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{{short description|Format for expressing mathematical formulae}}
{{
{{Use dmy dates|date=February 2021}}
{{Infobox technology standard
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}}
| authors = {{Collapsible list|title=Principal authors|
{{blist|Ron Ausbrooks|Stephen Buswell|David Carlisle|Giorgi Chavchanidze|Stéphane Dalmas|Stan Devitt|Angel Diaz|Sam Dooley|Roger Hunter|Patrick Ion|Michael Kohlhase|Azzeddine Lazrek|Paul Libbrecht|Bruce Miller|Robert Miner|Chris Rowley|Murray Sargent|Bruce Smith|Neil Soiffer|Robert Sutor|Stephen Watt}}
}}<ref name="w3c-standard-2nd-ed"/>
| website = {{ubl
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}}
| base_standards = [[XML]]
| related_standards = [[OpenMath]], [[OpenDocument]], [[Office Open XML]], {{abbr|[[OMDoc]]|Open Mathematical Documents}}
| abbreviation = MathML
}}
'''Mathematical Markup Language''' ('''MathML''') is a pair of [[mathematical markup language]]s, an application of [[XML]] for describing [[mathematics|mathematical]] notations and capturing both its structure and content
== History ==
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| url = https://www.w3.org/MarkUp/HTMLPlus/htmlplus_45.html
| date = 1993-11-08
}}</ref> MathML 1 was released as a W3C recommendation in April 1998 as the first [[XML]] language to be recommended by the [[W3C]]. Version 1.01 of the format was released in July 1999 and version 2.0 appeared in February 2001. Implementations of the specification appeared in [[Amaya (web editor)|Amaya 1.1]], [[
| title = Mozilla 1.0 Released!
| url = http://www.mozillazine.org/articles/article2278.html
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}}</ref> Also in 2015, the MathML Association was founded to support the adoption of the MathML standard.<ref>{{citation
| url = http://mathml-association.org/about.html
| archive-url = https://web.archive.org/web/20151002150927/http://mathml-association.org/about.html
| title = Mondial Association for Tools Handling MathML▼
| url-status = usurped
| archive-date = 2 October 2015
| access-date = 2016-06-20
| author1 = Deyan Ginev
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=== MathML Core ===
In August 2021, a new specification called ''MathML Core'' was published, described as the
| title = MathML Core
| url = https://www.w3.org/TR/2022/WD-mathml-core-20220504/#abstract
| date = 2022-05-04
| access-date = 2023-03-03
}}</ref> MathML Core set itself apart from MathML 3.0 by including detailed rendering rules and integration with [[CSS]], automated browser support testing resources, and focusing on a fundamental subset of MathML. An implementation was added to Chromium at the beginning of 2023.<ref name="igalia-chrome-109">{{cite web
| url = https://www.igalia.com/2023/01/10/Igalia-Brings-MathML-Back-to-Chromium.html
| title = Igalia Brings MathML Back to Chromium
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}}</ref>
Thus, the expression <math
<syntaxhighlight lang="xml">
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| mime = application/mathml-content+xml
| type code = <code>MMLc</code>
| uniform type = {{
| conforms to = {{mono|public.mathml}}
| extended from = [[#Generic MathML|Generic MathML]]
}}
Content MathML focuses on the semantics, or meaning, of the expression rather than its layout. Central to Content MathML is the {{code|lang=XML|<apply>}} element that represents function application. The function being applied is the first child element under {{code|lang=XML|<apply>}}, and its operands or parameters are the remaining child elements. Content MathML uses only a few attributes.
Tokens such as identifiers and numbers are individually marked up, much as for Presentation MathML, but with elements such as {{code|lang=XML|<ci>}} and {{code|lang=XML|<cn>}}. Rather than being merely another type of token, operators are represented by specific elements, whose mathematical semantics are known to MathML: {{code|lang=XML|<times>}}, {{code|lang=XML|<power>}}, etc. There are over a hundred different elements for different functions and operators.<ref>{{cite web
| url = http://www.w3.org/TR/MathML3/chapter4.html#contm.opel
| title = Content Markup
| website = W3.org
}}</ref>
For example, {{code|lang=XML|<apply><sin/><ci>x</ci></apply>}} represents <math>\sin(x)</math> and {{code|lang=XML|<apply><plus/><ci>x</ci><cn>5</cn></apply>}} represents <math>x+5</math>. The elements representing operators and functions are empty elements, because their operands are the other elements under the containing {{code|lang=XML|<apply>}}.
The expression <math>a x^2+b x+c</math> could be represented as
<syntaxhighlight lang="xml">
<math>
<apply>
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== Other standards ==
The [[International Organization for Standardization|ISO]]/[[International Electrotechnical Commission|IEC]] standard [[OpenDocument]] (ODF) natively supports MathML for mathematical content. OpenDocument is the default file format in office suites like [[LibreOffice]] and [[Collabora Online]], the MathML content is stored in the ODF files (e.g., .odt, .ods, .odp). Microsoft Office does not support MathML in its default office suite XML document format. Instead, it defines a different XML math syntax derived from older [[Microsoft Office]] products.
Another standard called [[OpenMath]] that has been more specifically designed (largely by the same people who devised Content MathML) for storing formulae semantically can be used to complement MathML. OpenMath data can be embedded in MathML using the {{code|lang=XML|1=<annotation-xml encoding="OpenMath">}} element. OpenMath ''content dictionaries'' can be used to define the meaning of {{code|lang=XML|<csymbol>}} elements. The following would define ''P''<sub>1</sub>(''x'') to be the first [[Legendre polynomial]]:
<syntaxhighlight lang="xml">
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The [[OMDoc]] format has been created for markup of larger mathematical structures than formulae, from statements like definitions, theorems, proofs, and examples, to complete theories and even entire text books. Formulae in OMDoc documents can either be written in Content MathML or in OpenMath; for presentation, they are converted to Presentation MathML.
== See also ==
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* [[KaTeX]]{{snd}}JavaScript library that converts LaTeX to MathML
* [[MathJax]]{{snd}}JavaScript library that converts LaTeX to MathML
* [[OpenDocument]] The ISO/IEC standard used by applications like [[LibreOffice]] and [[Collabora Online]] natively support MathML for mathematical content
== References ==
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{{W3C Standards}}
{{Web browsers}}
{{ISO standards}}
{{Authority control}}
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