Computer Algebra Systems (CAS)

Dr. Christoph Koutschan

Time and Place

Monday, 10:15 - 11:45, Room KG 419
First Meeting: 4 October 2010


The lecture is intended to give an overview on the big variety of CAS that are available nowadays, and to investigate and compare their abilities. It will start with an introduction to the two most popular general purpose CAS, namely Maple and Mathematica (and if time allows also to others like Axiom, Derive, Macsyma/ Maxima). For each of these CAS a short tutorial will be given and its limitations and common pitfalls will be discussed. The rest of the lecture will be dedicated to special purpose CAS from different areas of mathematics (like CoCoA, Macaulay, Singular, GAP, etc.).


By default, the lecture will be held in English. On agreement with all participants, we can also switch to German.


Participants can get a grade by either giving a talk about a CAS of their own choice or some other topic, or by taking an oral exam.
Here is a list of suggestions for such topics: topics.pdf (topics 3, 5, 8, 9 and 10 have already been chosen).
More topics have been proposed by Prof. Walther Neuper from TU Graz: CAS-topics-Neuper.pdf. These topics are related to the ISAC project. There are lots of open Master's theses within this project, and hence a talk in the CAS lecture could be a first step into this direction.


Here you can download all the material of the lectures held so far.

11.10.2010Mathematicaslides, notebook, pdf of notebook
18.10.2010Maple slides, Maple worksheet (pdf)
25.10.2010Principia slides, MMA examples (pdf), Maple examples (pdf)
08.11.2010Sage slides, Sage examples (pdf)
15.11.2010Axiom / FriCAS slides
22.11.2010ISAC ISAC project
29.11.2010GAP slides, GAP examples in Sage (pdf)
6.12.2010GeoGebra GeoGebra homepage
13.12.2010Modular Arithmetic 
17.1.2011 (1)Cylindrical Algebraic Decomposition slides, Mathematica Notebook (pdf)
17.1.2011 (2)Decidability Questions 
24.1.2011 (1)Singular slides, Singular homepage
24.1.2011 (2)PARI/GP slides, PARI homepage
31.1.2011Algebraic Numbers slides, Mathematica Notebook (pdf)

Christoph Koutschan