#### TU Kaiserslautern • Department of Mathematics • Winter Term 2015/16

# «Computer Algebra»

Prof. Dr. Mathias Schulze •
Dipl.-Math. Cornelia Rottner

## News

- The tutorial will start in the second week of the semester with an introduction to Singular. We will meet in the computer lab 48-419.

## Schedule

| weekday | time | room | instructor |

class | Tuesday | 08:15-09:45 | 48-438 | Mathias Schulze |

class | Thursday | 08:15-09:45 | 48-438 | Mathias Schulze |

tutorial | Monday | 10:00-11:30 | 48-436 | Cornelia Rottner |

## Prerequisites

- Einführung in das symbolische Rechnen (Introduction to symbolic computation)
- Commutative Algebra

## Content

Monomial orderings, division with remainder, normal forms, standard
bases, Bucherger's criterion, Mora's algorithm, ideal/module operations
(membership, radical membership, intersection, quotient, saturation,
elimination, ...),
free resolutions, Hilbert's syzygy theorem, (Noether) normalization,
primary decomposition, radical, Hilbert(-Samuel) series/polynomial,
singular locus, Ext/Tor.

## 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 Cornelia Rottner, 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.

## Credit

In order to obtain an Übungsschein you need to actively participate in the tutorial and achieve a total homework score of at least 40%.
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

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