Editing MathML (section)

=== Content MathML ===
{{Infobox file format
| name = Content MathML
| mime = application/mathml-content+xml
| type code = <code>MMLc</code>
| uniform type = {{mono|public.mathml.content}}
| 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>
		<plus/>
		<apply>
			<times/>
			<ci>a</ci>
			<apply>
				<power/>
				<ci>x</ci>
				<cn>2</cn>
			</apply>
		</apply>
		<apply>
			<times/>
			<ci>b</ci>
			<ci>x</ci>
		</apply>
		<ci>c</ci>
	</apply>
</math>
</syntaxhighlight>

Content MathML is nearly [[isomorphic]] to [[Binary expression tree|expressions]] in a [[Functional programming|functional language]] such as [[Scheme (programming language)|Scheme]] and other dialects of [[Lisp (programming language)|Lisp]]. {{code|lang=XML|<apply>...</apply>}} amounts to Scheme's {{code|lang=Scheme|(...)}}, and the many operator and function elements amount to Scheme functions. With this trivial literal transformation, plus un-tagging the individual tokens, the example above becomes:
<syntaxhighlight lang="scheme">
(plus
  (times a (power x 2))
  (times b x)
  c)
</syntaxhighlight>
This reflects the long-known close relationship between XML element structures, and [[Lisp (programming language)|LISP]] or Scheme [[S-expressions]].<ref>Steven DeRose. The SGML FAQ Book: Understanding the Relationship of SGML and XML, Kluwer Academic Publishers, 1997. {{isbn|978-0-7923-9943-8}}.</ref><ref>[[Canonical S-expressions#cite note-0]]</ref>

==== Wikidata annotation in Content MathML ====
According to the OM Society,<ref name="OpenMath">{{cite web
	| url = https://www.openmath.org/
	| title = OpenMath Home · OpenMath
	| website = www.openmath.org
}}</ref> OpenMath Content Dictionaries can be employed as collections of symbols and identifiers with declarations of their semantics{{snd}}names, descriptions and rules. A 2018 paper presented at the [[Special Interest Group on Information Retrieval|SIGIR]] conference<ref name="SchubotzScharpfGipp2018">{{cite journal
	| first1 = Moritz  | last1 = Schubotz
	| first2 = Philipp | last2 = Scharpf
	| first3 = Bela    | last3 = Gipp
	| title = Representing Mathematical Formulae in Content MathML using Wikidata.
	| url = http://ceur-ws.org/Vol-2132/paper5.pdf
	| date = 2018
	| journal = Birndl@sigir
}}</ref> proposed that the semantic knowledge base [[Wikidata]] could be used as an OpenMath Content Dictionary to link semantic elements of a mathematical formula to unique and language-independent Wikidata items.