The &RCWA; package provides methods for computations with the so-called 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 possible 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.