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Computing the Homology of Semialgebraic Sets I: Lax Formulas
[article]
2019
arXiv
pre-print
We describe and analyze an algorithm for computing the homology (Betti numbers and torsion coefficients) of closed semialgebraic sets given by Boolean formulas without negations over lax polynomial inequalities. 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. All previous algorithms solving this problem have doubly exponential complexity (and this
arXiv:1807.06435v3
fatcat:cpn6gnkhfndovf6v64w25qgiae