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.

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bch用户手册，该程序用于快速计算Baker-Campbell-Hausdorff和类似系列

本手册介绍了bch，这是一种用C编程语言编写的高效程序，用于快速计算Baker-Campbell-Hausdorff（BCH）和类似的Lie系列。Lie系列可以以Lyndon，经典Hall或ES Chibrikov的右标为基础表示。在林登基础上，事实证明这是特别有效的，在普通个人计算机上，对于20级以下的BCH系列，计算111013系数所需的时间不到半秒，并且需要的11MB内存可忽略不计。最高30度（程序可以处理的最高度）的条件下，74248451系数的计算需要55个小时，但仍仅需要适度的5.5GB内存。