Comment #7 on issue 1704 by mattpap: [PATCH] Integration of certain  
composite functions fails
http://code.google.com/p/sympy/issues/detail?id=1704

> Great!  I bought it with some of the money I had left on my card from  
> GSoC.
> Hopefully I can look at it over winter break, though I suspect I won't be  
> able
> to finish it until the summer.

It would be very helpful if you could implement some algorithms from this  
book.
Personally I went through this book a long ago, but at that time there  
weren't many
reasons for implementing too many of procedures described there, because to  
do this
properly you need a strong basis, i.e.: polynomial manipulation algorithms  
and
simplification/normalization functions. The first are still insufficient  
(e.g. lack
of factorization and gcd routines over algebraic number (function) fields)  
and the
other are almost non-existent (sad truth but truth). So actually you will  
spend 10
maybe 20 percent of time working on the integration toolbox and the rest on  
more
basic tools (in this context).

> Also, I am just finishing up my course in Abstract Algebra, so I think I  
> will
> also look through the Polynomials module and hopefully most of it will  
> make
> sense now (e.g., the Galois stuff).

You see, there are two worlds: symbolic manipulation (core) and computer  
algebra
(polys). The first one is the one a typical user sees (in a system like  
SymPy is).
The other world is usually hidden underneath and only not that often people  
use it on
its own. If you want to work on integration (or on any other problem of  
similar
complexity) you need understanding of this bottom layer, where (abstract)  
algebra is
a quite (read: very) useful toy.


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