The often elusive Poincar\'e recurrence can be witnessed in a completely
separable system. For such systems, the problem of recurrence reduces to the
classic mathematical problem of simultaneous Diophantine approximation of
multiple numbers. The latter problem then can be somewhat satisfactorily solved
by using the famous Lenstra-Lenstra-Lov\'{a}sz (LLL) algorithm, which is
implemented in the Mathematica built-in function \verb"LatticeReduce". The
procedure is illustrated with a harmonic chain. The incredibly large recurrence
times are obtained exactly. They follow the expected scaling law very well.Comment: 8 pages, 5 figure
