Extension:Math/Syntax

This page is outdated. It was written for an older version of MediaWiki and may not apply to the most recent version. If you have checked or updated this page and found the content to be suitable, please remove this notice. See the talk page for a possible discussion on this.

The Math extension uses a subset of TeX markup, including some extensions from LaTeX and AMS-LaTeX, to display mathematical formulas. It either generates SVG, MathML markup, or uses MathJax to render math on the client side, depending on user preferences and the complexity of the expression.

MathML and MathJax are planned to be used more in the future, with the SVG images becoming deprecated.

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.

Traditionally, math markup goes inside the XML-style tag math: ‎<math>...‎</math>.

As with all XML-style tags, one can use the function #tag: {{#tag:math|...}}; this is more versatile: the wikitext at the dots is first expanded before interpreting the result as TeX code. Thus it can contain parameters, variables, parser functions and templates. Note however that with this syntax double braces in the TeX code must have a space in between, to avoid confusion with their use in template calls etc. Also, to produce the character "|" inside the TeX code, use {{!}}.

In TeX, as in HTML, extra spaces and newlines are ignored.

The alt text of the images, which is displayed to visually impaired and other readers who cannot see the images, and is also used when the text is selected and copied, is equivalent to the TeX code that produced the image.

Apart from function and operator names, as is customary in mathematics for variables, 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. You can also define new function names using \operatorname{...}. For example, <math>\text{abc}</math> gives ${\displaystyle \text{abc}}$. You can also define new function names using \operatorname{...}.

The following symbols are reserved characters that either have a special meaning under LaTeX or are unavailable in all the fonts.

# $ % ^ & _ { } ~ \

Some of these can be entered with a backslash in front:

<math>\# \$ \% \& \_ \{ \} </math> → ${\displaystyle \#\$\%\mathrm{\&}\_\{\}}$

Others have special names:

<math> \hat{} \quad \tilde{} \quad \backslash </math> → ${\displaystyle \stackrel{}{^}\stackrel{}{~}\mathrm{\setminus }}$

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 about 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

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

Both HTML and TeX have advantages in some situations.

1. Formulas in HTML behave more like regular text.
2. The formula’s background and font size match the rest of HTML contents (this can be fixed on TeX formulas by using the commands \pagecolor and \definecolor) and the appearance respects CSS and browser settings while the typeface is conveniently altered to help you identify formulae.
3. Formulae typeset with HTML code will be accessible to client-side script links (a.k.a. scriptlets).
4. 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.
5. 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.
6. Formulae using HTML code will render as sharp as possible no matter what device is used to render them.

1. TeX is semantically more precise than HTML.
   1. In TeX, "<math>x</math>" means "mathematical variable ${\displaystyle x}$", 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 x and no information is lost. This requires diligence and more typing that could make the formula harder to understand as you type it.
2. One consequence of point 1 is that TeX code can be transformed into HTML, but not vice-versa (unless your wikitext follows the style of point 1.2). 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.
3. Another consequence of point 1 is that TeX can be converted to MathML (e.g. by MathJax) for browsers which support it, thus keeping its semantics and allowing the rendering to be better suited for the reader’s graphic device.
4. TeX is the preferred text formatting language of most professional mathematicians, scientists, and engineers writing in English. It is easier to persuade them to contribute if they can write in TeX.
5. 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.
6. 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 the browser generally capable to substitute a matching glyph from a different font family, it need not be the case for combined glyphs (compare ‘ a̅ ’ and ‘ a̅ ’).
7. When writing in TeX, editors need not worry about whether this or that version of this or that browser supports this or that HTML entity. The burden of these decisions is put on the software. This does not hold for HTML formulae, which can easily end up being rendered wrongly or differently from the editor’s intentions on a different browser.
8. TeX formulae, by default, render larger and are usually more readable than HTML formulae and are not dependent on client-side browser resources, such as fonts, and so the results are more reliably WYSIWYG.
9. 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.

In some cases it may be the best choice to use neither TeX nor the html-substitutes, but instead the simple ASCII symbols of a standard keyboard (see below, for an example).

\cfrac{2}{ c + \cfrac{2}{ d + \cfrac{1}{2} } } = a
\qquad
\dfrac{2}{ c + \dfrac{2}{ d + \dfrac{1}{2} } } = a

\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)

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

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

\begin{cases}
3x + 5y +  z &= 1 \\
7x - 2y + 4z &= 2 \\
-6x + 3y + 2z &= 3
\end{cases}

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

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

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

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

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

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

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.

Equations can use color:

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

  ${\displaystyle x^2}+2x-1$

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

  ${\displaystyle x_{1,2}=\frac{-b\pm \sqrt{b^2-4ac}}{2a}}$

See here for all named colors (archived) 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.

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>

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

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>

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

The phantom commands create empty horizontal and/or vertical space the same height and/or width of the argument.

Due to the default css

img.tex { vertical-align: middle; }

an inline expression like ${\displaystyle {\displaystyle \underset{-N}{\overset{N}{\int }}}{e}^{x}dx}$ 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.

There are two ways to render chemical sum formulae as used in chemical equations:

• <math chem>
• <chem>

<chem>X</chem> is short for <math chem>\ce{X}</math>.

(where X is a chemical sum formula)

Technically, <math chem> is a math tag with the extension mhchem enabled, according to the mathjax documentation.

Note, that the commands \cee and \cf are disabled, because they are marked as deprecated in the mhchem LaTeX package documentation.

If the formula reaches a certain "complexity", spaces might be ignored (<chem>A + B</chem> might be rendered as if it were <chem>A+B</chem> with a positive charge). In that case, write <chem>A{} + B</chem> (and not <chem>{A} + {B}</chem> as was previously suggested). This will allow auto-cleaning of formulae once the bug will be fixed and/or a newer mhchem version will be used.

See examples below.

<chem>C6H5-CHO</chem>
${\displaystyle \mathrm{C}{\phantom{A}}_6\mathrm{H}{\phantom{A}}_5-\mathrm{C}\mathrm{H}\mathrm{O}}$

<chem>\mathit{A} ->[\ce{+H2O}] \mathit{B}</chem>
${\displaystyle \mathit{A}\stackrel{+\mathrm{H}{\phantom{A}}_2\mathrm{O}}{\to }\mathit{B}}$

<math chem>A \ce{->[\ce{+H2O}]} B</math>
${\displaystyle A\stackrel{+\mathrm{H}{\phantom{A}}_2\mathrm{O}}{\to }B}$

<chem>SO4^2- + Ba^2+ -> BaSO4 v</chem>
${\displaystyle \mathrm{S}\mathrm{O}{\phantom{A}}_4{\phantom{A}}^{2-}+\mathrm{B}\mathrm{a}{\phantom{A}}^{2+}⟶\mathrm{B}\mathrm{a}\mathrm{S}\mathrm{O}{\phantom{A}}_4\downarrow }$

<chem>H2NCO2- + H2O <=> NH4+ + CO3^2-</chem>
${\displaystyle \mathrm{H}{\phantom{A}}_2\mathrm{N}\mathrm{C}\mathrm{O}{\phantom{A}}_2{\phantom{A}}^{-}+\mathrm{H}{\phantom{A}}_2\mathrm{O}\stackrel{-\rightharpoonup }{\leftharpoondown -}\mathrm{N}\mathrm{H}{\phantom{A}}_4{\phantom{A}}^{+}+\mathrm{C}\mathrm{O}{\phantom{A}}_3{\phantom{A}}^{2-}}$

<chem>H2O</chem>
${\displaystyle \mathrm{H}{\phantom{A}}_2\mathrm{O}}$

<chem>Sb2O3</chem>
${\displaystyle \mathrm{S}\mathrm{b}{\phantom{A}}_2\mathrm{O}{\phantom{A}}_3}$

<chem>H+</chem>
${\displaystyle \mathrm{H}{\phantom{A}}^{+}}$

<chem>CrO4^2-</chem>
${\displaystyle \mathrm{C}\mathrm{r}\mathrm{O}{\phantom{A}}_4{\phantom{A}}^{2-}}$

<chem>AgCl2-</chem>
${\displaystyle \mathrm{A}\mathrm{g}\mathrm{C}\mathrm{l}{\phantom{A}}_2{\phantom{A}}^{-}}$

<chem>[AgCl2]-</chem>
${\displaystyle [\mathrm{A}\mathrm{g}\mathrm{C}\mathrm{l}{\phantom{A}}_2]{\phantom{A}}^{-}}$

<chem>Y^{99}+</chem>
${\displaystyle \mathrm{Y}{\phantom{A}}^{99+}}$

<chem>Y^{99+}</chem>
${\displaystyle \mathrm{Y}{\phantom{A}}^{99+}}$

<chem>H2_{(aq)}</chem>
${\displaystyle \mathrm{H}{\phantom{A}}_2{\phantom{A}}_{(\mathrm{a}\mathrm{q})}}$

<chem>NO3-</chem>
${\displaystyle \mathrm{N}\mathrm{O}{\phantom{A}}_3{\phantom{A}}^{-}}$

<chem>(NH4)2S</chem>
${\displaystyle (\mathrm{N}\mathrm{H}{\phantom{A}}_4){\phantom{A}}_2\mathrm{S}}$

${\displaystyle a{x}^2+bx+c=0}$

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

${\displaystyle a{x}^2+bx+c=0}$

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

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

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

${\displaystyle 2=\left(\frac{(3-x)\times 2}{3-x}\right)}$

<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>
 

${\displaystyle {\displaystyle \underset{a}{\overset{x}{\int }}}{\displaystyle \underset{a}{\overset{s}{\int }}}f(y)dyds={\displaystyle \underset{a}{\overset{x}{\int }}}f(y)(x-y)dy}$

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

${\displaystyle {\displaystyle \sum _{m=1}^{\mathrm{\infty }}}{\displaystyle \sum _{n=1}^{\mathrm{\infty }}}\frac{m^{2}n}{3^m(m{3}^n+n{3}^m)}}$

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

${\displaystyle u^{″}+p(x)u^{\prime }+q(x)u=f(x),x>a}$

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

${\displaystyle \left|\overline{z}\right|=\left|z\right|,|(\overline{z}{)}^n|=|z{|}^n,\arg (z^n)=n\arg (z)}$

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

${\displaystyle \underset{z\to z_0}{\lim }f(z)=f(z_0)}$

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

${\displaystyle {\varphi }_n(\kappa )=\frac{1}{4{\pi }^2{\kappa }^2}{\displaystyle \underset{0}{\overset{\mathrm{\infty }}{\int }}}\frac{\sin (\kappa R)}{\kappa R}\frac{\partial }{\partial R}\left[R^2\frac{\partial D_n(R)}{\partial R}\right]dR}$

<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>

${\displaystyle {\varphi }_n(\kappa )=0.033C_n^2{\kappa }^{-11/3},\frac{1}{L_0}\ll \kappa \ll \frac{1}{l_0}}$

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

${\displaystyle f(x)=\{\begin{array}{ll}1& -1\le x<0\\ \frac{1}{2}& x=0\\ 1-x^2& \text{otherwise}\end{array}}$

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

${\displaystyle {}_p{F}_q(a_1,\dots ,a_p;c_1,\dots ,c_q;z)={\displaystyle \sum _{n=0}^{\mathrm{\infty }}}\frac{(a_1{)}_n\cdots (a_p{)}_n}{(c_1{)}_n\cdots (c_q{)}_n}\frac{z^n}{n!}}$

 <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>

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

Bug reports and feature requests should be reported on Phabricator with the tag Math.

• Converting between ParserFunctions syntax and TeX syntax
• Typesetting of mathematical formulas
• Score — extension for music markup
• Glossary of mathematical symbols

• A LaTeX tutorial
• LaTeX, A Short Course: Typesetting Mathematics
• 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
• Comprehensive List of Mathematical Symbols
• 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.