  
  [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, Chapter [14X5[0m explains caching data structures, whereas
  Chapter  [14X8[0m describes our implementation of AVL trees. 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 [14X9[0m
  to  use  the orbit-by-suborbit algorithms. Currently, Chapter [14X10[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 [14X11[0m shows an instructive
  examples for the more sophisticated usage of this package.
  
