Michael Joswig: Software
Specialized software is the key tool to help the mind doing research in mathematics. At the same time mathematical software bridges the gap between the diverse fields of mathematics and their application areas. See also my github page.
polymake
polymake is a software system for convex polytopes, simplicial complexes, and more. Co-authored with Ewgenij Gawrilow (now TomTom) and actively supported by many people [BibTeX-Entry]. If you are interested to see how polymake can be used, see the documentation or this extra page with references. This is a long term project first released in 1997.
- Get an idea of how to use the system from the polymake Miscellanea.
- Look up polymake at swMATH.
- Current versions of polymake are available as packages for Arch Linux, Debian, Ubuntu and other Linux systems.
- polymake extension TropicalCubics [download TropicalCubics-0.2.tar.xz], software companion to the paper The Schläfli fan, co-authored with Marta Panizzut and Bernd Sturmfels
- polymake extension polytropes [download polytropes-0.1.tar.xz], software companion to the paper The tropical geometry of shortest paths, co-authored with Benjamin Schröter. The extension itself is co-authored with Ewgenij Gawrilow.
mptopcom
This is a new parallel implementation of the down-flip reverse search algorithm for enumerating the (regular) triangulations of a point set. Co-authored with Skip Jordan and Lars Kastner. Our article Parallel enumeration of triangulations explains the method and reports on experimental results. Release of version 1.2 on 25 August 2020.
MatchTheNet
This small polymake side project is an educational game, which lets you play with 3-dimensional polytopes and their unfoldings. Co-authored with Georg Loho, Benjamin Lorenz and Rico Raber; presented at SoCG 2017. MatchTheNet is part of Imaginary.
OSCAR
We are currently developing a new computer algebra system, called "OSCAR". It is written in Julia, and it combines GAP, Singular, polymake and Antic. First draft of documentation.
The Julia interface to polymake is Polymake.jl; see also arXiv:2003.11381 I started to create Juypter notebooks to showcase features of Polymake.jl and Oscar.jl. Here are some of the topics:
In order to run the above: clone the entire subdirectories from github, use activate . and instantiate in Julia's REPL mode, while that is your working directory. Then you are good to go.
Project II.1 in SFB/TRR 195, with Mohamed Barakat, Wolfram Decker, Claus Fieker and Frank Lübeck. Researchers: Reimer Behrend, Sebastian Gutsche, William Hart
DGD Gallery
A new collection of geometric models.
RealLie
This is a small program which computes real representations of quasi-simple Lie groups. It is quite old but still functional and occasionally useful. Joint work with Richard Bödi.