I try to implement the Poincaré-Birkhoff-Witt basis of the free algebra. I defined the elements of this basis and a function which gives the expansion of an element of the free algebra on this basis; actually, it returns a dictionary whose keys are monomials and whose values are the corresponding coefficients. I would like to define a new basis of the free algebra, but I don't know which structure I should use. Is there a "canonical way"? Should I use a CombinatorialFreeModule? There might be some documentation I should have read before asking any question. Please tell me where I should have a look. Best, Matthieu
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