How to implement Non Commuting Multivariate Formal Power Series rings in SageMat

edit

Note that this is quite recent and probably not much tested.

Thank you for the answer! I tried it but didn't manage to do calculations with its elements. I should've mentioned that I needed to do so in the question. I should be able to, for example, calculate (a+1)^(-1) to be 1 - a + a^2 - a^3 + ... + O(..)

Errors I encountered:

G = F.completion()
G.algebra_generators()

Throws

TypeError: 'NotImplementedType' object is not callable

and

G.inject_variables()

Throws

ValueError: variable names have not yet been set using self._assign_names(...)

I've tried doing:

G._assign_names(['a', 'b'])
G.inject_variables()

But it throws:

AttributeError: 'LazyCompletionGradedAlgebra_with_category' object has no attribute 'gens'

Oh, just saw what you wrote 48 min ago. Welp, I guess this is the result of my tests.

I have edited my answer to explain how to define the generators.

Thank you so much! that solved my issue completely. Just wish I could upvote lol