On Mon, 10 Nov 2008 17:36:46 -0800 (PST)
cesarnda <[EMAIL PROTECTED]> wrote:

> 
> Actually this sum can't be done by Maxima, but Derive can do it (even
> an old version of derive). do you have an idea of how this problem is
> planning to be solved?

As Robert Dodier pointed out, Maxima can actually do the sum, it is
just a bug in the maxima interface which fails to call the right
function. As he also mentioned, Maxima could probably solve this problem
before any others.

Here is a paragraph from A = B [1], p. 74:

  R. W. Gosper, Jr., discovered his algorithm in conjunction with his
  work on the development of one of the first symbolic algebra
  programs, Macsyma. Because of his algorithm, Macsyma had a
  seemingly uncanny ability to find simple formulas for sums of the
  type (5.1.1).

[1] http://www.math.upenn.edu/~wilf/AeqB.html


Returning to the question of how Sage plans to handle this, the short
answer is "I am working on it." :) 

We will have a completely new implementation of summation, independent
of the one in Maxima. At the moment I have an implementation of the
theoretical framework which lets you solve much more complicated
sums than the ones above. Unfortunately, coming up with an interface
that spares the user from the gory details of the theory will still be a
challenge. Thus, it will be some time before these problems are
handled natively in Sage, but then Sage will (hopefully) be more capable
than the others out there. 


Cheers,

Burcin

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