The &RCWA; package provides methods for computations with Residue Class-Wise Affine 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 standard choice is R = \mathbb{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 3n+1 - conjecture. A regularly updated comprehensive annotated bibliography for this conjecture which has been compiled by Jeffrey C. Lagarias can be found at http://arxiv.org/abs/math.NT/0309224.

The bijective rcwa mappings of R form a proper subgroup of Sym(R), called RCWA(R). In general, computing 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( \mathbb{Z}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&uscore;e.pdf).