Abstract
We design polynomial-time algorithms for some particular cases of the volume computation problem and the integral points counting problem for convex polytopes. The basic idea is a reduction to the computation of certain exponential sums and integrals. We give elementary proofs of some known identities between these sums and integrals and prove some new identities.
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This research was partially supported by the Mittag-Leffler Institute.
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Barvinok, A.I. Computing the volume, counting integral points, and exponential sums. Discrete Comput Geom 10, 123–141 (1993). https://doi.org/10.1007/BF02573970
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DOI: https://doi.org/10.1007/BF02573970