GSOC 2014: Series expansion

[Avichal Dayal]

I'll be applying for GSOC this year and I'm interested in upgrading the series module.
The ideas page mentions about such a project. However it has been there for some 2-3 years now and I wanted to ask if someone has done some work independently on it. I don't see any GSOC project done on it by the way.

The ideas page nicely mentions the current situation and further developments to be made on it. However those were the views of a single person and as suggested I wanted to discuss it with the community

Series currently is represented as ordinary sympy expression using Add(terms).
However if we want to classify sequences and series, we might want to have a proper structure, maybe a separate object.
The project also talks about implementing formal power series. This will be made easier if we have a separate series class.
However the problem is of course that many modules specially limits uses series output directly (as they are sympy expressions)

I like the way ode module uses hints to solve equations. It is also proposed that solvers uses a similar thing.
So we can also use hints for series too, right? Problems like series(sin(x)*cos(x), x, 1000) are currently very slow. We can have
hints to tell which function must be used to expand it.

Other than this, it says to improve limit of series and order arithmetic. I'm trying to solve some bugs in series and limits,
also testing various limits and series from a standard school textbooks. What improvement is needed in order arithmetic?

Also if we make a separate class for series or sequences, we would move all the series methods currently placed in core/expr.py.
That would clean up expr.py a bit, right? Is a separate class for series favored by the community?
Also please share your views on this project.

Thank You,
Avichal Dayal

[Avichal Dayal]

Also I wanted to ask about 'The Lpoly2 Distributed polynomials in series'. It is the work of Mario Pernici which is upon review process now.
https://github.com/sympy/sympy/pull/609
How will it affect the series code?

I'm also a bit unclear of what the aim of this project. Apart from formal power series and asymptotic expansion
what else is the aim of this project?

[Ondřej Čertík]

Hi Avichal,

Sorry that nobody got in touch with you. I think there are couple
ideas how to improve the speed, as you mentioned, e.g.:

series(sin(x)*cos(x), x, 1000)

I am also interested in getting this done in CSymPy:

https://github.com/certik/csympy

and compare against Mathematica etc. for these series expansions, to
get decent speed. You can apply for CSymPy as well here.

Ondrej

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