Allow algorithm='sympy' in symbolic_sum function

[seblabbe]

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

CC: @kcrisman

Component: symbolics

Author: Sébastien Labbé

Branch/Commit: 16acdcf

Reviewer: Ralf Stephan

Issue created by migration from https://trac.sagemath.org/ticket/22004

[seblabbe]

Branch: u/slabbe/22004

[seblabbe]

Commit: aa2bcc1

[sagetrac-git]

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

a0f8d17

22004: Allow algorithm='sympy' in symbolic_sum function

[sagetrac-git]

Changed commit from aa2bcc1 to a0f8d17

[kcrisman]

comment:4

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

[kcrisman]

comment:5

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!

[sagetrac-git]

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

16acdcf

22004: fixing doc comment

[sagetrac-git]

Changed commit from a0f8d17 to 16acdcf