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Computing the Betti numbers of arrangements in practice
 Proceedings of the 8th International Workshop on Computer Algebra in Scientific Computing (CASC), LNCS 3718
, 2005
"... We describe an algorithm for computing the zeroth and the first Betti numbers of the union of n simply connected compact semialgebraic sets in R k, where each such set is defined by a constant number of polynomials of constant degrees. The complexity of the algorithm is O(n 3). We also describe an ..."
Abstract

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We describe an algorithm for computing the zeroth and the first Betti numbers of the union of n simply connected compact semialgebraic sets in R k, where each such set is defined by a constant number of polynomials of constant degrees. The complexity of the algorithm is O(n 3). We also describe an implementation of this algorithm in the particular case of arrangements of ellipsoids in R 3 and describe some of our results. 1