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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