It might be fun for somebody to extend Maxima's use of rootsof (see integrate_use_rootsof).
Maxima could do things such as rootsof(x^2-5) + rootsof(y^2-3) --> rootsof(q^4-16*q^2+4).
The four roots of q^4-16*q^2+4 are (+/-) sqrt(5) + sqrt(3), sqrt(5) (+/-) sqrt(3).
One problem would be to prevent Maxima from simplifying rootsof(x^2-5) - rootsof(x^2-3) --> 0.
Maybe we need a general scheme for preventing the general simplifier from doing xxx - xxx --> 0.
And what would be a simple representation for rootsof(sum((1)^(k + 1/2) / k,k,1,inf), by the way?
--Barton