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Re: [Axiom-developer] Design of Semantic Latex

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,
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

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.”


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