There is a problem with integrate_uses_rootof ...
(whoever wrote this might think about it..)
it would be nice to be able to differentiate the result of integration
uses rootsof.
unfortunately, it is likely to be quite hard to do this because lsum is
too general. You would have
to figure out if the summand was a symmetric function of the roots.
Having a sum_over_roots operation would solve this. I think Maple and
Mathematica do it.
Lsum can be used for other things..
RJF