Leandro Vendramin (Vrije Universiteit Brussel) Computational algebra: groups, rings and combinatorics. We present the computer algebra system GAP and use it to solve some research-level problems in algebra and combinatorics. The topics to investigate are groups, certain finite rings and some combinatorial structures associated with the Yang-Baxter equation (with applications in knot theory). GAP is a system for computational discrete algebra with emphasis on computational group theory.

Assistants

Arne van Antwerpen was the assistant to Leandro Vendramin for this course’s tutorials.

Arne is a postdoc at Vrije Universiteit Brussel (VUB) in Brussels, Belgium. He completed his PhD in 2020 at Vrije Universiteit Brussel under the supervision of Eric Jespers. His research interests include set-theoretic solutions of the Yang-Baxter equation, skew braces, finite group theory and finiteness conditions in ring theory.

Installing GAP

We strongly recommend that all participants have either SAGE or GAP installed before the lectures begin. To install SAGE, which comes with a GAP distribution, please see here. To install GAP, there are general instructions available here. If you would prefer not to install GAP, you can find an online alternative here.

Reading material for the course

1. Computer algebra with GAP by K. Piterman. and L. Vendramin.

Slides

1. First lecture.
2. Second lecture.
3. Third lecture.

Tutorial

1. The file with the FRACTRAN program PRIMEGAME is here.
2. The file generating the Look and Say sequence is here.