Dual Presentation with Math from one Source using GELLMU

1.  Introduction

A contemporary author writing an article for “dual presentation” has in mind both the classical printed presentation of an article and the online form of an article formatted in HTML. There are particular challenges when mathematics is involved because it is moderately difficult to produce correct mathematical markup for modern HTML documents.

While mathematics is a principal concern in this article, most of what is said here is relevant, though less critically so, for documents that do not involve mathematics.

There are two main approaches for achieving dual presentation that are relevant to the TeX community. (Texinfo, the language of the GNU Documentation System, also provides a route for dual presentation of articles without mathematical markup.)

1. Write a LaTeX article, and use a program that translates to HTML.

2. Write an article in a suitable XML document type, such as DocBook, and use standard software for generating LaTeX and HTML.

Both methods present challenges to authors who have been accustomed to using LaTeX. In particular, if mathematics is involved, there are no widely deployed XML document types that support author-level mathematical markup. Since mid-2002 mathematical content in the second-generation form of HTML has been supported by the two most widely deployed web browsers, but not many articles seem to have appeared on the web in this form so far. The most likely reason is difficulty of creation.

This article addresses the use of “generalized LaTeX”, as implemented in the GELLMU Project, to produce dual content from a single LaTeX-like source. (The overall system design in GELLMU is one for multiple outputs although at this time the standard implementation provides (i) printed output via standard LaTeX and (ii) HTML.)

A generalized LaTeX article under the GELLMU Project is essentially equivalent to an XML document under an author-level document type that may be called “GELLMU article”. Preparing documents this way combines the reliability of XML document transformation with most of the conveniences, such as newcommand macro substitutions, the use of blank lines for paragraph boundaries, and cross-referencing, that are available when writing LaTeX markup.

It should be emphasized that the GELLMU Project does not provide translation of classical LaTeX to HTML or to any XML document type. Of course, one may open a classical LaTeX document in an editor and invest time and energy to “port” it to GELLMU source, but there is no automation for this.

The task of translating legacy documents to HTML and to XML document types is difficult. In 2007 we are witness to more than 10 years of effort in this direction, and we still have no easy path, particularly when mathematics is involved. Nonetheless, translation, to the extent that it is reasonably possible, is very important because we have 30 years of legacy documents. (Most of the past translation efforts have been aimed at standard structured formats like HTML and the DocBook XML document type. It would be interesting to see if the translation task toward such standard formats can be improved by first translating toward an author-level document type, such as GELLMU article, that models structured LaTeX rather closely and then translating from there toward the original target.)

When a contemporary author has dual presentation in mind for new documents, writing classical LaTeX is no longer the best way to proceed because of the difficulty of translation from LaTeX to other formats. Writing for a suitable author-level XML document type is a much better way to have seamless dual presentation, and using the LaTeX-like front end offered by GELLMU makes it seem to the author very much like writing LaTeX.

In his talk preceding mine at TUG 2007 Chris Rowley ventured the idea that “peak TeX”, like “peak oil”, lies in the near future. In saying that I hope he is speaking of a peak in relative use by authors as markup source of the print-focused typesetting language that we have known. The other side of this is that if, as a community, we come to appreciate the usefulness of LaTeX-like markup, as opposed to classical LaTeX, as a general author front end for writing structured documents and then come to understand that practice as part of the TeX world and hone our techniques of formatting these structured documents for classical TeX-based typesetting, the future I imagine is one of more, not less, TeX.

2.  Writing Source Markup

This is GELLMU source for a short paragraph with a relatively simple mathematical display.

The following identity may be

regarded as a formulation of the

Weierstrass product for the Gamma

function.

\[ \int_{0}^{\infty} t^x

   e^{-t} \frac{dt}{t} \int:

   = \frac{1}{x}

   \prod_{k=1}^{\infty}

   \frac{\bal{1 + \frac{1}{k}}^x

    }{\bal{1 + \frac{x}{k}}}

   \prod: \]

Understanding the derivation of

this identity is reasonable for a

bright student of first year

undergraduate calculus in the

United States.

This source compiles to:

The following identity may be regarded as a formulation of the Weierstrass product for the Gamma function. $${\int }_0^{\infty }{t}^x{e}^{-t}\frac{dt}{t}=\frac{1}{x}\prod _{k=1}^{\infty }\frac{{\left(1+\frac{1}{k}\right)}^x}{\left(1+\frac{x}{k}\right)}$$ Understanding the derivation of this identity is reasonable for a bright student of first year undergraduate calculus in the United States.

The markup looks like classical LaTeX. In fact, except for the use of the zone closers \int: and \prod:, it would be classical LaTeX. It is generalized LaTeX.

The mandatory use of zone closers arises from the fact that the GELLMU system is not monolithic. Rather than being a single program, it is a suite of cross-platform component programs, each with a well-defined task, managed with a driver script. The first stage of processing operates at the level of syntax with almost no knowledge of markup vocabulary.¹ Because of this, GELLMU source, like texinfo source, has stricter syntactic requirements than plain TeX and classical LaTeX.

Other ways in which GELLMU source differs from classical LaTeX source include:

1. Command arguments must be explicitly braced.

2. There may be no white space between a command name and the delimiter (a brace or bracket) for its first argument or option.

3. There may be no white space separating the delimiters of the successive arguments and options of a command.

4. Braces for the argument of a superscript or subscript may be omitted only if the argument is a single character.

5. The semi-colon at the end of a command name (such as \latex; above) indicates that the command does not introduce content. Often this type of semi-colon may be omitted, and, beyond that for most purposes \foo; may be regarded as shorthand for \foo{}.

6. The command vocabulary is somewhat different.

3.  Another Example

Figure 1 provides a GELLMU rendition of an example posted to the UseNet newsgroup sci.math.research on 29 October 2002 (Message id: apmpvn$bpb$1.repost@nef.ens.fr), by David Madore of ENS comparing TeX markup to MathML markup in order to illustrate the undisputed point that no author would ever regularly want to write MathML directly.²

This is the GELLMU source underlying figure 1:

\macro{\=}{\ovbar}

\macro{\.}{\ovdot}

\newcommand{\b}[1]{\unbar{#1}}

In a letter to Godfrey Harold

Hardy, S\b{r}\={\i}\b{n}iv\={a}sa

R\={a}m\={a}\b{n}uja\b{n}

Aiya\.{n}k\={a}r asserts that

\[ \frac{1

 }{1+\frac{e^{-2\pi\sqrt{5}}

 }{1+\frac{e^{-4\pi\sqrt{5}}

 }{1+\frac{e^{-6\pi\sqrt{5}}

 }{\ldots}}}}

=

\bal{\frac{\sqrt{5}

 }{

 1+\sqrt[5]{5^{3/4}

 \bal{

  \frac{\sqrt{5}-1}{2}

 }^{5/2}-1}}

-\frac{\sqrt{5}+1}{2}}

e^{2\pi/\sqrt{5}} \]

In this markup, note first the use of GELLMU's \macro facility to provide emulation of classical LaTeX algorithmic accents with names that are not formed with letters. Further note the use of \bal{ ... } in place of the LaTeX usage \left( ... \right). GELLMU has various balancers of this type and will eventually have more. This is related to the fact that the markup is simply a “front” for an SGML document type where a name is needed. The processor for XHTML + MathML output will not tolerate unbalanced balancing characters in a math zone except as provided through these balancers and also through the list generator

The kinds of weak enforcement of mathematical semantics represented by such balancing provisions and by the requirement for explicit ending of sum, int, and prod containers is prelude to future optional incorporation of stronger mathematical semantics in the markup.

Madore is correct in suggesting that one doesn't want to look at the MathML markup for this, but the rendering by Firefox, somewhat enlarged, is captured in the screenshot that is figure 2.

4.  The Importance of XHTML + MathML

There are several reasons why it is important to have articles and course materials with mathematical content online in modern HTML, i.e., XHTML + MathML.

5.  Compiling an Article

6.  System Components

Regular GELLMU is a system assembled from modular components. Each step along the way produces an intermediate stage output that has its own sense and that, when things go wrong, provides opportunity both for diagnosis and intervention. A flow chart for regular GELLMU is found in figure 5.

In figure 5 what I call the “side door” is the second row entry showing the possibility of translation from source languages other than the markup of regular GELLMU into the author-level XML document type corresponding to the source markup of regular GELLMU.

One will note from the scroll that SGML/XML validation is done at several stages. This validation can be important for catching the author's mistakes. When there are error messages, it is possible and important to consult the scroll's last message regarding the stage of processing. Note in this regard that the translation from elaborated XML to XHTML + MathML takes place in 3 stages that are not shown on the chart but that may be seen in the example scroll.

7.  Further Information

Much more information may be found in the User Guide ([3]), the GELLMU Manual ([4]), and the GELLMU web site, http://www.albany.edu/~hammond/gellmu/. A link to an online version of this document with live links should be available at the GELLMU web site for several years.