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


                                Abstract

RCWA is a GAP 4 package which provides methods for computations with
the so-called [R]esidue [C]lass-[W]ise [A]ffine mappings (rcwa mappings
for short) and the groups generated by bijective mappings of this type.

The rcwa mappings are a type of mappings of certain euclidean rings R
into themselves. A possible choice is R = Z. Similar classes of mappings
are known as Generalized Collatz Mappings, Periodically Linear Functions
or Number Theoretic Functions with Periodic Rational Coefficients.
In fact, the development of this package has partly been motivated
by the Collatz- (3n+1-) conjecture. 

The bijective rcwa mappings of R form a proper subgroup of Sym(R), called
RCWA(R). In general, the computation with arbitrary mappings from R into
R is an algorithmically difficult task. The rcwa mappings provide a class
of mappings which are accessible to computations. The investigation of
rcwa mappings and groups generated by them is the central aim of this
package. 

An object of particular interest is the group RCWA(Z) of all residue
class-wise affine bijections of the integers.

Residue class-wise affine groups are introduced in the author's thesis
`Restklassenweise affine Gruppen'. This thesis is available at
http://elib.uni-stuttgart.de/opus/volltexte/2005/2448/.
A copy of it as well as an english translation is distributed with this
package (see thesis/thesis.pdf resp. thesis/thesis_e.pdf).


                              Requirements

The RCWA Package needs at least version 4.4 of GAP, is completely written
in the GAP language and does neither contain nor require external binaries.
Recent versions of the packages ResClasses, GRAPE and GAPDoc are needed.
The binaries of GRAPE are not needed, thus RCWA runs under Windows and on
the MacIntosh as well. 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
chapter `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

