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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