Comment #14 on issue 1028 by [email protected]: Sum().doit() doesn't do it
http://code.google.com/p/sympy/issues/detail?id=1028
I already submitted some changes.
I think one alternative is the one you mention, to have some heuristics,
and is the most doable in th short term. Other alternative that may work,
as posted in another issue, is to implement summation by parts and borrow
some logic from integrals. I will take a look at Karrs algorithm, seems
very powerful and fun to code.
I'm reviewing the concrete mathematics and other sources to find a list of
common summations. Maybe we could start a wiki page for that, since raising
a ticket for each one could be too much. I suggest to raise a ticket with
all non solved summations and a link to a wiki and to raise tickets for
extra functionalities needed to solve that sums.
The summations related to the binomial number may require lot of works
since there are so many different tricks.
Overall I think the summation module still need some review and
improvements. For example the one provided by smichr to further detect
cases in which to apply the telescopic method.
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