# What's the best symbolic approach to manipulating infinite/truncated power series?

I'm trying to do something similar to reversion of power series. In my case, the expression involves g(f(ax + b)) where g is a power series, f is the sum of two Taylor series, a and b are real constants. I'm hoping to identify a pattern in the coefficients of the resultant series. I'd like to manipulate the series with QQ coefficients and RR x. How should I define these series?

I'd like to then explore that expression replacing x (RR) with n (ZZ+) for further simplification. How do I convert an expression between ring types?

If these are series in

`x`

, why do you care whether`x`

is in`RR`

? Also, why not just work in the standard power series ring?