\documentclass[12pt]{article} %100\% % test comment removal \begin{document} \title{A Brief Description of LaTeXMathJax} \author{Peter Jipsen} \address{Chapman University} \date{Version: January 31, 2014 (update to new CDN on July 25, 2017)} \maketitle \begin{abstract} This is a short article that illustrates those aspects of LaTeX that are transformed by LaTeXMathJax into a html plus MathJax format. While limited in scope, LaTeXMathJax nonetheless is capable of transforming a large subset of those elements found in a typical LaTeX article into a MathJax empowered webpage. The goal of LaTeXMathJax is that of making pure latex coding a "web-friendly" enterprise. A look at the HTML source of this page reveals that it is in fact almost completely written in LaTeX and transformed client-side into HTML+CSS+MathJax. \end{abstract} \section{Introduction} LaTeXMathJax is complete rewrite of \href{http://math.etsu.edu/LaTeXMathML/}{LaTeXMathML} by Jeff Knisley (based on work of Douglas R. Woodall), which is itself an adaptation and extension of \href{http://www1.chapman.edu/\~jipsen/asciimath.html}{ASCIIMathML} by \href{http://www1.chapman.edu/\~jipsen}{Peter Jipsen}. Like ASCIIMathML, it transforms LaTeX code it finds among the HTML code for a web page into MathJax-typeset equations. This article is a brief introduction both to LaTeX and to how it can be used in conjunction with LaTeXMathJax to include mathematics in all browsers that support MathJax. \subsection{A Brief Description} \label{Browsers} To use LaTeXMathJax, your web-page header needs to have the following in the <head> of the webpage: \texttt{<script src="http://math.chapman.edu/\~jipsen/latexmathjax/latexmathjax.js"></script> <link rel="stylesheet" type="text/css"\newline href="http://math.chapman.edu/\~jipsen/latexmathjax/latexmathjax.css" />} % \subsection{Downloading LaTeXMathJax} To download and use LaTeXMathJax, you will need at least the Javascript .js file. The CSS style sheet is not involved in the typesetting of equations, but it is important for numbering equations, captioning figures, and so on. To download, right-click on the following links and choose "Save Target As...": \newline \ \href{http://math.chapman.edu/~jipsen/latexmathjax/latexmathjax.js}{Link to latexmathjax.js Javascript Code} \newline \ \href{http://math.chapman.edu/~jipsen/latexmathjax/latexmathjax.css}{Link to Standard Article Style Sheet} \newline If you download latexmathjax.js or latexmathjax.css, then the URL's in the script and link tags will need to point to the download locations. \[\colorbox{yellow}{Note: LaTeXMathJax is designed to automatically load MathJax from a cdn (content distribution network; see end of the latexmathjax.js file).}\] \[\colorbox{yellow}{Hence MathJax should not also be loaded at the top of the html file that loads LaTeXMathJax.js since this can cause conflicts preventing MathJax from loading properly.}\] \textbf{The remainder of this text is taken verbatim from Jeff Knisley's description of LaTeXMathML. Wherever ASCIIMathML is referenced, it should now be read as MathJax, and some of the material below does not apply to the current (mini) version of LaTeXMathJax.} \subsection{A Brief History} MathML is a low level mathematical markup language for the internet. The "low level" nature of MathML means that typesetting even the simplest expressions can be quite involved. For example, typesetting the equation $y=x^2$ in MathML requires the following MathML structure: \begin{verbatim}<math title="y=x^2"> <mstyle> <mi>y</mi> <mo>=</mo> <mrow> <msup> <mi>x</mi> <mn>2</mn> </msup> </mrow> </mstyle> </math> \end{verbatim} However, the power and possible applications of MathML more than justify its complexity. In the future, MathML will allow not only the display of equations, but also their storage in databases, their mathematical manipulation for research purposes, and alternative representations such as for the handicapped or in other languages. Indeed, many efforts are underway to take advantage of MathML. The low-level nature of MathML has also inspired many efforts to develop higher level methods for encoding mathematical expressions into MathML. Most notable for this project is \href{http://www1.chapman.edu/\~jipsen/asciimath.html}{ASCIIMathML} by \href{http://www1.chapman.edu/\~jipsen}{Peter Jipsen} of Chapman University, upon which LaTeXMathML is based. Dr. Jipsen's excellent tool allows certain text codes in html-encoded web pages to be transformed "on the fly" into MathML equivalent syntax. The \href{http://www1.chapman.edu/\~jipsen/asciimath.html}{ASCIIMathML} javascript file is now one of several similar technologies by Peter Jipsen that do everything from graphing to implementing a personal wiki. Having noticed that some ASCIIMathML codes are similar to LaTeX codes and motivated out of a desire for a more LaTeX-like experience, Dr. \href{http://www.maths.nottingham.ac.uk/personal/drw/}{Douglas R. Woodall} of the University of Nottingham transformed ASCIIMathML into the original \href{http://www.maths.nottingham.ac.uk/personal/drw/lm.html}{LaTeXMathML} which accomplishes the same task as Dr. Jipsen's ASCIIMathML but does so strictly with LaTeX codes. At about the same time, Dr. \href{http://www.math.wisc.edu/\~ram/}{Arun Ram} of the University of Wisconsin developed the \href{http://www.math.wisc.edu/\~ram/MathGlossary/mathmlguide.xml}{mathmlguide} which suggests standard practices for using html/xml+css+mathml in producing web-based mathematics (supported in part by the National Science Foundation under Grant No. DMS-0353038 ). The present version of LaTeXMathML extends the original to allow simple LaTeX articles to be transformed to html+css+mathml in accordance with (much of) the mathml style guide. It was produced by Dr. Jeff Knisley, from East Tennessee State University, and supported in part by a Howard Hughes Medical Institute initiative called the \href{http://math.etsu.edu/Symbiosis/}{Symbiosis Project} ( HHMI #52005872). This short article is an introduction to LaTeXMathML. The second section explores the typesetting of simple mathematical expressions. The third section describes the larger "logical" structures--in particular, the \texttt{\begin...\end} structures supported by LaTeXMathML--and the fourth section describes the interplay between traditional html formatting and the LaTeXMathML script. \section{Mathematical Expressions} % blank line after \section inserts additional space At the heart of both ASCIIMathML and LaTeXMathML is the desire to transform LaTeX-encoded mathematics into mathml equivalent structures. For example, the LaTeX code \texttt{\$y=x^2\$} is transformed into the mathml typeset expression $y=x^{2}$. LaTeX coding of mathematics is for the most part straightforward and logical. Inline mathematics is placed between dollar signs, as above, while displayed equations can be structured in several ways (details later). A relatively simple approach to displayed equations is to use either \$\$ ... \$\$ or \textbackslash[ ... \textbackslash], where ... represents the LaTeX codes for the math to be displayed. For example, the following is a displayed equation set off by \textbackslash [ and \textbackslash ]: \[ x\left( x-1\right) =x^{2}-x \] The LaTeX code for most mathematical objects includes a "backslash" before the name of the object. For example, the Greek letter "alpha" is entered as \texttt{\alpha}, which is subsequently rendered as $\alpha$. Some objects, such as fractions and square roots, require other mathematical objects. These follow immediately after the object name and are enclosed using braces { }. For example, the upper $\frac{1}{2}$ of the unit circle is encoded by \texttt{\$\$y=\sqrt{1-x^2}}\texttt{\$\$}, which results in $$y=\sqrt{1-x^{2}}$$ There are few exceptions to this simple approach, so that LaTeX encoding of mathematics depends in great part on knowing the codes for the mathematical objects to be so rendered. A list of many common objects is given at \href{http://www.maths.nottingham.ac.uk/personal/drw/lm.html}{LaTeXMathML}. Mathematical groupings are an important part of mathematical formatting. Grouping in LaTeX is accomplished using the \left and \right structures. For example, the expression on the right below uses the \left(...\right) structure, while the one on the left does not. % Creates a comment until end of line! \[ \frac{d}{dx}(\frac{x^{2}}{\sqrt{1-x^{2}}}) \quad \text{or} \quad \frac{d}{dx}\left( \frac{x^{2}}{\sqrt{1-x^{2}}}\right) \] Also, an empty line indicates to LaTeX that a new paragraph should begin. YOU SHOULD AVOID EMPTY LINES INSIDE EQUATIONS!!! Another way of organizing and grouping mathematical objects is via an array structure. In LaTeX, arrays are produced using the begin{array}{aligncode}...\end{array} structure, as is the case with the rotation matrix below: \[ R\left( \theta \right) =\left[ \begin{array}{cc} \cos \left( \theta \right) & -\sin \left( \theta \right) \\ \sin \left( \theta \right) & \cos \left( \theta \right) \end{array} \right] \] Moreover, combinations of \left...\right and arrays can be used to create a large number of mathematical structures, such as a representation of a piecewise-defined function. Below is an example for the \emph{characteristic function} of an interval $\left[ a,b\right]$. \textbf{NOTE: You MUST USE \lt for "less than" and \gt for "greater than" because the symbols > and < are used to form HTML tags.} \[ \chi _{\left[ a,b\right] }\left( x\right) =\left\{ \begin{array}{ccc} 1 & \mbox{if} & a\leq x\leq b \\ 0 & \mbox{if} & x \lt a ~ \mbox{or} ~ x\gt b \end{array} \right. \] There are many guides to LaTeX coding that are readily available, including \cite{LaTeXMathMLcite} and the beginner's tutorial by \href{http://ctan.tug.org/tex-archive/info/lshort/english/lshort.pdf}{Tobias Oetiker et al}, which also comes in a number of \href{http://ctan.tug.org/tex-archive/info/lshort/}{different translations}. For a quick, high-level overview of the history, power, and purpose of LaTeX, see \href{http://www.techscribe.co.uk/ta/latex-introduction.pdf}{Mike Unwalla's one-page description} in the 2006 'Communicator'. There is also a \href{http://en.wikibooks.org/wiki/LaTeX}{LaTeX wikibook} . Finally, the free download \href{http://www.dessci.com/en/products/texaide/}{TeXaide} from Design Science provides a ``point and click'' method for producing LaTeX codes for mathematical expressions. They can be ``cut and pasted'' into web pages like this one that are to be transformed using LaTeXMathML. \section{Larger Structures} Mathematics is communicated not only through symbols and expressions, but also through larger logical structures such as arrays of equations, numbered equations, definitions, theorems, and examples. LaTeX can implement practically any such logical structure, but LaTeXMathML implements only a subset of the LaTeX structures and leaves the rest to html and css implementation. Let's take a look at the logical structures provided by LaTeXMathML using a top-down approach. To begin with, we can place title, authors, addresses, and date at the beginning of a web page, along with an abstract and keywords. The next level of structure is the section, which we have already seen, followed by subsections and subsubsections. For example, the phrase ``Begin...End Structures'' below is the title of a subsection. \subsection{Begin...End Structures} After the section, subsection, subsubsection structures, the next level of structure are the \begin ... \end structures known as \emph{environments.} LaTeXMathML implements the following environments: itemize, enumerate, figure, definition, proposition (a short, nearly obvious theorem), lemma (a result that precedes a proof of a theorem), theorem, proof, corollary (follows immediately from a theorem), example, and exercise. Let's explore environments by developing the ``theory'' of when two measured quantities are commensurate with one another (i.e., rationally related). % To end of line is comment. A line with only space starts a new paragraph \begin{definition} Let us define a variable $A$ to be commensurate with a variable $B$ if there exist non-zero integers $m,n\in \mathbb{Z}$ such that $$ mA=nB.$$ \end{definition} Notice that environments can contain both inline and displayed equations. They can also contain html coding (later). Moreover, the following \ % a single backslash surrounded by space inserts a non-breaking space, so line is not empty proposition should be immediate. % Do not use multiple \ for spacing (i.e., no \ \ \ ). Use actual spacing commands. \begin{proposition} $A$ is commensurate with $B$ if and only if $B$ is commensurate with $A.$ \end{proposition} \begin{proof} Follows immediately from the fact that $mA=nB$ is the same as $nB=mA$ (reflexivity of equality). \end{proof} The structure after the proposition environment is the \emph{proof} environment. Environment and section styles are controlled using CSS style sheets. The default is latexmathjaxmini.css, which adds the structure ``\textbf{Proof:}'' at the beginning of the environment and the block at the end. The css style sheet can be edited to change this rendering. % \begin{proposition} Integer coefficient linear combinations of commensurate variables are commensurate to both variables. \end{proposition} \begin{proof}\label{NoEQN} If $nA=mB$ for $m,n\in \mathbb{Z}$ and $C=jA+kB$ for $j,k\in \mathbb{Z}$, then \begin{eqnarray*} mC &=&jmA+kmB \\ &=&jmA+knA \\ &=&A\left( jm+kn\right) \end{eqnarray*} which completes the proof since $\left(jm+kn\right)\in\mathbb{Z}$ \end{proof} Also, by default, all numbering is by section count and environment count once a section has been defined (and is only by environment count if no sections are used). To the extent allowed by a given browser's CSS support, this numbering scheme can be modified to include subsections, subsubsections, and other features. The lemma, theorem, corollary, example, and exercise environments are similarly employed. \subsection{Equation Arrays and Numbering} There are many different ways of producing displayed equations, such as using double dollar signs, using backslash bracket combinations, or using any of the \emph{displaymath, equation, equation*, eqnarray, }or \emph{eqnarray*} environments. The equation and eqnarray environments generate numbers, while the other environments (the starred, in particular) do not \emph{unless they contain a label} (more later). Eqnarrays are used to define arrays of equations, which are arrays of rows with each row containing the same number of elements. Elements in each row are separated by ampersands &, and rows are separated using \\ \begin{lemma} The variables $A$ and $A^{2}$ are not commensurate. \end{lemma} \proof The key here is that $A$ and $A^{2}$ can vary, meaning their values are not fixed. Thus, given any fixed $m$ and $n, $ we have \begin{eqnarray} mA &=& nA^{2} \\ mA-nA^{2} &=&0 \\ A\left( m-nA\right) &=&0 \end{eqnarray} which implies that $A=\frac{m}{n}$ is constant.\endproof Here we see three new features -- namely, the old style proof and endproof objects (in contrast to the proof environment). Specifically, \textbackslash proof creates the word "Proof:" and \textbackslash endproof creates a black box. Also, the proof above includes a numbered eqnarray structure, one we will refer back to later. The number exists because it contains a \emph{label}. Labels mark points in a document that we want to refer back to later (using the \ref{..} structure ). In contrast, the eqnarray structure in the \href{#NoEQN}{proof} of Proposition 3.2 does not include a number. Notice that \textbf{to this point, there are no errors in entering LaTeX codes}. Unlike a LaTeX compiler which stops when it encounters an error, the LaTeXMathML script keeps plugging away (hopefully) as best as it can. For example, if we incorrectly had entered \endpproof, then LaTeXMathML leaves it as it found it while a traditional LaTeX compiler might stop compiling and ask for guidance. While convenient given small errors and simple documents, LaTeXMathML's tendency to "keep on going" may make errors more difficult to locate, especially in larger structures. It may thus be advantageous to make sure the document compiles as traditional LaTeX first. % \begin{theorem} The product of commensurate variables is not commensurate with either variable. \end{theorem} % \begin{proof} If $A$ and $B$ are commensurate, then $\exists m,n\in \mathbb{Z} \ni mA=nB$. Since we can write $$ 4AB=\left( A+B\right) ^{2}-\left( A-B\right) ^{2} $$ the quantity $4AB$ is commensurate to the combination of $\left( A+B\right) ^{2}-\left( A-B\right) ^{2}.$ The lemma implies that $\left( A+B\right) ^{2}$ is not commensurate to $A+B,$ and a calculation similar to (\ref{LemmaEquationArray}) shows that the combination is not commensurate to any linear combination of $A$ or $B,$ thus proving the theorem. \end{proof} Again, we see two more structures -- namely, the displaymath environment that does not number the equation (unless it contains a label) and the ref command which points back to the eqnarray in the lemma (REF COMMANDS ARE CASE\ SENSITIVE). Clicking on the ref will move the page focus to that equation, and the browser back button will move it back. \subsubsection{More with Labels, References, and Citations} A label can also be placed into any \begin..\end structure, and if a counter scheme exists for that structure, then a ref will display that value. For example, the second corollary below contains a label that is ref'ed in the example that follows. \begin{corollary} The $n^{th}$ root, $n \ne 1,$ of a variable is not commensurate with the original variable. \end{corollary} \begin{corollary} \label{CorollaryLabel}The ratio of commensurate variables is not commensurate with either variable. \end{corollary} We omit the proofs because we want to point out the label in the corollary -- and that the default numbering does not reference the subsection (but can be changed with appropriate CSS if supported). \begin{example} Suppose \label{theexample} a factory makes different sizes of square sheets of paper, and suppose that $S$ denotes the length of a side of a given square sheet \textbf{in centimeters} and $T$ denotes the length of a side of a given square \textbf{in meters.} Then $S=100~T,$ so $S$ and $T$ are commensurate. However, if a sheet of paper is exactly $\sqrt{2}$ cm in length, then its area is $2$ $cm^2$, and there is no way to rationally relate $\sqrt{2}$ to $2.$ Thus, $S^{2}$ and $S$ are not commensurate (because the measurements themselves need not be rational numbers!). Also, notice that the word variable in Corollary \ref{CorollaryLabel} is of key importance, since \[ \frac{S}{T}=100\quad \text{is constant}. \] \ \end{example} The reference back to the Corollary is a link with the Corollary's number. In the last equation, we use space-creating objects like quad and \~. Also, each backslash surrounded only by text inserts a single space. Referencing an item in the bibliography is done using the \textbf{cite} command. It works like a ref, only it shows the bibliographic entry heading for an item in the references, which can be either numerical or a label. For example, for more information on commensurate variables, see \cite{CCM}. (Given appropriate CSS support and a couple of LaTeXMathML.js modifications, Harvard style citations could be easily produced). \section{LaTeXMathML and HTML} It is possible to use HTML instead of LaTeX to create structures. For example, both this \href{#LemmaEquationArray}{LateX Link} and this HTML link point back to the equation array in the lemma above. We've also seen html and LaTeX working together via the html "pre" tag. It is imperative, however, that ONLY LATEX CODES ARE USED IN FORMATTING LATEX EQUATIONS. For example, we cannot use an html "bold" tag to create bold inside an equation array. Instead, we would need to use \\textbf{bold text}. However, html tags can be used inside of non-equation, non-table, and non-figure environments. \subsection{Figures and Tables} Figures and tables can be typeset using either LaTeX or HTML. Below is an example in which the first image is via the html img tag, while the second uses the figure environment. \begin{exercise} Suppose the figure below was drawn on a rubber sheet which is stretched uniformly in all directions.The labeled quantities vary as the rubber sheet is stretched. Which of these labeled quantities are commensurate with each other? \end{exercise} \begin{exercise} Which products of variables are commensurate in Figure \ref{Exercise2Image}? \begin{figure} \label{Exercise2Image} \includegraphics{EquilateralTriangle.gif} \caption{Same image as above} \end{figure} \end{exercise} As these examples show, the html image can include img style properties (such as a border). However, we have no means of numbering or referencing the image by number. The LaTeX version allows no image styles but does provide a straightforward means of labeling and captioning the image. Tables can be defined using either HTML or LaTeX. We will only consider the LaTeX table structure here, which must contain \textbf{only} LaTeX code (no html) and \textbf{only} inline math. \begin{verbatim} \begin{table} \begin{tabular}{lcr} First & $x^2+y^2$ & $\frac ab$ \\ Second & 0 & Table Cell \\ Third & $y=\sqrt{1-x^2}$ & End \end{tabular} \caption{This is a LaTeX Table} \end{table} \end{verbatim} The resulting table is shown below: \begin{table} \begin{tabular}{lcr} First & $x^2+y^2$ & $\frac ab$ \\ Second & 0 & Table Cell \\ Third & $y=\sqrt{1-x^2}$ & End \end{tabular} \caption{This is a LaTeX Table} \end{table} Only simple table structures are supported--hlines and vertical bars are ignored. However, tables are of the class LaTeXtable and each has a unique id of LaTeXtable#, where # is a positive integer, so that CSS styles can be applied to any or all of the tables. Also, the \\displaystyle command will cause inline mathematics to be typeset as if displayed. \subsection{Lists and Colors} Similarly, numbered and bulleted lists can be rendered using either LaTeX or HTML, and in both cases, items in the list can contain inline math, displayed math, or just about anything. For example, first let's consider the LaTeX \textbf{enumerate} environment \begin{enumerate} \item First Numbered Item \item Second Numbered Item \begin{enumerate} \item Second Item Sublist one with equation \[ \frac {\pi^n-1} {\pi-1} = \sum_{j=0}^{n-1} \pi^j \] where $\pi = 3.14159\ldots$. \item Second Item Sublist Two \end{enumerate} \item Third Numbered Item \end{enumerate} Now let's look at the LaTeX \textbf{itemize} environment: \begin{itemize} \item First bulleted item \item Second bulleted item \item Bulleted item C \end{itemize} These can be easily reproduced using the HTML ol (ordered list) and ul (unordered list) environments. The list above is reproduced below using the ul tag.

- First bulleted item
- Second bulleted item
- Bulleted item C

- First bulleted item
- Second bulleted item
- Bulleted item C

The measures $a$ and $b$ are commensurate if $\frac a b$ is rational. %

This will also compile in a LaTeX compiler, although the color information is in HTML and will not be used by a LaTeX compiler. Another alternative is to place LaTeX directly into an HTML "container" (div, pre, p, etcetera) whose class is \textbf{LaTeX}. The LaTeXMathML script checks for such containers, and if none exist, then it assumes it should transform the entire web page. If such a "Container" does exist, however, then it will transform LaTeX into MathML+HTML+CSS only within those containers. For example, in order for LaTeX comments and whitespace to be transformed correctly within Internet Explorer, any code to be transformed should be place within an html "div" tag which is itself within an html "pre" tag with a class of "LaTeX", as shown below: <pre class="LaTeX"> <div> LaTeX code to be transformed by LaTeXMathML </div></pre> This web page contains 3 such structures -- the first beginning before the title and ending below this line,

the second inside of a "font" tag which turns this text red,but which does not include this text so that LaTeX such as $y=x^2$ is not transformed into MathML, and the third from

here to the end of the page. The second actually uses a "span" instead of a "div", in the form \begin{verbatim} <font color="red" > <pre class="LaTeX"> <span> the second inside of a "font" tag which turns this text red </span></pre> </font> \end{verbatim} A simple script can be used to obtain only the code inside of LaTeX class containers before compiling with a LaTeX compiler. This allows LaTeX and HTML to be mixed meaningfully on a web page in a way that does not interfere with LaTeX compiling of the LaTeX on the page. Also, the pre-div structure allows LaTeXMathML to overcome some (but not all) of the shortcomings of Internet Explorer. (\textbf{Note:} I have not yet written such a script, but doing so is very straightforward). \section{Future Directions} The goal of LaTeXMathML is that of making pure latex coding a "web-friendly" enterprise. In particular, LaTeX differs enough from html and xml to allow it to be nearly seamlessly incorporated into the web environment. Thus, the ideal for LaTeXMathML is as an engine that \begin{itemize} \item maps LaTeX structures to html and/or MathML structures and \item uses CSS style files for styling (in parallel to .sty files in LaTeX). \end{itemize} Unfortunately, browser support for CSS2 is problematic at best, and support for CSS3 is non-existent, so that in the present effort, many features are not CSS by default. To the extent that support exists, CSS features can be enabled by modifying the LaTeXMathML.standardarticle.css style sheet (see stylesheet comments for details). There are bound to be many, many errors produced by this effort, some of which are due to inconsistencies across browsers. Fortunately, there are alternatives to LaTeXMathML, although each with their own sets of advantages and disadvantages (for example, LaTeX variants such as \cite{Itex2MMlcite} and \cite{TTMcite} ). Also, many of the implementations (tables, for example) are limited in scope. One important issue that should be addressed is that LaTeX documents are typically much, much longer than a typical webpage. A way to address this might be to develop collapsing sections. This could be accomplished by mapping sections into "divs" and allowing the always-visible headings to toggle between displayed and not-displayed. This would have the added benefit of allowing LaTeXMathML.js to work on a section-by-section basis and give the appearance of accelerated rendering. Another important issue is CSS versus XSL. The choice of CSS over XSL is due to the mathml guide and to the familiarity many users may have with CSS. Browser support for CSS is poor but hopefully improving (many improvements have already been made on an ad-hoc basis -- see, for example, \cite{IE7cite}, which I have yet to get to work with the latest version of IE but which has worked in the past). Enabling commented items in the LaTeXMathML.standard.css stylesheet will allow Firefox to use CSS for all features -- including counters -- except for cites and references. As a mathematician, I try to always keep in mind that it is the mathematics that is most important and not the formatting itself. But as a colleague once noted, "If formatting wasn't important, all our journals would be Xerox copies of legal pads." Hopefully, LaTeXMathML can be a tool that allows us to focus on mathematics and yet enables us to use the power of the internet in communicating that mathematics to ourselves and others. \textbf{Note: }Click \href{torturetest.htm}{here} for LaTeXMathML Torture test. \begin{thebibliography}{9} \bibitem{Doob} Doob, Michael. \textit{A Gentle Introduction to LaTeX: A Manual for Self-study}, Department of Mathematics, The University of Manitoba Winnipeg, Manitoba, Canada, \url{http://ctan.tug.org/tex-archive/info/gentle/gentle.pdf} \bibitem{IE7cite}Edwards, Dean. \textit{IE7}, March, 2007, \url{http://dean.edwards.name/IE7/} \bibitem[[Itex2MMl]]{Itex2MMlcite}Gartside, Paul. \textit{Itex2MML}, Department of Mathematics, University of Pittsburgh, March 2001, \url{http://pear.math.pitt.edu/mathzilla/itex2mml.html} \bibitem[[TTM]]{TTMcite}Hutchinson, Ian. \textit{TTM, A TeX to MathML Translator}, \url{http://hutchinson.belmont.ma.us/tth/mml/} \bibitem{x} The LateX Project. \url{http://www.latex-project.org/intro.html} \bibitem[[LaTeXMathML]]{LaTeXMathMLcite}Woodall, Douglas R. \textit{LaTeXMathML}, School of Mathematical Sciences, the University of Nottingham, University Park, Nottingham, \url{http://www.maths.nottingham.ac.uk/personal/drw/lm.html} \bibitem{CCM}Wikipedia contributors. \textit{Commensurability (mathematics)}, Wikipedia, The Free Encyclopedia,10 May 2007, retrieved on 25 May 2007, \url{http://en.wikipedia.org/w/index.php?title=Commensurability_\%28mathematics\%29}, Page Version ID: 129899760 \end{thebibliography} \ There is also a simple appendix system using the appendix command (used only once): \appendix \section{Technical Appendix} Below are a few insights into the inner workings of LaTeXMathML.js for those who might want to modify it, as well as some information about the CSS used in LaTeXMathML.standardarticle.css. \subsection{A Brief Description of LateXMathML.standardarticle.css} In extending LaTeXMathML, an attempt was made to match structures in LaTeX with their most natural counterparts in html (in particular, in the document object model). Thus, sections, subsections, and subsubsections are mapped to headings H2, H3, and H4 (as was done in the mathmlguide), while labels, references, and citations are mapped to anchors--i.e., the "a" tags. Environments are mapped to DIV elements, while figures and displayed equations are mapped to html tables in order to accommodate numbering and captions. Script Generated text--such as numbers and the word "references" are placed into "span" elements. This means that if pseudo-classes and CSS counters are to be used, the script generated text can be suppressed by setting \begin{center} span.environment { display: none } \end{center} in the .css style file. The relevant CSS classes are classified according to dom element type in the html table below. The Divs and Counters column identifies elements that have countered associated with them. In the CSS counter specifications, the counter names are the same as the classNames.

Divs | Divs & Counters | Tables | Other |

title | definition | displayequation | section = H2 |

author | proposition | figure | subsection = H3 |

address | lemma | LaTeXtable | subsubsection = H4 |

date | theorem | itemize = ul | |

abstract | corollary | enumerate = ol | |

keyword | example | ref = a | |

thebibliography | exercise | cite = a |