Allow algorithm='sympy' in symbolic_sum function

[slabbe]

I want this to work:

sage: n = var('n')
sage: sum(1/((2*n+1)^2-4)^2, n, 0, Infinity, algorithm='sympy')

See ​this question on ask.sagemath.org

[git]

Branch pushed to git repo; I updated commit sha1. New commits:

​a0f8d17

22004: Allow algorithm='sympy' in symbolic_sum function

[kcrisman]

(Incidentally, the example here, which doesn't work right with Maxima, may be related to ​https://sourceforge.net/p/maxima/bugs/3236/.)

[kcrisman]

Also,

         sage: symbolic_sum(1/(1+k^2), k, -oo, oo, algorithm = 'giac')           # optional - giac
         (pi*e^(2*pi) - pi*e^(-2*pi))/(e^(2*pi) + e^(-2*pi) - 2)
+    SymPy can't solve that summation::
+

You will need an extra blank line for formatting. I'd also say that Maxima can't do the sum in this ticket, not that Sage per se can't - indeed, Sage can after this patch!

[git]

Branch pushed to git repo; I updated commit sha1. New commits:

​16acdcf

22004: fixing doc comment

[slabbe]

On my screen, the extra blank line is already there. Can you confirm this problem?

I wrote Maxima instead of Sage. Needs review!

[kcrisman]

Huh, now it appears fine. Go figure.

Wish I had time to do proper review :( don't even have up-to-date Sage (compiling). These comments are what I could do for now, and as long as someone checks it works right and "corner cases" don't yield errors you haven't caught, I definitely say positive review!

[rws]

I really see no problem with this addition. Now that there is a symbolic sum in Sage the conversion of unsolved sums from SymPy will only need a small SymPy patch (in the SymPy repo or in build/pkgs/sympy) to work.

[vbraun]

Author name is missing...