  
  
                             [1XThe [5XSCO[0m[1X Package Manual[0m
  
  
                       [1XSimplicial Cohomology of Orbifolds[0m
  
  
                               Version 2008.08.24
  
  
                                  August 2008
  
  
                                 Simon Goertzen
  
  
  
  Simon Goertzen
      Email:    [7Xmailto:simon.goertzen@rwth-aachen.de[0m
      Homepage: [7Xhttp://wwwb.math.rwth-aachen.de/goertzen/[0m
      Address:  Lehrstuhl B für Mathematik
                RWTH Aachen
                Templergraben 64
                52062 Aachen
                (Germany)
  
  
  
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  [1XAbstract[0m
  This document explains the primary uses of the [5XSCO[0m 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]).
  
  
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  [1XCopyright[0m
  © 2007-2008 by Simon Goertzen
  
  This  package  may  be distributed under the terms and conditions of the GNU
  Public License Version 2.
  
  
  -------------------------------------------------------
  [1XAcknowledgements[0m
  The [5XSCO[0m 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[0m  in  its  current functionality is dependent on the [5XGAP[0m
  package [5Xhomalg[0m by M. Barakat [BR08], as it relies on [5Xhomalg[0m to do the actual
  computations. This manual was created with the help of the [5XGAPDoc[0m package by
  M. Neunhöffer and F. Lübeck.
  
  
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  [1XContents (SCO)[0X
  
  1 Introduction
    1.1 Overview over this manual
    1.2 Installation of the [5XSCO[0m Package
  2 Usage
    2.1 The Examples Script
    2.2 Working Manually
  3 Examples
    3.1 Example 1: Klein Bottle
    3.2 Example 2: V_4
    3.3 Example 3: The "Teardrop" orbifold
  4 [5XSCO[0m methods and functions
    4.1 Methods and functions for orbifold triangulations
      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 Methods and functions for simplicial sets
      4.2-1 SimplicialSet
      4.2-2 SimplicialSet
      4.2-3 ComputeNextDimension
      4.2-4 Extend
    4.3 Methods and functions for matrix creation and computation
      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 An Overview of the [5XSCO[0m package source code
  
  
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