### 课程题目：Some efficient algorithms in real algebraic geometry

Mohab Safey El Din, Laboratoire d'Informatique de Paris 6, France

This course will overview the most recent developments of computer algebra algorithms for real solving polynomial systems. It will be subdivided in three parts. First, we will introduce the notions of real and real closed fields and algorithms for univariate solving. Next, we will switch to multivariate situations in order to compute sample points in real solution sets to polynomial systems. Finally, we will study algorithms for performing quantifier elimination over the reals.