It's funny, I've been diving into a lot of math I haven't used in a while lately (via the Coursera "Robotics Specialization"). Since I don't particularly trust

It's funny, I've been diving into a lot of math I haven't used in a while lately (via the Coursera "Robotics Specialization"). Since I don't particularly trust myself to do huge amounts of symbolic manipulation/integration/etc on paper, I've picked up Maxima as a CAS to try to keep track of it all. More than once, I've gotten some set of equations into a form that I'm ready to use to do numerical iteration/gradient descent/whatever, and Maxima just kind of... pops out a closed form solution for the problem I'm trying to solve. My basic approach to straddle the symbolic/numeric divide is to keep things symbolic until the last minute and then substitute in the boundary conditions/constants/whatever at the end and see what pops out. If Maxima pops out a closed form solution, I'll analyze that geometrically to make sure it makes sense and isn't just a quirk of the specific boundary conditions I've chosen, and if it doesn't really have a closed form solution, I'll use the simplified equations and run them through a solver of whatever kind (ODE, gradient descent, etc).