Open source
Software
Software we have developed or contributed to in a leading role. Everything is open source under the GNU GPL or MIT licence, as indicated in each repository.
Polyhedral Omega
The Polyhedral Omega algorithm from “Polyhedral Omega: a New Algorithm for Solving Linear Diophantine Systems” (Breuer & Zafeirakopoulos) was first implemented in Python/Sage and is now developed in Julia by members of the lab. You can try the Sage version in this public CoCalc worksheet.
Polyhedral Omega for Optimization
The first implementation of Polyhedral Omega applied to integer linear programming, presented as a software presentation at ISSAC 2024. Still under heavy development as an alcyon.jl package.
alcyon.jl
The umbrella project for the lab’s implementations: a Julia computer algebra system for ALgorithms for Combinatorics, geometrY, Optimization and Number theory.
PTOPO
Maple package computing the geometry and topology of parametric curves, from “PTOPO: Computing the geometry and the topology of parametric curves” (Katsamaki, Rouillier, Tsigaridas & Zafeirakopoulos). See the project page for more information and pictures.
math-data
Infrastructure for a database of version-controlled mathematical data and datasets, built for benchmarking mathematical software and for training machine learning models. It grew out of years of benchmarking our code against existing implementations; benchit was the first attempt.
LaTeX
Packages that grew out of macro collections. polyhedra.sty draws polyhedra, polytopes, cones and hyperplanes in TikZ and is available on CTAN. The GTU styles are for students and researchers at Gebze Technical University.