1################################################################################ 2## 3## simpcomp / generate.gd 4## 5## Generate simplicial complexes or construct them using existing 6## complexes. 7## 8## $Id$ 9## 10################################################################################ 11 12## GAPDoc include 13## <#GAPDoc Label="generate"> 14## <Section Label="sec:FromScratch"> 15## <Heading>Creating an <C>SCSimplicialComplex</C> object from a facet list</Heading> 16## 17## 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. 18## 19## <#Include Label="SCFromFacets"/> 20## <#Include Label="SC"/> 21## <#Include Label="SCFromDifferenceCycles"/> 22## <#Include Label="SCFromGenerators"/> 23## 24## </Section> 25## 26## <#Include Label="isosig"/> 27## 28## <Section Label="sec:Standard"> 29## <Heading>Generating some standard triangulations</Heading> 30## 31## <#Include Label="SCBdCyclicPolytope"/> 32## <#Include Label="SCBdSimplex"/> 33## <#Include Label="SCEmpty"/> 34## <#Include Label="SCSimplex"/> 35## <#Include Label="SCSeriesTorus"/> 36## <#Include Label="SCSurface"/> 37## <#Include Label="SCFVectorBdCrossPolytope"/> 38## <#Include Label="SCFVectorBdCyclicPolytope"/> 39## <#Include Label="SCFVectorBdSimplex"/> 40## </Section> 41## 42## <Section Label="sec:Series"> 43## <Heading>Generating infinite series of transitive triangulations</Heading> 44## 45## <#Include Label="SCSeriesAGL"/> 46## <#Include Label="SCSeriesBrehmKuehnelTorus"/> 47## <#Include Label="SCSeriesBdHandleBody"/> 48## <#Include Label="SCSeriesBid"/> 49## <#Include Label="SCSeriesC2n"/> 50## <#Include Label="SCSeriesConnectedSum"/> 51## <#Include Label="SCSeriesCSTSurface"/> 52## <#Include Label="SCSeriesD2n"/> 53## <#Include Label="SCSeriesHandleBody"/> 54## <#Include Label="SCSeriesHomologySphere"/> 55## <#Include Label="SCSeriesK"/> 56## <#Include Label="SCSeriesKu"/> 57## <#Include Label="SCSeriesL"/> 58## <#Include Label="SCSeriesLe"/> 59## <#Include Label="SCSeriesLensSpace"/> 60## <#Include Label="SCSeriesPrimeTorus"/> 61## <#Include Label="SCSeriesSeifertFibredSpace"/> 62## <#Include Label="SCSeriesS2xS2"/> 63## 64## </Section > 65## <Section Label="sec:RegularAndChiralMaps"> 66## <Heading>A census of regular and chiral maps</Heading> 67## 68## <#Include Label="highlysymmetricsurfaces"/> 69## 70## See also <Ref Func="SCSurface" /> for example triangulations of all compact closed surfaces 71## with transitive cyclic automorphism group. 72## 73## </Section > 74## <Section Label="sec:generateFromOld"> 75## <Heading>Generating new complexes from old</Heading> 76## 77## <#Include Label="SCCartesianPower"/> 78## <#Include Label="SCCartesianProduct"/> 79## <#Include Label="SCConnectedComponents"/> 80## <#Include Label="SCConnectedProduct"/> 81## <#Include Label="SCConnectedSum"/> 82## <#Include Label="SCConnectedSumMinus"/> 83## <#Include Label="SCDifferenceCycleCompress"/> 84## <#Include Label="SCDifferenceCycleExpand"/> 85## <#Include Label="SCStronglyConnectedComponents"/> 86## 87## </Section> 88## 89## <#Include Label="fromgroup"/> 90## 91## <#Include Label="class3mflds"/> 92## 93## <#/GAPDoc> 94 95DeclareAttribute("SCConnectedComponents",SCIsPolyhedralComplex); 96DeclareAttribute("SCStronglyConnectedComponents",SCIsSimplicialComplex); 97 98DeclareOperation("SCCartesianPower",[SCIsSimplicialComplex,IsInt]); 99DeclareOperation("SCCartesianProduct",[SCIsSimplicialComplex,SCIsSimplicialComplex]); 100DeclareOperation("SCConnectedProduct",[SCIsSimplicialComplex,IsInt]); 101DeclareOperation("SCConnectedSum",[SCIsSimplicialComplex,SCIsSimplicialComplex]); 102DeclareOperation("SCConnectedSumMinus",[SCIsSimplicialComplex,SCIsSimplicialComplex]); 103DeclareOperation("SCFromDifferenceCycles",[IsList]); 104DeclareOperation("SCFromGenerators",[IsPermGroup,IsList]); 105 106DeclareGlobalFunction("SCBdCrossPolytope"); 107DeclareGlobalFunction("SCBdCyclicPolytope"); 108DeclareGlobalFunction("SCBdSimplex"); 109DeclareGlobalFunction("SCDifferenceCycleCompress"); 110DeclareGlobalFunction("SCDifferenceCycleExpand"); 111DeclareGlobalFunction("SCEmpty"); 112DeclareGlobalFunction("SCFVectorBdCrossPolytope"); 113DeclareGlobalFunction("SCFVectorBdCyclicPolytope"); 114DeclareGlobalFunction("SCFVectorBdSimplex"); 115DeclareGlobalFunction("SCSeriesAGL"); 116DeclareGlobalFunction("SCSeriesBdHandleBody"); 117DeclareGlobalFunction("SCSeriesBid"); 118DeclareGlobalFunction("SCSeriesBrehmKuehnelTorus"); 119DeclareGlobalFunction("SCSeriesC2n"); 120DeclareGlobalFunction("SCSeriesConnectedSum"); 121DeclareGlobalFunction("SCSeriesCSTSurface"); 122DeclareGlobalFunction("SCSeriesD2n"); 123DeclareGlobalFunction("SCSeriesHandleBody"); 124DeclareGlobalFunction("SCSeriesHomologySphere"); 125DeclareGlobalFunction("SCSeriesK"); 126DeclareGlobalFunction("SCSeriesKu"); 127DeclareGlobalFunction("SCSeriesL"); 128DeclareGlobalFunction("SCSeriesLe"); 129DeclareGlobalFunction("SCSeriesLensSpace"); 130DeclareGlobalFunction("SCSeriesNSB1"); 131DeclareGlobalFunction("SCSeriesNSB2"); 132DeclareGlobalFunction("SCSeriesNSB3"); 133DeclareGlobalFunction("SCSeriesPrimeTorus"); 134DeclareGlobalFunction("SCSeriesSeifertFibredSpace"); 135DeclareGlobalFunction("SCSimplex"); 136DeclareGlobalFunction("SCSeriesTorus"); 137DeclareGlobalFunction("SCSurface"); 138DeclareGlobalFunction("SCSeriesS2xS2"); 139