>
> I think we should rather represent series as a Series class, roughly 
> equivalent to SeriesData in Mathematica: 
>
> http://reference.wolfram.com/mathematica/ref/SeriesData.html<http://www.google.com/url?q=http%3A%2F%2Freference.wolfram.com%2Fmathematica%2Fref%2FSeriesData.html&sa=D&sntz=1&usg=AFQjCNGUrewTF7qnSvMywwXBrTqnr9qneg>
>  
>

This is a bit undocumented (as all in Mathematica, usually).  For example,
it's not so clear what kind of coefficients are allowed.
 

> The Series class would interact with SymPy similar to how Poly works in 
> SymPy. 
> The Series would represent a series expansion in one variable (I don't 
> have opinions about multiple variables yet), so it would remember the 
> terms in some suitable format (see below, just like for Polys, there 
> are more options on the internal representation) and the order of the 
> series. Then, when you print it, it will print it just like we 
> currently do, with the "O(x^2)" term, though that's just how it is 
> printed. 
>

Not sure if this is a Series class job.  I mean, to remember terms.

The Series should be build on (or to be itself) the ground of
some stream-like entity, that can do actual arithmetic.
Memoization/caching - another issue.
 

> If you look at how GiNaC does it
>

It looks, like it can only formal power series and laurent (just like
sage?).  We want more?

Open ideas: 
>
> * I don't like that Order requires special handling in Add: 
>
> https://github.com/sympy/sympy/blob/master/sympy/core/add.py#L237<https://www.google.com/url?q=https%3A%2F%2Fgithub.com%2Fsympy%2Fsympy%2Fblob%2Fmaster%2Fsympy%2Fcore%2Fadd.py%23L237&sa=D&sntz=1&usg=AFQjCNFg_9hCCBrkVjHKxInryZlS4ADe6g>
>  
>

That's another issue.  But arithmetics (not differential
calculus!) with O makes sense. 

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