  
  [1X1 [33X[0;0YIntroduction[133X[101X
  
  
  [1X1.1 [33X[0;0YMotivation for this package[133X[101X
  
  [33X[0;0YThis  package  is about orbit enumeration. It bundles fundamental algorithms
  for   orbit  enumeration  as  well  as  more  sophisticated  special-purpose
  algorithms for very large orbits.[133X
  
  [33X[0;0YThe  fundamental  methods are basically an alternative implementation to the
  orbit algorithms in the [5XGAP[105X 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.[133X
  
  [33X[0;0YThe  higher  level  algorithms  basically implement the idea to enumerate an
  orbit  [21Xby  suborbits[121X  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 [21Xpush-the-button-tools[121X but require a
  considerable amount of knowledge from the [21Xpilot[121X.[133X
  
  [33X[0;0YQuite  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.[133X
  
  
  [1X1.2 [33X[0;0YOverview over this manual[133X[101X
  
  [33X[0;0YChapter  [14X2[114X  describes  the installation of this package. Chapter [14X3[114X describes
  our  reimplementation  of the basic orbit algorithm. Chapter [14X4[114X describes our
  toolbox for hash tables, Chapter [14X5[114X explains caching data structures, whereas
  Chapter  [14X8[114X describes our implementation of AVL trees. Chapter [14X6[114X covers tools
  to  use  random  methods  in  groups.  Chapter [14X7[114X 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[114X
  to  use  the orbit-by-suborbit algorithms. Currently, Chapter [14X10[114X 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[114X shows an instructive
  examples for the more sophisticated usage of this package.[133X
  
  
  [1X1.3 [33X[0;0YFeedback[133X[101X
  
  [33X[0;0YFor  bug  reports,  feature  requests  and suggestions, please use our issue
  tracker ([7Xhttps://github.com/gap-packages/orb/issues[107X).[133X
  
