First we present algorithms for the construction and analysis of near-rings of functions on finite groups. In particular we show how to construct a transformation near-ring from a given set of generating functions and how to solve the membership problem for such a near-ring. Secondly we give a construction of BIB-designs from planar near-rings.
Implementations of the described algorithms are part of the GAP-package Sonata that has been developed at the University of Linz, Austria. Sonata is part of SAGE since 2006. We will demonstrate various examples by using a combination of these computer algebra systems.