symbolic integtn/diffn of Maxima best of any open source system??

(CY and RJF being quoted here)
| > Some of Axiom's capabilities in indefinite symbolic
| > integration of algebraic functions are, I think, superior.
| 
| Really?  I thought algebraic functions were the closest thing
| to a simple case of integration out there.  How do they improve
| on us?  (And what should we do to catch up?)

I imagine that by `algebraic functions', RJF means solutions
to algebraic equations, e.g., y as a function of x defined
by
     y^3 + 2y + 6 = x^5 + 1

Going out on a limb here, i'd be surprised if the problem in
full generality were tractable at all, but special cases
are, of course (y^2 = 1 - x^2), and one would want to handle
as many special cases as possible.

[And if the general case _is_ tractable, somebody please correct
me and point me to the literature.]

dan