MathML

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For help writing formulae in Wikipedia, please see Help:Formula.

Mathematical Markup Language (MathML) is an application of XML for describing mathematical notation and capturing both its structure and content. It aims at integrating mathematical formulae into World Wide Web documents. It is a recommendation of the W3C math working group.

1 History
2 Presentation and semantics
3 Example
4 Software support
5 Other standards
6 See also
7 References
8 External links

[edit] History

The specification of version 1.01 of the format was released in July 1999 and version 2.0 appeared in February 2001. In October 2003, the second edition of MathML Version 2.0 was published as the final release by the W3C math working group. In June 2006 the W3C has rechartered the MathML Working Group to produce a MathML 3 Recommendation until February 2008.

MathML was originally designed before the finalization of XML namespaces. As such, MathML markup is often not namespaced, and applications that deal with MathML, such as the Mozilla browsers, do not require a namespace. For applications that wish to namespace MathML, the recommended namespace URI is http://www.w3.org/1998/Math/MathML.

[edit] Presentation and semantics

MathML deals not only with the presentation but also the meaning of formula components (the latter part of MathML is known as “Content MathML”). Because the meaning of the equation is preserved separate from the presentation, how the content is communicated can be left up to the user. For example, web pages with MathML embedded in them can be viewed as normal web pages with many browsers but visually impaired users can also have the same MathML read to them through the use of screen readers (e.g. using the MathPlayer plugin for Internet Explorer).

[edit] Example

The well-known quadratic formula:

$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$

would be marked up using TeX syntax like this:

x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}

in troff/eqn like this:

x={-b +- sqrt{b sup 2 - 4ac}} over 2a

in OpenOffice.org Math like this (both are valid):

x={-b plusminus sqrt {b^2 - 4 ac}} over {2 a}
x={-b +- sqrt {b^2 - 4ac}} over 2a

and like this in Presentation MathML (the representation is an expression tree made up from layout elements like mfrac or msqrt elements):

<math xmlns="http://www.w3.org/1998/Math/MathML">
 <mi>x</mi>
 <mo>=</mo>
 <mfrac>
  <mrow>
   <mrow>
    <mo>-</mo>
    <mi>b</mi>
   </mrow>
   <mo>&PlusMinus;</mo>
   <msqrt>
    <msup>
     <mi>b</mi>
     <mn>2</mn>
    </msup>
    <mo>-</mo>
    <mrow>
     <mn>4</mn>
     <mo>&InvisibleTimes;</mo>
     <mi>a</mi>
     <mo>&InvisibleTimes;</mo>
     <mi>c</mi>
    </mrow>
   </msqrt>
  </mrow>
  <mrow>
   <mn>2</mn>
   <mo>&InvisibleTimes;</mo>
   <mi>a</mi>
  </mrow>
 </mfrac>
</math>

and finally like this in Content MathML (the representation is an expression tree for the functional structure elements like apply (for function application) or eq (for the equality relation) elements:

<math xmlns="http://www.w3.org/1998/Math/MathML">
  <apply>
    <eq/>
    <ci>x</ci>
    <apply>
      <frac/>
      <apply/>
        <csymbol definitionURL="http://www.example.com/mathops/multiops.html#plusminus"><mo>&PlusMinus;</mo></csymbol>
        <apply>
          <minus/>
          <ci>b</ci>
        </apply>
        <apply>
          <sqrt/>
          <apply>
            <minus/>
            <apply>
              <power/>
              <ci>b</ci>
              <cn>2</cn>
            </apply>
            <apply>
              <times/>
              <cn>4</cn>
              <ci>a</ci>
              <ci>c</ci>
            </apply>
          </apply>
        </apply>
      </apply>
      <apply>
        <times/>
        <cn>2</cn>
        <ci>a</ci>
      </apply>
    </apply>
  </apply>
</math>

In the expression tree above, elements like times are defined by the MathML specification and stand for mathematical functions that are applied to sibling expressions that are interpreted as arguments. The csymbol element is a generic extension element that means whatever is specified in the document referred to in the definitionURL attribute.

Although less compact compared to TeX, the XML structuring promises to make it widely usable and allows for instant display in applications such as Web browsers and facilitates a straightforward interpretation of its meaning in mathematical software products. MathML is not intended to be written or edited directly by humans.^[1]

[edit] Software support

[edit] Editors

Some editors with native MathML support (including copy and paste of MathML) are Publicon from Wolfram Research and SciWriter from soft4science.

MathML is also supported by major office products such as OpenOffice.org and KOffice and by mathematical software products such as Mathematica and the Windows version of the Casio ClassPad 300.

[edit] Conversion

Several utilities for converting mathematical expressions to MathML are available, including converters [1] between TeX and MathML. ConTeXt does the reverse and uses TeX for typesetting MathML (usually resulting in PDF documents). MathType from Design Science allows users to create equations in a WYSIWYG window and export them as MathML. Also, Wolfram Research provides a web page to convert typed mathematical expressions to MathML.

GNU TeXmacs is a what-you-see-is-what-you-get editor with extensive support for mathematics. Converters exist for presentation MathML in both directions. TeXmacs can be used to write mathematical articles which are exported to XHTML with embedded MathML. Another WYSIWYG MathML-as-is editor, Formulator MathML Weaver [2] provides a means for importing/exporting MathML with support for some abstract entities such as &ExponentialE; and &DifferentialD;. The W3C Browser/Editor Amaya can also be mentioned as a WYSIWYG MathML-as-is editor.

[edit] Web browsers

Of the major web browsers, those that directly support the format are recent versions of Gecko browsers (e.g., Firefox and Camino).[3] Other browsers support the format using external plugins. For example, Internet Explorer supports MathML using the Design Science MathPlayer plugin.

[edit] Web conversion

ASCIIMath [4] provides a JavaScript library to re-write a convenient Wiki-like text syntax used inline in web pages into MathML on the fly; it works in browsers with MathML support or plug-ins. LaTeXMathML [5] does the same for (a subset of) the standard LaTeX math syntax.

Blahtex is a TeX-to-MathML converter intended for use with MediaWiki, which may possibly add MathML support into Wikipedia, in addition to the current HTML and PNG output options.

[edit] Support of Software Developers

Support of MathML format accelerates software application development in such various topics, as computer-aided education (distance learning, electronic textbooks and other classroom materials); automated creation of attractive reports; computer algebra systems; authoring, training, publishing tools (both for web and desktop-oriented), and many other applications for mathematics, science, business, economics, etc. Several software vendors propose a component edition of their MathML editors, thus providing the easy way for software developers to insert mathematics rendering/editing/processing functionality in their applications. For example, Formulator ActiveX Control [6] from Hermitech Laboratory can be incorporated into an application as a MathML-as-is editor, Design Science propose a toolkit for building web pages that include interactive math (WebEQ™ Developers Suite, [7]).

[edit] Software Support

A number of software products indirectly support MathML. Geometry Expressions is an interactive geometry program that supports importing and exporting expressions as MathML via copy and paste.

[edit] Other standards

Another standard called OpenMath which has been designed (largely by the same people who devised Content MathML) more specifically for storing formulae semantically can also be used to complement MathML.

The OMDoc format has been created for markup of larger mathematical structures than formulae, from statements like definitions, theorems, proofs, or example, to theories and text books. Formulae in OMDoc documents can either be written in Content MathML or in OpenMath; for presentation, they are converted to Presentation MathML.

The Ecma Office Open XML (OOXML) standard defines an incompatible XML math syntax, derived from Microsoft Office products.

[edit] See also

[edit] References

^ Buswell, Steven; Devitt, Stan; Diaz, Angel; et al (7 July 1999). Mathematical Markup Language (MathML™) 1.01 Specification (Abstract). Retrieved on 26 September, 2006. “While MathML is human-readable it is anticipated that, in all but the simplest cases, authors will use equation editors, conversion programs, and other specialized software tools to generate MathML.”

[edit] External links

W3C Math Home — Contains the specifications, a FAQ, and a list of supporting software.
Latest MathML Recommendation
Zvon MathML Reference
MathML in Mozilla
MIT's instructions, MathML on Win/Mac/Linux
GNU TeXmacs: the free wysiwyg editing platform
MathML Renderer — MathML rendering engine for the .NET Framework; Enables server-side MathML to bitmap conversion.
MathType — A Design Science application for authoring math equations, which can be exported in a variety of formats (including MathML)
MathPlayer — A plugin from Design Science that allows Internet Explorer to display MathML.
MathFlow — A suite of Design Science products which enable XML workflow tools to interpret, create, edit, and export MathML.
MathML Central — Website containing utilities to display, plot, and convert any mathematical expression to and from MathML.
The OpenMath Standard
GtkMathView — A rendering engine for MathML markup
Itex - LaTeX-like language for generating MathML
itexToMML - Enhancement to the original itex2mml translator
MathML in ConTeXt - Example framework/demo page for conversion of MathML into PDF using ConTeXt (wiki page)
SciWriter — Scientific XML-based WYSIWYM editor with native MathML support; Supports also export to LaTeX
ASCIIMath — A JavaScript library for converting Wiki-like syntax into MathML
LaTeXMathML — A JavaScript program to dynamically translate LaTeX math notation to Presentation MathML
Formulator MathML Suite A Hermitech Laboratory software for authoring mathematical equations in MathML format (both Presentation and Content Markup)

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Categories: Markup languages | Mathematical tools | W3C standards | XML-based standards