Computing the betti numbers of arrangements in practice

Authors:
Saugata Basu;Michael Kettner
Affiliations:
School of Mathematics, Georgia Institute of Technology, Atlanta, GA;School of Mathematics, Georgia Institute of Technology, Atlanta, GA
Venue:
CASC'05 Proceedings of the 8th international conference on Computer Algebra in Scientific Computing
Year:
2005

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Abstract

We describe an algorithm for computing the zero-th and the first Betti numbers of the union of n simply connected compact semi-algebraic sets in ℝk, where each such set is defined by a constant number of polynomials of constant degrees. The complexity of the algorithm is O(n3). We also describe an implementation of this algorithm in the particular case of arrangements of ellipsoids in ℝ3 and describe some of our results.