Computer Algebra (326.031)
Winter semester 2022/2023
Carsten Schneider


Time:   Thurdays, 10:15 - 11:45
Room:  HS 12

In the last decades big parts of mathematics has been algorithmized and many mathematical problems (or problems coming from natural and technical sciences that can be modeled in mathematics) can be solved with the computer. A major contribution for this algorithmic revolution is the computer algebra. This lecture aims at introducing the most crucial algorithms in this field and illustrating how they can be used for non-trivial applications.

We discuss constructive symbolic methods for simplification of expressions and solving algebraic (i.e., polynomial) systems of equations. Among others, the following algorithms are explored:

Some slides accomplishing the lecture can be found in the pdf-file CA.pdf. In addition, some concrete examples discussed in the lexture can be also found within the Mathematica notebook Examples.nb

The lecture is partially based on


Time:   Thurdays, 12:00 - 12:45
Room:  HS 12
Exercise instructor: Günter Landsmann (landsmann@risc.jku.at)

The exercises start on October 13. Always the week before homeworks are posed on an exercise sheet that will be accessible below. At the beginning of the exercise class the participants indicate which homeworks they have carried out. Based on that the participants are selected in order to present the solutions. The homeworks themselves consist of concrete calculations by using a CA system, proving some simple statements that are needed in the lecture, or considering further aspects that are not treated in the lecture. In particular, little programming exercises might be posed.

List of exercise sheets

    for 13.10.2022:    ca-ex-01.pdf
    for 20.10.2022:    ca-ex-02.pdf
    for 27.10.2022:    ca-ex-03.pdf
    for 03.11.2022:    ca-ex-04.pdf
    for 10.11.2022:    ca-ex-05.pdf
    for 17.11.2022:    ca-ex-06.pdf
    for 24.11.2022:    ca-ex-07.pdf
    for 01.12.2022:    ca-ex-08.pdf
    for 15.12.2022:    ca-ex-09.pdf
    for 12.01.2023:    ca-ex-10.pdf
    for 19.01.2023:    ca-ex-11.pdf
    for 26.01.2023:    ca-ex-12.pdf