Computer Algebra Systems (CAS)
Dr. Christoph Koutschan
Time and Place
Monday, 10:15  11:45, Room KG 419
First Meeting: 4 October 2010
Content
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.).
Language
By default, the lecture will be held in English.
On agreement with all participants, we can also switch to German.
Assessment
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:
CAStopicsNeuper.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.
Material
Here you can download all the material of the lectures held so far.
Date  Topic  Material 
04.10.2010  Introduction  slides 
11.10.2010  Mathematica  slides, notebook, pdf of notebook 
18.10.2010  Maple 
slides,
Maple worksheet (pdf)

25.10.2010  Principia 
slides,
MMA examples (pdf),
Maple examples (pdf)

08.11.2010  Sage 
slides,
Sage examples (pdf)

15.11.2010  Axiom / FriCAS 
slides

22.11.2010  ISAC 
ISAC project

29.11.2010  GAP 
slides,
GAP examples in Sage
(pdf)

6.12.2010  GeoGebra 
GeoGebra homepage

13.12.2010  Modular 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

31.1.2011  Algebraic Numbers 
slides,
Mathematica Notebook
(pdf)

Christoph Koutschan