  
  [1m[4m[31m11. A demo session with SimpComp[0m
  
  This chapter contains the transcript of a demo session with SimpComp that is
  intended  to give an insight into what things can be done with this package.
  Of  course  this  only  scratches  the  surface of the functions provided by
  SimpComp,  see  chapters  [1m4.[0m  through  [1m9.[0m  for further functions provided by
  SimpComp.
  
  
  [1m[4m[31m11.1 Creating a [22m[32mSCSimplicialComplex[1m[4m[31m object[0m
  
  Simplicial  complex  objects can either be created from a facet list, from a
  function  generating  triangulations  of  standard complexes or by expanding
  difference   cycles.  There  are  also  functions  creating  new  simplicial
  complexes  from  old,  see  chapter  [1m4.[0m  which will be described in the next
  sections.
  
  [22m[35m-----------------------------  Log  ------------------------------[0m
    [22m[35mgap> #first run functionality test on simpcomp[0m
    [22m[35mgap> SCRunTest();[0m
    [22m[35m+ test simpcomp package, version 1.1.21[0m
    [22m[35m+ GAP4stones: 69988[0m
    [22m[35mtrue[0m
    [22m[35mgap> #all ok[0m
    [22m[35mgap> c1:=SCFromFacets([[1,2],[2,3],[3,1]]);[0m
    [22m[35m[SimplicialComplex[0m
    [22m[35m[0m
    [22m[35m Properties known: Dim, Facets, Name, VertexLabels.[0m
    [22m[35m[0m
    [22m[35m Name="unnamed complex 1"[0m
    [22m[35m Dim=1[0m
    [22m[35m[0m
    [22m[35m/SimplicialComplex][0m
    [22m[35mgap> c2:=SCBdSimplex(2);[0m
    [22m[35m[SimplicialComplex[0m
    [22m[35m[0m
    [22m[35m Properties known: AutomorphismGroup, AutomorphismGroupOrder, [0m
    [22m[35m                   AutomorphismGroupStructure, AutomorphismGroupTransitivity, [0m
    [22m[35m                   Chi, Dim, F, Facets, Generators, HasBounday, Homology, [0m
    [22m[35m                   IsConnected, IsStronglyConnected, Name, TopologicalType, [0m
    [22m[35m                   VertexLabels.[0m
    [22m[35m[0m
    [22m[35m Name="S^1_3"[0m
    [22m[35m Dim=1[0m
    [22m[35m AutomorphismGroupStructure="S3"[0m
    [22m[35m AutomorphismGroupTransitivity=3[0m
    [22m[35m Chi=0[0m
    [22m[35m F=[ 3, 3 ][0m
    [22m[35m Homology=[ [ 0, [ ] ], [ 1, [ ] ] ][0m
    [22m[35m IsConnected=true[0m
    [22m[35m IsStronglyConnected=true[0m
    [22m[35m TopologicalType="S^1"[0m
    [22m[35m[0m
    [22m[35m/SimplicialComplex][0m
    [22m[35mgap> c3:=SCFromDifferenceCycles([[1,1,6],[3,3,2]]);[0m
    [22m[35m[SimplicialComplex[0m
    [22m[35m[0m
    [22m[35m Properties known: Dim, Facets, Name, VertexLabels.[0m
    [22m[35m[0m
    [22m[35m Name="complex from diffcycles [ [ 1, 1, 6 ], [ 3, 3, 2 ] ]"[0m
    [22m[35m Dim=2[0m
    [22m[35m[0m
    [22m[35m/SimplicialComplex][0m
    [22m[35mgap> [0m
  [22m[35m------------------------------------------------------------------[0m
  
  
  [1m[4m[31m11.2 Working with a [22m[32mSCSimplicialComplex[1m[4m[31m object[0m
  
  As  described  in  section  [1m3.2[0m  there  are two several ways of accessing an
  object  of  type [22m[32mSCSimplicialComplex[0m. An example for the two equivalent ways
  is given below. The preference will be given to the object oriented notation
  in this demo session. The code listed below
  
  [22m[35m-----------------------------  Log  ------------------------------[0m
    [22m[35mgap> c:=SCBdSimplex(3);; # create a simplicial complex object[0m
    [22m[35mgap> SCFVector(c);[0m
    [22m[35m[ 4, 6, 4 ][0m
    [22m[35mgap> SCSkel(c,0);[0m
    [22m[35m[ [ 1 ], [ 2 ], [ 3 ], [ 4 ] ][0m
    [22m[35mgap> [0m
  [22m[35m------------------------------------------------------------------[0m
  
  is equivalent to
  
  [22m[35m-----------------------------  Log  ------------------------------[0m
    [22m[35mgap> c:=SCBdSimplex(3);; # create a simplicial complex object[0m
    [22m[35mgap> c.F;[0m
    [22m[35m[ 4, 6, 4 ][0m
    [22m[35mgap> c.Skel(0);[0m
    [22m[35m[ [ 1 ], [ 2 ], [ 3 ], [ 4 ] ][0m
    [22m[35mgap> [0m
  [22m[35m------------------------------------------------------------------[0m
  
  
  [1m[4m[31m11.3 Calculating properties of a [22m[32mSCSimplicialComplex[1m[4m[31m object[0m
  
  SimpComp  provides  a  variety  of  functions  for calculating properties of
  simplicial  complexes,  see  chapter  [1m4.[0m.  All  these  properties  are  only
  calculated once and stored in the simplicial complex object.
  
  [22m[35m-----------------------------  Log  ------------------------------[0m
    [22m[35mgap> c1.F;     [0m
    [22m[35m[ 3, 3 ][0m
    [22m[35mgap> c1.FaceLattice;[0m
    [22m[35m[ [ [ 1 ], [ 2 ], [ 3 ] ], [ [ 1, 2 ], [ 1, 3 ], [ 2, 3 ] ] ][0m
    [22m[35mgap> c1.AutomorphismGroup;[0m
    [22m[35mS3[0m
    [22m[35mgap> c1.Generators;[0m
    [22m[35m[ [ [ 1, 2 ], 3 ] ][0m
    [22m[35mgap> c3.Facets;[0m
    [22m[35m[ [ 1, 2, 3 ], [ 1, 2, 8 ], [ 1, 3, 6 ], [ 1, 4, 6 ], [ 1, 4, 7 ], [0m
    [22m[35m  [ 1, 7, 8 ], [ 2, 3, 4 ], [ 2, 4, 7 ], [ 2, 5, 7 ], [ 2, 5, 8 ], [0m
    [22m[35m  [ 3, 4, 5 ], [ 3, 5, 8 ], [ 3, 6, 8 ], [ 4, 5, 6 ], [ 5, 6, 7 ], [0m
    [22m[35m  [ 6, 7, 8 ] ][0m
    [22m[35mgap> c3.F;[0m
    [22m[35m[ 8, 24, 16 ][0m
    [22m[35mgap> c3.G;[0m
    [22m[35m[ 4 ][0m
    [22m[35mgap> c3.H;[0m
    [22m[35m[ 5, 11, -1 ][0m
    [22m[35mgap> c3.ASDet;[0m
    [22m[35m186624[0m
    [22m[35mgap> c3.Chi;[0m
    [22m[35m0[0m
    [22m[35mgap> c3.Generators;[0m
    [22m[35m[ [ [ 1, 2, 3 ], 16 ] ][0m
    [22m[35mgap> c3.HasBoundary;[0m
    [22m[35mfalse[0m
    [22m[35mgap> c3.IsConnected;[0m
    [22m[35mtrue[0m
    [22m[35mgap> c3.IsCentrallySymmetric;[0m
    [22m[35mtrue[0m
    [22m[35mgap> c3.Vertices;[0m
    [22m[35m[ 1, 2, 3, 4, 5, 6, 7, 8 ][0m
    [22m[35mgap> c3.ConnectedComponents;[0m
    [22m[35m[ [SimplicialComplex[0m
    [22m[35m    [0m
    [22m[35m     Properties known: Dim, Facets, Name, VertexLabels.[0m
    [22m[35m    [0m
    [22m[35m     Name="Connected component #1 of complex from diffcycles [ [ 1, 1, 6 ], [ \[0m
    [22m[35m3, 3, 2 ] ]"[0m
    [22m[35m     Dim=2[0m
    [22m[35m    [0m
    [22m[35m    /SimplicialComplex] ][0m
    [22m[35mgap> c3.UnknownProperty;[0m
    [22m[35m#I  SCPropertyObject: unhandled property 'UnknownProperty'. Handled properties\[0m
    [22m[35m are [ "Equivalent", "IsKStackedSphere", "IsManifold", "IsMovable", "Move", [0m
    [22m[35m  "Moves", "RMoves", "ReduceAsSubcomplex", "Reduce", "ReduceEx", "Copy", [0m
    [22m[35m  "Recalc", "ASDet", "AutomorphismGroup", "AutomorphismGroupInternal", [0m
    [22m[35m  "Boundary", "ConnectedComponents", "Dim", "DualGraph", "Chi", "F", [0m
    [22m[35m  "FaceLattice", "FaceLatticeEx", "Faces", "FacesEx", "Facets", "FacetsEx", [0m
    [22m[35m  "FpBetti", "FundamentalGroup", "G", "Generators", "GeneratorsEx", "H", [0m
    [22m[35m  "HasBoundary", "HasInterior", "Homology", "Incidences", "IncidencesEx", [0m
    [22m[35m  "Interior", "IsCentrallySymmetric", "IsConnected", "IsEmpty", [0m
    [22m[35m  "IsEulerianManifold", "IsHomologySphere", "IsInKd", "IsKNeighborly", [0m
    [22m[35m  "IsOrientable", "IsPM", "IsPure", "IsShellable", "IsStronglyConnected", [0m
    [22m[35m  "MinimalNonFaces", "MinimalNonFacesEx", "Name", "Neighborliness", [0m
    [22m[35m  "Orientation", "Skel", "SkelEx", "SpanningTree", [0m
    [22m[35m  "StronglyConnectedComponents", "Vertices", "VerticesEx", [0m
    [22m[35m  "BoundaryOperatorMatrix", "HomologyBasis", "HomologyBasisAsSimplices", [0m
    [22m[35m  "HomologyInternal", "CoboundaryOperatorMatrix", "Cohomology", [0m
    [22m[35m  "CohomologyBasis", "CohomologyBasisAsSimplices", "CupProduct", [0m
    [22m[35m  "IntersectionForm", "IntersectionFormParity", [0m
    [22m[35m  "IntersectionFormDimensionality", "Load", "Save", "ExportPolymake", [0m
    [22m[35m  "ExportLatexTable", "ExportJavaView", "LabelMax", "LabelMin", "Labels", [0m
    [22m[35m  "Relabel", "RelabelStandard", "RelabelTransposition", "Rename", [0m
    [22m[35m  "SortComplex", "UnlabelFace", "AlexanderDual", "CollapseGreedy", "Cone", [0m
    [22m[35m  "DeletedJoin", "Difference", "HandleAddition", "Intersection", [0m
    [22m[35m  "IsIsomorphic", "IsSubcomplex", "Isomorphism", "IsomorphismEx", "Join", [0m
    [22m[35m  "Link", "Links", "Neighbors", "NeighborsEx", "Shelling", "ShellingExt", [0m
    [22m[35m  "Shellings", "Span", "Star", "Stars", "Suspension", "Union", [0m
    [22m[35m  "VertexIdentification", "Wedge", "DetermineTopologicalType", "Dim", [0m
    [22m[35m  "Facets", "VertexLabels", "Name", "Vertices", "IsConnected", [0m
    [22m[35m  "ConnectedComponents" ].[0m
    [22m[35m[0m
    [22m[35mfail[0m
    [22m[35mgap> [0m
  [22m[35m------------------------------------------------------------------[0m
  
  
  [1m[4m[31m11.4 Creating new complexes from a [22m[32mSCSimplicialComplex[1m[4m[31m object[0m
  
  [22m[35m-----------------------------  Log  ------------------------------[0m
    [22m[35mgap> c4:=c3+c3;[0m
    [22m[35m[SimplicialComplex[0m
    [22m[35m[0m
    [22m[35m Properties known: Dim, Facets, Name, VertexLabels, Vertices.[0m
    [22m[35m[0m
    [22m[35m Name="complex from diffcycles [ [ 1, 1, 6 ], [ 3, 3, 2 ] ]#+-complex from dif\[0m
    [22m[35mfcycles [ [ 1, 1, 6 ], [ 3, 3, 2 ] ]"[0m
    [22m[35m Dim=2[0m
    [22m[35m[0m
    [22m[35m/SimplicialComplex][0m
    [22m[35mgap> SCRename(c4,"T^2#T^2");[0m
    [22m[35mtrue[0m
    [22m[35mgap> SCLink(c4,1);[0m
    [22m[35m[SimplicialComplex[0m
    [22m[35m[0m
    [22m[35m Properties known: Dim, Facets, Name, VertexLabels.[0m
    [22m[35m[0m
    [22m[35m Name="lk(1) in T^2#T^2"[0m
    [22m[35m Dim=1[0m
    [22m[35m[0m
    [22m[35m/SimplicialComplex][0m
    [22m[35mgap> SCStar(c4,[1,2]);[0m
    [22m[35m[SimplicialComplex[0m
    [22m[35m[0m
    [22m[35m Properties known: Dim, Facets, Name, VertexLabels.[0m
    [22m[35m[0m
    [22m[35m Name="star([ 1, 2 ]) in T^2#T^2"[0m
    [22m[35m Dim=2[0m
    [22m[35m[0m
    [22m[35m/SimplicialComplex][0m
    [22m[35mgap> SCRename(c3,"T^2");[0m
    [22m[35mtrue[0m
    [22m[35mgap> SCConnectedProduct(c3,4);[0m
    [22m[35m[SimplicialComplex[0m
    [22m[35m[0m
    [22m[35m Properties known: Dim, Facets, Name, VertexLabels, Vertices.[0m
    [22m[35m[0m
    [22m[35m Name="T^2#+-T^2#+-T^2#+-T^2"[0m
    [22m[35m Dim=2[0m
    [22m[35m[0m
    [22m[35m/SimplicialComplex][0m
    [22m[35mgap> SCCartesianProduct(c2,c2);[0m
    [22m[35m[SimplicialComplex[0m
    [22m[35m[0m
    [22m[35m Properties known: Dim, Facets, Name, TopologicalType, VertexLabels.[0m
    [22m[35m[0m
    [22m[35m Name="S^1_3xS^1_3"[0m
    [22m[35m Dim=2[0m
    [22m[35m TopologicalType="S^1xS^1"[0m
    [22m[35m[0m
    [22m[35m/SimplicialComplex][0m
    [22m[35mgap> SCCartesianPower(c2,3);[0m
    [22m[35m[SimplicialComplex[0m
    [22m[35m[0m
    [22m[35m Properties known: Dim, Facets, Name, TopologicalType, VertexLabels.[0m
    [22m[35m[0m
    [22m[35m Name="(S^1_3)^3"[0m
    [22m[35m Dim=3[0m
    [22m[35m TopologicalType="(S^1)^3"[0m
    [22m[35m[0m
    [22m[35m/SimplicialComplex][0m
    [22m[35mgap> [0m
  [22m[35m------------------------------------------------------------------[0m
  
  
  [1m[4m[31m11.5 Homology related calculations[0m
  
  SimpComp  relies  on  the  GAP  package  homology  [DH+04]  for its homology
  computations  but  provides  further  (co-)homology  related  functions, see
  chapter [1m5.[0m.
  
  [22m[35m-----------------------------  Log  ------------------------------[0m
    [22m[35mgap> s2s2:=SCCartesianProduct(SCBdSimplex(3),SCBdSimplex(3));[0m
    [22m[35m[SimplicialComplex[0m
    [22m[35m[0m
    [22m[35m Properties known: Dim, Facets, Name, TopologicalType, VertexLabels.[0m
    [22m[35m[0m
    [22m[35m Name="S^2_4xS^2_4"[0m
    [22m[35m Dim=4[0m
    [22m[35m TopologicalType="S^2xS^2"[0m
    [22m[35m[0m
    [22m[35m/SimplicialComplex][0m
    [22m[35mgap> SCHomology(s2s2);[0m
    [22m[35m[ [ 0, [  ] ], [ 0, [  ] ], [ 2, [  ] ], [ 0, [  ] ], [ 1, [  ] ] ][0m
    [22m[35mgap> SCHomologyInternal(s2s2);[0m
    [22m[35m[ [ 0, [  ] ], [ 0, [  ] ], [ 2, [  ] ], [ 0, [  ] ], [ 1, [  ] ] ][0m
    [22m[35mgap> SCHomologyBasis(s2s2,2);[0m
    [22m[35m[ [ 1, [ [ 1, 70 ], [ -1, 12 ], [ 1, 2 ], [ -1, 1 ] ] ], [0m
    [22m[35m  [ 1, [ [ 1, 143 ], [ -1, 51 ], [ 1, 29 ], [ -1, 25 ] ] ] ][0m
    [22m[35mgap> SCHomologyBasisAsSimplices(s2s2,2);[0m
    [22m[35m[ [ 1, [0m
    [22m[35m      [ [ 1, [ 2, 3, 4 ] ], [ -1, [ 1, 3, 4 ] ], [ 1, [ 1, 2, 4 ] ], [ -1, [ 1[0m
    [22m[35m                    , 2, 3 ] ] ] ], [0m
    [22m[35m  [ 1, [ [ 1, [ 5, 9, 13 ] ], [ -1, [ 1, 9, 13 ] ], [ 1, [ 1, 5, 13 ] ], [0m
    [22m[35m          [ -1, [ 1, 5, 9 ] ] ] ] ][0m
    [22m[35mgap> SCCohomologyBasis(s2s2,2);[0m
    [22m[35m[ [ 1, [0m
    [22m[35m      [ [ 1, 122 ], [ 1, 115 ], [ 1, 112 ], [ 1, 111 ], [ 1, 93 ], [ 1, 90 ], [0m
    [22m[35m          [ 1, 89 ], [ 1, 84 ], [ 1, 83 ], [ 1, 82 ], [ 1, 46 ], [ 1, 43 ], [0m
    [22m[35m          [ 1, 42 ], [ 1, 37 ], [ 1, 36 ], [ 1, 35 ], [ 1, 28 ], [ 1, 27 ], [0m
    [22m[35m          [ 1, 26 ], [ 1, 25 ] ] ], [0m
    [22m[35m  [ 1, [ [ 1, 213 ], [ 1, 201 ], [ 1, 192 ], [ 1, 189 ], [ 1, 159 ], [0m
    [22m[35m          [ 1, 150 ], [ 1, 147 ], [ 1, 131 ], [ 1, 128 ], [ 1, 125 ], [0m
    [22m[35m          [ 1, 67 ], [ 1, 58 ], [ 1, 55 ], [ 1, 39 ], [ 1, 36 ], [ 1, 33 ], [0m
    [22m[35m          [ 1, 10 ], [ 1, 7 ], [ 1, 4 ], [ 1, 1 ] ] ] ][0m
    [22m[35mgap> SCCohomologyBasisAsSimplices(s2s2,2);[0m
    [22m[35m[ [ 1, [ [ 1, [ 4, 8, 12 ] ], [ 1, [ 3, 8, 12 ] ], [ 1, [ 3, 7, 12 ] ], [0m
    [22m[35m          [ 1, [ 3, 7, 11 ] ], [ 1, [ 2, 8, 12 ] ], [ 1, [ 2, 7, 12 ] ], [0m
    [22m[35m          [ 1, [ 2, 7, 11 ] ], [ 1, [ 2, 6, 12 ] ], [ 1, [ 2, 6, 11 ] ], [0m
    [22m[35m          [ 1, [ 2, 6, 10 ] ], [ 1, [ 1, 8, 12 ] ], [ 1, [ 1, 7, 12 ] ], [0m
    [22m[35m          [ 1, [ 1, 7, 11 ] ], [ 1, [ 1, 6, 12 ] ], [ 1, [ 1, 6, 11 ] ], [0m
    [22m[35m          [ 1, [ 1, 6, 10 ] ], [ 1, [ 1, 5, 12 ] ], [ 1, [ 1, 5, 11 ] ], [0m
    [22m[35m          [ 1, [ 1, 5, 10 ] ], [ 1, [ 1, 5, 9 ] ] ] ], [0m
    [22m[35m  [ 1, [ [ 1, [ 13, 14, 15 ] ], [ 1, [ 9, 14, 15 ] ], [ 1, [ 9, 10, 15 ] ], [0m
    [22m[35m          [ 1, [ 9, 10, 11 ] ], [ 1, [ 5, 14, 15 ] ], [ 1, [ 5, 10, 15 ] ], [0m
    [22m[35m          [ 1, [ 5, 10, 11 ] ], [ 1, [ 5, 6, 15 ] ], [ 1, [ 5, 6, 11 ] ], [0m
    [22m[35m          [ 1, [ 5, 6, 7 ] ], [ 1, [ 1, 14, 15 ] ], [ 1, [ 1, 10, 15 ] ], [0m
    [22m[35m          [ 1, [ 1, 10, 11 ] ], [ 1, [ 1, 6, 15 ] ], [ 1, [ 1, 6, 11 ] ], [0m
    [22m[35m          [ 1, [ 1, 6, 7 ] ], [ 1, [ 1, 2, 15 ] ], [ 1, [ 1, 2, 11 ] ], [0m
    [22m[35m          [ 1, [ 1, 2, 7 ] ], [ 1, [ 1, 2, 3 ] ] ] ] ][0m
    [22m[35mgap> PrintArray(SCIntersectionForm(s2s2));[0m
    [22m[35m[ [  0,  1 ],[0m
    [22m[35m  [  1,  0 ] ][0m
    [22m[35mgap> c:=s2s2+s2s2;[0m
    [22m[35m[SimplicialComplex[0m
    [22m[35m[0m
    [22m[35m Properties known: Dim, Facets, Name, VertexLabels, Vertices.[0m
    [22m[35m[0m
    [22m[35m Name="S^2_4xS^2_4#+-S^2_4xS^2_4"[0m
    [22m[35m Dim=4[0m
    [22m[35m[0m
    [22m[35m/SimplicialComplex][0m
    [22m[35mgap> PrintArray(SCIntersectionForm(c));[0m
    [22m[35m[ [   0,  -1,   0,   0 ],[0m
    [22m[35m  [  -1,   0,   0,   0 ],[0m
    [22m[35m  [   0,   0,   0,  -1 ],[0m
    [22m[35m  [   0,   0,  -1,   0 ] ][0m
    [22m[35mgap> [0m
  [22m[35m------------------------------------------------------------------[0m
  
  
  [1m[4m[31m11.6 Bistellar flips[0m
  
  [22m[35m-----------------------------  Log  ------------------------------[0m
    [22m[35mgap> beta4:=SCBdCrossPolytope(4);;    [0m
    [22m[35mgap> s3:=SCBdSimplex(4);;             [0m
    [22m[35mgap> SCEquivalent(beta4,s3);[0m
    [22m[35m#I  round 0, move: [ [ 2, 6, 7 ], [ 3, 4 ] ][0m
    [22m[35m[ 8, 25, 34, 17 ][0m
    [22m[35m#I  round 1, move: [ [ 2, 7 ], [ 3, 4, 5 ] ][0m
    [22m[35m[ 8, 24, 32, 16 ][0m
    [22m[35m#I  round 2, move: [ [ 2, 5 ], [ 3, 4, 8 ] ][0m
    [22m[35m[ 8, 23, 30, 15 ][0m
    [22m[35m#I  round 3, move: [ [ 2 ], [ 3, 4, 6, 8 ] ][0m
    [22m[35m[ 7, 19, 24, 12 ][0m
    [22m[35m#I  round 4, move: [ [ 6, 8 ], [ 1, 3, 4 ] ][0m
    [22m[35m[ 7, 18, 22, 11 ][0m
    [22m[35m#I  round 5, move: [ [ 8 ], [ 1, 3, 4, 5 ] ][0m
    [22m[35m[ 6, 14, 16, 8 ][0m
    [22m[35m#I  round 6, move: [ [ 5 ], [ 1, 3, 4, 7 ] ][0m
    [22m[35m[ 5, 10, 10, 5 ][0m
    [22m[35m#I  SCReduceComplexEx: complexes are bistellarly equivalent.[0m
    [22m[35mtrue[0m
    [22m[35mgap> SCBistellarOptions.WriteLevel;   [0m
    [22m[35m0[0m
    [22m[35mgap> SCBistellarOptions.WriteLevel:=1;[0m
    [22m[35m1[0m
    [22m[35mgap> SCEquivalent(beta4,s3);          [0m
    [22m[35m#I  SCLibInit: made directory "~/PATH" for user library.[0m
    [22m[35m#I  SCIntFunc.SCLibInit: index not found -- trying to reconstruct it.[0m
    [22m[35m#I  SCLibUpdate: rebuilding index for ~/PATH.[0m
    [22m[35m#I  SCLibUpdate: rebuilding index done.[0m
    [22m[35m[0m
    [22m[35m#I  round 0, move: [ [ 2, 4, 6 ], [ 7, 8 ] ][0m
    [22m[35m[ 8, 25, 34, 17 ][0m
    [22m[35m#I  round 1, move: [ [ 2, 4 ], [ 5, 7, 8 ] ][0m
    [22m[35m[ 8, 24, 32, 16 ][0m
    [22m[35m#I  round 2, move: [ [ 4, 5 ], [ 1, 7, 8 ] ][0m
    [22m[35m[ 8, 23, 30, 15 ][0m
    [22m[35m#I  round 3, move: [ [ 4 ], [ 1, 6, 7, 8 ] ][0m
    [22m[35m[ 7, 19, 24, 12 ][0m
    [22m[35m#I  SCLibAdd: saving complex to file "complex_ReducedComplex_7_vertices_3_2009\[0m
    [22m[35m-10-27_11-40-00.sc".[0m
    [22m[35m#I  round 4, move: [ [ 2, 6 ], [ 3, 7, 8 ] ][0m
    [22m[35m[ 7, 18, 22, 11 ][0m
    [22m[35m#I  round 5, move: [ [ 2 ], [ 3, 5, 7, 8 ] ][0m
    [22m[35m[ 6, 14, 16, 8 ][0m
    [22m[35m#I  SCLibAdd: saving complex to file "complex_ReducedComplex_6_vertices_5_2009\[0m
    [22m[35m-10-27_11-40-00.sc".[0m
    [22m[35m#I  round 6, move: [ [ 5 ], [ 1, 3, 7, 8 ] ][0m
    [22m[35m[ 5, 10, 10, 5 ][0m
    [22m[35m#I  SCLibAdd: saving complex to file "complex_ReducedComplex_5_vertices_6_2009\[0m
    [22m[35m-10-27_11-40-00.sc".[0m
    [22m[35m#I  SCLibAdd: saving complex to file "complex_ReducedComplex_5_vertices_7_2009\[0m
    [22m[35m-10-27_11-40-00.sc".[0m
    [22m[35m#I  SCReduceComplexEx: complexes are bistellarly equivalent.[0m
    [22m[35mtrue[0m
    [22m[35mgap> myLib:=SCLibInit("~/PATH"); # copy path from above             [0m
    [22m[35m[Simplicial complex library. Properties:[0m
    [22m[35mCalculateIndexAttributes=true[0m
    [22m[35mNumber of complexes in library=4[0m
    [22m[35mIndexAttributes=[ "Name", "Date", "Dim", "F", "G", "H", "Chi", "Homology" ][0m
    [22m[35mLoaded=true[0m
    [22m[35mPath="/home/spreerjn/reducedComplexes/2009-10-27_11-40-00/"[0m
    [22m[35m][0m
    [22m[35mgap> s3:=myLib.Load(3);[0m
    [22m[35m[SimplicialComplex[0m
    [22m[35m[0m
    [22m[35m Properties known: Chi, Date, Dim, F, Faces, Facets, G, H, Homology, [0m
    [22m[35m                   IsConnected, Name, VertexLabels.[0m
    [22m[35m[0m
    [22m[35m Name="ReducedComplex_5_vertices_6"[0m
    [22m[35m Dim=3[0m
    [22m[35m Chi=0[0m
    [22m[35m F=[ 5, 10, 10, 5 ][0m
    [22m[35m G=[ 0, 0 ][0m
    [22m[35m H=[ 1, 1, 1, 1 ][0m
    [22m[35m Homology=[ [ 0, [ ] ], [ 0, [ ] ], [ 0, [ ] ], [ 1, [ ] ] ][0m
    [22m[35m IsConnected=true[0m
    [22m[35m[0m
    [22m[35m/SimplicialComplex][0m
    [22m[35mgap> s3:=myLib.Load(2);[0m
    [22m[35m[SimplicialComplex[0m
    [22m[35m[0m
    [22m[35m Properties known: Chi, Date, Dim, F, Faces, Facets, G, H, Homology, [0m
    [22m[35m                   IsConnected, Name, VertexLabels.[0m
    [22m[35m[0m
    [22m[35m Name="ReducedComplex_6_vertices_5"[0m
    [22m[35m Dim=3[0m
    [22m[35m Chi=0[0m
    [22m[35m F=[ 6, 14, 16, 8 ][0m
    [22m[35m G=[ 1, 0 ][0m
    [22m[35m H=[ 2, 2, 2, 1 ][0m
    [22m[35m Homology=[ [ 0, [ ] ], [ 0, [ ] ], [ 0, [ ] ], [ 1, [ ] ] ][0m
    [22m[35m IsConnected=true[0m
    [22m[35m[0m
    [22m[35m/SimplicialComplex][0m
    [22m[35mgap> t2:=SCCartesianProduct(SCBdSimplex(2),SCBdSimplex(2));;[0m
    [22m[35mgap> t2.F;[0m
    [22m[35m[ 9, 27, 18 ][0m
    [22m[35mgap> SCBistellarOptions.WriteLevel:=0;[0m
    [22m[35m0[0m
    [22m[35mgap> SCBistellarOptions.LogLevel:=0;  [0m
    [22m[35m0[0m
    [22m[35mgap> mint2:=SCReduceComplex(t2);    [0m
    [22m[35m[ true, [SimplicialComplex[0m
    [22m[35m    [0m
    [22m[35m     Properties known: Dim, Facets, Name, VertexLabels.[0m
    [22m[35m    [0m
    [22m[35m     Name="unnamed complex 85"[0m
    [22m[35m     Dim=2[0m
    [22m[35m    [0m
    [22m[35m    /SimplicialComplex], 32 ][0m
    [22m[35mgap> [0m
    [22m[35m			[0m
  [22m[35m------------------------------------------------------------------[0m
  
