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I am looking for a program that for a given word in a free Lie algebra calculate the coefficients of the word with respect to the Hall basis. Can you suggest me a program?

Thanks

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There is the following GAP package (and related ones), which I would recommend:

Willem de Graaf and Serena Cicalo, LieRing — a GAP package.

The command "FreeLieRing" enables definition and computations in the free Lie algebra, including Hall bases.

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