  
  [1X2 [33X[0;0YUsage[133X[101X
  
  [33X[0;0YThere  are  different  ways  to  use  [5XSCO[105X.  Please  note that for the actual
  computations  the  [5Xhomalg[105X  package  is  required, and you will need both the
  [5XRingsForHomalg[105X  and  the  [5XGaussForHomalg[105X  package  to  make  use of the full
  computational  capabilities.  For  your  information,  [5XRingsForHomalg[105X offers
  support  for  external  computer algebra systems and the rings they support,
  while  [5XGaussForHomalg[105X  extends  [5XGAP[105X  functionality  with  regards  to sparse
  matrices and computations over fields and [22Xℤ / ⟨ p^n ⟩[122X.[133X
  
  
  [1X2.1 [33X[0;0YThe Examples Script[133X[101X
  
  [33X[0;0YRegardless  of  the  extend of your installation, you will always be able to
  call  the  example  script  [11XSCO/examples/examples.g[111X. This script is not only
  callable in-[5XGAP[105X by [2XSCO_Examples[102X ([14X4.3-6[114X), but also automatically checks which
  packages you have installed and provides you with the available options. The
  example script is designed to take you through the ring creation process and
  then   load   one   of   the   files   of   your   choice   located  in  the
  [11XSCO/examples/orbifolds/[111X  directory.  In  there  you  will find a lot of test
  files  with  small  0-  or  1-dimensional  orbifolds,  but also the complete
  triangulations  of  the  17  orbifolds  corresponding  to  the 2-dimensional
  wallpaper  groups  (these should be exactly the uncapitalized files, ranging
  from  [11Xp1.g[111X  to  [11Xp6m.g[111X).  Computing  the cohomology of these orbifolds was an
  important part of my diploma thesis [G\t08].[133X
  
  [33X[0;0YPlease  note that the variables [3XM[103X, [3Xiso[103X, and [3Xmu[103X in the orbifold files have to
  keep their name for the example script to work correctly. Refer to chapter [14X3[114X
  for concrete examples.[133X
  
  
  [1X2.2 [33X[0;0YWorking Manually[133X[101X
  
  [33X[0;0YOnce  you  are familiar with the example script and want to try out your own
  triangulations,   it   is   best   to   create  your  own  [11X.g[111X  file  in  the
  [11XSCO/examples/orbifolds/[111X  directory,  then  call the script again. If for any
  reason  you  do  not  want to create a file or work with the script, you can
  always  do  every  step  by  hand.  Check  [14X4[114X  if you need to know more about
  specific methods and functions. The basic steps are:[133X
  
  [30X    [33X[0;6YDefine a list of maximum simplices[133X
  
  [30X    [33X[0;6YIf applicable, define an isotropy record[133X
  
  [30X    [33X[0;6YIf applicable, define a list encoding the [22Xμ[122X-map[133X
  
  [30X    [33X[0;6YFrom the above data, create an orbifold triangulation[133X
  
  [30X    [33X[0;6YDefine the simplicial set of the orbifold triangulation[133X
  
  [30X    [33X[0;6YCreate a [5Xhomalg[105X ring [22XR[122X[133X
  
  [30X    [33X[0;6YCreate boundary or coboundary matrices over [22XR[122X[133X
  
  [30X    [33X[0;6YCalculate their homology or cohomology[133X
  
