Hi

Sympy currently lacks a class based representation for series expansions.
Though the current approach works well, it has its problems, like- all 
types of
series are lumped under one name, issues with infinite series, etc. 
Moreover, such
an implementation, if successful, can also be ported to C++, which will be 
much
faster. Hence, I would like to give series expansion a class representation.

There has been a lot of dicussion here : 
https://groups.google.com/forum/#!searchin/sympy/series/sympy/hiRuIHa8ImA/JLOBsMr9yUcJ

This approach builds on ring_series.py and Ondrej's implementation here
https://github.com/certik/sympy/blob/59492520b443ea5f0ef31fc018e9bc700b93b818/a.py

is even faster than the existing one based on ring_series.

I found another approach here 
https://github.com/sympy/sympy/wiki/UD-Sequences-and-formal-power-series-prototype

which uses sequences to construct power series. There was an attempt to 
follow
this approach in https://github.com/sympy/sympy/pull/7846 using formula 
based
power series, but the PR is yet to be merged.

How do the two approaches compare? What are the expectations from such a 
class
based representation?

Regards

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