# «Computer Algebra»

## Schedule

 Class: Tue: 08:15 - 09:45 (48 - 438) Thu: 13:45 - 15:15 (48 - 438) Tutorial: Tue: 15:30 - 17:00 (48 - 436)

## Homework

There will be weekly homework assignments posted on this page, typically posted on Thursday and due on the next Thursday by 10:00 am. Please hand in your solutions by the respective due date in the office of Raul Epure, room 48-427. You may (and you are encouraged to) turn in your homework in teams of 3. However, each of you needs to be able to present your team's solutions during the tutorial.

 Sheet 1 due April 25 10:00 am (pdf) Sheet 2 due May 2 10:00 am (pdf) Sheet 3 due May 9 10:00 am (pdf) Sheet 4 due May 16 10:00 am (pdf) Sheet 5 due May 23 10:00 am (pdf) Sheet 6 due May 29 10:00 am (pdf) Sheet 7 due June 6 10:00 am (pdf) Sheet 8 due June 13 10:00 am (pdf) Sheet 9 due June 19 10:00 am (pdf) Sheet 10 due June 27 10:00 am (pdf) Sheet 11 due July 4 10:00 am (pdf) Project due July 11 10:00 am (pdf)

## Programming

Every two weeks the homework will contain a programming exercise. We are going to use the computer algebra system SINGULAR. On the SINGULAR homepage you can find a manual and examples for the code. You can download and install SINGULAR on every operating system like OS X, Windows, Linux, but you can also use the preinstalled version on the computers, which you can find in the math department. In order to see how SINGULAR works you can have a look at these examples. We will also give a short introduction in the first example class on April 24. During the course of the semester we will create a SINGULAR library. You can download the template here. Here you can find a SINGULAR library with solutions to the programming exercises.

## Credit

In order to obtain an Übungsschein you need to actively participate in the tutorial and achieve a total homework score of at least 50%. Active participation means regular attendance and presenting a solution of a homework problem (at least once).

For credit points you need to pass an oral exam after the end of the semester.

## Literature

The lecture weill be based on certain chapters of the book:

• G.-M. Greuel, G. Pfister: A Singular Introduction to Commutative Algebra

Other books we can recommend are the following:

• D. A. Cox, J. Little, D. O'Shea: Ideals, Varieties, and Algorithms
• H. Schenck: Computational Algebraic Geometry
• W. Decker, Ch. Lossen: Computing in Algebraic Geometry - A Quick Start using Singular