Polyhedral Omega

The Polyhedral Omega algorithm presented in “Polyhedral Omega: a New Algorithm for Solving Linear Diophantine Systems” (joint work with Felix Breuer) is implemented originally in Python/Sage and currently developed in JuliaLang with other members of the alcyon lab.

Actively developed as part of alcyon.jl

Actively developed as standalone package

Outdated Python/Sage implementation

Polyhedral Omega for Optimization

The first implementation of Polyhedral Omega applied to ILP (Integer Linear Programming). Still under heavy development as an alcyon.jl package. Presented in ISSAC 2024 (software presentation).

Very unstable. Use at own risk.

PTOPO

The Maple package for the implementation of the algorithm presented in PTOPO: Computing the geometry and the topology of parametric curve (joint work with Christina Katsamaki, Fabrice Rouillier and Elias Tsigaridas). See the page of the project for more information and nice pictures.

math-data

math-data is a project providing the infrastructure for a database of version-controlled mathematical data and datasets. The primary motivation for us was benchmarking mathematical software as well as training machine learning models.

math-data both as a project and as codebase grew out of years of benchmarking my code against existing implementations. Everyone wants to see benchmarks, but nobody wants to do them because it is a lot of work (that doesn’t count academically).

My first attempt to organize a benchmarking system can be found in benchit (but only for historical reasons, not production stable/tested).

Only a curiosity. Do not use.

alcyon.jl

alcyon.jl is an umbrella project for implementations in the ALCYON lab. As expected, it is a Julia package implementing ALgorithms for Combinatorics, geometrY, Optimization and Number theory.

The registry needed to install the packages.

The template if you want to contribute a package.

LaTeX

LaTeX is excellent for increasing productivity, except if you enjoy writing macros/packages too much. After wasting countless hours writing macros for the future, here are some packages that may be useful to others.

Polyhedra.sty

A LaTeX package for drawing polyhedra (and polytopes and cones and hyperplanes) in tikz. Grew out of my macros collection while writing my thesis. Available in CTAN.

Gebze Technical University LaTeX styles

Beamer style file for the Final Project (Bitirme Projesi)

Latex styles for BAP research project reports

Other

Wordpress plugin to create a research institution management system and webpage. Probably outdated.