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Wintersemester 2010/2011
Prof. Franz Winkler
Dr. Günter Landsmann
Computeralgebra (326.017)

Time: Tue 15:30 - 18:00
Place: HS 13
First Lecture: Tue 05.10.2010, HS 13
Exam: Tue 25.01.2011, 16:00 - 17:30 in HS 17

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 mode:
The course is a combination (KV) of lectures (VO) and exercises (UE). The exercises consist of homework exercises and projects. There will be 2 exercise sheets which will be available below in pdf-format. A project comprises a theme, problems, solutions, examples and an algorithm. On October 12, 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 January 18 in a 15 minutes' talk by a group member.

Lecture notes:
0-Titel.pdf
1-What-Is.pdf
2-1-Groebner-Intro.pdf
2-2-Groebner-Rob.pdf
2-3-Groebner-Theory.pdf
2-3-Groebner-Theory-ex.pdf
2-4-Groebner-Application.pdf
3-GCD.pdf
4-Resultants.pdf
5-references.pdf
Time schedule:Date-Type -Topics
05.10.VOKap.1 What is Computer Algebra ?
Kap.2.1 introduction to Gröbner bases
Kap.2.2 Gröbner bases in Robotics
12.10UE 1. Exercise sheet, Project organisation
19.10.VOGröbner bases, Kap.2.3
09.11.VOGröbner bases, Kap.2.3
16.11.VOGröbner bases, Kap.2.3
23.11.VOGröbner bases, Kap.2.4
30.11.UE 2. Exercise sheet
07.12.VOGCD, Kap.3
14.12.VOGCD, Kap.3
11.01.VOResultants, Kap.4
18.01.UEProject presentations
25.01.VOEXAM (KLAUSUR) 16:00 - 17:30 in HS 17
ohne Unterlagen / no books
Klausur-25012011-angaben.pdf
Klausur-25012011-ergebnis.pdf
Project abstracts: CA-Projects.pdf
Diploma thesis: DA-Thema-Schreiner.pdf