Ring Series Improvement and Series Inversion

[Cédric Travelletti]

Hi everyone

I'm currently trying to improve ring_series by adding the series expansion of the Sine Integral.

I'm having some trouble with series inversion.

I have to use rs_series_inversion in order to perform some division. The problem is that series inversion doesn't always work.
For example:

R, x, y = ('x, y', QQ)
rs_series_inversion(x + x*y, 4)


This throws a NotImplementedError.

Would anyone have any advice on this? I was thinking about catching the exception and just using 1/p in that case.

Also, when writing tests, I'm having trouble with the assertions, I'm getting ASSERTION ERRORS, even when both side of the equation are the same.
Are there some pitfalls when testing expression equality that I should be aware of? (I noticed that these errors only show up when including higher order terms.)

Any suggestion would be appreciated.

Bests

Cédric