In the winter semester 2023/24, I will read a four-hours lecture course

Algorithmic Commutative Algebra

(with tutorials). On the one hand, the course will introduce some theoretical concepts from commutative algebra and algebraic geometry like the interconnection between polynomial ideals and varieties (the zero sets of polynomials). On the other hand, algorithms for effective computations with ideals and for solving polynomial equations are covered. As fundamental tools for such tasks Gröbner bases and triangular sets will be studied. Prerequisities are only basic notions from algebra like rings and ideals.

Used Literature:

• D.A. Cox, J. Little, D. O'Shea: Using Algebraic Geometry, Springer
• W. Decker, C. Lossen: Computing in Algebraic Geometry, Springer
• G.-M. Greuel, G. Pfister: A Singular Introduction to Commutative Algebra, Springer
• M. Kreuzer, L. Robbiano: Computational Commutative Algebra 2, Springer
• H. Schenck: Computational Algebraic Geometry, Cambridge University Press

Time/Location: Tuesday and Thursday 11:00-13:00, Room 2420
Beginn: 19. October

Tutorials:

The tutorials are organised by Matthias Seiß.