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syntax/ responses to felt@math.wsu

From: Richard J. Fateman <fateman@CS.Berkeley.EDU>
Date: Thu, 7 May 1998 11:24:40 -0700 (PDT)
Message-Id: <199805071824.LAA12059@peoplesparc.CS.Berkeley.EDU>
To: www-math@w3.org

* Here are my questions:
*1) Are we really trying to come up with a standard way to code *and
*display* all common mathematical expressions, such as the differential
*operator?  This seems like an admirable but impossible task.  If you
*ask 10 mathematicians how to display the differential operator, you
*will get 5 different answers.  So, for automated search-ability, are
*we giving up quite a bit of display flexibility?

No, you should be able to show the same object differently.  Ideally
you would search for the semantically relevant indicator.  That
is $x^2$ might be semantically "the real valued variable
x raised to the power 2"  but $d^2/dx^2$  would be "derivative of order 2
with respect to x".  You could search for "derivative". or "power".

I don't know how MathML would, in particular represent these things
because I haven't followed the details as they have evolved

*2) If there are translators from LaTeX to MathML, how can this `context'
*possibly be included?  LaTeX did not meet the needs of MathML because it
*is only display oriented (i.e. the same expression may stand for two
*different ideas, depending on context), but how can a translator add such

Mostly, people lie that they can translate from LaTeX to MathML.  They
assume a context for your LaTeX that allows them to impute semantics.
I have a program that does this, and it assumes that $ax$ means a*x
but $\cos x$  does NOT mean cos*x  but cos(x). Does it work? Sometimes.
Try to translate $2,3,5,7,11,\cdots$ into MathML.

*3) Why is automated searching for math syntax so important?  If I am
*searching for a paper on trigonometry, I would search for `trigonometry',
*not \cos (or the MathML equivalent).  Or is it searching within a document
*that we are talking about?

I have a web program that searches for integral formulas in a table of
integrals. It is a prototype for an application that might search for material
in math or other journals.  Without a math-search engine
you can only search for words in chapter headings, like "Bessel".
Is this a generally useful thing to do? I think it is better
to be able to find the specific formulas involving the product
of two Bessel functions, if that is what you need.  MathML
has not, so far as I know, addressed the needs for conveying
a pattern or template of expressions that arise implicitly
in a table of integrals.  I am unaware of any interested alternative
(challenging) prototype problem, and this is really unfortunate:

The typical MathML demo examples (getting computer algebra system A to talk
to computer algebra system B and/or its front end and/or a display
program) are unlikely to push much of anything technologically, and
the structure hypothesized in the large volume of work proposed in
automating all of mathematics seems to be in need of a benchmark.
Most of the efforts in demos that I've seen
require only that you talk about a SUBSET of what computer algebra
systems talk about.  

I have offered this integration benchmark, but no one else has bitten:  If you
cannot encode Gradshteyn & Rhyzik's Table of Integrals, then
you should rethink what you are doing.  If you believe you CAN
encode it, provide some pages.  Handwaving is unacceptable.
I have done a few thousand (oddly enough by translating with
a clever parser from TeX) and have hundreds that probably can't
be done except by hand.

If you want to see what can be done if you DO incorporate
even a small table of integrals into a program (encoding math)
see http://http.cs.berkeley.edu/~fateman/htest.html .

*Again, I appologize if I am rehashing old material. 

Probably. but isn't that the purpose of the internet?:)

* For what my vote is
*worth, I would rather stick to a display-only language, tell the browser
*developers to include a LaTeX compiler, and be done with it. 

That's available already.

*  However, I
*can understand that searching for context-based material might be
*important to some people.

Yep. If you came up with a benchmark that would demonstrate 
how this might be important to some people in your area of expertise,
that would give the MathML workers something to chew on!

Richard Fateman
Received on Thursday, 7 May 1998 14:25:59 UTC

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