Wrong documentation for sum() function?

[Michael]

When ask sage about the function sum()

sage: sum?

I get told to use it the following way:

sage: sum(expression, k, 1, n)

which should give me back the summation of "expression" over the index
k from 1 to n.
Unfortunately this gives me an error message like "summation index
needed".

I found out searching the internet that writing instead:

sum(expression for k in (1..n))

works. So I'm assuming that the documentation is outdated. Maybe this
is well know, but I hope it is ok to post this here.

Cheers
Michael

[Juan Luis Varona]

Dear Michael and Minh,

>
> > So I'm assuming that the documentation is outdated. Maybe this
> > is well know, but I hope it is ok to post this here.
>

> Could you try the examples in the documentation at [1] and see if it's
> what you wanted?
>
> [1]http://www.sagemath.org/doc/reference/sage/misc/functional.html#sage....
>
> --
> Regards
> Minh Van Nguyen

Great!
I have seen in the documentation of [1], and I have seen the notation
sum(1/k^4, k, 1, oo) that is also new for me.

But I want to make a comment, also from this documentation. It says
sum(1/(1+k^2), k, -oo, oo, algorithm = 'mathematica') # optional
-- requires mathematica

OK, I understand that sage do not kown how to evaluate
sum(1/(1+k^2), k, -oo, oo)

But it answer 0 , that is wrong!!!

(I have yet 4.3.1; I'm waiting 4.3.4 to update my sage)

Yours,

Juan Luis Varona

[Juan Luis Varona]

Dear Minh,

>
> > OK, I understand that sage do not kown how to evaluate
> > sum(1/(1+k^2), k, -oo, oo)
>
> > But it answer     0      , that is wrong!!!
>

> Both Sage 4.3.3 and 4.3.4 give the same wrong answer:
>
> [mvngu@sage sage-4.3.4]$ sage
> ----------------------------------------------------------------------
> | Sage Version 4.3.3, Release Date: 2010-02-21                       |
> | Type notebook() for the GUI, and license() for information.        |
> ----------------------------------------------------------------------
> sage: k = var("k")
> sage: sum(1/(1+k^2), k, -oo, oo)
> 0
>
> [mvngu@sage sage-4.3.4]$ ./sage
> ----------------------------------------------------------------------
> | Sage Version 4.3.4, Release Date: 2010-03-19                       |
> | Type notebook() for the GUI, and license() for information.        |
> ----------------------------------------------------------------------
> sage: k = var("k")
> sage: sum(1/(1+k^2), k, -oo, oo)
> 0
>
> Here is the answer from Maple:
>
> [mvngu@sage ~]$ maple
>     |\^/|     Maple 12 (X86 64 LINUX)
> ._|\|   |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2008
>  \  MAPLE  /  All rights reserved. Maple is a trademark of
>  <____ ____>  Waterloo Maple Inc.
>       |       Type ? for help.> sum(1 / (1 + k^2), k=-infinity..infinity);
>
>                                   Pi coth(Pi)
>
> And the answer from Mathematica:
>
> [mvngu@sage ~]$ math
> Mathematica 6.0 for Linux x86 (64-bit)
> Copyright 1988-2007 Wolfram Research, Inc.
>
> In[1]:= Sum[1 / (1 + k^2), {k, -Infinity, Infinty}]
>
>         I
> Out[1]= - (PolyGamma[0, -I - Infinty] - PolyGamma[0, I - Infinty])
>         2

>
> > (I have yet 4.3.1; I'm waiting 4.3.4 to update my sage)
>

> Unfortunately, updating to Sage 4.3.4 won't even fix the above issue
> with the sum() command. The above issue with the sum() command is now
> tracked at ticket #8582:
>
> http://trac.sagemath.org/sage_trac/ticket/8582
>

Thanks for include it as a ticket.

Juan Luis

PD: Mathematica 7.0 also gives the correct answer Pi Coth[Pi]]