I have been working on free algebras with Sage for a while and I could add some features that might be useful. For example, I could implement the Poincaré-Birkhoff-Witt basis of a free algebra. To do so, I use the standard factorisation and the Lyndon factorisation of the word that corresponds to a monomial. Hence, I think that I should add a coercion of words into elements of the free algebra and conversely. I do not know if this is a good idea. where I have to put these "maps" (in the code of FreeAlgebraElement? of FreeMonoidElement? of FreeAlgebra?). If anyone can help me... Matthieu
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