  
  [1X1 [33X[0;0YIntroduction[133X[101X
  
  [33X[0;0YThis  package is a collection of functions that I wrote for various research
  projects  (e.g.,  [Gra08],  [dG11], [GE09], [Gra11], [GVY12]). The reason to
  collect them in a package is to avoid them getting lost. Secondly, I believe
  that the functions may be of wider interest.[133X
  
  [33X[0;0YApart  from  this  one,  this manual has four chapters. The second describes
  various  functions  that did not fit in any of the other chapters. They vary
  from  short  utility  functions  to  functions  implementing  rather complex
  algorithms.  The  remaining  three  chapters are all devoted to a particular
  area.[133X
  
  [33X[0;0YThe  third  chapter  contains (descriptions of) functions for computing with
  the classification of the nilpotent orbits in simple Lie algebras. There are
  functions  for  creating  the  orbits  and for computing representatives. We
  refer  to [CM93] for an overview of the theory of nilpotent orbits in simple
  Lie algebras.[133X
  
  [33X[0;0YThe  fourth chapter is dedicated to finite order automorphisms of the simple
  Lie  algebras and the corresponding [22Xθ[122X-groups. The finite order automorphisms
  have  been classified by Kac, up to conjugacy in the automorphism group. For
  the  background on this we refer to [Hel78]. The classification is described
  in  terms  of  so-called  Kac  diagrams. The package contains a function for
  creating  all automorphisms of a given simple Lie algebra, of a given finite
  order.[133X
  
  [33X[0;0YThe  eigenspaces  of an automorphism of finite order of a simple Lie algebra
  form a grading of that Lie algebra. Moreover, the 0-component is a reductive
  subalgebra,  acting  on  the  1-component.  The 0-component corresponds to a
  reductive  reductive group, also acting on the 1-component. This group (with
  its  action)  is called a [22Xθ[122X-group. It was introduced and studied in the 70-s
  by  Vinberg  ([Vin75]  ,  [Vin76],  [Vin79])  The package has a function for
  listing the nilpotent orbits of this group.[133X
  
  [33X[0;0YThe  fifth  chapter has functions for working with semisimple subalgebras of
  semisimple  Lie  algebras.  The  package  contains  a database of semisimple
  subalgebras  of the simple subalgebras of ranks up to 8. Moreover, there are
  functions  for  computing  the  semisimple  subalgebras  of  semisimple  Lie
  algebras  on  the  fly.  Finally,  there  are  some  functions for computing
  branching rules.[133X
  
  [33X[0;0YWe remark that the package needs the package [5XQuaGroup[105X.[133X
  
