Many years ago, when I was a grad student, I bought a student-discount copy of Mathematica, the symbolic computer algebra system. It was crucial to finishing my doctoral thesis: I pretty quickly got beyond the point where I could safely do the algebra involved in my research by hand without making a fatal mistake somewhere. I knew some people who
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It really seems as if the built-in graphics haven't gone very far since then, and everyone else seems to sort of imitate that style. Part of it is probably a no-nonsense attitude among scientists and mathematicians that you don't want to seem like you're trying to put something over by making your graphics look like something out of Hollywood or a video game. But sometimes it seems as if conventions determined by antique technical limitations are hobbling things unnecessarily.
Though I know it can interface with external packages to do fancier things.
Right now, there's this entertaining competition going on between SymPy's symbolic integration routines and the Maxima ones that Sage uses by default. SymPy seems to be the one under more active development; it may already be a more powerful integrator than Maxima, but Maxima's faster because it uses more compiled native code. Presumably if/when that changes, Sage will switch over.
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