
                              The RCWA Package
                              ================


                                  Abstract

RCWA is a  GAP 4  package which provides methods  for investigating [R]esidue
[C]lass-[W]ise [A]ffine groups  by means of computation.  In principle,  this
package can deal at least with the following types of groups:

 - Finite groups.
 - Free groups of finite rank.
 - Free products of finitely many finite groups, thus in particular
   the modular group PSL(2,Z).
 - Direct products of such groups.
 - Wreath products of such groups with finite groups and with (Z,+).

Among these groups there are finitely generated groups which are not finitely
presented, and such with  unsolvable membership problem.  Further, any finite
group embeds into some divisible torsion group which RCWA can deal with.
    With the help of  this package,  the author has found  a countable simple
group which is generated by involutions interchanging disjoint  residue clas-
ses of the integers and which contains all the above groups.


                                Requirements

The RCWA package needs at least GAP 4.4.7, ResClasses 2.3.5, GRAPE 4.0, Poly-
cyclic 1.1  and GAPDoc 0.999.  All required packages are already present in a
standard GAP installation.  RCWA can be used under UNIX, under Windows and on
the MacIntosh.  It is completely written in the GAP language and does neither
contain  nor require  external binaries.  In particular,  warnings concerning
missing binaries when GRAPE is loaded can savely be ignored.


                                Installation

Like any other GAP package,  RCWA must be installed in the pkg/  subdirectory
of the GAP distribution.  This is accomplished by extracting the distribution
file in this directory.   When you have done this you can load the package as
usual via LoadPackage( "rcwa" );.
    For further advice  on questions of technical nature please see the chap-
ter `Auxiliary functions' in the manual.

                                    ---

If you have problems with this package, wish to make comments or suggestions,
or if you find bugs, please send e-mail to

Stefan Kohl, kohl@mathematik.uni-stuttgart.de

