSteinberg</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap6.html#X7B88925386E197AC">6.9-2 SCAutomorphismGroup</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap6.html#X7A33B8177A7ACD3A">6.9-3 SCAutomorphismGroupInternal</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap6.html#X78F6EF808047772C">6.9-4 SCAutomorphismGroupSize</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap6.html#X7EAC3A5D7A3339BB">6.9-5 SCAutomorphismGroupStructure</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap6.html#X7E9D5C257F88E5E0">6.9-6 SCAutomorphismGroupTransitivity</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap6.html#X836DC73380EA7414">6.9-7 SCBoundary</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap6.html#X812AE7397B4FC88E">6.9-8 SCDehnSommervilleCheck</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap6.html#X859C3981831B4B81">6.9-9 SCDehnSommervilleMatrix</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap6.html#X80B33CAF7B5476C0">6.9-10 SCDifferenceCycles</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap6.html#X82351AAE793DCB68">6.9-11 SCDim</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap6.html#X798175C58050DDBD">6.9-12 SCDualGraph</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap6.html#X788BAE187D584103">6.9-13 SCEulerCharacteristic</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap6.html#X81F8071385FD9C1D">6.9-14 SCFVector</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap6.html#X7F8B561C823DDDBA">6.9-15 SCFaceLattice</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap6.html#X7AE0029985BD0775">6.9-16 SCFaceLatticeEx</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap6.html#X7F6FE9B27B8D6922">6.9-17 SCFaces</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap6.html#X7B40DFE780A47109">6.9-18 SCFacesEx</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap6.html#X7BDD568184E3419D">6.9-19 SCFacets</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap6.html#X87DC942881235E25">6.9-20 SCFacetsEx</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap6.html#X79F60850875BB683">6.9-21 SCFpBettiNumbers</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap6.html#X875963367A7745FB">6.9-22 SCFundamentalGroup</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap6.html#X7B9F77A885E1BABE">6.9-23 SCGVector</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap6.html#X863CA73D7F66B295">6.9-24 SCGenerators</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap6.html#X789F8FC77FC0E701">6.9-25 SCGeneratorsEx</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap6.html#X84FBF0A685547ECD">6.9-26 SCHVector</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap6.html#X796EBADE7803C622">6.9-27 SCHasBoundary</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap6.html#X7C2A5B4D7E77E444">6.9-28 SCHasInterior</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap6.html#X7A0547F67BBB6546">6.9-29 SCHeegaardSplittingSmallGenus</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap6.html#X7C7335667C162AFA">6.9-30 SCHeegaardSplitting</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap6.html#X864978877E7D4DA0">6.9-31 SCHomologyClassic</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap6.html#X7B0C12F5780FDD9B">6.9-32 SCIncidences</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap6.html#X7B4CA6FE78A9880F">6.9-33 SCIncidencesEx</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap6.html#X862926A079F6DFC2">6.9-34 SCInterior</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap6.html#X8123A6E282CD0174">6.9-35 SCIsCentrallySymmetric</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap6.html#X81AF20DC814B51A6">6.9-36 SCIsConnected</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap6.html#X860375D980E9A801">6.9-37 SCIsEmpty</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap6.html#X83E01C957D2F2458">6.9-38 SCIsEulerianManifold</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap6.html#X843C3E7F79D8093F">6.9-39 SCIsFlag</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap6.html#X83F0246384A766F2">6.9-40 SCIsHeegaardSplitting</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap6.html#X7E66FE0C83A3D371">6.9-41 SCIsHomologySphere</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap6.html#X87BC29AF878E7FD8">6.9-42 SCIsInKd</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap6.html#X7F4BECCA7E67B1B2">6.9-43 SCIsKNeighborly</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap6.html#X78C860DC851167F7">6.9-44 SCIsOrientable</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap6.html#X79DFCA08808665B7">6.9-45 SCIsPseudoManifold</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap6.html#X7AAA757F842EA23A">6.9-46 SCIsPure</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap6.html#X7EA4F4DB78758652">6.9-47 SCIsShellable</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap6.html#X7A2BD5657BBE1CC7">6.9-48 SCIsStronglyConnected</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap6.html#X7B935899849C8E40">6.9-49 SCMinimalNonFaces</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap6.html#X7DE069A0823BD56E">6.9-50 SCMinimalNonFacesEx</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap6.html#X82A224DF787A97BE">6.9-51 SCNeighborliness</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap6.html#X7AC2427184B44C65">6.9-52 SCNumFaces</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap6.html#X78DACE3478340DB8">6.9-53 SCOrientation</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap6.html#X8026B46F8236124D">6.9-54 SCSkel</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap6.html#X84ACF7D580FE8B76">6.9-55 SCSkelEx</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap6.html#X7E770DE27938B140">6.9-56 SCSpanningTree</a></span>
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<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap6.html#X8284003382F863A0">6.10 <span class="Heading">Operations on simplicial complexes</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap6.html#X818757A17DA5CFFC">6.10-1 SCAlexanderDual</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap6.html#X82D22356858062D6">6.10-2 SCClose</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap6.html#X7CF53D8D7E0FA702">6.10-3 SCCone</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap6.html#X800BDDD878DFCBDB">6.10-4 SCDeletedJoin</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap6.html#X7FB3D29178076EB4">6.10-5 SCDifference</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap6.html#X7C8D11C684825ADC">6.10-6 SCFillSphere</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap6.html#X7DCB16857D49EC37">6.10-7 SCHandleAddition</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap6.html#X7B4BE2C783E6D0BF">6.10-8 SCIntersection</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap6.html#X85659EC77DFF8183">6.10-9 SCIsIsomorphic</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap6.html#X81D9CC438313F589">6.10-10 SCIsSubcomplex</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap6.html#X8623B92580E8B4E4">6.10-11 SCIsomorphism</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap6.html#X86576B7287686E2B">6.10-12 SCIsomorphismEx</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap6.html#X86AC8D81837CC677">6.10-13 SCJoin</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap6.html#X8482E1F67C927BB7">6.10-14 SCNeighbors</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap6.html#X7F8FBEF17ACD0D4F">6.10-15 SCNeighborsEx</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap6.html#X7EDA334983025D3D">6.10-16 SCShelling</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap6.html#X7F967A717D4E41C0">6.10-17 SCShellingExt</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap6.html#X8373598C7FF5D28E">6.10-18 SCShellings</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap6.html#X7987AAE481C31F38">6.10-19 SCSpan</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap6.html#X7AAA4669793C57DC">6.10-20 SCSuspension</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap6.html#X81DA367A813F7599">6.10-21 SCUnion</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap6.html#X7D5639CB87A0D3F1">6.10-22 SCVertexIdentification</a></span>
<span class="ContSS"><br /><span class="nocss"> </span><a href="chap6.html#X7E7B17317D1B618D">6.10-23 SCWedge</a></span>
</div></div>
</div>
<h3>6 <span class="Heading">Functions and operations for <code class="code">SCSimplicialComplex</code></span></h3>
<p><a id="X7A93E4B08536E2C8" name="X7A93E4B08536E2C8"></a></p>
<h4>6.1 <span class="Heading">Creating an <code class="code">SCSimplicialComplex</code> object from a facet list</span></h4>
<p>This section contains functions to generate or to construct new simplicial complexes. Some of them obtain new complexes from existing ones, some generate new complexes from scratch.</p>
<p><a id="X7B5A874584FF34A7" name="X7B5A874584FF34A7"></a></p>
<h5>6.1-1 SCFromFacets</h5>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ SCFromFacets</code>( <var class="Arg">facets</var> )</td><td class="tdright">( method )</td></tr></table></div>
<p>Returns: simplicial complex of type <code class="code">SCSimplicialComplex</code> upon success, <code class="keyw">fail</code> otherwise.</p>
<p>Constructs a simplicial complex object from the given facet list. The facet list <var class="Arg">facets</var> has to be a duplicate free list (or set) which consists of duplicate free entries, which are in turn lists or sets. For the vertex labels (i. e. the entries of the list items of <var class="Arg">facets</var>) an ordering via the less-operator has to be defined. Following Section 4.11 of the <strong class="pkg">GAP</strong> manual this is the case for objects of the following families: rationals <code class="code">IsRat</code>, cyclotomics <code class="code">IsCyclotomic</code>, finite field elements <code class="code">IsFFE</code>, permutations <code class="code">IsPerm</code>, booleans <code class="code">IsBool</code>, characters <code class="code">IsChar</code> and lists (strings) <code class="code">IsList</code>.</p>
<p>Internally the vertices are mapped to the standard labeling <span class="SimpleMath">1..n</span>, where <span class="SimpleMath">n</span> is the number of vertices of the complex and the vertex labels of the original complex are stored in the property ''VertexLabels'', see <code class="func">SCLabels</code> (<a href="chap4.html#X826E9B4482AF2671"><span class="RefLink">4.2-3</span></a>) and the <code class="code">SCRelabel..</code> functions like <code class="func">SCRelabel</code> (<a href="chap4.html#X7B6011907B74EDDA"><span class="RefLink">4.2-6</span></a>) or <code class="func">SCRelabelStandard</code> (<a href="chap4.html#X78E22E3B787DDE90"><span class="RefLink">4.2-7</span></a>).</p>
<div class="example"><pre>
gap> c:=SCFromFacets([[1,2,5], [1,4,5], [1,4,6], [2,3,5], [3,4,6], [3,5,6]]);
<SimplicialComplex: unnamed complex 12 | dim = 2 | n = 6>
gap> c:=SCFromFacets([["a","b","c"], ["a","b",1], ["a","c",1], ["b","c",1]]);
<SimplicialComplex: unnamed complex 13 | dim = 2 | n = 4>
</pre></div>
<p><a id="X7B5470FD7E2320DE" name="X7B5470FD7E2320DE"></a></p>
<h5>6.1-2 SC</h5>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ SC</code>( <var class="Arg">facets</var> )</td><td class="tdright">( method )</td></tr></table></div>
<p>Returns: simplicial complex of type <code class="code">SCSimplicialComplex</code> upon success, <code class="keyw">fail</code> otherwise.</p>
<p>A shorter function to create a simplicial complex from a facet list, just calls <code class="func">SCFromFacets</code> (<a href="chap6.html#X7B5A874584FF34A7"><span class="RefLink">6.1-1</span></a>)(<var class="Arg">facets</var>).</p>
<div class="example"><pre>
gap> c:=SC(Combinations([1..6],5));
<SimplicialComplex: unnamed complex 14 | dim = 4 | n = 6>
</pre></div>
<p><a id="X827D29DD79A82CFA" name="X827D29DD79A82CFA"></a></p>
<h5>6.1-3 SCFromDifferenceCycles</h5>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ SCFromDifferenceCycles</code>( <var class="Arg">diffcycles</var> )</td><td class="tdright">( method )</td></tr></table></div>
<p>Returns: simplicial complex of type <code class="code">SCSimplicialComplex</code> upon success, <code class="keyw">fail</code> otherwise.</p>
<p>Creates a simplicial complex object from the list of difference cycles provided. If <var class="Arg">diffcycles</var> is of length <span class="SimpleMath">1</span> the computation is equivalent to the one in <code class="func">SCDifferenceCycleExpand</code> (<a href="chap6.html#X8510B6CF85070A28"><span class="RefLink">6.6-8</span></a>). Otherwise the induced modulus (the sum of all entries of a difference cycle) of all cycles has to be equal and the union of all expanded difference cycles is returned.</p>
<p>A <span class="SimpleMath">n</span>-dimensional difference cycle <span class="SimpleMath">D = (d_1 : ... : d_n+1)</span> induces a simplex <span class="SimpleMath">∆ = ( v_1 , ... , v_n+1 )</span> by <span class="SimpleMath">v_1 = d_1</span>, <span class="SimpleMath">v_i = v_i-1 + d_i</span> and a cyclic group action by <span class="SimpleMath">Z_σ</span> where <span class="SimpleMath">σ = ∑ d_i</span> is the modulus of <span class="SimpleMath">D</span>. The function returns the <span class="SimpleMath">Z_σ</span>-orbit of <span class="SimpleMath">∆</span>.</p>
<p>Note that modulo operations in <strong class="pkg">GAP</strong> are often a little bit cumbersome, since all integer ranges usually start from <span class="SimpleMath">1</span>.</p>
<div class="example"><pre>
gap> c:=SCFromDifferenceCycles([[1,1,6],[2,3,3]]);;
gap> c.F;
[ 8, 24, 16 ]
gap> c.Homology;
[ [ 0, [ ] ], [ 2, [ ] ], [ 1, [ ] ] ]
gap> c.Chi;
0
gap> c.HasBoundary;
false
gap> SCIsPseudoManifold(c);
true
gap> SCIsManifold(c);
true
</pre></div>
<p><a id="X804A0B1F85B333C2" name="X804A0B1F85B333C2"></a></p>
<h5>6.1-4 SCFromGenerators</h5>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ SCFromGenerators</code>( <var class="Arg">group</var>, <var class="Arg">generators</var> )</td><td class="tdright">( method )</td></tr></table></div>
<p>Returns: simplicial complex of type <code class="code">SCSimplicialComplex</code> upon success, <code class="keyw">fail</code> otherwise.</p>
<p>Constructs a simplicial complex object from the set of <var class="Arg">generators</var> on which the group <var class="Arg">group</var> acts, i.e. a complex which has <var class="Arg">group</var> as a subgroup of the automorphism group and a facet list that consists of the <var class="Arg">group</var>-orbits specified by the list of representatives passed in <var class="Arg">generators</var>. Note that <var class="Arg">group</var> is not stored as an attribute of the resulting complex as it might just be a subgroup of the actual automorphism group. Internally calls <code class="code">Orbits</code> and <code class="func">SCFromFacets</code> (<a href="chap6.html#X7B5A874584FF34A7"><span class="RefLink">6.1-1</span></a>).</p>
<div class="example"><pre>
gap> #group: AGL(1,7) of order 42
gap> G:=Group([(2,6,5,7,3,4),(1,3,5,7,2,4,6)]);;
gap> c:=SCFromGenerators(G,[[ 1, 2, 4 ]]);
<SimplicialComplex: complex from generators under unknown group | dim = 2 | n \
= 7>
gap> SCLib.DetermineTopologicalType(c);
<SimplicialComplex: complex from generators under unknown group | dim = 2 | n \
= 7>
</pre></div>
<p><a id="X867E1FF580230E20" name="X867E1FF580230E20"></a></p>
<h4>6.2 <span class="Heading">Isomorphism signatures</span></h4>
<p>This section contains functions to construct simplicial complexes from isomorphism signatures and to compress closed and strongly connected weak pseudomanifolds to strings.</p>
<p>The isomorphism signature of a closed and strongly connected weak pseudomanifold is a representation which is invariant under relabelings of the underlying complex and thus unique for a combinatorial type, i.e. two complexes are isomorphic iff they have the same isomorphism signature.</p>
<p>To compute the isomorphism signature of a closed and strongly connected weak pseudomanifold <span class="SimpleMath">P</span> we have to compute all canonical labelings of <span class="SimpleMath">P</span> and chose the one that is lexicographically minimal.</p>
<p>A canonical labeling of <span class="SimpleMath">P</span> is determined by chosing a facet <span class="SimpleMath">∆ ∈ P</span> and a numbering <span class="SimpleMath">1, 2, ... , d+1</span> of the vertices of <span class="SimpleMath">∆</span> (which in turn determines a numbering of the co-dimension one faces of <span class="SimpleMath">∆</span> by identifying each face with its opposite vertex). This numbering can then be uniquely extended to a numbering (and thus a labeling) on all vertices of <span class="SimpleMath">P</span> by the weak pseudomanifold property: start at face <span class="SimpleMath">1</span> of <span class="SimpleMath">∆</span> and label the opposite vertex of the unique other facet <span class="SimpleMath">δ</span> meeting face <span class="SimpleMath">1</span> by <span class="SimpleMath">d+2</span>, go on with face <span class="SimpleMath">2</span> of <span class="SimpleMath">∆</span> and so on. After finishing with the first facet we now have a numbering on <span class="SimpleMath">δ</span>, repeat the procedure for <span class="SimpleMath">δ</span>, etc. Whenever the opposite vertex of a face is already labeled (and also, if the vertex occurs for the first time) we note this label. Whenever a facet is already visited we skip this step and keep track of the number of skippings between any two newly discovered facets. This results in a sequence of <span class="SimpleMath">m-1</span> vertex labels together with <span class="SimpleMath">m-1</span> skipping numbers (where <span class="SimpleMath">m</span> denotes the number of facets in <span class="SimpleMath">P</span>) which then can by encoded by characters via a lookup table.</p>
<p>Note that there are precisely <span class="SimpleMath">(d+1)! m</span> canonical labelings we have to check in order to find the lexicographically minimal one. Thus, computing the isomorphism signature of a large or highly dimensional complex can be time consuming. If you are not interested in the isomorphism signature but just in the compressed string representation use <code class="func">SCExportToString</code> (<a href="chap6.html#X7E95E36680C188C4"><span class="RefLink">6.2-1</span></a>) which just computes the first canonical labeling of the complex provided as argument and returns the resulting string.</p>
<p>Note: Another way of storing and loading complexes is provided by simpcomp's library functionality, see Section 13.1 for details.
<p><a id="X7E95E36680C188C4" name="X7E95E36680C188C4"></a></p>
<h5>6.2-1 SCExportToString</h5>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ SCExportToString</code>( <var class="Arg">c</var> )</td><td class="tdright">( function )</td></tr></table></div>
<p>Returns: string upon success, <code class="keyw">fail</code> otherwise.</p>
<p>Computes one string representation of a closed and strongly connected weak pseudomanifold. Compare <code class="func">SCExportIsoSig</code> (<a href="chap6.html#X80098C5F7B80A621"><span class="RefLink">6.2-2</span></a>), which returns the lexicographically minimal string representation.</p>
<div class="example"><pre>
gap> c:=SCSeriesBdHandleBody(3,9);;
gap> s:=SCExportToString(c); time;
"deffg.h.f.fahaiciai.i.hai.fbgeiagihbhceceba.g.gag"
3
gap> s:=SCExportIsoSig(c); time;
"deefgaf.hbi.gbh.eaiaeaicg.g.ibf.heg.iff.hggcfffgg"
11
</pre></div>
<p><a id="X80098C5F7B80A621" name="X80098C5F7B80A621"></a></p>
<h5>6.2-2 SCExportIsoSig</h5>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ SCExportIsoSig</code>( <var class="Arg">c</var> )</td><td class="tdright">( method )</td></tr></table></div>
<p>Returns: string upon success, <code class="keyw">fail</code> otherwise.</p>
<p>Computes the isomorphism signature of a closed, strongly connected weak pseudomanifold. The isomorphism signature is stored as an attribute of the complex.</p>
<div class="example"><pre>
gap> c:=SCSeriesBdHandleBody(3,9);;
gap> s:=SCExportIsoSig(c);
"deefgaf.hbi.gbh.eaiaeaicg.g.ibf.heg.iff.hggcfffgg"
</pre></div>
<p><a id="X7E915DA7821DD513" name="X7E915DA7821DD513"></a></p>
<h5>6.2-3 SCFromIsoSig</h5>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ SCFromIsoSig</code>( <var class="Arg">str</var> )</td><td class="tdright">( method )</td></tr></table></div>
<p>Returns: a SCSimplicialComplex object upon success, <code class="keyw">fail</code> otherwise.</p>
<p>Computes a simplicial complex from its isomorphism signature. If a file with isomorphism signatures is provided a list of all complexes is returned.</p>
<div class="example"><pre>
gap> s:="deeee";;
gap> c:=SCFromIsoSig(s);;
gap> SCIsIsomorphic(c,SCBdSimplex(4));
true
</pre></div>
<div class="example"><pre>
gap> s:="deeee";;
gap> PrintTo("tmp.txt",s,"\n");;
gap> cc:=SCFromIsoSig("tmp.txt");
[ <SimplicialComplex: unnamed complex 9 | dim = 3 | n = 5> ]
gap> cc[1].F;
[ 5, 10, 10, 5 ]
</pre></div>
<p><a id="X79072405786FEA0B" name="X79072405786FEA0B"></a></p>
<h4>6.3 <span class="Heading">Generating some standard triangulations</span></h4>
<p><a id="X7E04DD807AF33B78" name="X7E04DD807AF33B78"></a></p>
<h5>6.3-1 SCBdCyclicPolytope</h5>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ SCBdCyclicPolytope</code>( <var class="Arg">d</var>, <var class="Arg">n</var> )</td><td class="tdright">( function )</td></tr></table></div>
<p>Returns: simplicial complex of type <code class="code">SCSimplicialComplex</code> upon success, <code class="keyw">fail</code> otherwise.</p>
<p>Generates the boundary complex of the <var class="Arg">d</var>-dimensional cyclic polytope (a combinatorial <span class="SimpleMath">d-1</span>-sphere) on <var class="Arg">n</var> vertices, where <span class="SimpleMath">n≥ d+2</span>.</p>
<div class="example"><pre>
gap> SCBdCyclicPolytope(3,8);
<SimplicialComplex: Bd(C_3(8)) | dim = 2 | n = 8>
</pre></div>
<p><a id="X839F3BD37DBA3F3C" name="X839F3BD37DBA3F3C"></a></p>
<h5>6.3-2 SCBdSimplex</h5>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ SCBdSimplex</code>( <var class="Arg">d</var> )</td><td class="tdright">( function )</td></tr></table></div>
<p>Returns: simplicial complex of type <code class="code">SCSimplicialComplex</code> upon success, <code class="keyw">fail</code> otherwise.</p>
<p>Generates the boundary of the <span class="SimpleMath">d</span>-simplex <span class="SimpleMath">∆^d</span>, a combinatorial <span class="SimpleMath">d-1</span>-sphere.</p>
<div class="example"><pre>
gap> SCBdSimplex(5);
<SimplicialComplex: S^4_6 | dim = 4 | n = 6>
</pre></div>
<p><a id="X856E48967BBFCF0E" name="X856E48967BBFCF0E"></a></p>
<h5>6.3-3 SCEmpty</h5>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ SCEmpty</code>( )</td><td class="tdright">( function )</td></tr></table></div>
<p>Returns: simplicial complex of type <code class="code">SCSimplicialComplex</code> upon success, <code class="keyw">fail</code> otherwise.</p>
<p>Generates an empty complex (of dimension <span class="SimpleMath">-1</span>), i. e. a <code class="code">SCSimplicialComplex</code> object with empty facet list.</p>
<div class="example"><pre>
gap> SCEmpty();
<SimplicialComplex: empty complex | dim = -1 | n = 0>
</pre></div>
<p><a id="X7A23532F7A8A3988" name="X7A23532F7A8A3988"></a></p>
<h5>6.3-4 SCSimplex</h5>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ SCSimplex</code>( <var class="Arg">d</var> )</td><td class="tdright">( function )</td></tr></table></div>
<p>Returns: simplicial complex of type <code class="code">SCSimplicialComplex</code> upon success, <code class="keyw">fail</code> otherwise.</p>
<p>Generates the <var class="Arg">d</var>-simplex.</p>
<div class="example"><pre>
gap> SCSimplex(3);
<SimplicialComplex: B^3_4 | dim = 3 | n = 4>
</pre></div>
<p><a id="X8664A90879248282" name="X8664A90879248282"></a></p>
<h5>6.3-5 SCSeriesTorus</h5>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ SCSeriesTorus</code>( <var class="Arg">d</var> )</td><td class="tdright">( function )</td></tr></table></div>
<p>Returns: simplicial complex of type <code class="code">SCSimplicialComplex</code> upon success, <code class="keyw">fail</code> otherwise.</p>
<p>Generates the <span class="SimpleMath">d</span>-torus described in <a href="chapBib.html#biBKuehnel86HigherDimCsaszar">[K\t86]</a>.</p>
<div class="example"><pre>
gap> t4:=SCSeriesTorus(4);
<SimplicialComplex: 4-torus T^4 | dim = 4 | n = 31>
gap> t4.Homology;
[ [ 0, [ ] ], [ 4, [ ] ], [ 6, [ ] ], [ 4, [ ] ], [ 1, [ ] ] ]
</pre></div>
<p><a id="X87C67A0087F645C1" name="X87C67A0087F645C1"></a></p>
<h5>6.3-6 SCSurface</h5>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ SCSurface</code>( <var class="Arg">g</var>, <var class="Arg">orient</var> )</td><td class="tdright">( function )</td></tr></table></div>
<p>Returns: simplicial complex of type <code class="code">SCSimplicialComplex</code> upon success, <code class="keyw">fail</code> otherwise.</p>
<p>Generates the surface of genus <var class="Arg">g</var> where the boolean argument <var class="Arg">orient</var> specifies whether the surface is orientable or not. The surfaces have transitive cyclic group actions and can be described using the minimum amount of <span class="SimpleMath">O(operatornamelog (g))</span> memory. If <var class="Arg">orient</var> is <code class="code">true</code> and <var class="Arg">g</var><span class="SimpleMath">≥ 50</span> or if <var class="Arg">orient</var> is <code class="code">false</code> and <var class="Arg">g</var><span class="SimpleMath">≥ 100</span> only the difference cycles of the surface are returned</p>
<div class="example"><pre>
gap> c:=SCSurface(23,true);
<SimplicialComplex: S_23^or | dim = 2 | n = 88>
gap> c.Homology;
[ [ 0, [ ] ], [ 46, [ ] ], [ 1, [ ] ] ]
gap> c.TopologicalType;
"(T^2)^#23"
gap> c:=SCSurface(23,false);
<SimplicialComplex: S_23^non | dim = 2 | n = 21>
gap> c.Homology;
[ [ 0, [ ] ], [ 22, [ 2 ] ], [ 0, [ ] ] ]
gap> c.TopologicalType;
"(RP^2)^#23"
</pre></div>
<div class="example"><pre>
gap> dc:=SCSurface(345,true);
[ [ 1, 1, 1374 ], [ 2, 343, 1031 ], [ 343, 345, 688 ] ]
gap> c:=SCFromDifferenceCycles(dc);
<SimplicialComplex: complex from diffcycles [ [ 1, 1, 1374 ], [ 2, 343, 1031 ]\
, [ 343, 345, 688 ] ] | dim = 2 | n = 1376>
gap> c.Chi;
-688
gap> dc:=SCSurface(12345678910,true); time;
[ [ 1, 1, 24691357816 ], [ 2, 4, 24691357812 ], [ 3, 3, 24691357812 ],
[ 4, 12345678907, 12345678907 ] ]
0
</pre></div>
<p><a id="X831315CD80BA3654" name="X831315CD80BA3654"></a></p>
<h5>6.3-7 SCFVectorBdCrossPolytope</h5>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ SCFVectorBdCrossPolytope</code>( <var class="Arg">d</var> )</td><td class="tdright">( function )</td></tr></table></div>
<p>Returns: a list of integers of size <code class="code">d + 1</code> upon success, <code class="keyw">fail</code> otherwise.</p>
<p>Computes the <span class="SimpleMath">f</span>-vector of the <span class="SimpleMath">d</span>-dimensional cross polytope without generating the underlying complex.</p>
<div class="example"><pre>
<span class="GAPprompt">gap></span> <span class="GAPinput">SCFVectorBdCrossPolytope(50);</span>
[ 100, 4900, 156800, 3684800, 67800320, 1017004800, 12785203200,
137440934400, 1282782054400, 10518812846080, 76500457062400,
497252970905600, 2907017368371200, 15365663232819200, 73755183517532160,
322678927889203200, 1290715711556812800, 4732624275708313600,
15941471244491161600, 49418560857922600960, 141195888165493145600,
372243705163572838400, 906332499528699084800, 2039248123939572940800,
4241636097794311716864, 8156992495758291763200, 14501319992459185356800,
23823597130468661657600, 36146147370366245273600, 50604606318512743383040,
65296266217435797913600, 77539316133205010022400, 84588344872587283660800,
84588344872587283660800, 77337915312079802204160, 64448262760066501836800,
48771658304915190579200, 33370081998099867238400, 20535435075753764454400,
11294489291664570449920, 5509506971543692902400, 2361217273518725529600,
878592473867432755200, 279552150776001331200, 74547240206933688320,
16205921784116019200, 2758454771764428800, 344806846470553600,
28147497671065600, 1125899906842624 ]
</pre></div>
<p><a id="X7C010361858F0214" name="X7C010361858F0214"></a></p>
<h5>6.3-8 SCFVectorBdCyclicPolytope</h5>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ SCFVectorBdCyclicPolytope</code>( <var class="Arg">d</var>, <var class="Arg">n</var> )</td><td class="tdright">( function )</td></tr></table></div>
<p>Returns: a list of integers of size <code class="code">d+1</code> upon success, <code class="keyw">fail</code> otherwise.</p>
<p>Computes the <span class="SimpleMath">f</span>-vector of the <var class="Arg">d</var>-dimensional cyclic polytope on <var class="Arg">n</var> vertices, <span class="SimpleMath">n≥ d+2</span>, without generating the underlying complex.</p>
<div class="example"><pre>
<span class="GAPprompt">gap></span> <span class="GAPinput">SCFVectorBdCyclicPolytope(25,198); </span>
[ 198, 19503, 1274196, 62117055, 2410141734, 77526225777, 2126433621312,
50768602708824, 1071781612741840, 20256672480820776, 346204947854027808,
5395027104058600008, 48354596155522298656, 262068846498922699590,
940938105142239825104, 2379003007642628680027, 4396097923113038784642,
6062663500381642763609, 6294919173643129209180, 4911378208855785427761,
2840750019404460890298, 1183225500922302444568, 335951678686835900832,
58265626173398052500, 4661250093871844200 ]
</pre></div>
<p><a id="X7C3E0F7687AC966E" name="X7C3E0F7687AC966E"></a></p>
<h5>6.3-9 SCFVectorBdSimplex</h5>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ SCFVectorBdSimplex</code>( <var class="Arg">d</var> )</td><td class="tdright">( function )</td></tr></table></div>
<p>Returns: a list of integers of size <code class="code">d + 1</code> upon success, <code class="keyw">fail</code> otherwise.</p>
<p>Computes the <span class="SimpleMath">f</span>-vector of the <span class="SimpleMath">d</span>-simplex without generating the underlying complex.</p>
<div class="example"><pre>
gap> SCFVectorBdSimplex(100);
[ 101, 5050, 166650, 4082925, 79208745, 1267339920, 17199613200,
202095455100, 2088319702700, 19212541264840, 158940114100040,
1192050855750300, 8160963550905900, 51297485177122800, 297525414027312240,
1599199100396803290, 7995995501984016450, 37314645675925410100,
163006083742200475700, 668324943343021950370, 2577824781465941808570,
9373908296239788394800, 32197337191432316660400, 104641345872155029146300,
322295345286237489770604, 942094086221309585483304,
2616928017281415515231400, 6916166902815169575968700,
17409661513983013070541900, 41783187633559231369300560,
95696978128474368620010960, 209337139656037681356273975,
437704928371715151926754675, 875409856743430303853509350,
1675784582908852295948146470, 3072271735332895875904935195,
5397234129638871133346507775, 9090078534128625066688855200,
14683973016669317415420458400, 22760158175837441993901710520,
33862674359172779551902544920, 48375249084532542217003635600,
66375341767149302111702662800, 87494768693060443692698964600,
110826707011209895344085355160, 134919469404951176940625649760,
157884485473879036845412994400, 177620046158113916451089618700,
192119641762857909630770403900, 199804427433372226016001220056,
199804427433372226016001220056, 192119641762857909630770403900,
177620046158113916451089618700, 157884485473879036845412994400,
134919469404951176940625649760, 110826707011209895344085355160,
87494768693060443692698964600, 66375341767149302111702662800,
48375249084532542217003635600, 33862674359172779551902544920,
22760158175837441993901710520, 14683973016669317415420458400,
9090078534128625066688855200, 5397234129638871133346507775,
3072271735332895875904935195, 1675784582908852295948146470,
875409856743430303853509350, 437704928371715151926754675,
209337139656037681356273975, 95696978128474368620010960,
41783187633559231369300560, 17409661513983013070541900,
6916166902815169575968700, 2616928017281415515231400,
942094086221309585483304, 322295345286237489770604,
104641345872155029146300, 32197337191432316660400, 9373908296239788394800,
2577824781465941808570, 668324943343021950370, 163006083742200475700,
37314645675925410100, 7995995501984016450, 1599199100396803290,
297525414027312240, 51297485177122800, 8160963550905900, 1192050855750300,
158940114100040, 19212541264840, 2088319702700, 202095455100, 17199613200,
1267339920, 79208745, 4082925, 166650, 5050, 101 ]
</pre></div>
<p><a id="X814FE0267D7C54A9" name="X814FE0267D7C54A9"></a></p>
<h4>6.4 <span class="Heading">Generating infinite series of transitive triangulations</span></h4> | | |
