This is a continuation of question1 and question2, though reading them is not needed to understand this one.
Here is the code in which I tried doing what was specified in the question:
n = 2
R = FreeAlgebra(ZZ, 'X', n, degrees = [1]*n)
RR = R.completion()
RM = R.monoid()
R_gens = R.gens()
RR_gens = tuple(RR(x) for x in R.gens())
RM_gens = RM.gens()
print(f"{R_gens=}")
print(f"{RR_gens=}")
print(f"{RM_gens=}")
r = R_gens[0]
print(f"{r=}")
print(f"{r.coefficient(RM_gens[0])=}")
print(f"{r.coefficient(RM_gens[1])=}")
rr = RR_gens[0]
print(f"{rr=}")
# print(f"{rr.coefficient(RM_gens[0])}")
# print(f"{rr.coefficient(RR_gens[0])}")
print(f"{rr.coefficient(R_gens[0])}")
The last 3 prints are different methods in which I try doing this. The first Throws:
TypeError: unsupported operand parent(s) for >=: 'Free monoid on 2 generators (X0, X1)' and 'Integer Ring'
The second Throws:
TypeError: tuple indices must be integers or slices, not LazyCompletionGradedAlgebra_with_category.element_class
The third doesn't throw an error, but returns the integer 0.
I've tried varying the formal power series in many ways, and the monomial for which I request the coefficient without success, the results are the same for the above 3 methods.
FrédéricC, thank you for all the help so far, and do let me know if there are things I can/should do to improve future questions and/or give back to the community.
