On 8/25/07, Rafael de Pelegrini Soares <rafael at enq.ufrgs.br> wrote:
> Have you found an answer for your question about 'Differentiate into a
> sum' posted last month on this list?
For the record, the question was ...
On 7/1/07, Jordi Gutierrez Hermoso <jordigh <at> gmail.com> wrote:
> How can I do something like finding the derivative wrt to x[r] of some
> function of the sum sum(a[k]*x[k], k, 1, n)?
I think we should be able to come up with something if we
express a solution abstractly first and then figure out how to
represent that in Maxima.
As a first cut, which is probably wrong, maybe something like
diff (sum (foo (x [f (i)]), i, 1, n), x [j])
=> sum (diff (foo (x [k]), x [k]), k in { i s.t. j = f (i) })
It's not clear to me how to generalize this to multiple subscripted
variables in the summand e.g. foo(x[f(i)], x[g(i)]). Plus it might
well be completely off the mark. Anyway it's fun to think about.
best
Robert Dodier