  
  [1X1 Introduction[0X
  
  
  [1X1.1 Motivation for this package[0X
  
  This  package  is about orbit enumeration. It bundles fundamental algorithms
  for   orbit  enumeration  as  well  as  more  sophisticated  special-purpose
  algorithms for very large orbits.
  
  The  fundamental  methods are basically an alternative implementation to the
  orbit algorithms in the [5XGAP[0m library. We tried to make them more flexible and
  more  efficient  at  the  same  time, therefore backwards compatibility with
  respect  to  the  user  interface  had  to  be  given  up. In addition, more
  information about how an orbit was produced is retained and is available for
  further  usage.  These  orbit  enumeration  algorithms  build  on  even more
  fundamental code for hash tables.
  
  The  higher  level  algorithms  basically implement the idea to enumerate an
  orbit  "by  suborbits"  with  respect  to one or more subgroups. While these
  orbit-by-suborbit  algorithms  are  much  more efficient in many cases, they
  very  often  need  careful and sometimes difficult preparations by the user.
  They are definitely not intended to be "push-the-button-tools" but require a
  considerable amount of knowledge from the "pilot".
  
  Quite  a  bit  of  the  code in this package consists in fact of interactive
  tools  to  enable  users  to  prepare  the  data  for  the orbit-by-suborbit
  algorithms to work.
  
  
  [1X1.2 Overview over this manual[0X
  
  Chapter  [14X2[0m  describes  the installation of this package. Chapter [14X3[0m describes
  our  reimplementation  of the basic orbit algorithm. Chapter [14X4[0m describes our
  toolbox  for  hash  tables,  whereas  Chapter  [14X6[0m  covers tools to use random
  methods  in  groups.  Chapter [14X7[0m describes a lot of tools to search in groups
  and  orbits.  These  techniques  are  basically intended to provide the data
  structures  necessary  to  run  the  code  described in Chapter [14X8[0m to use the
  orbit-by-suborbit  algorithms. Currently, Chapter [14X9[0m is an empty placeholder.
  In some future version of this package it will contain a description of code
  which helps users to find nice quotients of modules which is also needed for
  the  orbit-by-suborbit algorithms. However, since the interface to this code
  is  not  yet  stable,  we  chose not to document it as of now, in particular
  because it relies on other not yet published packages as of the time of this
  writing.  Finally,  Chapter  [14X10[0m  shows  an instructive examples for the more
  sophisticated usage of this package.
  
