  This manual describes bch, an efficient program written in the C programming
language for the fast computation of the Baker-Campbell-Hausdorff (BCH) and
similar Lie series. The Lie series can be represented in the Lyndon basis, in
the classical Hall basis, or in the right-normed basis of E.S. Chibrikov. In
the Lyndon basis, which proves to be particularly efficient for this purpose,
the computation of 111013 coefficients for the BCH series up to terms of degree
20 takes less than half a second on an ordinary personal computer and requires
negligible 11MB of memory. Up to terms of degree 30, which is the maximum
degree the program can handle, the computation of 74248451 coefficients takes
55 hours but still requires only a modest 5.5GB of memory.
