All good remarks. > The "rewrite engine" ambitions for Fungrim seem potentially misplaced. It would probably be better to contribute to an existing open source

All good remarks. > The "rewrite engine" ambitions for Fungrim seem potentially misplaced. It would probably be better to contribute to an existing open source state-of-the-art CAS like Fricas For the record, I have contributed to several existing open source computer algebra systems (not Fricas though). I honestly don't think anyone has found the right foundations for computer algebra systems yet. Nor do I even think that there can necessarily be a "one size fits all solution" that works better than a multitude of specialized systems for different tasks. Fricas gets some things right where others don't, but it has its own weaknesses. I think it's valuable to explore different approaches. This possible future direction for Fungrim is more of a research project, and in any case, I think it's complementary to much of the work that is already being done on other open source computer algebra systems. Sorry that this is still a bit vague. I have more specific issues in mind, but I don't have time to elaborate in this HN comment. I hope to do a better writeup in the future! > WTF! Only if one uses Wolfram Alpha exclusively! Or Maple, or Maxima, or SymPy, or Sage, or... even Fricas. Despite its type system, Fricas has the same problem as the rest with overzealous simplification. One of the very first examples in the Fricas book, "integrate (1/(x^2 + a),x)" gives a result that isn't valid when a = 0... And that's without even digging to look for something more subtle that will be more likely to catch the user off guard. > Try Fricas. I admit that I haven't tried Fricas in a long time, but I'm also confident that I wouldn't need to look hard to find examples. Here is just one quote from the Fricas book: "FriCAS can compute some forward Laplace transforms, mostly of elementary functions not involving logarithms, although some cases of special functions are handled." Mathematica, on the other hand, handles a huge number of Laplace transforms involving logarithms and special functions (largely using Meijer G-function methods in combination with internal lookup tables and many different heuristics). How well does Fricas support definite integration with piecewise functions or functions involving branch cuts? Mathematica has improved a lot in this area in the last few years (even if it isn't perfect). Of course, I'm sure Fricas has its strong areas too, and Mathematica is terrible in some areas. > "Automagical" interfaces suck, they will inevitably break when you stray just a bit from the intended path. It is better to have a typed language like Fricas has. Oh, I do agree completely about the problem with automagical interfaces that work until they don't :) Nevertheless, even "automagic" that breaks down at some point is great for discovery and prototyping. I think in many cases, we can do a better job providing interfaces that scale smoothly between automatic and user-controlled.