The polymake XML file format
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.
cs.MS↗
arXiv subjects
Ewgenij Gawrilow
Publications and source records attributed to Ewgenij Gawrilow.
Computing convex hulls and counting integer points with polymake
The main purpose of this paper is to report on the state of the art of computing integer hulls and their facets as well as counting lattice points in convex polytopes. Using the polymake system we explore various algorithms and implementations. Our experience in this area is summarized in ten "rules of thumb".
math.CO↗
Drawing polytopal graphs with polymake
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 methods displayed are implemented in the software system polymake.
math.CO↗
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.
math.CO↗