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\Chapter{Introduction}

\index{carat}

This package contains GAP interface routines to {\CARAT}, 
a package of programs for the computation with crystallographic
groups. {\CARAT} is implemented in C, and has been developed by
J.~Opgenorth, W.~Plesken, and T.~Schulz at Lehrstuhl~B f\accent127ur 
Mathematik, RWTH Aachen. The algorithms used by {\CARAT} are described 
in \cite{OPS98}. 

{\CARAT} is to a large extent complementary to the GAP 4 package
{\Cryst}. In particular, it provides routines for the computation 
of normalizers and conjugators of finite unimodular groups in $GL(n,Z)$,
and routines for the computation of Bravais groups, which are all 
missing in {\Cryst}.  Furthermore, {\CARAT} provides also a catalogue of 
Bravais groups up to dimension 6. {\Cryst} automatically loads {\CARAT}
when it is available, and makes use of its functions where necessary. 
The present package thereby extends the functionality of {\Cryst} 
considerably.

{\CARAT} itself is NOT part of this package. However, for your convenience,
and with the permission of the {\CARAT} authors, a copy of {\CARAT} 
has been included. It is this version with which the interface routines 
have been tested. The most recent version of {\CARAT} can be obtained at 
the {\CARAT} Home Page

\beginitems
&
\URL{http://wwwb.math.rwth-aachen.de/carat/}
\enditems
 
The {\GAP} interface routines to {\CARAT} have been written by

\beginitems
&
Franz G\accent127ahler\hfill\break
Fakult\accent127at f\accent127ur Mathematik\hfill\break
Universit\accent127at Bielefeld\hfill\break
Postfach 10 01 31\hfill\break
D-33501 Bielefeld\hfill\break
\Mailto{gaehler@math.uni-bielefeld.de}
\enditems

to whom bug reports regarding these interface routines should be
addressed. 

Bug reports regarding {\CARAT} itself should be sent to
\Mailto{carat@momo.math.rwth-aachen.de}.