%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%
%W  matreps.tex           GAP documentation                  Bettina Eick
%W                                                          Werner Nickel
%%
%H  $Id: matreps.tex,v 1.4 2003/10/24 12:05:36 werner Exp $
%%

\Chapter{Matrix Representations}

This chapter describes functions which compute matrix representations
for pcp-groups.  So far the routines in this package are only able to
compute matrix representations for torsion-free nilpotent groups.

\>UnitriangularMatrixRepresentation( G )

computes a faithful representation of a torsion-free nilpotent group
<G> as unipotent lowertriangular matrices over the integers.  The
pc-presentation for <G> must not contain any power relations.  The
algorithm is described in \cite{dGN02}.

\>IsMatrixRepresentation( <G>, <matrices> )

checks if the map defined by maping the i-th generator of the
pcp-group <G> to the i-th matrix of <matrices> defines a homomorphism.

