Unipot is a package for GAP 4 [GAP04]. The version 1.0 of this package was the content of my diploma thesis [Hal00].
Let U be a unipotent subgroup of a Chevalley group of type L(K). Then it is generated by the elements x_r(t) for all r∈ Φ^+,t∈ K. The roots of the underlying root system Φ are ordered according to the height function. Each element of U is a product of the root elements x_r(t). By Theorem 5.3.3 from [Car89] each element of U can be uniquely written as a product of root elements with roots in increasing order. This unique form is called the canonical form.
The main purpose of this package is to compute the canonical form of an element of the group U. To this end we have implemented the unipotent subgroups of Chevalley groups and their elements as GAP objects and installed some operations for them. One method for the operation Comm uses Chevalley's commutator formula, which we have implemented, too.
We use the root systems and the structure constants available in GAP from the simple Lie algebras, and the same ordering of roots.
If you use Unipot to solve a problem or publish some result that was partly obtained using Unipot, I would appreciate it if you would cite Unipot, 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.
Specifically, please refer to:
[Hal02] Sergei Haller. Unipot --- a system for computing with elements
of unipotent subgroups of Chevalley groups, July 2002.
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