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truncated exponential series over ring of matrices over symbolic ring

I want to do the following:


I then want to define a function as the first several terms of the exponential series exp(gamma). Something like


This will return an error like: 'too many values to unpack'

I only want to work with this function formally until I need to specify a value of n and eventually solve for the value f(i), g(i) in terms of some other parameters (yet to be defined in this code). What are some ways to clean this up so I can work with the truncated power series with matrix coefficients?

A possibly simpler but related question is how does one build a function that will sum several powers of a matrix?