In the summer term 2012, I will teach a course

Polynomial Computer Algebra

(with exercises). Although the course is officially a course with two hours per week, I will deliver four hours per week but stop at mid-term.

After linear equations, the next simplest class of problems are polynomial equations. In this course we will study how various computational problems with polynomials can be solved effectively. It consists of two parts. The first part is concerned with polynomial arithmetics. Topics will be fast multiplication, GCD computation and factorisation. The second part will introduce Gröbner bases and apply them to various problems with polynomial ideals.

Literature:

• J. von zur Gathen, J. Gerhard: Modern Computer Algebra, Cambridge University Press
• W.W. Adams, P. Loustaunau: An Introduction to Gröbner Bases, AMS
• T. Becker, V. Weispfenning: Gröbner Bases: A Computational Approach to Commutative Algebra, Springer
• D.A. Cox, J. Little, D. O'Shea: Ideals, Varieties, and Algorithms, Springer
• R. Fröberg: An Introduction to Gröbner Bases, Wiley
• M. Kreuzer, L. Robbiano: Computational Commutative Algebra 1, Springer

Time/Location: Tuesday 11:00-13:00, Room 2420; Thursday 09:00-11:00, Room 0450
Begin: 10. April

Exercises

The exercises will be organised by Michael Schweinfurter. The weekly assignments will be published on this web page. In the exercises we will use the freely available computer algebra system CoCoA; an introduction will be given at the beginning of the course.