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Mathematica is at a disadvantage since it worries about getting everything perfectly right, i.e. it cares about branch cuts and domains. I can cook up plenty of
by knzhou 7y ago
Mathematica is at a disadvantage since it worries about getting everything perfectly right, i.e. it cares about branch cuts and domains. I can cook up plenty of examples engineered to have these issues, which I could do (naively) but which Mathematica would choke on (when trying to solve it properly). All of the examples that Mathematica couldn't solve seem to be of this form. If you actually want it to stand a chance, you have to put in appropriate Assumptions, not just toss it in.
That said, I'm still extremely surprised this works that well. I would be very curious to test this interactively.
- amelius 7y agoYou could take a 2-step approach, where you first take the "fuzzy" approach, and then later try to correct for possible oversights (which is just simple bookkeeping).
- mlevental 7y agohow exactly would you do that? how would you know when the fuzzy search has failed?
- amelius 7y agoYou plug the result back into the equation, then simplify the equation until you get a tautology. Of course, the "simplify" step can be difficult, but it's usually a lot simpler than solving equations.