polymake is a modular software system to study and visualize objects from various fields of discrete mathematics, especially convex polytopes, finite simplicial complexes, graphs, and (as of version 2.1) tropical geometry. For basic usage the user specifies an object (e.g., a polytope) and issues queries to the polymake system in order to learn about properties of this object, without the need to specify which algorithms to use in order to compute the desired results. In this way the system behaves much like an expert system.

While also previous versions allowed extensions in both, Perl and C++, the new version 2.1 introduces high-level Perl scripts as a new key feature. This allows to use polymake in a much more flexible way, for instance, to conveniently obtain census data of large classes of objects, but also to ease more intricate constructions of polytopes and other objects.

The presentation will be focused on how the users with different programming skills (starting from zero) can productively use and extend polymake functionality.

polymake is an open source project designed to run in a UNIX-alike environment. It is available for download at http://www.math.tu-berlin.de/polymake.