Radical computations of zero-dimensional ideals and real root counting

The computation of the radical of a zero-dimensional ideal plays an important role in various areas of computer algebra. A bunch of different methods have been published to meet this task (see e.g. [4,8,11,13–17]). The method presented in this paper is strongly connected to a recent approach to the real root counting problem as described in [2,18]. It provides a lot of information for real root counting already in the process of calculating the radical. In this sense this approach is well-suited for real root counting problems.