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.
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.
This is a brandnew 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 arXiv preprint explains the method and reports on experimental results. Release of version 1.0 on March 28, 2018.
Thanks to Sebastian Gutsche, Marek Kaluba, Benjamin Lorenz and Sascha Timme we already have a first tech preview (as of November 2018):
In order to run the above: (1) Use Linux or MacOS; Windows 10 may work with the Linux subsystem. (2) Download polymake snapshot (from Nov 16, 2018 or later), build and install into, e.g., "/installed/at". (3) Then set "export POLYMAKE_CONFIG=/installed/at/bin/polymake-config" and possibly also "export LD_LIBRARY_PATH=/installed/at/lib:". Add package Polymake.jl to julia and build. Then proceed, e.g., with the notebook above.