Hi,
On Thu, 26 Mar 2009 09:31:09 -0700 (PDT)
Patrick <[email protected]> wrote:
> I'd like to count the iterations of a loop nest by evaluating a sum.
> Consider the following loop nest:
>
> for (k = 0; k < N; k++)
> for (i = k+1; i < N; i++)
> for (j = k+1; j <= i; j++)
> ...
>
> I'd like to count the total number of iterations of that loop nest.
> I've used mathematica a bit, and you could solve this problem with
> something like this:
>
> Sum[1, {k, 0, N}, {i, k+1, N}, {j, k+1, i-1}]
>
> The result should be in terms of N. For this loop nest the closed
> form is:
>
> 1 / 6 * (1 + N) * (N^2 - N)
>
> I've been trying to figure out how to do this sort of problem in Sage,
> but I have been unsuccessful. Any help would be greatly appreciated.
Unfortunately Sage doesn't have native code to find closed forms for
sums at the moment. You will have to use maxima directly to solve this problem.
I have an implementation of various (mostly theoretical) parts of
symbolic summation algorithms, but it has no user interface. I expect
to push this code in Sage at the end of May, after I sort the user
interface out and add some other basic dependencies in Sage.
Cheers,
Burcin
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