Este artículo explica como redactar funciones matemáticas utilizando el lenguaje MathML. Al igual que HTML, MathML puede describirse con etiquetas y atributos. HTML puede volverse interminable cuando tu documento contiene estructuras avanzadas como listas o tablas pero afortunadamente existen varios generadores, desde simple notaciones, editores WYSIWYG y otros Sistemas de Administración de Contenido (CMS) utilizados para la creación de páginas web.
Las notaciones Matemáticas son aún más complejas con estructuras que contienen fracciones, raíces cuadradas o matrices que seguramente requerirán sus propias etiquetas. Como consecuencia, las buenas herramientas de redacción de MathML son importantes y más adelante describimos algunas opciones. En particular, el équipo MathML de Mozilla ha creado TeXZilla, un convertor de LaTeX a MathML compatible con Unicode, para ser utilizado en muchos scenari descrito ahí. Desde luego, la lista no es de ninguna manera definitiva y estás invitado a revisar la Lista de Software MathML de W3C donde puedes encontrar diferentes herramientas.
Hay que señalar que por diseño, MathML está bien integrado en HTML5 y particularmente puedes utilizar las características Web comunes como CSS, DOM, Javascript o SVG. Esto está fuera del ámbito de este artículo pero cualquiera con conocimientos básicos de lenguajes Web será capaz de combinar fácilmente estas características con MathML. Revisa nuestros demos y referencias de MathML para más detalles.
Fundamentos
Utilizar MathML en páginas HTML
Puedes utilizar MathML dentro de un documento HTML5:
<!DOCTYPE html> <html> <head> <title>MathML in HTML5</title> </head> <body> <h1>MathML in HTML5</h1> <p> Square root of two: <math> <msqrt> <mn>2</mn> </msqrt> </math> </p> </body> </html>
Content MathML no esta soportado por el navegador. Es recomendable convertir tu content MathML markup en Presentation MathML antes de publicarlo, por ejemplo con la ayuda de la hoja de calculo ctop.xsl . Las herramientas mencionadas en esta pagina generan Presentation MathML.
Para navegadores sin soporte a MathML
Desafortunadamente, algunos navegadores no son capaces de renderizar ecuaciones MathML o tienen un soporte limitado. Por lo tanto necesitará usar MathML polyfill para proveer el renderizado. Si necesita solo construcciones matematicas básicas tales como las utilizadas en esta wiki de MDN entonces una pequeña hoja de cálculo mathml.css podria ser suficiente. Para usarlo, solo inserta una linea en el header de tu documento:
<script src="https://fred-wang.github.io/mathml.css/mspace.js"></script>If you need more complex constructions, you might instead consider using the heavier MathJax library as a MathML polyfill:
<script src="https://fred-wang.github.io/mathjax.js/mpadded.js"></script>Note that these two scripts perform feature detection of the mspace or mpadded elements (see the browser compatibility table on these pages). If you don't want to use this link to GitHub but instead to integrate these polyfills or others in your own project, you might need the detection scripts to verify the level of MathML support. For example the following function verifies the MathML support by testing the mspace element (you may replace mspace with mpadded):
function hasMathMLSupport() {
var div = document.createElement("div"), box;
div.innerHTML = "<math><mspace height='23px' width='77px'/></math>";
document.body.appendChild(div);
box = div.firstChild.firstChild.getBoundingClientRect();
document.body.removeChild(div);
return Math.abs(box.height - 23) <= 1 && Math.abs(box.width - 77) <= 1;
}Alternatively, the following UA string sniffing will allow to detect the rendering engines with native MathML support (Gecko and WebKit). Note that UA string sniffing is not the most reliable method and might break from version to version:
var ua = navigator.userAgent;
var isGecko = ua.indexOf("Gecko") > -1 && ua.indexOf("KHTML") === -1 && ua.indexOf('Trident') === -1;
var isWebKit = ua.indexOf('AppleWebKit') > -1 && ua.indexOf('Chrome') === -1;Mathematical fonts
Note: browsers can only use a limited set of mathematical fonts to draw stretchy MathML operators. However, implementation of the OpenType MATH table is in progress in Gecko & WebKit. This will provide a generic support for mathematical fonts and simplify the settings described in this section.
To get a good mathematical rendering in browsers, some MathML fonts are required. It's a good idea to provide to your visitors a link to the MDN page that explains how to install MathML fonts. Alternatively, you can just make them available as Web fonts. You can get these fonts from the MathML-fonts add-on ; the xpi is just a zip archive that you can fetch and extract for example with the following command:
wget https://addons.mozilla.org/firefox/downloads/latest/367848/addon-367848-latest.xpi -O mathml-fonts.zip; \
unzip mathml-fonts.zip -d mathml-fontsThen copy the mathml-fonts/resource/ directory somewhere on your Web site and ensure that the woff files are served with the correct MIME type. Finally, include the mathml-fonts/resource/mathml.css style sheet in your Web pages, for example by adding the following rule to the default style sheet of your Web site:
@import url('/path/to/resource/mathml.css');You then need to modify the font-family on the <math> elements and, for Gecko, the on ::-moz-math-stretchy pseudo element too. For example to use STIX fonts:
math {
font-family: STIXGeneral;
}
::-moz-math-stretchy {
font-family: STIXNonUnicode, STIXSizeOneSym, STIXSize1, STIXGeneral;
}
Try the MathML torture test to compare the rendering of various fonts and the CSS rules to select them.
Utilizar MathML en documentos XML (XHTML, EPUB, etc.)
Si por alguna razón necesitas utilizar MathML en documentos XML, asegúrate de cumplir con los requisitos habituales: documentos bien realizados, el uso correcto de la especificación MIME, el prefijo MathML "https://www.w3.org/1998/Math/MathML" en la raíz <math>. Por ejemplo, la versión XHTML del ejemplo anterior luce de esta manera:
<?xml version="1.0" encoding="UTF-8"?> <!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.1 plus MathML 2.0//EN" "https://www.w3.org/Math/DTD/mathml2/xhtml-math11-f.dtd"> <html xmlns="https://www.w3.org/1999/xhtml"> <head> <title>XHTML+MathML Example</title> </head> <body> <h1>XHTML+MathML Example</h1> <p> Square root of two: <math xmlns="https://www.w3.org/1998/Math/MathML"> <msqrt> <mn>2</mn> </msqrt> </math> </p> </body> </html>
Note that if you use MathML as a standalone .mml or .svg documents or inside an EPUB book, it may not always be possible to use MathJax as a polyfill for rendering engines without MathML support. Hence whether MathML can be handled will vary according to the tools used to read these documents.
Utilizar MathML en correos electrónicos
Los clientes de correos modernos pueden enviar y recibir correos electrónicos en el formato HTML5 y por lo tanto pueden manejar expresiones de tipo MathML. Asegúrate de tener las opciones de "Enviar como HTML" y "Ver como HTML" habilitadas. En Thunderbird, puedes utilizar el comando "Insertar HTML" para pegar tu código HTML+MathML. MathBird es un complemento conveniente de Thunderbird para insertar este tipo de expresiones MathML utilizando la sintaxis AsciiMath.
De nuevo, la forma en como MathML es manejada y la calidad de cómo se muestran estas expresiones depende del cliente de correo electrónico. Aún si tu navegador es compatible con MathML, tu servicio de correo electrónico puede evitar que envíes o recibas correos con expresiones MathML.
Conversion from a Simple Syntax
There are many simple notations (e.g. wiki or markdown syntaxes) to generate HTML pages. The same is true for MathML: for example ASCII syntaxes as used in calculators or the more powerful LaTeX language, very popular among the scientific community. In this section, we present some of these tools to convert from a simple syntax to MathML.
- pros:
- Writing mathematical expressions may only require a standard text editor.
- Many tools are available, some of them are compatible with the classical LaTeX-to-pdf workflow.
- This gives access to advanced features of LaTeX like macros.
- cons:
- This may be harder to use: people must learn a syntax, typos in the code may easily lead to parsing or rendering errors etc
- The interface is not user-friendly: only code editor without immediate display of the mathematical expression.
- None of the syntax has been standardized, making cross-compatibility between converters difficult. Even the popular LaTeX language keeps having new packages added.
Client-side Conversion
In a Web environment, the most obvious method to convert a simple syntax into a DOM tree is to use Javascript and of course many libraries have been developed to perform that task.
- pros:
- This is very easy setup: only a few Javascript and CSS files to upload and/or a link to add to your document header.
- This is a pure Web-based solution: everything is done by the browsers and no other programs must be installed or compiled.
- cons:
- This won't work if the visitor has Javascript disabled.
- The MathML code is not exposed to Web crawlers (e.g. those of math search engines or feed aggregators). In particular, your content won't show up properly on Planet.
- The conversion must be done at each page load, may be slow and may conflict with the HTML parsing (e.g. "<" for tags or "$" for money amounts)
- You may need to synchronize the Javascript converter with other Javascript programs on your page.
TeXZilla has an <x-tex> custom element, that can be used to write things like
<x-tex>\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1</x-tex>
and get it automatically converted into MathML. This is still a work-in-progress, but could be improved in the future thanks to Web Components and shadow DOM. Alternatively, you can use the more traditional Javascript parsing of expressions at load time as all the other tools in this section do.
One simple client-side conversion tools is ASCIIMathML. Just download the ASCIIMathML.js script and copy it to your Web site. Then on your Web pages, add a <script> tag to load ASCIIMathML and the mathematical expressions delimited by ` (grave accent) will be automatically parsed and converted to MathML:
<html>
<head>
...
<script type="text/javascript" src="ASCIIMathML.js"></script>
...
</head>
<body>
...
<p>blah blah `x^2 + y^2 = r^2` blah ...
...LaTeXMathML is a similar script that allows to parse more LaTeX commands. The installation is similar: copy LaTeXMathML.js and LaTeXMathML.standardarticle.css, add links in the header of your document and the LaTeX content of your Web page marked by the "LaTeX" class will be automatically parsed and converted to HTML+MathML:
<head>
...
<script type="text/javascript" src="LaTeXMathML.js"></script>
<link rel="stylesheet" type="text/css" href="LaTeXMathML.standardarticle.css" />
...
</head>
<body>
...
<div class="LaTeX">
\documentclass[12pt]{article}
\begin{document}
\title{LaTeXML Example}
\maketitle
\begin{abstract}
This is a sample LaTeXML document.
\end{abstract}
\section{First Section}
$$ \sum_{n=1}^{+\infty} \frac{1}{n^2} = \frac{\pi^2}{6} $$
\end{document}
</div>
...jqMath is another script to parse a simple LaTeX-like syntax but which also accepts non-ASCII characters like √{∑↙{n=1}↖{+∞} 6/n^2} = π to write . The installation is similar: download and copy the relevant Javascript and CSS files on your Web site and reference them in your page header (see the COPY-ME.html file from the zip archive for an example). One of the advantage of jqMath over the previous scripts is that it will automatically add some simple CSS rules to do the mathematical layout and make the formulas readable on browsers with limited MathML support.
Another way to work around the lack of MathML support in some browsers is to use MathJax. However, note that you may find conflicts and synchronization issues between MathJax and the Javascript libraries previously mentioned. So if you really want to use MathJax as a MathML polyfill, you'd better use its own LaTeX/ASCIIMath parsers too. Note that on the one hand MathJax has better parsing and rendering support but on the other hand it is much bigger, more complex and slower than the previous Javascript libraries. Fortunately, you can use MathJax's CDN so that you don't need to install it on your Web server. Also, the slowest part of MathJax is currently its HTML-CSS / SVG output modes so we recommend to use the Native MathML output for Gecko-based browsers. Hence a typical configuration to use the AMS-LaTeX input is:
...
<script type="text/x-mathjax-config">
MathJax.Hub.Config({
MMLorHTML: { prefer: { Firefox: "MML" } }
});
</script>
<script type="text/javascript"
src="https://cdn.mathjax.org/mathjax/latest/MathJax.js?config=TeX-AMS-MML_HTMLorMML">
</script>
</head>
<body>
\[ \tau = \frac{x}{y} + \sqrt{3} \]
...Note that the dollar delimiters are not used by default. To use the ASCIIMathML input instead, just replace TeX-AMS-MML_HTMLorMML by AM-MML_HTMLorMML. MathJax has many other features, see the MathJax documentation for further details.
Command-line Programs
An alternative way is to parse the simple syntax before publishing your web pages. That is, you use command-line programs to generate them and publish these static pages on your server.
- pros:
- You get static Web pages: the LaTeX source don't need to be parsed at each page load, the MathML code is exposed to Web crawlers and you can put them easily on any Web server.
- Binary programs may run faster than Javascript programs and can be more sophisticated e.g. have a much complete LaTeX support or generate other formats like EPUB.
- You can keep compatibility with other tools to generate pdf e.g. you can use the same .tex source for both latex and latexml.
- cons:
- This requires to install programs on your computer, which may be a bit more difficult or they may not be available on all platforms.
- You must run the programs on your computer and have some kind of workflow to get the Web pages at the end ; that may be a bit tedious.
- Binary programs are not appropriate to integrate them in a Mozilla extension or XUL application.
TeXZilla can be used from the command line and will essentially have the same support as itex2MML described below. However, the stream filter behavior is not implemented yet.
If you only want to parse simple LaTeX mathematical expressions, you might want to try tools like itex2MML or Blahtex. The latter is often available on Linux distributions. Let's consider the former, which was originally written by Paul Gartside at the beginning of the Mozilla MathML project and has been maintained by Jacques Distler since then. It's a small stream filter written in C/C++ and generated with flex and bison ; in particular it is very fast. Install flex/bison as well as the classical compiler and make tools. On Unix, you can then download itex2MML, build and install it:
wget https://golem.ph.utexas.edu/~distler/blog/files/itexToMML.tar.gz; \
tar -xzf itexToMML.tar.gz; \
cd itex2MML/itex-src;
make
sudo make installNow suppose that you have a HTML page with TeX fragments delimited by dollars:
input.html
...
</head>
<body>
<p>$\sqrt{a^2-3c}$</p>
<p>$$ {\sum_{i=1}^N i} = \frac{N(N+1)}{2} $$</p>
</body>
</html>Then to generate the HTML page input.html with TeX expressions replaced by MathML expressions, just do
cat input.html | itex2MML > output.html
There are even more sophisticated tools to convert arbitrary LaTeX documents into HTML+MathML. For example TeX4ht is often included in TeX distributions and has an option to use MathML instead of PNG images. This command will generate an XHTML+MathML document foo.xml from a foo.tex LaTeX source:
mk4ht mzlatex foo.tex # Linux/Mac platforms mzlatex foo.tex # Windows platform
LaTeXML is another tool that is still actively developed but the release version is rather old, so you'd better install the development version. In particular, this version can generate HTML5 and EPUB documents. Here is the command to execute in order to create a foo.html Web page from the foo.tex LaTeX source:
latexml --dest foo.xml foo.tex latexmlpost --dest foo.html --format=html5 foo.xml
If you want to have a MathJax fallback for non-Gecko browsers, copy the Javascript lines given above into a mathjax.js file and use the --javascript parameter to tell LaTeXML to include that file:
latexmlpost --dest foo.html --format=html5 --javascript=mathjax.js foo.xml
If your LaTeX document is big, you might want to split it into several small pages rather putting everything in a single page. This is especially true if you use the MathJax fallback above, since in that case MathJax will take a lot of time to render the equations in non-Gecko browsers. Use the --splitat parameter for that purpose. For example, this will split the pages at the \section level:
latexmlpost --dest foo.html --format=html5 --splitat=section foo.xml
Finally, to generate an EPUB document, you can do
latexmlc --dest foo.epub --splitat=section foo.xml
Server-side Conversion
- pros:
- Conversion is done server-side and the MathML output can be cached, which is more efficient and cleaner than client-side conversion.
- cons:
- This might be a bit more difficult to set up, since you need some admin right on your server.
TeXZilla can be used as a Web server in order to perform server-side LaTeX-to-MathML conversion. LaTeXML can also be used as a deamon to run server-side. Mathoid is another tool based on MathJax that is also able to perform additional MathML-to-SVG conversion.
Instiki is a Wiki that integrates itex2MML to do server-side conversion. In future versions, MediaWiki will support server-side conversion too.
Graphical Interface
Input Box
TeXZilla has several interfaces, including a CKEditor plugin used on MDN, an online demo, a Firefox add-on or a FirefoxOS Webapp. Abiword contains a small equation editor, based on itex2MML. Bluegriffon is a mozilla-based Wysiwyg HTML editor and has an add-on to insert MathML formulas in your document, using ASCII/LaTeX-like syntax.
WYSIYWG Editors
Firemath is an extension for Firefox that provides a WYSIWYG MathML editor. A preview of the formula is displayed using the rendering engine of Mozilla. The generated MathML code is available at the bottom. Use the text field for token elements and buttons to build advanced constructions. Once you are done, you can save your document as a XHTML page.
OpenOffice and LibreOffice have an equation editor (File → New → Formula). It is semi-WYSIWYG: you enter the source of the formula using the equation panel/keyboard and a preview of the formula is regularly refreshed. The editor uses its own syntax "StarMath" for the source but MathML is also generated when the document is saved. To get the MathML code, save the document as mml and open it with any text editor. Alternatively, you can extract the odf file (which is actually a zip archive) and open an xml file called content.xml.
Amaya is the W3C's web editor, which is able to handle MathML inside XHTML documents. Use the Elements and the Special Chars panels to create various advanced mathematical constructs. Simple text such as a+2 is automatically parsed and the appropriate MathML markup is generated. Once you are done, you can directly save your XHTML page and open it in Mozilla.
Optical Character & Handwriting Recognition
Inftyreader is able to perform some Optical Character Recognition, including translation of mathematical equations into MathML. Other tools can do handwriting recognition such as the Windows Math Input Panel
or the online converter Web Equation.
Original Document Information
- Author(s): Frédéric Wang
- Other Contributors: Florian Scholz
- Last Updated Date: April 2, 2011
- Copyright Information: Portions of this content are © 2010 by individual mozilla.org contributors; content available under a Creative Commons license | Details.