Symbolic Computation Group

I will discuss algorithms for solving polynomial systems, some applications which motivated their development (from cryptology), and part of the machinery that runs behind the scenes. Emphasis will be put on two points:

* These high-level applications rely on a set of classical, basic subroutines, such as polynomial multiplication. The importance of these basic algorithms, and of their implementation, cannot be overstated. Don't waste a factor of 2!
* Polynomial system solving relates to objects of geometric nature. Hence, geometry should be used as a guideline to design and analyze such algorithms.

The talk aims at giving an outlook of how this circle of ideas is evolving,and of what future development may be expected.