Computing symbolic derivatives and integrals, simplifying algebraic expressions, arithmetic with arbitrary length integers, solving simple ODE, computing limits and series, things like that.
Maxima is a fine piece of software, and I’m a huge proponent of its development, but doesn’t compete in the breadth or depth of Mathematica (or Maple) at all.
It certainly competes due to the fact of being free software, which is a strong requirement of my workflow. I can try Mathematica and Maple (and love them), but ultimately I have to end using a free software solution.
