For those who didn't see, the final paper was posted with many updates https://arxiv.org/abs/1912.01412. The newest version addresses some of the things that were discussed here, and makes more use of SymPy, including demonstrating some integrals that SymPy cannot solve, as well as making it clearer how SymPy was used to check the results of integration.
Aaron Meurer On Tue, Oct 8, 2019 at 8:16 PM oldk1331 <[email protected]> wrote: > > (This mail is copied from my response at maxima mailing list.) > > My opinion on this paper: > > First, their dataset (section 4.1) can be greatly improved using > existing integration theory, Risch algorithm says that every elementary > function integration can be reduced to 3 cases: transcendental (only > contains rational functions and exp/log/tan, other trigonometric > functions can transform to 'tan'), algebraic (only contains rational > functions and nth-root ^), and mixed-case. > > So their method to prepare the dataset concentrates greatly on the > transcendental cases, extremely lacks algebraic cases. And they uses > only numbers from -5 to 5. I think it scales badly for wider ranges of > numbers. > > For transcendental cases, I think FriCAS has fully implemented this > branch of Risch algorithm, so it should always give correct result. For > algebraic cases, I highly doubt that this ML program can solve > integrate(x/sqrt(x^4 + 10*x^2 - 96*x - 71), x) = > log((x^6+15*x^4+(-80)*x^3+27*x^2+(-528)*x+781)*(x^4+10*x^2+(-96)*x+(-71))^(1/2)+(x^8+20*x^6+(-128)*x^5+54*x^4+(-1408)*x^3+3124*x^2+10001))/8 > > In fact, I doubt that this program can solve some rational function > integration that requires Lazard-Rioboo-Trager algorithm to get > simplified result. > > So I think this ML program has many flaws, but we can't inspect it. > > > I'm also curious (and sceptical) on just how well a neural network can > > "learn" symbolic mathematics and specifically an integration > > algorithm. Another interesting thing to do would be to try to train a > > network to integrate rational functions, to see if it can effectively > > recreate the algorithm (for those who don't know, there is a complete > > algorithm which can integrate any rational function). My guess is that > > this sort of thing is still beyond the capabilities of a neural > > network. > > I totally agree. > > - Qian > > -- > You received this message because you are subscribed to the Google Groups > "sympy" group. > To unsubscribe from this group and stop receiving emails from it, send an > email to [email protected]. > To view this discussion on the web visit > https://groups.google.com/d/msgid/sympy/ca99c7a0-b372-82cb-74e6-2ff978f40d54%40gmail.com. -- You received this message because you are subscribed to the Google Groups "sympy" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To view this discussion on the web visit https://groups.google.com/d/msgid/sympy/CAKgW%3D6LCHjJhz06Y-N3RwNS8g8wAbi274ke5rc77L%2BWnORUHuw%40mail.gmail.com.
