OperatorGB

Software package for Gröbner basis computations in the free algebra, with dedicated methods for automatising the proofs of operator statements. In particular, the package provides several methods for searching for elemnts of certain forms in noncommutative polynomial ideals.

The latest versions for SageMath and Mathematica can be found on github: Sage version, Mathematica version

SignatureGB (beta version)

This SageMath package allows to do computations with noncommutative signature Gröbner bases of two-sided ideals in the free algebra. So far, this is only a beta version with an actual release coming soon.

The latest version can be found on github.

Additional material for papers

• The SageMath implementation of the main algorithm from the paper
  
  C. Hofstadler, T. Verron. Short proofs of ideal membership, 10 pages, 2023. arXiv
  
  together with the benchmark examples presented in the paper is available here. Please see the README file included in the downloaded folder for information on installation and usage.
• The SageMath implementation of the algorithm from the paper
  
  C. Hofstadler, T. Verron. Signature Gröbner bases in free algebras over rings. 9 pages, 2023. DOI | arXiv
  
  together with the benchmark examples presented in the paper is available here. Please see the README file included in the downloaded folder for information on installation and usage.
• The Mathematica notebook accompanying the paper
  
  C. Hofstadler, T. Verron. Signature Gröbner bases, bases of syzygies and cofactor reconstruction in the free algebra, Journal of Symbolic Computations, 31 pages, 2022. DOI | arXiv
  
  together with a Mathematica version of the package is available here.
• The Mathematica notebook accompanying the paper
  
  C. Hofstadler, C.G. Raab, G. Regensburger, Computing elements of certain form in ideals to prove properties of operators, submitted, 26 pages, 2021. arXiv
  
  together with a Mathematica version of the package is available here.
  

Thermal image object detection

In a recent project, we developed and trained a neural network to detect humans in thermal images over occluded terrain, which can be particularly useful for search and rescue operations for example. For further information on the project itself, please see this blog post. The Matlab code can be obtained from this github repository.

GraphDrawing

A simple Java application that allows to visualize graphs in several different styles. This project was done together with Lukas Wögerer and can be obtained from my github page.

ore_algebra

As part of my Bachelor’s thesis I contributed to the SageMath package ore_algebra, which is a Sage package for doing computations with Ore operators and is developed by Manuel Kauers, Marc Mezzarobba, and Frederik Johansson. See here for further information.

Terms of use

Unless otherwise stated, the software provided on this web site is free; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. The programs are distributed in the hope that they will be useful, but without any warranty; without even the implied warranty of merchantability or fitness for a particular purpose. See the GNU General Public License for more details.