  
  [1X1 [33X[0;0YPreface[133X[101X
  
  [33X[0;0Y[5XUnipot[105X  is  a package for [5XGAP[105X 4 [GAP04]. The version 1.0 of this package was
  the content of my diploma thesis [Hal00].[133X
  
  [33X[0;0YLet  [22XU[122X be a unipotent subgroup of a Chevalley group of type [22XL(K)[122X. Then it is
  generated  by  the  elements  [22Xx_r(t)[122X  for  all [22Xr∈ Φ^+,t∈ K[122X. The roots of the
  underlying  root system [22XΦ[122X are ordered according to the height function. Each
  element of [22XU[122X is a product of the root elements [22Xx_r(t)[122X. By Theorem 5.3.3 from
  [Car89]  each  element  of  [22XU[122X  can  be uniquely written as a product of root
  elements  with  roots  in  increasing  order. This unique form is called the
  canonical form.[133X
  
  [33X[0;0YThe  main  purpose  of  this  package is to compute the canonical form of an
  element  of  the  group  [22XU[122X.  To  this  end we have implemented the unipotent
  subgroups  of  Chevalley  groups  and  their  elements  as  [5XGAP[105X  objects and
  installed  some  operations for them. One method for the operation [10XComm[110X uses
  Chevalley's commutator formula, which we have implemented, too.[133X
  
  
  [1X1.1 [33X[0;0YRoot Systems[133X[101X
  
  [33X[0;0YWe  use  the  root systems and the structure constants available in [5XGAP[105X from
  the simple Lie algebras, and the same ordering of roots.[133X
  
  
  [1X1.2 [33X[0;0YCiting Unipot[133X[101X
  
  [33X[0;0YIf  you use [5XUnipot[105X to solve a problem or publish some result that was partly
  obtained  using [5XUnipot[105X, I would appreciate it if you would cite [5XUnipot[105X, just
  as you would cite another paper that you used. (Below is a sample citation.)
  Again I would appreciate if you could inform me about such a paper.[133X
  
  [33X[0;0YSpecifically, please refer to:[133X
  
  [4X[32X  Example  [32X[104X
    [4X[28X[Hal02] Sergei Haller. Unipot --- a system for computing with elements[128X[104X
    [4X[28X        of unipotent subgroups of Chevalley groups, July 2002.[128X[104X
  [4X[32X[104X
  
