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Mailing list for the LaTeX3 project <[log in to unmask]>
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From:
"William F. Hammond" <[log in to unmask]>
Date:
Sat, 12 Dec 1998 18:32:46 -0500
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Mailing list for the LaTeX3 project <[log in to unmask]>
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This is a text/plain rendition (with some human intervention) of
http://math.albany.edu/~hammond/gellmu/authordtd/mathbench.html .

                 What is a Reasonable Authoring DTD
                   under SGML or XML for MathML?

                         William F. Hammond

                         1. A Few Examples

1. Compound fractions:
                   {{a}/{b}}/{{c}/{d}} = {a d}/{b c}.
2. The formula for solving the quadratic equation a x^2 + b x + c = 0
   (in a field of characteristic <> 2):
                x = {-b {+/-} SQRT{b^2 - 4 a c}}/{2 a} .
3. Mixed function application and multiplication:
                           sin a x cos b x .
4. Newton's binomial series:
(1 + t)^r = SUM[_{k=0}^{INFTY} {r(r - 1)(r - 2)...(r - k + 1)}/{k!} t^k] .

5. Stokes's Theorem in space:
    INT[INT[_S (curl F . N) d sigma]] = INT[_{\partial S}(F . T)d s] .

6. The continued fraction for the golden mean:
        {1 + SQRT{5}}/{2} = {1}/{1+{1}/{1+{1}/{1+{1}/{1+...}}}}.

7. The inline math representation

                           Gal(\bar{ Q }/Q)

   for a centrally important object that one might choose to declare
   as the symbol "galQ", once a command \mathsym has been
   implemented for use in a GELLMU document preamble (not to be
   confused with an SGML preamble).

                        2. Generating MathML

There is an issue for authoring related to MathML [1], the rather
verbose XML language developed by the World Wide Web Consortium (W3C)
HTML Math Working Group during the period 1996-1998.

How can we set all of the above mathematics examples in a succinct
SGML authoring language that admits robust processing to MathML and
that uses reasonably succinct mathematical notation based on the long
tradition of Western mathematical notation?

The purpose of my draft on notation at the URL
http://www.albany.edu/~hammond/gellmu/notation [2] is to explain what
additional information is needed in this document to eliminate the
need for guessing in automated rendering of the examples above, as
marked up in the XML version of this document, into MathML in a fully
automated way. Note that no guessing is needed to render this document
in either HTML, with mathematics set crudely but reasonably, nor to
render it in LaTeX. (Perhaps one may not fully appreciate this latter
point without examining the XML version [3] of this document.)

Note that under the unrealized part of my design a math symbol may be
declared in a GELLMU document preamble with the usage:

        \mathsym{symbol-name}{symbol-type}[symbol-rendering] .

In this symbol-name is an alphanumeric string (case-sensitive)
beginning with a letter. The second argument symbol-type is an
alpha-numeric string that may also include possibly a few other string
characters such as `/', `-', `>', `<', `,', `.', `*', etc. (Under the
didactic GELLMU document type definition a command name for each
non-alphanumeric keyboard character is provided in order to provide
flexible handling of such characters in various possible output
formats.) It is intended that the type information be
context-specific, possibly under a general framework that is not yet
specified. The optional third argument is a generic instruction, in an
unspecified format that will eventually need to be specified, for
generic rendering as would be used if there were no symbol declaration
for the symbol. Absent a third argument the rendering of the symbol
should simply be

                     <space>symbol-name<space> .

(In LaTeX the ``space'' might be a small space.) Note further that
when my GNU Emacs Lisp processor transliterates the GELLMU markup for
mathsym to SGML, it will simply convert the argument markup to tagged
format.

The command name mathsym will be one of very few names that acquires a
meaning in my design for GELLMU outside of the SGML document type
definition (as well as therein) that is a legal name in GELLMU source.
Most other such names generated by the transliterator violate the
naming rule: a name must be alpha-numeric with the first character a
letter and the first digit, if any, not the digit zero. These names do
appear in the document type definition.

A processor for the target LaTeX should remember any symbol
declarations in the GELLMU preamble and set each occurrence inside one
of the math modes without a generic rendering-instruction using the
LaTeX command \mbox on the default generic rendering. If one is
processing both for LaTeX and for MathML, then it would be sensible to
use an early SGML-to-SGML processor to mark all declared symbols
inside math modes. Such a declared symbol name, e.g. galQ, should not
be confused with a corresponding command name \galQ; the latter must
be in the DTD but not the former. (The two need not be related in any
way.)

The reader is invited to do one or more of the following:
  * point out inadequacies in my draft on notation.
  * improve my draft on notation.
  * provide code to render the above examples:
  _________________________________________________________________

References

   1. http://www.w3.org/Math/
   2. http://www.albany.edu/~hammond/gellmu/notation
   3. http://www.albany.edu/~hammond/gellmu/authordtd/

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