I'm not sure why you did not post to sage-support.  Here are some suggestions:

1. Remove the first line of your script (with var())  which serves no purpose.
2. In both functions initialize g by g=1/2, not g(x) = .
3. Expressions like sin(n*pi*x) where both n and z are exact integers
will be treated as symbolic expressions, which is not what you want.
I suggest forcing to real arithmetic by using pi = RR.pi() or similar.

John

On Mon, Jun 6, 2011 at 11:34 AM, Ignas Anikevicius
<[email protected]> wrote:
> Hello,
>
> This is my first message to this list, but I hope, that I have not
> broken any rules here. I am writing because I have noticed a strange
> thing, which I think should not happen.
>
> I needed to test my maths solutions, so I thought I would just use a
> loop to get sage generate the first 600 terms of a particular Fourier
> series. But then I remembered that sage has a sum function. So I also
> tried the sum function. However, I noticed a very big performance
> difference which I did not expect. I was wondering if someone could
> explain me why there is such a difference in the performance although
> the actual result is the same? Or is the native sum function more clever
> or what?
>
> The output of the script and the script itself are attached. Note that I
> did not bother to wait for the native sum function to sum 1000 terms, as
> it took eternity to finish.
>
> Cheers,
> Ignas A.
>
>
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