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

Date: Thu, 7 May 1998 11:24:40 -0700 (PDT)

Message-Id: <199805071824.LAA12059@peoplesparc.CS.Berkeley.EDU>

To: www-math@w3.org

Responses... * 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 *context? 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 FatemanReceived on Thursday, 7 May 1998 14:25:59 UTC

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