  
  [1X1 [33X[0;0YIntroduction[133X[101X
  
  
  [1X1.1 [33X[0;0YGeneral aims of [5XCongruence[105X[101X[1X package[133X[101X
  
  [33X[0;0YThe  [5XGAP[105X package [5XCongruence[105X provides functions to construct several types of
  canonical  congruence  subgroups  in  [22XSL_2(ℤ)[122X,  and  also intersections of a
  finite number of such subgroups.[133X
  
  [33X[0;0YFurthermore,  it  implements  the algorithm for generating Farey symbols for
  congruence  subgroups  and  using  them  to  produce a system of independent
  generators for these subgroups.[133X
  
  [33X[0;0YUsing  the  package,  one can also determine indices of congruence subgroups
  and  their  intersections  in  [22XSL_2(ℤ)[122X  and  in  other congruence subgroups,
  generate  their  random  elements  and check element memberships. Success of
  other  group  theoretical constructions mostly depends on whether they could
  be expressed in terms of group generators or not.[133X
  
  [33X[0;0YFor  the theoretical backround, we refer to [LLT95b], [LLT95a], [CLLT93] and
  [Kul91].[133X
  
  
  [1X1.2 [33X[0;0YInstallation and system requirements[133X[101X
  
  [33X[0;0Y[5XCongruence[105X  is  distributed  in standard formats ([11Xtar.gz[111X, [11Xtar.bz2[111X, [11X-win.zip[111X)
  and can be obtained from [7Xhttp://www.cs.st-andrews.ac.uk/~alexk/congruence/[107X.[133X
  
  [33X[0;0Y[5XCongruence[105X  does  not  use  external  binaries and, therefore, works without
  restrictions  on the operating system. It requires at least version [5XGAP[105X 4.5,
  and no compatibility with previous releases of [5XGAP[105X 4 is guaranteed.[133X
  
  [33X[0;0YInstallation  of the package is standard and follows the guidelines from the
  [5XGAP[105X  manual (see [14X'Reference: Installing a GAP Package'[114X. After the package is
  installed,  you  can  start  [5XGAP[105X  and  load the [5XCongruence[105X package using the
  command:[133X
  
  [4X[32X  Example  [32X[104X
    [4X[28X[128X[104X
    [4X[25Xgap>[125X [27XLoadPackage("congruence");[127X[104X
    [4X[28X[128X[104X
  [4X[32X[104X
  
