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

Hi everyone,

As the title says, I need to use Non Commuting Multivariate Formal Power Series rings (Over P-adics) for my masters research, and while I found Non Commuting Multivariate Polynomial rings (e.g. the FreeAlgebra) and Multivariate Formal Power Series rings, I haven't found something that mixes both.

Is there some terminology for this that I'm missing? Or a simple way to implement this in sage?

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

Hi everyone,

As the title says, I need to use Non Commuting Multivariate Formal Power Series rings (Over P-adics) for my masters research, and while I found Non Commuting Multivariate Polynomial rings (e.g. the FreeAlgebra) and Multivariate Formal Power Series rings, I haven't found something that mixes both.

Is there some terminology for this that I'm missing? Or a simple way to implement this in sage?

Edit: I need to be able to do calculations with its generators. For example, (a+1)^(-1) should be 1 - a + a^2 - a^3 + ... + O(..) when 'a' is a generator.