Abstract
An algorithm for solving systems of linear Diophantine inequalities, which uses the apparatus of generating functions, is studied. After describing the algorithm, estimates are obtained for its labour content, the ranges of its effective application are found, the connection is established with problems of exact integration of finite trigonometric polynomials, some characteristics of the critical lattices of certain domains are evaluated, and the admissible lattice of the shifted hyper-cube is constructed.
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