This talk is a tutorial about an old algorithm in computer
algebra, which is not as widely known as it deserves: Collins's algorithm for cylindrical algebraic decomposition. This algorithm is capable of solving the quantifier elimination problem for real closed fields, and is thus useful for answering various questions about systems of multivariate polynomial inequalities, very much as Groebner bases are useful for answering questions about systems of equations. In the talk, we want togive the basic (geometric) intuition of the algorithm as well as a collection of typical use cases.
Forschungs-