On the computation of the homology of semialgebraic sets

We describe a numerical algorithm to compute the homology
groups of semialgebraic sets.

The algorithm is numerically stable.

Its running time is unbounded (for some input data the algorithm loops
forever) but it has the following property: out of a set of measure
2^{-N} (here N is the input size) the running time is bounded by 2^{N^3}.