RISC-Linz RISC-Linz Research Institute for Symbolic Computation  

Wintersemester 2009/2010
Prof. Franz Winkler
Dr. Günter Landsmann
Computeralgebra (326.017)

Time: Tue 15:30 - 18:00
Place: HS 13
First Lecture: Tue 06.10.2009, HS 13
Final Exam: Tue 26.01.2010
16:00 - 18:00, HS 10

A theoretical and practical introduction into the area of computer algebra will be presented. In particular we deal with the constructive symbolic solution of systems of algebraic (i.e. polynomial) equations. We will cover the theory of Gröbner bases, Euclid's algorithm for GDCs of polynomials, and the method of resultants.

The course will follow the appropriate chapters in:

F. Winkler: Polynomial Algorithms in Computer Algebra,
Springer-Verlag Wien New York, 1996
(ISBN 3-211-82759-5)

Participants are expected to be acquainted with the basic notions in algebra and algorithm theory.

Lecture notes: Kap00.pdf
Kap02-1.pdf Kap02-1-tacnode.pdf
Kap02-4.pdf Kap02-4-curves.pdf Kap02-4-surface.pdf Kap02-4-syz-proofs.pdf Kap02-4-resolution.pdf

Lecture mode:
The course is a combination (KV) of lectures and exercises. The exercises (UE) consist of homework exercises and projects. There will be 3 exercise sheets which can be found below in pdf-format. A project comprises a theme, problems, solutions, examples and an algorithm. On October 20th, after discussing the first bunch of exercises, the projects will be allocated to groups of students, one project a group. The members of each group are expected to work out the theme, compile the theory behind, discuss examples and develop an algorithm capable of solving the corresponding problems. All this should be summarized in a paper of 5 to 8 pages to be presented on 19th of October in a 15 minutes' talk by a group member.

Time schedule:Date-Type-Topics
6.10.VOKap.1 What is Computer Algebra ?
Kap.2.1 introduction to Gröbner bases
Kap.2.2 Gröbner bases in Robotics
13.10.VOGröbner bases, Kap.2.3
20.10.UE 1. Exercise sheet, Project organisation
27.10.VOGröbner bases, Kap.2.3
03.11.VOGröbner bases, Kap.2.3
10.11.UE 2. Exercise sheet
17.11.VOGröbner bases, Kap.2.4
24.11.VOGröbner bases, Kap.2.4
01.12.UE 3. Exercise sheet
15.12.VOGCD, Kap.3
12.01.VOResultants, Kap.4
19.01.UEProject presentations
26.01.VOKLAUSUR 16:00 - 17:30, in HS 10
ohne Unterlagen / no books
Klausurangaben: klausur.pdf
Klausurbeurteilung: klausur-26012010-ergebnis.pdf
Endnote: noten-ca.pdf

Project abstracts: ca-projects.pdf
Project groups: ca-projectgroups.pdf