[GAP Forum] The RCWA Package

[Bettina Eick]

Dear GAP Forum,

it is my pleasure to announce the new Gap package
                `RCWA - Residue Class-Wise Affine Groups'
by Stefan Kohl.

The package contains methods to create and compute with rcwa mappings;
that is, with residue class-wise affine mappings over an euclidian ring.
The Collatz mapping

    T : Z -> Z defined by f(n) = n/2 if n is even and
                          f(n) = (3n+1)/2 if n is odd

is a rcwa mapping and it is the basis for the (still open) Collatz
conjecture asking whether an iterated application of T to any positive
integer eventually yields 1.

Further, the pacakge contains methods to create and compute with groups
of bijective rcwa mappings over an euclidian ring. In particular, the
package has been designed to investigate the group RCWA(Z) which is the
group of all bijective rcwa mappings over Z.

The groups RCWA(R) for euclidian rings R are interesting infinite groups
whose structure is not well known at current. The RCWA package provides
a first approach towards investigating these groups.

The package is currently available under
http://www.cip.mathematik.uni-stuttgart.de/~kohlsn/rcwa.html.

Best wishes,
              Bettina Eick