Computing the volume,counting integral points,and exponential sums |
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| Authors: | Alexander I Barvinok |
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| Institution: | (1) I. M. Sechenov Institute of Evolutionary Physiology and Biochemistry, Academy of Sciences of Russia, 44 M. Thorez Prospect, 194223 St. Petersburg, Russia;(2) Present address: Department of Mathematics, Royal Institute of Technology, S-10044 Stockholm, Sweden |
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| 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.
This research was partially supported by the Mittag-Leffler Institute. |
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