What are and how do we compute Tropical Polytopes (software for tight spans and other tropical polytopes)?
Tropical polytopes have recently been introduced by Develin and Sturmfels. They form a class of polyhedral complexes which generalize tight spans of finite metric spaces (and this is one reason why they are relevant for phylogenetic analysis). This renewed discrete geometry viewpoint on the subject paves the way to employ established algorithmic methods and to use existing software for standard problems in phylogenetics.
We report on recent implementations within the open source software framework polymake; see www.math.tu-berlin.de/polymake. These will become available with the new version 2.1, scheduled to be available by the time of this talk.