Equations

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MediaWiki uses a subset of AMS-LaTeX markup, a superset of LaTeX markup which is in turn a superset of TeX markup, for mathematical formulae. It generates either PNG images or simple HTML markup, depending on user preferences and the complexity of the expression. In the future, as more browsers are smarter, it will be able to generate enhanced HTML or even MathML in many cases. (See blahtex for information about current work on adding MathML support.)

More precisely, MediaWiki filters the markup through Texvc, which in turn passes the commands to TeX for the actual rendering. Thus, only a limited part of the full TeX language is supported; see below for details.

To have math rendered in a particular MediaWiki installation, one has to set $wgUseTeX = true; in LocalSettings.php.

Technicals

Syntax

Math markup goes inside <math> ... </math>. The edit toolbar has a button for this.

Similar to HTML, in TeX extra spaces and newlines are ignored.

The TeX code has to be put literally: MediaWiki templates, predefined templates, and parameters cannot be used within math tags: pairs of double braces are ignored and "#" gives an error message. However, math tags work in the then and else part of #if, etc. See Template:Tim for more information.

Rendering

The PNG images are black on white (not transparent). These colors, as well as font sizes and types, are independent of browser settings or CSS. Font sizes and types will often deviate from what HTML renders. Vertical alignment with the surrounding text can also be a problem. The css selector of the images is img.tex. It should be pointed out that solutions to most of these shortcomings have been proposed by Maynard Handley, but have not been implemented yet.

The alt text of the PNG images, which is displayed to visually impaired and other readers who cannot see the images, defaults to the wikitext that produced the image, excluding the <math> and </math>. You can override this by explicitly specifying an alt attribute for the math element. For example, <math alt="Square root of pi">\sqrt{\pi}</math> generates an image <math alt="square root of pi">\sqrt{\pi}</math> whose alt text is "Square root of pi".

Apart from function and operator names, as is customary in mathematics, variables and letters are in italics; digits are not. For other text, (like variable labels) to avoid being rendered in italics like variables, use \text, \mbox, or \mathrm. For example, <math>\text{abc}</math> gives <math>\text{abc}</math>. This does not work for special characters, they are ignored unless the whole <math> expression is rendered in HTML:

• <math>\text {abcdefghijklmnopqrstuvwxyzàáâãäåæçèéêëìíîïðñòóôõö÷øùúûüýþÿ}</math>
• <math>\text {abcdefghijklmnopqrstuvwxyzàáâãäåæçèéêëìíîïðñòóôõö÷øùúûüýþÿ}\,</math>

gives:

• <math>\text {abcdefghijklmnopqrstuvwxyzàáâãäåæçèéêëìíîïðñòóôõö÷øùúûüýþÿ}</math>
• <math>\text {abcdefghijklmnopqrstuvwxyzàáâãäåæçèéêëìíîïðñòóôõö÷øùúûüýþÿ}\,</math>

TeX vs HTML

Before introducing TeX markup for producing special characters, it should be noted that, as this comparison table shows, sometimes similar results can be achieved in HTML (see Help:Special characters).

The codes on the left produce the symbols on the right, but the latter can also be put directly in the wikitext, except for ‘=’.

α β γ δ ε ζ
η θ ι κ λ μ ν
ξ ο π ρ  σ ς
τ υ φ χ ψ ω
Γ Δ Θ Λ Ξ Π
Σ Φ Ψ Ω

∫ ∑ ∏ √ − ± ∞
≈ ∝ {{=}} ≡ ≠ ≤ ≥ 
× · ÷ ∂ ′ ″
∇ ‰ ° ∴ Ø ø
∈ ∉ 
∩ ∪ ⊂ ⊃ ⊆ ⊇
¬ ∧ ∨ ∃ ∀ 
⇒ ⇔ → ↔ ↑ 
ℵ - – — 

The project has settled on both HTML and TeX because each has advantages in some situations.

Pros of HTML

1. Formulas in HTML behave more like regular text. In-line HTML formulae always align properly with the rest of the HTML text and, to some degree, can be cut-and-pasted. The formula’s background and font size match the rest of HTML contents and the appearance respects CSS and browser settings while the typeface is conveniently altered to help you identify formulae. The display of a formula entered using mathematical templates can be conveniently altered by modifying the templates involved; this modification will affect all relevant formulae without any manual intervention. Formulae typeset with HTML code will be accessible to client-side script links (a.k.a. scriptlets).
2. Pages using HTML code for formulae will load faster.
3. The HTML code, if entered diligently, will contain all semantic information to transform the equation back to TeX or any other code as needed. It can even contain differences TeX does not normally catch, e.g. {{math|''i''}} for the imaginary unit and {{math|<VAR>i</VAR>}} for an arbitrary index variable.

Pros of TeX

1. TeX is semantically more precise than HTML.
   1. In TeX, "<math>x</math>" means "mathematical variable <math>x</math>", whereas in HTML "x" is generic and somewhat ambiguous.
   2. On the other hand, if you encode the same formula as "{{math|<VAR>x</VAR>}}", you get the same visual result Template:Math and no information is lost. This requires diligence and more typing that could make the formula harder to understand as you type it. However, since there are far more readers than editors, this effort is worth considering.

   One consequence of this is that TeX code can be transformed into HTML, but not vice-versa.Template:Ref This means that on the server side we can always transform a formula, based on its complexity and location within the text, user preferences, type of browser, etc. Therefore, where possible, all the benefits of HTML can be retained, together with the benefits of TeX. It is true that the current situation is not ideal, but that is not a good reason to drop information/contents. It is more a reason to help improve the situation. Another consequence of this is that TeX can be converted to MathML for browsers which support it, thus keeping its semantics and allowing the rendering to be better suited for the reader’s graphic device.

2. TeX is the preferred text formatting language of most professional mathematicians, scientists, and engineers. It is easier to persuade them to contribute if they can write in TeX. TeX has been specifically designed for typesetting formulae, so input is easier and more natural if you are accustomed to it, and output is more aesthetically pleasing if you focus on a single formula rather than on the whole containing page. Once a formula is done correctly in TeX, it will render reliably, whereas the success of HTML formulae is somewhat dependent on browsers or versions of browsers. Another aspect of this dependency is fonts: the serif font used for rendering formulae is browser-dependent and it may be missing some important glyphs. While browsers are generally able to substitute a matching glyph from a different font family, this may not work for combined glyphs (compare ‘ Template:IPA ’ and ‘ a̅ ’).Template:Ref
3. TeX formulae, by default, render larger and are usually more readable than HTML formula and are not dependent on client-side browser resources, such as fonts, and so the results are more reliably WYSIWYG.
4. While TeX does not assist you in finding HTML codes or Unicode values (which you can obtain by viewing the HTML source in your browser), cutting and pasting from a TeX PNG in Wikipedia into simple text will return the LaTeX source.

Template:Note unless your wikitext follows the style of point 1.2

Template:Note The entity support problem is not limited to mathematical formulae though; it can be easily solved by using the corresponding characters instead of entities, as the character repertoire links do, except for cases where the corresponding glyphs are visually indiscernible (e.g. &ndash; for ‘–’ and &minus; for ‘−’).

Functions, symbols, special characters

For a little more semantics on these symbols, see the brief TeX Cookbook

Larger expressions

Subscripts, superscripts, integrals

Fractions, matrices, multilines

\begin{matrix}
  x & y \\
  z & v 
\end{matrix}

\begin{vmatrix}
  x & y \\
  z & v 
\end{vmatrix}

\begin{Vmatrix}
  x & y \\
  z & v
\end{Vmatrix}

\begin{bmatrix}
  0      & \cdots & 0      \\
  \vdots & \ddots & \vdots \\ 
  0      & \cdots & 0
\end{bmatrix}

\begin{Bmatrix}
  x & y \\
  z & v
\end{Bmatrix}

\begin{pmatrix}
  x & y \\
  z & v 
\end{pmatrix}

\bigl( \begin{smallmatrix}
  a&b\\ c&d
\end{smallmatrix} \bigr)

 a&b\\ c&d

f(n) = 
\begin{cases} 
  n/2,  & \mbox{if }n\mbox{ is even} \\
  3n+1, & \mbox{if }n\mbox{ is odd} 
\end{cases}

 n/2,  & \mbox{if }n\mbox{ is even} \\ 
 3n+1, & \mbox{if }n\mbox{ is odd} 

\begin{align}
 f(x) & = (a+b)^2 \\
      & = a^2+2ab+b^2 \\
\end{align}

f(x) & = (a+b)^2 \\
     & = a^2+2ab+b^2 \\

\begin{alignat}{2}
 f(x) & = (a-b)^2 \\
      & = a^2-2ab+b^2 \\
\end{alignat}

f(x) & = (a-b)^2 \\
     & = a^2-2ab+b^2 \\

\begin{array}{lcl}
  z        & = & a \\
  f(x,y,z) & = & x + y + z  
\end{array}

 z        & = & a \\
 f(x,y,z) & = & x + y + z  

\begin{array}{lcr}
  z        & = & a \\
  f(x,y,z) & = & x + y + z     
\end{array}

 z        & = & a \\
 f(x,y,z) & = & x + y + z     

<math>f(x) \,\!</math>
<math>= \sum_{n=0}^\infty a_n x^n </math>
<math>= a_0+a_1x+a_2x^2+\cdots</math>

\begin{cases}
    3x + 5y +  z \\
    7x - 2y + 4z \\
   -6x + 3y + 2z 
\end{cases}

\begin{array}{|c|c||c|} a & b & S \\
\hline
0&0&1\\
0&1&1\\
1&0&1\\
1&1&0\\
\end{array}

Parenthesizing big expressions, brackets, bars

You can use various delimiters with \left and \right:

Alphabets and typefaces

Texvc cannot render arbitrary Unicode characters. Those it can handle can be entered by the expressions below. For others, such as Cyrillic, they can be entered as Unicode or HTML entities in running text, but cannot be used in displayed formulas.

Mixed text faces

Color

Equations can use color:

• {\color{Blue}x^2}+{\color{YellowOrange}2x}-{\color{OliveGreen}1}

  <math>{\color{Blue}x^2}+{\color{YellowOrange}2x}-{\color{OliveGreen}1}</math>

• x_{1,2}=\frac{-b\pm\sqrt{\color{Red}b^2-4ac}}{2a}

  <math>x_{1,2}=\frac{-b\pm\sqrt{\color{Red}b^2-4ac}}{2a}</math>

See here for all named colorskpss supported by LaTeX.

Note that color should not be used as the only way to identify something, because it will become meaningless on black-and-white media or for color-blind people. See Wikipedia:Manual of Style#Color coding.

Formatting issues

Spacing

Note that TeX handles most spacing automatically, but you may sometimes want manual control.

Automatic spacing may be broken in very long expressions (because they produce an overfull hbox in TeX):

<math>0+1+2+3+4+5+6+7+8+9+10+11+12+13+14+15+16+17+18+19+20+\cdots</math>

<math>0+1+2+3+4+5+6+7+8+9+10+11+12+13+14+15+16+17+18+19+20+\cdots</math>

This can be remedied by putting a pair of braces { } around the whole expression:

<math>{0+1+2+3+4+5+6+7+8+9+10+11+12+13+14+15+16+17+18+19+20+\cdots}</math>

<math>{0+1+2+3+4+5+6+7+8+9+10+11+12+13+14+15+16+17+18+19+20+\cdots}</math>

Alignment with normal text flow

Due to the default CSS

<source lang="CSS">img.tex { vertical-align: middle; }</source>

an inline expression like <math>\int_{-N}^{N} e^x\, dx</math> should look good.

If you need to align it otherwise, use <math style="vertical-align:-100%;">...</math> and play with the vertical-align argument until you get it right. However, how it looks may depend on the browser and the browser settings.

Also note that if you rely on this workaround, if/when the rendering on the server gets fixed in future releases, as a result of this extra manual offset your formulae will suddenly be aligned incorrectly. So use it sparingly, if at all.

Forced PNG rendering

To force the formula to render as PNG, add \, (small space) at the end of the formula (where it is not rendered). This will force PNG if the user is in "HTML if simple" mode, but not for "HTML if possible" mode (math rendering settings in preferences).

You can also use \,\! (small space and negative space, which cancel out) anywhere inside the math tags. This does force PNG even in "HTML if possible" mode, unlike \,.

This could be useful to keep the rendering of formulae in a proof consistent, for example, or to fix formulae that render incorrectly in HTML (at one time, a^{2+2} rendered with an extra underscore), or to demonstrate how something is rendered when it would normally show up as HTML (as in the examples above).

For instance:

This has been tested with most of the formulae on this page, and seems to work perfectly.

You might want to include a comment in the HTML so people don't "correct" the formula by removing it:

<!-- The \,\! is to keep the formula rendered as PNG instead of HTML. Please don't remove it.-->

Commutative diagrams

To make a commutative diagram, there are three steps:

1. write the diagram in TeX
2. convert to SVG
3. upload the file to Wikimedia Commons

Diagrams in TeX

Xy-pic (online manual) is the most powerful and general-purpose diagram package in TeX.

Simpler packages include:

• AMS's amscd
• Paul Taylor's diagrams
• François Borceux Diagrams

The following is a template for Xy-pic, together with a hack to increase the margins in dvips, so that the diagram is not truncated by over-eager cropping (suggested in TUGboat:kpss TUGboat, Volume 17 1996, No. 3):

\documentclass{amsart}
\usepackage[all, ps, dvips]{xy} % Loading the XY-Pic package 
                                % Using postscript driver for smoother curves
\usepackage{color}              % For invisible frame
\begin{document}
\thispagestyle{empty} % No page numbers
\SelectTips{eu}{}     % Euler arrowheads (tips)
\setlength{\fboxsep}{0pt} % Frame box margin
{\color{white}\framebox{{\color{black}$$ % Frame for margin

\xymatrix{ % The diagram is a 3x3 matrix
%%% Diagram goes here %%%
}

$$}}} % end math, end frame
\end{document}

Convert to SVG

Once you have produced your diagram in LaTeX (or TeX), you can convert it to an SVG file using the following sequence of commands:

pdflatex file.tex
pdfcrop --clip file.pdf tmp.pdf
pdf2svg tmp.pdf file.svg
(rm tmp.pdf at the end)

If you do not have pdflatex (which is unlikely) you can also use the commands

latex file.tex
dvipdfm file.dvi

to get a PDF version of your diagram. The pdfcrop and pdf2svg utilities are needed for this procedure.

In general, you will not be able to get anywhere with diagrams without TeX and Ghostscript, and the inkscape program is a useful tool for creating or modifying your diagrams by hand. There is also a utility pstoedit which supports direct conversion from Postscript files to many vector graphics formats, but it requires a non-free plugin to convert to SVG, and regardless of the format, this editor has not been successful in using it to convert diagrams with diagonal arrows from TeX-created files.

These programs are:

• a working TeX distribution, such as TeX Live
• Ghostscript
• pstoedit
• Inkscape

Upload the file

Template:Seealso Template:Seealso

As the diagram is your own work, upload it to Wikimedia Commons, so that all projects (notably, all languages) can use it without having to copy it to their language's Wiki. (If you've previously uploaded a file to somewhere other than Commons, to Commons.)

Check size

Before uploading, check that the default size of the image is neither too large nor too small by opening in an SVG application and viewing at default size (100% scaling), otherwise adjust the -y option to dvips.

Name

Make sure the file has a meaningful name.

Upload

Login to Wikimedia Commons, then upload the file; for the Summary, give a brief description.

Now go to the image page and add a description, including the source code, using this template:

{{Information
|Description =
{{en| Description [[:en:Link to WP page|topic]]
}}
|Source=Created as per: [[:en:meta:Help:Displaying a formula#Commutative diagrams]]
<pre>
% TeX source here
</pre>
|Date = The Creation Date, like 1999-12-31
|Author = [[User:YourUserName|Your Real Name]]
|Permission = {{self|PD-self (or other license)|author=[[User:YourUserName|Your Real Name]]}}
}}

[[Category:Commutative diagrams]]

Source code

• Include the source code in the image page, in the Source section of the Information template, so that the diagram can be edited in future.
• Include the complete .tex file, not just the fragment, so future editors do not need to reconstruct a compilable file.
• (Don't include it in the Summary section, which is just supposed to be a summary.)

License

The most common license for commutative diagrams is PD-self; some use PD-ineligible, especially for simple diagrams, or other licenses. Please do not use the GFDL, as it requires the entire text of the GFDL to be attached to any document that uses the diagram.

Description

If possible, link to a Wikipedia page relevant to the diagram.

Category

Include [[Category:Commutative diagrams]], so that it appears in commons:Category:Commutative diagrams. There are also subcategories, which you may choose to use.

Include image

Now include the image on the original page via [[Image:Diagram.svg]]

Examples

A sample conforming diagram is commons:Image:PSU-PU.svg.

Examples

<math>ax^2 + bx + c = 0</math>

<math>ax^2 + bx + c = 0</math>

<math>ax^2 + bx + c = 0\,\!</math>

<math>ax^2 + bx + c = 0\,\!</math>

<math>x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}</math>

<math>x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}</math>

<math>2 = \left( \frac{\left(3-x\right) \times 2}{3-x} \right)</math>

<math>2 = \left(
 \frac{\left(3-x\right) \times 2}{3-x}
 \right)</math>

<math>S_{\text{new}} = S_{\text{old}} - \frac{ \left( 5-T \right) ^2} {2}</math>

 <math>S_{\text{new}} = S_{\text{old}} - \frac{ \left( 5-T \right) ^2} {2}</math>
 

<math>\int_a^x \!\!\!\int_a^s f(y)\,dy\,ds = \int_a^x f(y)(x-y)\,dy</math>

<math>\int_a^x \!\!\!\int_a^s f(y)\,dy\,ds
 = \int_a^x f(y)(x-y)\,dy</math>

<math>\sum_{m=1}^\infty\sum_{n=1}^\infty\frac{m^2\,n}{3^m\left(m\,3^n+n\,3^m\right)}</math>

<math>\sum_{m=1}^\infty\sum_{n=1}^\infty\frac{m^2\,n}
 {3^m\left(m\,3^n+n\,3^m\right)}</math>

<math>u + p(x)u' + q(x)u=f(x),\quad x>a</math>

<math>u'' + p(x)u' + q(x)u=f(x),\quad x>a</math>

<math>|\bar{z}| = |z|, |(\bar{z})^n| = |z|^n, \arg(z^n) = n \arg(z)</math>

<math>|\bar{z}| = |z|,
 |(\bar{z})^n| = |z|^n,
 \arg(z^n) = n \arg(z)</math>

<math>\lim_{z\rightarrow z_0} f(z)=f(z_0)</math>

<math>\lim_{z\rightarrow z_0} f(z)=f(z_0)</math>

<math>\phi_n(\kappa)
= \frac{1}{4\pi^2\kappa^2} \int_0^\infty \frac{\sin(\kappa R)}{\kappa R}  \frac{\partial}{\partial R}  \left[R^2\frac{\partial D_n(R)}{\partial R}\right]\,dR</math>

<math>\phi_n(\kappa) =
 \frac{1}{4\pi^2\kappa^2} \int_0^\infty
 \frac{\sin(\kappa R)}{\kappa R}
 \frac{\partial}{\partial R}
 \left[R^2\frac{\partial D_n(R)}{\partial R}\right]\,dR</math>

<math>\phi_n(\kappa) = 0.033C_n^2\kappa^{-11/3},\quad \frac{1}{L_0}\ll\kappa\ll\frac{1}{l_0}</math>

<math>\phi_n(\kappa) = 
 0.033C_n^2\kappa^{-11/3},\quad
 \frac{1}{L_0}\ll\kappa\ll\frac{1}{l_0}</math>

<math>f(x) = \begin{cases}1 & -1 \le x < 0 \\
\frac{1}{2} & x = 0 \\ 1 - x^2 & \mbox{otherwise}\end{cases}</math>

<math>
 f(x) =
 \begin{cases}
 1 & -1 \le x < 0 \\
 \frac{1}{2} & x = 0 \\
 1 - x^2 & \mbox{otherwise}
 \end{cases}
 </math>

<math>{}_pF_q(a_1,\dots,a_p;c_1,\dots,c_q;z) = \sum_{n=0}^\infty \frac{(a_1)_n\cdots(a_p)_n}{(c_1)_n\cdots(c_q)_n}\frac{z^n}{n!}</math>

 <math>{}_pF_q(a_1,\dots,a_p;c_1,\dots,c_q;z)
 = \sum_{n=0}^\infty
 \frac{(a_1)_n\cdots(a_p)_n}{(c_1)_n\cdots(c_q)_n}
 \frac{z^n}{n!}</math>

<math> \frac {a}{b}</math>   <math> \tfrac {a}{b} </math>
<math> \frac {a}{b}\  \tfrac {a}{b} </math>

<math>S=\frac{1}{2}dD\sin\alpha </math>
<math>S=\frac{1}{2}dD\sin\alpha </math>

<math>V=\frac{1}{6}\pi h[3(r_1^2+r_2^2)+h^2]</math>
<math>V=\frac{1}{6}\pi h[3(r_1^2+r_2^2)+h^2]</math>

Bug reports

Discussions, bug reports and feature requests should go to the Wikitech-l mailing list. These can also be filed on Mediazilla under MediaWiki extensions.

See also

• Typesetting of mathematical formulas
• Proposed m:Music markup and Help:Musical symbols
• Table of mathematical symbols
• mw:Extension:Blahtex, or blahtex: a LaTeX to MathML converter for Wikipedia
• General help for editing a Wiki page
• Mimetex alternative for another way to display mathematics using Mimetex.cgi
• Wikipedia:Math Sandbox
• commons:Category:Images which should use TeX

External links

• A LaTeX tutorial.
• A paper introducing TeX—see page 39 onwards for a good introduction to the maths side of things.
• A paper introducing LaTeX—skip to page 49 for the math section. See page 63 for a complete reference list of symbols included in LaTeX and AMS-LaTeX.
• The Comprehensive LaTeX Symbol List—symbols not found here may be documented there.
• AMS-LaTeX guide.
• A set of public domain fixed-size math symbol bitmaps.
• MathML: A product of the W3C Math working group, is a low-level specification for describing mathematics as a basis for machine to machine communication.

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