This article is cited in 1 scientific paper (total in 1 paper)
On Voronoi's cylindric minima theorem
A. V. Ustinov
Institute for Applied Mathematics, Khabarovsk Division, Far-Eastern Branch of the Russian Academy of Sciences, Khabarovsk
Voronoi's algorithm for computing a system of fundamental units of a complex number field is based on a geometric properties of 3-dimensional lattices. This algorithm is based on Voronoi's theorem about cylindric minima for a lattice in general position. In the original proof and it's refinement published by Delone and Faddeev some significant cases were skipped. In the present we give a complete proof of Voronoi's theorem. The result is extended to arbitrary lattices.
lattice, Voronoi algorithm.
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MSC: Primary 11H06; Secondary 11H55
A. V. Ustinov, “On Voronoi's cylindric minima theorem”, Dal'nevost. Mat. Zh., 11:2 (2011), 213–221
Citation in format AMSBIB
\paper On Voronoi's cylindric minima theorem
\jour Dal'nevost. Mat. Zh.
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