I will review a simple and efficient algorithm for the certified computation of S, which
only needs to compute projections of the solutions but no further algebraic manipulations.
It computes a separating direction l as well as isolating boxes for all solutions for the cost of O(d) projections of the solutions. It is worthwhile to remark that, for d=2, the worst case bit complexity of our method matches the current record bound as achieved by much more involved algorithms.