Computing the Homology of Semialgebraic Sets. II: General formulas
Abstract
We describe and analyze a numerical algorithm for computing the homology (Betti numbers and torsion coefficients) of semialgebraic sets given by Boolean formulas. The algorithm works in weak exponential time. This means that outside a subset of data having exponentially small measure, the cost of the algorithm is single exponential in the size of the data. This extends the work in Part I to arbitrary semialgebraic sets.
All previous algorithms proposed for this problem have doubly exponential complexity .
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