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.

翻译：本手册描述了bch,这是用C编程语言编写的快速计算Baker-Campbell-Hausdorf(BCH)和类似Liet系列的高效程序,Lyendon系列可以以Lyndon为基础、古典大厅为基础或E.S.Chibrikov的右无线为基础。在Lyndon(证明在这方面特别有效)的基础上,计算BCH系列直至20级的111013系数需要普通个人计算机不到半秒半,需要可忽略不计的11MB内存。在第30级(这是方案所能处理的最大程度),计算74248451系数需要55小时,但仍只需要少量5.5GB内存。