Help:Formula

Welcome!

Hello, Formula, and welcome to Wikipedia. Thank you for your contributions; I hope you like the place and decide to stay!

Please read The Five Pillars of Wikipedia to help you get to know this place, and you might want to look at What Wikipedia is not to see what is and isn't suitable for Wikipedia.

And remember, don't submit copyrighted work without permission. By submitting your work, you promise you wrote it yourself or copied it from public domain resources — this does not include most web pages.

I hope you enjoy editing here and being a Wikipedian! By the way, please be sure to sign your name on Talk pages using four tildes (~~~~) to produce your name and the current date. If you have any questions, see the help pages or ask a question. Again, welcome! - Other languages: , , , , , , ,

TeX

MediaWiki uses 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.

Math markup goes inside <math> ... </math>. Line breaks within these tags are fine, and aren't rendered. They're a good idea to keep the raw markup clear (for instance, a line break after each term or row of a matrix).

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. The css selector of the images is img.tex.

In the case of a non-white page background, the white background of the formula effectively highlights it, which can be an advantage or a disadvantage.

One may want to avoid using TeX markup as part of a line of regular text, as the formulae don't align properly and the font size, as said, usually does not match.

The alt attribute of the TeX images (the text that shows up in the hover box) is the wikitext that produced them, excluding the <math> and </math>.

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

Functions, symbols, special characters

(see also Help:Special characters)

Feature	Syntax	How it looks rendered
std. functions (good)	\sin x + \ln y +\operatorname{sgn} z	$\sin x+\ln y+\operatorname {sgn} z$
std. functions (wrong)	sin x + ln y + sgn z	$sinx+lny+sgnz\,$
Modular arithm.	s_k \equiv 0 \pmod{m}	$s_{k}\equiv 0{\pmod {m}}$
Derivatives	\nabla \partial x dx \dot x \ddot y	$\nabla \ \partial x\ dx\ {\dot {x}}\ {\ddot {y}}$
Sets	\forall x \not\in \varnothing \subseteq A \cap \bigcap B \cup \bigcup \exists \{x,y\} \times C	$\forall x\not \in \varnothing \subseteq A\cap \bigcap B\cup \bigcup \exists \{x,y\}\times C$
Logic	p \land \bar{q} \to p\lor \lnot q	$p\land {\bar {q}}\to p\lor \lnot q$
Root	\sqrt{2}\approx 1.4	${\sqrt {2}}\approx 1.4$
Root	\sqrt[n]{x}	${\sqrt[{n}]{x}}$
Relations	\sim \simeq \cong \le \ge \equiv \not\equiv \approx \ne \propto	$\sim \ \simeq \ \cong \ \leq \ \geq \ \equiv \ \not \equiv \ \approx \ \neq \ \propto$
Geometric	\triangle \angle \perp \\| 45^\circ	$\triangle \ \angle \perp \\|\ 45^{\circ }$
Arrows	\leftarrow \rightarrow \leftrightarrow \longleftarrow \longrightarrow \mapsto \longmapsto \nearrow \searrow \swarrow \nwarrow \uparrow \downarrow \updownarrow	$\leftarrow \ \rightarrow \ \leftrightarrow$ $\longleftarrow \ \longrightarrow$ $\mapsto \ \longmapsto$ $\nearrow \ \searrow \ \swarrow \ \nwarrow$ $\uparrow \ \downarrow \ \updownarrow$
Arrows	\Leftarrow \Rightarrow \Leftrightarrow \Longleftarrow \Longrightarrow \Longleftrightarrow \Uparrow \Downarrow \Updownarrow	$\Leftarrow \ \Rightarrow \ \Leftrightarrow$ $\Longleftarrow \ \Longrightarrow \ \Longleftrightarrow$ $\Uparrow \ \Downarrow \ \Updownarrow$
Special	\oplus \otimes \pm \mp \hbar \wr \dagger \ddagger \star * \ldots \circ \cdot \times \bullet \infty \vdash \models	$\oplus \otimes \pm \mp \hbar \wr \dagger \ddagger \star *\ldots$ $\circ \cdot \times \bullet \ \infty \ \vdash \ \models$
Lowercase \mathcal has some extras	\mathcal {45abcdenpqstuvwx}	${\mathcal {45abcdenpqstuvwx}}$

Subscripts, superscripts, integrals

Feature	Syntax	How it looks rendered
Superscript	a^2	$a^{2}$	$a^{2}\,\!$
Subscript	a_2	$a_{2}$	$a_{2}\,\!$
Grouping	a^{2+2}	$a^{2+2}$	$a^{2+2}\,\!$
Grouping	a_{i,j}	$a_{i,j}$	$a_{i,j}\,\!$
Combining sub & super	x_2^3	$x_{2}^{3}$
Derivative (good)	x'	$x'$	$x'\,\!$
Derivative (wrong in HTML)	x^\prime	$x^{\prime }$	$x^{\prime }\,\!$
Derivative (wrong in PNG)	x\prime	$x\prime$	$x\prime \,\!$
Derivative dots	\dot{x}, \ddot{x}	${\dot {x}},{\ddot {x}}$
Underlines & overlines	\hat a \bar b \vec c \widehat {d e f} \overline {g h i} \underline {j k l}	${\hat {a}}\ {\bar {b}}\ {\vec {c}}\ {\widehat {def}}\ {\overline {ghi}}\ {\underline {jkl}}$
Sum	\sum_{k=1}^N k^2	$\sum _{k=1}^{N}k^{2}$
Product	\prod_{i=1}^N x_i	$\prod _{i=1}^{N}x_{i}$
Limit	\lim_{n \to \infty}x_n	$\lim _{n\to \infty }x_{n}$
Integral	\int_{-N}^{N} e^x\, dx	$\int _{-N}^{N}e^{x}\,dx$
Line Integral	\oint_{C} x^3\, dx + 4y^2\, dy	$\oint _{C}x^{3}\,dx+4y^{2}\,dy$

Fractions, matrices, multilines

Feature

Syntax

How it looks rendered

Fractions

\frac{2}{4} or {2 \over 4}

{\frac {2}{4}}

Binomial coefficients

{n \choose k}

{n \choose k}

Small Fractions

\begin{matrix} \frac{2}{4} \end{matrix}

{\begin{matrix}{\frac {2}{4}}\end{matrix}}

Matrices

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

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

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

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

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

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

Case distinctions

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

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

Multiline equations

\begin{matrix}f(n+1) & = & (n+1)^2 \\ \ & = & n^2 + 2n + 1 \end{matrix}

{\begin{matrix}f(n+1)&=&(n+1)^{2}\\\ &=&n^{2}+2n+1\end{matrix}}

Alternative multiline equations (using tables)


{|
|-
|<math>f(n+1)</math>
|<math>=(n+1)^2</math>
|-
|
|<math>=n^2 + 2n + 1</math>
|}

$f(n+1)\,\!$	$=(n+1)^{2}\,\!$
	$=n^{2}+2n+1\,\!$

Fonts

Feature	Syntax	How it looks rendered
Greek letters	\alpha \beta \gamma \Gamma \phi \Phi \Psi\ \tau \Omega	$\alpha \ \beta \ \gamma \ \Gamma \ \phi \ \Phi \ \Psi \ \tau \ \Omega$
Blackboard bold	x\in\mathbb{R}\sub\mathbb{C}	$x\in \mathbb {R} \subset \mathbb {C}$
boldface (vectors)	\mathbf{x}\cdot\mathbf{y} = 0	$\mathbf {x} \cdot \mathbf {y} =0$
boldface (greek)	\boldsymbol{\alpha} + \boldsymbol{\beta} + \boldsymbol{\gamma}	${\boldsymbol {\alpha }}+{\boldsymbol {\beta }}+{\boldsymbol {\gamma }}$
Fraktur typeface	\mathfrak{a} \mathfrak{B}	${\mathfrak {a}}{\mathfrak {B}}$
Script	\mathcal{ABC}	${\mathcal {ABC}}$
Hebrew	\aleph \beth \gimel \daleth	$\aleph \ \beth \ \gimel \ \daleth$
non-italicised characters	\mbox{abc}	${\mbox{abc}}$	${\mbox{abc}}\,\!$
mixed italics (bad)	\mbox{if} n \mbox{is even}	${\mbox{if}}n{\mbox{is even}}$	${\mbox{if}}n{\mbox{is even}}\,\!$
mixed italics (good)	\mbox{if }n\mbox{ is even}	${\mbox{if }}n{\mbox{ is even}}$	${\mbox{if }}n{\mbox{ is even}}\,\!$

Parenthesizing big expressions, brackets, bars

Feature	Syntax	How it looks rendered
Not good	( \frac{1}{2} )	$({\frac {1}{2}})$
Better	\left ( \frac{1}{2} \right )	$\left({\frac {1}{2}}\right)$

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

Feature	Syntax	How it looks rendered
Parentheses	\left ( A \right )	$\left(A\right)$
Brackets	\left [ A \right ]	$\left[A\right]$
Braces	\left \{ A \right \}	$\left\{A\right\}$
Angle brackets	\left \langle A \right \rangle	$\left\langle A\right\rangle$
Bars and double bars	\left \| A \right \| and \left \\| B \right \\|	$\left\|A\right\|and\left\\|B\right\\|$
Delimiters can be mixed, as long as \left and \right match	\left [ 0,1 \right ) \left \langle \psi \right \|	$\left[0,1\right)$ $\left\langle \psi \right\|$
Use \left. and \right. if you don't want a delimiter to appear:	\left . \frac{A}{B} \right \} \to X	$\left.{\frac {A}{B}}\right\}\to X$

Spacing

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

Feature	Syntax	How it looks rendered
double quad space	a \qquad b	$a\qquad b$
quad space	a \quad b	$a\quad b$
text space	a\ b	$a\ b$
text space without PNG conversion	a \mbox{ } b	$a{\mbox{ }}b$
large space	a\;b	$a\;b$
medium space	a\>b	[not supported]
small space	a\,b	$a\,b$
no space	ab	$ab\,$
negative space	a\!b	$a\!b$

Align with normal text flow

If you desperately need to insert an expression like $\int _{-N}^{N}e^{x}\,dx$ in the normal text flow, you can use a HTML <font> tag for vertical alignment:

<font style="vertical-align:-100%;"><math>...</math></font>

Forced PNG rendering

If you must, it is possible to force the formula to render as PNG, without affecting the display of the formula, by adding \, (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 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:

Syntax	How it looks rendered
a^{2+2}	$a^{2+2}$
a^{2+2} \,	$a^{2+2}\,$
a^{\,\!2+2}	$a^{\,\!2+2}$
\int_{-N}^{N} e^x\, dx	$\int _{-N}^{N}e^{x}\,dx$
\int_{-N}^{N} e^x\, dx \,	$\int _{-N}^{N}e^{x}\,dx\,$
\int_{-N}^{N} e^x\, dx \,\!	$\int _{-N}^{N}e^{x}\,dx\,\!$