#### TU Kaiserslautern • Department of Mathematics • Winter Term 2013/14

# «Computer Algebra»

**Supervision:**
Mathias Schulze &
Yue Ren

**Meetings:**
class | Tuesday | 11:45-13:15h, 48-438 |

class | Thursday | 11:45-13:15h, 48-438 |

tutorial | Wednesday | 15:30-17:00h, 48-582 |

## Content

Monomial orderings, division with remainder, normal forms, standard bases, Bucherger's criterion, Mora's algorithm, ideal / module operations
(membership, radicalmembership, intersection, quotient, saturation, elimination, ...),
free resolutions, Hilbert's syzygy theorem, Noether normalization, primary decomposition, Hilbert series/polynomial.
## Tutorial

The tutorial will be held by Yue Ren. The deadline for regular signups has ended. For late signups, please contact Yue Ren.
## Homework

There will be weekly homework assignments posted on this page. Typically assignments will be posted on Thursday, and are due on Tuesday, the week after the next by 12:00. Please hand in your solutions
by the respective due date in the office of Yue Ren, room 48-420. 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