SymPy makes math fun again
The times I have used CAS to help with algebraic simplification, I've found the same problem, regardless of using SymPy or the more feature-filled Mathematica: the package's rules for simplification often obscure useful forms that lead to insight. The CAS gives you the correct result, of course, but I end up having to apply significant post-processing to the result by forcing substitutions that can take almost as much time as doing the algebra by hand.<p>As a simple example, consider the transfer function of a RLC circuit from basic electronics. It might contain a expression of the form: s^2 + (R/L) * s + 1/(LC). What's often helpful is to express this in terms of the unitless form 1 + s/(Q * w0) + (s/w0)^2, where w0 is the resonance frequency and Q is the quality factor. In a complicated example with more components, the value of w0 might be related to the simple form of 1/sqrt(LC) by some unitless factor, or there's some other helpful way to write things that neatly relate it to the basic case, but SymPy/Mathematica will drag its feet showing you that. I wish there was more done on improving the insight and meaningfulness of results from CAS to the experimenter.