computational-group-theory

Project in Computational Group Theory for COMPSCI 380 at The University of Auckland.

Supervisors

Cris Calude and Eamonn O'Brien

Project Goals and Outline

The rough project outline is (currently) as follows:

1. Complete a significant number of exercises of the book Presentations of Groups by D. L. Johnson. COMPLETED. The majority of the exercises from the first four chapters have been completed. I have read further than this of course. In the future I may come back and complete more of the exercises.

2. Write an implementation of an algorithm of the computation of the Smith Normal Form of an matrix with integer entries. Such a procedure was discussed in Maths 720, as it can be used to compute the factors described in the fundamental theorem of finitely generated abelian groups. COMPLETED. See magma folder and report.

3. Read relevant literature on implementation-specific considerations around the algorithm implemented in (2), for example, how to deal with integer overflow. Write a report on these considerations and improve the implementation using the knowledge gained from this. Run the algorithm on non-trivial test cases. COMPLETED. See report.

This project has been submitted for assessment as at 30th October 2017.

Usage

Clone this repository. To read the solutions to the exercises, compile exercises/johnson.tex using your preferred LaTeX distribution. To read the report, compile report/report.tex. All of the magma code is included in the folder magma.