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Re: [Maxima-discuss] ML for symbolic math
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From: Richard F. <fa...@be...> - 2019-10-01 23:58:10
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Try typing an expression into Wolfram Alpha. It guesses what you might want to know about and includes a plot or several. I tried Exp[-x^2*Sin[x]] for example. Not so great, but it tries. Regarding the larger issue of how to populate integral refernce handbooks with new integration formulas, or the equivalent for on-line resources, there are lots of ways of approaching this, e.g. via generating functions, series expansions and recognition, studies of special functions, and perhaps some other methods. Ted Einwohner and I looked at some for our online table lookup program Tilu. Not very successful though. The idea of "running differentiation backwards" doesn't seem to have any plausible methods. The idea of doing integrals without some significant effort at recognizing patterns also seems implausible, and the fact that certain problems easily stated as integrals also turn out to be recursively undecidable puts some constraints on solving this. In particular, if you can't tell if an expression is zero or not, how can you compute its integral? I'm sure that there are great applications for AI in vision, playing games with finite size boards, and presumably lots of other areas. I would not trust an AI to translate natural language of delicate political considerations, and there appear to be substantive issues in the hot topic of automated driving. Throwing enormous computational ML power doesn't keep Tesla crashes out of the news. symbolic math seems to fall more in the realm of symbolic "AI" or GOFAI -- good old fashioned AI -- using logic, ontologies, models,, etc. You can come up with hack solutions... like encode all calculus texts and their answer books, and do vision lookup, but that only solves the task of cheating on your calculus homework. Not doing calculus. If there is a program using ML to do integration, how about publishing it? Or at least publishing the test set? If I am mistaken and there is an actual success, say rivaling CAS programs in breadth, scope, accuracy etc,, it would certainly be interesting! RJF 19 6:01 PM, Henry Baker wrote: > The same way that AI/ML spam filters work: thumbs up or thumbs down. > > If the AI/ML has access to a large # of Maxima users, then it can get a bit of the "wisdom of the crowd". > > Google uses similar kinds of technology to determine what people want in their search results. > > Netflix uses similar kinds of technology to determine what you might want to watch. > > At 01:10 PM 10/1/2019, ΣταῦÏος ΜακÏάκης wrote: >> But how is that famous AI supposed to know what you want? If your input is [sin(x),cos(x)] do you want a parametric plot (a circle) or two line plots? Do you want one cycle? multiple cycles? What about tan(x) -- where do you clip the y axis? Or do you use a logistic curve to fit it all in a finite space? If your input is [2,4,4,4,5,6,7,8,8,8,9], is that [x,y]=[[1,2],[2,4],[3,4],[4,4]...] -- a bar chart, a scatterplot, or connected by lines? -- or a histogram like [x,y]=[[2,1],[4,3],[5,1], ...] or a smoothed density plot (with what parameters?)? etc etc. >> >> On Tue, Oct 1, 2019 at 3:49 PM Henry Baker <hb...@pi...> wrote: >> I just want to say "plot something interesting from these equations", or >> "plot x,y", and the AI/ML system will figure out how to do this. >> >> I don't want to have to spend a full day reading the Maxima plotting >> manual every time, which is about what usually it takes me, since I >> only do this every couple of years, and by the next time, I've forgotten >> all of the commands and switches. >> >> At 12:34 PM 10/1/2019, Raymond Toy wrote: >>>>>>>> "Henry" == Henry Baker <hb...@pi...> writes: >>>   Henry> I don't know about generic AI/ML for Maxima, but I would >>>   Henry> appreciate an AI/ML approach to *graphing* and more >>>   Henry> generally to *plotting*. >>> >>>   Henry> There are so many bells & whistles on the plotting >>>   Henry> mechanisms that an AI/ML program could exhaustively >>>   Henry> memorize & suggest possible plots. Once I could see what >>>   Henry> options the AI/ML program chose, I could then edit these to >>>   Henry> fine tune the plot. >>> >>> I'm a bit confused on what yuo want an AI to do here. Do you want the >>> AI to figure out how to choose how many points to plot to make the >>> curve sufficiently smooth? Somethine else? >>> >>> -- >>> Ray > > > _______________________________________________ > Maxima-discuss mailing list > Max...@li... > https://lists.sourceforge.net/lists/listinfo/maxima-discuss |