Computational Aspects of Commutative Algebra and Algebraic Geometry

Goals of this Dagstuhl Seminar

Modern computer algebra systems allow the computation of complicated examples in Commutative Algebra, Algebraic Geometry and Arithmetic Geometry. During the last couple of years such computations have helped to predict and check many theorems. Vice versa, inspired by complicated examples coming from theory, computer algebra developers have refined their algorithms and implementations. The main goals of this meeting were to:

• give developers of computer algebra systems and those who apply computer algebra in their theoretical research the possibility of exchanging ideas,
• to initiate cooperation between developers of different computer algebra systems,
• to present new algorithms and systems and recent theoretical developments as well.

In order to achieve our goals we kept the number of talks to roughly four per day. This allowed plenty of time for discussions at a blackboard or in front of a terminal, software demonstrations and introductionary tutorials, or other activities like a meeting on OpenMath.