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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… (More)
polymake is a software package designed for the study of the combinato rics and the geometry of convex polytopes and polyhedra. It offers access to a wide variety of algorithms and tools within a common framework. As a key design feature it allows to incorporate the functionality of a great variety of other software packages in a modular way. polymake is… (More)
We study a so-called static approach for the problem of routing vehicles conflict-free through a given street network. In fact, we assume that routes are computed without taking time-dependences into account and collisions are avoided via a particular reservation procedure. In this context, the task is to cope with two arising problems: the appearance of… (More)
The mathematical software system polymake provides a wide range of functions for convex polytopes, simplicial complexes, and other objects.
This note wants to explain how to obtain meaningful pictures of (possibly high-dimensional) convex polytopes, triangulated manifolds, and other objects from the realm of geometric combinatorics such as tight spans of finite metric spaces and tropical polytopes. In all our cases we arrive at specific, geometrically motivated, graph drawing problems. The… (More)
We describe an XML file format for storing data from computations in algebra and geometry. We also present a formal specification based on a RELAX-NG schema.