Defect polytopes and counter-examples with polymake

polymake and Lattice Polytopes

The polymake software system deals with convex polytopes and related objects from geometric combinatorics. This note reports on a new implementation of a subclass for lattice polytopes. The features displayed are enabled by recent changes to the polymake core, which will be discussed briefly.

polymake: a Framework for Analyzing Convex Polytopes

Fe b 20 09 POLYMAKE AND LATTICE POLYTOPES

The polymake software system deals with convex polytopes and related objects from geometric combinatorics. This note reports on a new implementation of a subclass for lattice polytopes. The features displayed are enabled by recent changes to the polymake core, which will be discussed briefly.

Proof-Like Counter-Examples

Counter-examples explain why a desired temporal logic property fails to hold, and as such considered to be the most useful form of output from modelcheckers. Reported explanations are typically short and described in terms of states and transitions of the model; as a result, they can be effectively used for debugging. However, counter-examples are not available for every CTL property and are of...

Geometric Reasoning with polymake

The mathematical software system polymake provides a wide range of functions for convex polytopes, simplicial complexes, and other objects. A large part of this paper is dedicated to a tutorial which exemplifies the usage. Later sections include a survey of research results obtained with the help of polymake so far and a short description of the technical background.