MA Help:Math markup

Contents → Math markup

MediaWiki uses LaTeX markup to render mathematical formulas as SVG images. LaTeX markup goes inside <math> ... </math> tags. 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).

This page contains selected examples of math markup that can be used in Memory Alpha articles. For more detailed information, see Help:Displaying a formula at Wikipedia.

Special characters[]

Feature	Syntax	How it looks rendered
std. functions (good)	\sin x + \ln y + \sgn z	$\sin x + \ln y +\operatorname{sgn} z$
std. functions (wrong)	sin x + ln y + sgn z	$sin x + ln y + sgn z$
Modular arithmetic	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 \exists \empty \emptyset \varnothing	$\forall \exists \empty \emptyset \varnothing$
	\in \ni \not \in \notin \subset \subseteq \supset \supseteq	$\in \ni \not \in \notin \subset \subseteq \supset \supseteq$
	\cap \bigcap \cup \bigcup \biguplus \setminus \smallsetminus	$\cap \bigcap \cup \bigcup \biguplus \setminus \smallsetminus$
Logic	p \land \bar{q} \to p\lor \lnot q	$p \land \bar{q} \to p\lor \lnot q$
Roots	\sqrt{2}\approx 1.4	$\sqrt{2}\approx 1.4$
Roots	\sqrt[n]{x}	$\sqrt[n]{x}$
Relations	\sim \simeq \cong \le \ge \equiv \not\equiv \approx \ne	$\sim \ \simeq \ \cong \ \le \ \ge \ \equiv \ \not\equiv \ \approx \ \ne$
Geometric	\Diamond \Box \triangle \angle \perp \mid \nmid \\| 45^\circ	$\Diamond \Box \triangle \angle \perp \mid \nmid \\| 45^\circ$
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 \dagger \ddagger \star \circ \cdot \times \bullet \infty \ell \mho \Finv \Re \Im \wp \complement \diamondsuit \heartsuit \clubsuit \spadesuit \Game \flat \natural \sharp	${\displaystyle \oplus \otimes \pm \mp \hbar \dagger \ddagger \star \circ \cdot \times \bullet\ \infty}$ $\ell \mho \Finv \Re \Im \wp \complement \diamondsuit \heartsuit \clubsuit \spadesuit \Game \flat \natural \sharp$

Subscripts and superscripts[]

Feature	Syntax	How it looks rendered
Superscript	a^2	$a^2$
Subscript	a_2	$a_2$
Grouping	a^{2+2}	$a^{2+2}$
Grouping	a_{i,j}	$a_{i,j}$
Combining sub & super	x_2^3	$x_2^3$
Derivative (good)	x'	$x'$
Underlines and overlines	\hat a \bar b \vec c \widehat {d e f} \overline {g h i} \underline {j k l}	$\hat a \ \bar b \ \vec c \ \widehat {d e f} \ \overline {g h i} \ \underline {j k l}$
Arrows	A \xleftarrow{n+\mu-1} B \xrightarrow[T]{n\pm i-1} C	$A \xleftarrow{n+\mu-1} B \xrightarrow[T]{n\pm i-1} C$
Overbraces	\overbrace{ 1+2+\cdots+100 }^{5050}	$\overbrace{ 1+2+\cdots+100 }^{5050}$
Underbraces	\underbrace{ a+b+\cdots+z }_{26}	$\underbrace{ a+b+\cdots+z }_{26}$
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	${\displaystyle \int_{-N}^{N} e^x\, dx }$
Line Integral	\oint_{C} x^3\, dx + 4y^2\, dy	$\oint_{C} x^3\, dx + 4y^2\, dy$

Fractions, matrices, and multilines[]

Feature	Syntax	How it looks rendered
Fractions	\frac{2}{4} or {2 \over 4}	$\frac{2}{4}$
Binomial coefficients	{n \choose k}	${n \choose k}$
Matrices	\begin{pmatrix} x & y \\ z & v \end{pmatrix}	${\displaystyle \begin{pmatrix} x & y \\ z & v \end{pmatrix}}$
	\begin{bmatrix} 0 & \cdots & 0 \\ \vdots & \ddots & \vdots \\ 0 & \cdots & 0\end{bmatrix}	${\displaystyle \begin{bmatrix} 0 & \cdots & 0 \\ \vdots & \ddots & \vdots \\ 0 & \cdots & 0\end{bmatrix} }$
	\begin{Bmatrix} x & y \\ z & v \end{Bmatrix}	${\displaystyle \begin{Bmatrix} x & y \\ z & v \end{Bmatrix}}$
	\begin{vmatrix} x & y \\ z & v \end{vmatrix}	${\displaystyle \begin{vmatrix} x & y \\ z & v \end{vmatrix}}$
	\begin{Vmatrix} x & y \\ z & v \end{Vmatrix}	${\displaystyle \begin{Vmatrix} x & y \\ z & v \end{Vmatrix}}$
	\begin{matrix} x & y \\ z & v \end{matrix}	${\displaystyle \begin{matrix} x & y \\ z & v \end{matrix}}$
Case distinctions	f(n) = \left \{ \begin{matrix} n/2, & \mbox{if }n\mbox{ is even} \\ 3n+1, & \mbox{if }n\mbox{ is odd} \end{matrix} \right.	$f(n) = \left \{ \begin{matrix} n/2, & \mbox{if }n\mbox{ is even} \\ 3n+1, & \mbox{if }n\mbox{ is odd} \end{matrix} \right.$
Multiline equations	\begin{matrix}f(n+1) & = & (n+1)^2 \\ \ & = & n^2 + 2n + 1 \end{matrix}	$\begin{matrix}f(n+1)&=& (n+1)^2 \\ \ & =& n^2 + 2n + 1\end{matrix}$

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-italicized characters	\mbox{abc}	$\mbox{abc}$
Mixed italics (bad)	\mbox{if} n \mbox{is even}	$\mbox{if} n \mbox{is even}$
Mixed italics (good)	\mbox{if }n\mbox{ is even}	$\mbox{if }n\mbox{ is even}$

Parenthesizing big expressions[]

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	$a\ b$
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	$a\!b$

External links[]

LaTeX at Wikipedia
A Gentle Introduction to TeX at The CTAN archive – a PDF document introducing TeX; see page 39 onward for a good introduction to the math side of things
The Comprehensive LaTeX Symbol List at The CTAN archive – a complete list of symbols available in LaTeX

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