Tutorial: Extension writing

MathJax is designed in a way that makes it easy to write extensions. Examples can be found in the MathJax third party extensions repository; see also Third-party Extensions.

In this tutorial, we are going to see how to write your own MathJax extension. No specific prerequisites are assumed, except that you already have a local installation and of course some familiarity with how to use MathJax.

The Big Picture

We suppose that you have a copy of MathJax in a MathJax/ directory and that the URL http://localhost/MathJax/ points to that directory. We also assume that you have a local Web server running at http://localhost/ ; this is not mandatory but will avoid issues with the cross-origin security policy.

First, note that the source code of MathJax is “packed” so that the JavaScript files are smaller and take less time to download. These files are not easy to read and edit, so for development purposes we will work with the MathJax/unpacked/ directory. Hence you should load the unpacked MathJax.js to run MathJax on your pages. For example if you write a file like

MathJax/unpacked/test0.html

<!doctype html>
<html>
  <head>
    <title>testcase</title>
    <meta charset="utf-8">
    <script type="text/javascript"
            src="http://localhost/MathJax/unpacked/MathJax.js?config=TeX-MML-AM_CHTML">
    </script>
  </head>
  <body>
    <p>TeX: \(\frac a b\)</p>
    <p>MathML: <math><msqrt><mi>x</mi></msqrt></math></p>
    <p>AsciiMath: `a^2 + b^2 = c^2`</p>
  </body>
</html>

then the page http://localhost/MathJax/unpacked/test0.html should contain formatted equations corresponding to the TeX, MathML and AsciiMath sources.

MathJax.js is the main file, which initializes MathJax and loads all its components. The most important ones are represented in the diagram below. The input modes (in blue) are located in unpacked/jax/input/ and transform the corresponding given input text into MathJax’s internal strutures (in red) located in unpacked/jax/element (only one format at the moment, essentially “MathML”). Then this internal structure is rendered by the output modes (in green) located in unpacked/jax/output. The MathJax extensions are located in unpacked/extensions/ and can modify or extend the MathJax components.

One feature of MathJax is that other Javascript files are loaded only when they are necessary. Extensions generally use other components so you must be sure that they are already loaded before running the extension. Similarly, the extension may need to indicate when it is ready so that other components can use it. Synchronizing your code with MathJax is explained in the MathJax documentation but we will review the rules when needed.

A Simple measureTime Extension

In this section, we are willing to write a small extension that indicates at the bottom of the page how much time MathJax has taken to typeset the page. First we create the following Javascript file:

// unpacked/extensions/measureTime.js

MathJax.HTML.addElement(document.body, "div", {style: {color: "red"}}, ["Hello World!"]);
MathJax.Ajax.loadComplete("[MathJax]/extensions/measureTime.js");

The first line is just using the convenient MathJax.HTML to create a <div style="color: red;">Hello World!</div> element. The second line will tell MathJax that measureTime.js has been successfully loaded. Again, we refer to Synchronizing your code with MathJax for details. Now modify test0.html and insert a text/x-mathjax-config script just before the one loading MathJax. Use that to add measureTime.js to the list of extensions to load:

<!-- MathJax/test/test1.html -->

...
    <script type="text/x-mathjax-config">
       MathJax.Hub.config.extensions.push("measureTime.js");
    </script>
    <script type="text/javascript"
            src="http://localhost/MathJax/unpacked/MathJax.js?config=TeX-MML-AM_CHTML">
...

The page http://localhost/MathJax/unpacked/test1.html should now render the same as test0.html, except that a red “Hello World!” message is appended at the end of the page!

Our goal is now to replace that message by something like “Typeset by MathJax in 2 second(s)”. A quick look at the MathJax Startup Sequence shows that the extensions are loaded before the typesetting pass. Also, the typesetting starts with a “Begin Typeset” signal and ends by a “End Typeset” signal. The startup sequence ends by a final “End” signal. In order to add listeners for these signals are sent, we use MathJax.Hub.Register.StartupHook.

Writing the extension is now straighforward. We save the data specific to the measureTime extension in a MathJax.Extension.measureTime object. When we listen the start and end typeset signals we set the corresponding startTime and endTime members to the current time. Finally when we listen the final End signal, we append the desired div (note that the previous version appended it immediately):

// unpacked/extensions/measureTime.js

MathJax.Extension.measureTime = {};

MathJax.Hub.Register.StartupHook("Begin Typeset", function () {
  MathJax.Extension.measureTime.startTime = (new Date()).getTime();
});

MathJax.Hub.Register.StartupHook("End Typeset", function () {
  MathJax.Extension.measureTime.endTime = (new Date()).getTime();
});

MathJax.Hub.Register.StartupHook("End", function () {
  var delta = (MathJax.Extension.measureTime.endTime - MathJax.Extension.measureTime.startTime) / 1000.;
  MathJax.HTML.addElement(document.body, "div", null,
                          ["Typeset by MathJax in " + delta + " second(s)"]);
});

MathJax.Ajax.loadComplete("[MathJax]/extensions/measureTime.js");

Now load test1.html again (clearing the browser cache if necessary) and verify if you see the desired “Typeset by MathJax in … seconds” message.

Note that this was a basic extension to demonstrate the extension mechanism but it obviously has some limitations; e.g. only the typeset time is measured (not the whole MathJax execution time), the message is not updated when you switch the rendering mode via the menu, the message is not localizable, etc.

Extension to define TeX macros

TeX already has a macro mechanism to define new commands from those already available. This mechanism exists in MathJax, too, and one can rely on it to create a MathJax extension that defines a collection of TeX macros. Consider the following example:

//unpacked/extensions/TeX/Taylor.js

MathJax.Hub.Register.StartupHook("TeX Jax Ready", function () {
  MathJax.InputJax.TeX.Definitions.Add({
    macros: {
      expexpansion: ["Macro", "\\sum_{n=0}^{+\\infty} \\frac{x^n}{n!}"],
      taylor: ["Macro","\\sum_{n=0}^{+\\infty} \\frac{{#1}^{(n)} \\left({#2}\\right)}{n!} {\\left( {#3} - {#2} \\right)}^n", 3],
      taylorlog: ["Macro","\\sum_{n=1}^{+\\infty} {(-1)}^{n+1} \\frac{#1^n}{n}", 1],
      taylorsin: ["Macro","\\sum_{n=0}^{+\\infty} \\frac{{(-1)}^n}{(2n+1)!} {#1}^{2n+1}", 1]
    }
  });
});

MathJax.Ajax.loadComplete("[MathJax]/extensions/TeX/Taylor.js");

The structure is similar to the measureTime extension: we wait until the TeX input is ready by listening the appropriate signal. Then we extend the set of TeX macros with some definitions. For example

expexpansion: ["Macro", "\\sum_{n=0}^{+\\infty} \\frac{x^n}{n!}"]

will define a TeX command for the exponential series. Note these definitions are given in Javascript strings, so you need to escape some special characters: for example double backslashes are used. If your macro has parameters, you must specify the expected number thus the 3 at the end of the array in

taylor: ["Macro","\\sum_{n=0}^{+\\infty} \\frac{{#1}^{(n)} \\left({#2}\\right)}{n!} {\\left( {#3} - {#2} \\right)}^n", 3],

Finally, you can use the Taylor extension in a test page:

<!--MathJax/unpacked/test2.html-->

...
<script type="text/x-mathjax-config">
  MathJax.Hub.Config({ TeX: { extensions: ["Taylor.js"] }});
</script>
...

<body>
\[ \exp(x) = \expexpansion \]

\[ f(x) = \taylor{f}{x}{a} \]


\[ \log(1+h) = \taylorlog{h} \text{ for } |h| \lt 1 \]

\[ \sin\left(\frac{\epsilon}{3}\right) =
   \taylorsin{\left(\frac{\epsilon}{3}\right)} \]
</body>

Dealing with Dependencies

Suppose that we want to create another extension Taylor2.js that uses some command from Taylor.js. Hence Taylor2 depends on Taylor and we should do some synchronization. We have already seen that the Taylor extension waits for the “TeX Jax Ready” signal before defining the macros. In order to inform the Taylor2 extensions when it is ready, the Taylor extension must itself send a “TeX Taylor Ready” signal. The appropriate place for that is of course after the macros are defined:

// unpacked/extensions/TeX/Taylor.js

MathJax.Hub.Register.StartupHook("TeX Jax Ready", function () {
  MathJax.InputJax.TeX.Definitions.Add({
    ...
  });
  MathJax.Hub.Startup.signal.Post("TeX Taylor Ready");
});

MathJax.Ajax.loadComplete("[MathJax]/extensions/TeX/Taylor.js");

Now define Taylor2.js as follows:

// unpacked/extensions/TeX/Taylor2.js

MathJax.Hub.Register.StartupHook("TeX Jax Ready", function () {
  MathJax.InputJax.TeX.Definitions.Add({
    macros: {
      sinexpansion: ["Extension", "Taylor"]
    }
  });
});

MathJax.Hub.Register.StartupHook("TeX Taylor Ready", function () {
  MathJax.Hub.Insert(MathJax.InputJax.TeX.Definitions, {
    macros: {
      sinexpansion: ["Macro", "\\taylorsin{x}"]
    }
  });
});

MathJax.Ajax.loadComplete("[MathJax]/extensions/TeX/Taylor2.js");

When the input Jax is ready, \sinexpansion will be define as a function that loads the Taylor extension and restarts the processing afterward. When the Taylor extension is ready, \sinexpansion becomes the wanted \\taylorsin{x} definition. Now, you can use this command in a test3 page. Note that only the Taylor2 extension is specified in the list of extensions to load (Taylor will be loaded when the sinexpansion macro is first used).

<!--MathJax/unpacked/test3.html-->

...
<script type="text/x-mathjax-config">
  MathJax.Hub.Config({ TeX: { extensions: ["Taylor2.js"] }});
</script>
...

<body>
\[ \sin(x) = \sinexpansion \]
...

We won’t give the details in this tutorial, but note that other MathJax components have similar methods to stop, wait for an extension, and restart the execution again.

More Advanced Extensions

In general, writing more sophisticated extensions require a good understanding of the MathJax codebase. Although the public MathJax API is available in the documentation, this is not always the case for the internal code. The rule of thumb is thus to read the relevant jax.js files in unpacked/jax (if necessary the Javascript files they can load, too) and to make your extension redefine or expand the code.

Here is an example. We modify the behavior of \frac so that the outermost fractions are drawn normally but those that have a \frac ancestor are drawn bevelled. We also define a new command \bfrac that draws bevelled fractions by default. It has an optional parameter to indicate whether we want a bevelled fraction and can take values “auto” (like \frac), “true” or “false”. One has to read carefully the TeX parser to understand how this extension is working.

//unpacked/extensions/bevelledFraction.js

MathJax.Hub.Register.StartupHook("TeX Jax Ready", function () {
  MathJax.InputJax.TeX.Definitions.Add({
    macros: {
      frac: "Frac",
      bfrac: "BFrac"
    }
  }, null, true);
  MathJax.InputJax.TeX.Parse.Augment({
    Frac: function (name) {

      var old = this.stack.env.bevelled; this.stack.env.bevelled = true;
      var num = this.ParseArg(name);
      var den = this.ParseArg(name);
      this.stack.env.bevelled = old;

      var frac = MathJax.ElementJax.mml.mfrac(num, den);
      frac.bevelled = this.stack.env.bevelled;
      this.Push(frac);
    },
    BFrac: function (name) {

      var bevelled = this.GetBrackets(name);
      if (bevelled === "auto")
        bevelled = this.stack.env.bevelled;
      else
        bevelled = (bevelled !== "false");

      var old = this.stack.env.bevelled; this.stack.env.bevelled = true;
      var num = this.ParseArg(name);
      var den = this.ParseArg(name);
      this.stack.env.bevelled = old;

      var frac = MathJax.ElementJax.mml.mfrac(num, den);
      frac.bevelled = bevelled;
      this.Push(frac);
    }
  });

});

MathJax.Ajax.loadComplete("[MathJax]/extensions/TeX/mfracBevelled.js");

Again you can use this command in a test4 page.

<!--MathJax/unpacked/test4.html-->

...
<script type="text/x-mathjax-config">
  MathJax.Hub.Config({ TeX: { extensions: ["mfracBevelled.js"] }});
</script>
...

\[ \frac a b \]
\[ \frac {\frac a b}{\frac c d} \]
\[ \bfrac a b \]
\[ \bfrac[true] a b \]
\[ \bfrac[false] a b \]
\[ \bfrac[auto] a b \]
\[ \frac {\bfrac[auto] a b}{\bfrac[false] a b} \]
\[ \bfrac {\frac a b}{\bfrac[auto] a b} \]

...