Mathematical markup languages

A mathematical markup language is a computer notation for representing mathematical formulae, based on mathematical notation. Specialized markup languages are necessary because computers normally deal with linear text and more limited character sets (although increasing support for Unicode is obsoleting very simple uses). A formally standardized syntax also allows a computer to interpret otherwise ambiguous content, for rendering or even evaluating. For computer-interpretable syntaxes, the most popular are TeX/LaTeX and MathML.

Notations for human input

Popular languages for input by humans and interpretation by computers include TeX^[1]/LaTeX^[2] and Eqn.^[3]

Computer algebra systems such as Macsyma, Mathematica, Maple, and MATLAB each have their own syntax.

When the purpose is informal communication with other humans, syntax is often ad hoc, sometimes called "ASCII math notation". Academics sometimes use syntax based on TeX due to familiarity with it from writing papers. Those used to programming languages may also use shorthands like "!" for $\neg$. Web pages may also use a limited amount of HTML to mark up a small subset, for example superscripting.^[4] Ad-hoc syntax requires context to interpret ambiguous syntax, for example ">=" could be "implies" or "greater than or equal to", and "dx/dy" is likely to denote a derivative, but strictly speaking could also mean a finite quantity dx divided by dy.

Examples

TeX	eqn	ad-hoc ASCII	ad-hoc Unicode	formula
$a^2$	a sup 2	a^2	a²	a2
$\sum_{k=1}^N k^2$	sum from { k = 1 } to N { k sup 2 }	sum_{k=1}^N k^2	Σ_{k=1}^N k²	$\sum_{k=1}^N k^2$
$\neg a > 2 \Rightarrow a \le 2$		!(a > 2) => a <= 2	¬ a > 2 ⇒ a ≤ 2	$\neg a > 2 \Rightarrow a \le 2$

Markup languages for computer interchange

Markup languages optimized for computer-to-computer communication include MathML,^[5] OpenMath, and OMDoc. These are designed for verbosity and to minimize ambiguity. However, the verbosity makes them clumsier for humans to type directly.^[5]

Conversion

Many input, rendering, and conversion tools exist.

Microsoft Word includes Equation Editor, a limited version of MathType. These allow entering formulae using a graphical user interface, and converting to standard markup languages such as MathML. SciWriter is another GUI that can generate MathML and LaTeX.^[6]

ASCIIMathML, a JavaScript program, can convert ad-hoc ASCII notation to MathML.^[7]

References

1. ^ Donald E. Knuth. The TeXbook (Computers and Typesetting, Volume A). Reading, Massachusetts: Addison-Wesley, 1984. ISBN 0-201-13448-9.
2. ^ Lamport. LaTeX: A document preparation system, 2nd edition User's guide and reference manual. ISBN. http://www.latex-project.org/guides/books.html. 
3. ^ Brian W. Kernighan and Lorinda L. Cherry. A System for Typesetting Mathematics, Communications of the ACM 18 (1975), 151–157.
4. ^ Drexel University (2007). "Math Typesetting for the Internet". http://mathforum.org/typesetting/index.html. Retrieved 2007-04-16. 
5. ^ ^{a b} Buswell, Stephen; Devitt, Stan; Diaz, Angel; et al. (7 July 1999). "Mathematical Markup Language (MathML) 1.01 Specification (Abstract)". http://www.w3.org/TR/REC-MathML/#abstract. Retrieved 2007-04-13. "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." 
6. ^ "SciWriter". Archived from the original on 2007-01-22. http://web.archive.org/web/20070122005920/http://www.soft4science.com/products/sciwriter/index.html. Retrieved 2007-04-13. 
7. ^ Peter Jipsen (August 2005). "ASCIIMathML". http://www1.chapman.edu/~jipsen/mathml/asciimath.html. Retrieved 2007-04-13. 

External links

• MathML official website