Hi,

> > I went through the paper "Symbolic summation with radical
> > expression" and I found myself unable to understand many points due
> > to my insufficient mathematical background

The whole topic of symbolic summation requires a
very strong background on (abstract) algebra. That's
one reason why it is rated as "very hard".

BTW this paper contains only additional information
describing extensions to the Karr algorithm.

Maybe we should group the references according to importance.

> > I haven't done any abstract algebra.
> > However, I went through the idea list and found the idea "SYMBOLIC
> > COMPUTATION OF INTEGRALS BY RECURRENCE" interesting. I went through
> > Michael Barnett's paper and it seemed approachable to me with my
> > mathematical background. Also I saw that integration is currently
> > done using Risch-Norman Algorithm, and it needs to be improved.
> 
> I guess this last detail is the essential one.  In my opinion, if you
> understand the article sufficiently well to write a good proposal, you
> are quite fit to actually implement the necessary functionality.

I don't think that this algorithm is enough work for a whole
gsoc project. It is only a single technique applicable to some
(rather special) integration problems.

Never the less it would be nice to have it to extend the integration
facilities of sympy.

Also there is at least one other gsoc thread about this topic.
(But I could not find these mails right now.)

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