本稿では MathML を用いて数式を表現する方法を説明します。 HTML と同じように、 MathML はタグと属性によって記述されます。文書中に箇条書きや表のような高度な構造がある場合 HTML は煩雑になってしまいますが、幸いなことに単純な記法で表を生成することができるツールや、 WYSIWYG な編集ができるツール、その他さまざまなコンテンツ管理システムであったりと，ウェブページを書き下ろすのに助けになるものはたくさんあります。
数式を表現しようと思うともっと複雑です。数学には分数や平方根、行列など独自のタグが必要になるような構造がいろいろあるからです。ですから、優良な MathML エディターが求められます。以下ではその幾つかについて述べていきます。取り分け、 Mozilla の MathML 開発チームが開発中の TeXZilla は、 JavaScript 製 Unicode LaTeX-MathML コンバーターであり、本稿で紹介されているような多くの場面で用いられることを想定しています。無論、本稿のツール紹介ではすべてを網羅している訳ではありませんから、是非とも W3C が発行する MathML ソフトウェア一覧をチェックして他のツールも見てみてください。
なお設計上、 MathML は HTML5 によく統合されており、特に CSS, DOM, Javascript, SVG のような通常のウェブ機能を使用できることができます。これはこのドキュメントの範囲外ですが、ウェブ言語の基本的な知識があれば、誰でも簡単にこれらの機能を MathML と組み合わせることができます。詳細については、デモや MathML リファレンスのページをご覧ください。
HTML5 文書内部では表示 MathML が使えます。
<!DOCTYPE html>
<html>
<head>
<title>HTML5におけるMathML</title>
</head>
<body>
<h1>HTML5におけるMathML</h1>
<p>
2の平方根は
<math>
<msqrt>
<mn>2</mn>
</msqrt>
</math>
</p>
</body>
</html>
ブラウザーは内容 MathML に対応していません。なので、文章を公開する際には ctop.xsl スタイルシートを使うなどして Content MathML マークアップを Presentation MathML に変換するのが良いでしょう。本稿で紹介するツールはいずれも Presentation MathML を生成します。
残念ながら、ブラウザーによっては MathML の方程式をレンダリングできなかったり、対応が限定されていたりします。そのため、代替レンダリングを提供するためには MathML ポリフィルを使用する必要があります。この MDN wiki で使われているような基本的な数学的な構造だけを必要とする場合は、小さな mathml.css スタイルシートで十分かもしれません。これを使うには、文書のヘッダーに一行だけ挿入してください。
<script src="https://fred-wang.github.io/mathml.css/mspace.js"></script>
ただ、もっと高度な表現も使いたいという場合にはもう少し大きい MathJax ライブラリを用いると良いでしょう。
<script src="https://fred-wang.github.io/mathjax.js/mpadded-min.js"></script>
これら 2 つのスクリプトは mspace または mpadded 要素の機能検出を行うことに注意してください (これらのページのブラウザー互換性表を参照してください)。また、良好な MathML の対応のないブラウザーのためにページの上部に警告を表示し、ユーザーに上記のフォールバックのいずれかを選択させるための同様のスクリプトもあります。
<script src="https://fred-wang.github.io/mathml-warning.js/mpadded-min.js"></script>
GitHub へのこのリンクを使わずに、これらのポリフィルや他のポリフィルを自分のプロジェクトに統合したい場合は、 MathML のサポートレベルを検証するための検出スクリプトが必要になるかもしれません。例えば、以下の関数は mspace 要素をテストすることで MathML への対応を検証しています (mspace を mpadded に置き換えても構いません)。
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;
}
あるいは、以下の UA 文字列スニッフィングは、ネイティブの MathML 対応があるレンダリングエンジン (Gecko と WebKit) を検出することを可能にします。UA 文字列スニッフィングは最も信頼性の高い方法ではなく、バージョンによっては壊れてしまう可能性があることに注意してください。
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;
In order to get a good layout or to allow different style, it's important to have mathematical fonts available. It's always good to provide a link to MDN's Font Instructions, so that your visitors can verify whether they have appropriate fonts installed on their system. It's also good to provide a fallback with Web fonts.
Prior to Gecko 31.0 {{GeckoRelease("31.0")}}, it was a bit tedious to setup math fonts, see the font instructions for Mozilla 2.0. For Gecko 31.0 {{GeckoRelease("31.0")}}, this is much simpler and is compatible with any Web rendering engine with MathML support. For example, here is a minimal stylesheet to use Latin Modern for the text and Latin Modern Math for the mathematics:
@namespace url('http://www.w3.org/1999/xhtml');
@namespace m url('http://www.w3.org/1998/Math/MathML');
body, m|mtext {
font-family: Latin Modern;
}
m|math {
font-family: Latin Modern Math;
}
You can then use the @font-face rule as usual to provide WOFF fallback for Latin Modern and Latin Modern Math. See this GitHub repository to get WOFF fonts and sample CSS stylesheets to use on your Web site and check its test page.
If for some reason you need to use MathML in XML documents, be sure to satisfy the usual requirements: well-formed document, use of correct MIME type, MathML namespace "http://www.w3.org/1998/Math/MathML" on <math> roots. For example, the XHTML version of the previous example looks like this:
<?xml version="1.0" encoding="UTF-8"?> <!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.1 plus MathML 2.0//EN" "http://www.w3.org/Math/DTD/mathml2/xhtml-math11-f.dtd"> <html xmlns="http://www.w3.org/1999/xhtml"> <head> <title>XHTML+MathML例</title> </head> <body> <h1>XHTML+MathML例</h1> <p> 2の平方根は <math xmlns="http://www.w3.org/1998/Math/MathML"> <msqrt> <mn>2</mn> </msqrt> </math> である。 </p> </body> </html>
Modern mail clients may send and receive emails in the HTML5 format and thus can use MathML expressions. Be sure to have the "send as HTML" and "view as HTML" options enabled. In Thunderbird, you can use the "Insert HTML" command to paste your HTML+MathML code. MathBird is a convenient add-on for Thunderbird to insert such MathML expressions using the AsciiMath input syntax. Moreover, a LaTeX-to-MathML input box has also been integrated into SeaMonkey since version 2.28 and into Thunderbird since version 31. Again, the way MathML is handled and the quality of the MathML rendering depends on the mail client. Even if your browser supports MathML, your Webmail may prevent you to send or receive mails with MathML inside.
Gecko-based instant messaging clients can integrate a Javascript-based text-to-MathML converter (mentioned below) and then render the MathML expressions generated from the (plaintext) instant messages. For example, there is an Instantbird add-on that handles LaTeX expressions.
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.
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.
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} = π² 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.
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.
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 http://golem.ph.utexas.edu/~distler/blog/files/itexToMML.tar.gz; \ tar -xzf itexToMML.tar.gz; \ cd itex2MML/itex-src; make sudo make install
Now 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用 mzlatex foo.tex # Windows用
Note that tex4ebook relies on TeX4ht to generate EPUB documents.
LaTeXML is another tool that can generate HTML5 and EPUB documents. Windows users can watch this video tutorial. Given a foo.tex LaTeX file, you can use these simple commands:
latexmlc --dest foo.html foo.tex # HTML5文書foo.htmlを生成 latexmlc --dest foo.epub foo.tex # EPUB文書foo.epubを生成
To handle the case of browsers without MathML support, you can use the --javascript parameter to tell LaTeXML to include one of the fallback scripts:
latexmlc --dest foo.html --javascript=https://fred-wang.github.io/mathml.css/mspace.jsfoo.tex # 予備的CSSを追加 latexmlc --dest foo.html --javascript=https://fred-wang.github.io/mathjax.js/mpadded-min.jsfoo.tex # 予備的MathJaxを追加
If your LaTeX document is big, you might want to split it into several small pages rather than putting everything in a single large page. For example, this will split the pages at the \section level:
latexmlc --dest foo.html --splitat=section foo.tex
TeXZilla、LaTeXML、MathoidはサーバーサイドのLaTeX-to-MathMLコンバーターとして使うことができます。Wikiエンジンである Instiki や MediaWiki はLaTeX数式をMathMLに変換する機能をサポートしています。
TeXZilla has several interfaces, including a CKEditor plugin used on MDN, an online demo, a Firefox add-on or a FirefoxOS Webapp. It has also been integrated into SeaMonkey since version 2.28 and into Thunderbird since version 31. Abiword contains a small equation editor, based on itex2MML. Finally, Bluegriffon has an add-on to insert MathML formulas in your document, using ASCII/LaTeX-like syntax.
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.
LyX is a graphical LaTeX editor, which has built-in support for XHTML+MathML export and can be configured to use similar LaTeX-to-(X)HTML converters. You can for example, you can configure it to use LaTeXML HTML5/EPUB export.
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.
OCRソフトの Inftyreader を用いると数式をMathMLとして読み込むことができます。また、Windows Math Input Panel やWeb上で使える Web Equation を用いると手書きの数式をMathMLに変換する事ができます。