Actually Doing It! : A Computational Introduction to Polyhedral Geometry Actually Doing It! : A Computational Introduction to Polyhedral GeometryThe minicourse deals with various computational problems associated with convex polyhedra in general dimension. Typical problems include the feasibility problem (is the convex polytope empty?), the representation conversion problem (between halfspace and vertex representations), the polytope volume computation, the construction of hyperplane arrangements and zonotopes, the computation of integrals and counting of lattice points. We aim to show some of the most important algorithms to solve such problems. All these essential algorithms have applications in a wide variety of topics including discrete optimization, game theory, algebraic and enumerative combinatorics, probability and statistics, cryptography and others.
Polymake is designed to run on any linux system including MacOS X. It is a special ``perl-like'' language. Once you have that polytope in memory, you can ask Polymake to compute many more properties about it. For this, Polymake relies mostly on software written by others, these include CDD, LattE, LRS, JAVAVIEW, etc, etc.