  
  
                             [1XThe [5XSCO[105X Package Manual[101X
  
  
                       [1XSimplicial Cohomology of Orbifolds[101X
  
  
                               Version 2015.11.06
  
  
                                  August 2011
  
  
                                 Simon Görtzen
  
  
  
  Simon Görtzen
      Email:    [7Xmailto:simon.goertzen@rwth-aachen.de[107X
      Homepage: [7Xhttp://wwwb.math.rwth-aachen.de/goertzen/[107X
      Address:  [33X[0;14YLehrstuhl B für Mathematik[133X
                [33X[0;14YRWTH Aachen[133X
                [33X[0;14YTemplergraben 64[133X
                [33X[0;14Y52062 Aachen[133X
                [33X[0;14Y(Germany)[133X
  
  
  
  -------------------------------------------------------
  [1XAbstract[101X
  [33X[0;0YThis document explains the primary uses of the [5XSCO[105X package. Included in this
  manual  is a documented list of the most important methods and functions you
  will  need.  For  the  theoretical  basis of this package please refer to my
  diploma thesis and the corresponding paper (work in progress; [Gör08a]).[133X
  
  
  -------------------------------------------------------
  [1XCopyright[101X
  [33X[0;0Y© 2007-2011 by Simon Görtzen[133X
  
  [33X[0;0YThis  package  may  be distributed under the terms and conditions of the GNU
  Public License Version 2.[133X
  
  
  -------------------------------------------------------
  [1XAcknowledgements[101X
  [33X[0;0YThe [5XSCO[105X package would not have been possible without the theoretical work by
  I.  Moerdijk  and  D. A. Pronk concerning simplicial cohomology of orbifolds
  [MP99].  Many  thanks  to  these  two,  as  well  as Mohamed Barakat and the
  Lehrstuhl  B  für Mathematik at RWTH Aachen University in general. It should
  be  noted  that  [5XSCO[105X  in  its  current functionality is dependent on the [5XGAP[105X
  package [5Xhomalg[105X by M. Barakat [BR08], as it relies on [5Xhomalg[105X to do the actual
  computations. This manual was created with the help of the [5XGAPDoc[105X package by
  M. Neunhöffer and F. Lübeck.[133X
  
  
  -------------------------------------------------------
  
  
  [1XContents (SCO)[101X
  
  1 [33X[0;0YIntroduction[133X
    1.1 [33X[0;0YOverview over this manual[133X
    1.2 [33X[0;0YInstallation of the [5XSCO[105X Package[133X
  2 [33X[0;0YUsage[133X
    2.1 [33X[0;0YThe Examples Script[133X
    2.2 [33X[0;0YWorking Manually[133X
  3 [33X[0;0YExamples[133X
    3.1 [33X[0;0YExample 1: Klein Bottle[133X
    3.2 [33X[0;0YExample 2: [22XV_4[122X[133X
    3.3 [33X[0;0YExample 3: The "Teardrop" orbifold[133X
  4 [33X[0;0Y[5XSCO[105X methods and functions[133X
    4.1 [33X[0;0YMethods and functions for orbifold triangulations[133X
      4.1-1 OrbifoldTriangulation
      4.1-2 Vertices
      4.1-3 Simplices
      4.1-4 Isotropy
      4.1-5 Mu
      4.1-6 MuData
      4.1-7 InfoString
    4.2 [33X[0;0YMethods and functions for simplicial sets[133X
      4.2-1 SimplicialSet
      4.2-2 SimplicialSet
      4.2-3 ComputeNextDimension
      4.2-4 Extend
    4.3 [33X[0;0YMethods and functions for matrix creation and computation[133X
      4.3-1 BoundaryOperator
      4.3-2 CreateBoundaryMatrices
      4.3-3 Homology
      4.3-4 CreateCoboundaryMatrices
      4.3-5 Cohomology
      4.3-6 SCO_Examples
  A [33X[0;0YAn Overview of the [5XSCO[105X package source code[133X
  
  
  [32X
