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From: | Richard Fateman |
Subject: | Re: [Axiom-developer] Design of Semantic Latex |
Date: | Sat, 27 Aug 2016 09:14:27 -0700 |
User-agent: | Mozilla/5.0 (Windows NT 10.0; WOW64; rv:45.0) Gecko/20100101 Thunderbird/45.2.0 |
Designation of branch cuts is sometimes
denoted by natural language.
While the end points are specific -- depend of singularities -- the cuts can be moved for convenience, and this is done often to evaluate contour integrals, for example. Take up a book on complex analysis and see what problems you have as you try to encode the statements, or especially the homework problems. I tried this decades ago with the text I used, https://www.amazon.com/Functions-Complex-Variable-Technique-Mathematics/dp/0898715954 but probably any other text would do. I think the emphasis on handbook or reference book representation is natural, and I have certainly pursued this direction myself. However what you/we want to be able to encode is mathematical discourse. This goes beyond "has the algorithm reproduced the reference value for an integration." Can you encode in semantic latex a description of the geometry of the (perhaps infinitely layered) contour of a complex function? You might wonder if this is important, but then note that questions of this sort appear in the problem section for chapter 1. Here's the challenge then. Take a mathematics book and "encode" it so that a program (hypothetically) could answer the problems at the end of each chapter. You do not need special functions and integral tables to find problems that are too hard to handle. I just found this http://news.mit.edu/2014/computer-system-automatically-solves-word-problems-0502 I think the problem, algebra word problems, which has been addressed repeatedly since 1965 or so, is already difficult. While I think (judging solely by the news article -- I was unaware of this work -- which apparently used Macsyma) this is low quality, it is hard to be sure. Maybe their problems can be be related to your ambitions. A quote from the article above, The system’s ability to perform fairly well even when trained chiefly on raw numerical answers is “super-encouraging,” Knight adds. “It needs a little help, but it can benefit from a bunch of extra data that you haven’t labeled in detail.” RJF |
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