MA Help:Math markup

Help 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	$\sin x + \ln y +\operatorname{sgn} z$ {\displaystyle \sin x+\ln y+\operatorname {sgn} z}
std. functions (wrong)	sin x + ln y + sgn z	$sin x + ln y + sgn z$ {\displaystyle sinx+lny+sgnz}
Modular arithmetic	s_k \equiv 0 \pmod{m}	$s_k \equiv 0 \pmod{m}$ {\displaystyle s_{k}\equiv 0{\pmod {m}}}
Derivatives	\nabla \partial x dx \dot x \ddot y	$\nabla \ \partial x \ dx \ \dot x\ \ddot y$ {\displaystyle \nabla \ \partial x\ dx\ {\dot {x}}\ {\ddot {y}}}
Sets	\forall \exists \empty \emptyset \varnothing	$\forall \exists \empty \emptyset \varnothing$ {\displaystyle \forall \exists \emptyset \emptyset \varnothing }
	\in \ni \not \in \notin \subset \subseteq \supset \supseteq	$\in \ni \not \in \notin \subset \subseteq \supset \supseteq$ {\displaystyle \in \ni \not \in \notin \subset \subseteq \supset \supseteq }
	\cap \bigcap \cup \bigcup \biguplus \setminus \smallsetminus	$\cap \bigcap \cup \bigcup \biguplus \setminus \smallsetminus$ {\displaystyle \cap \bigcap \cup \bigcup \biguplus \setminus \smallsetminus }
Logic	p \land \bar{q} \to p\lor \lnot q	$p \land \bar{q} \to p\lor \lnot q$ {\displaystyle p\land {\bar {q}}\to p\lor \lnot q}
Roots	\sqrt{2}\approx 1.4	$\sqrt{2}\approx 1.4$ {\displaystyle {\sqrt {2}}\approx 1.4}
Roots	\sqrt[n]{x}	$\sqrt[n]{x}$ {\displaystyle {\sqrt[{n}]{x}}}
Relations	\sim \simeq \cong \le \ge \equiv \not\equiv \approx \ne	$\sim \ \simeq \ \cong \ \le \ \ge \ \equiv \ \not\equiv \ \approx \ \ne$ {\displaystyle \sim \ \simeq \ \cong \ \leq \ \geq \ \equiv \ \not \equiv \ \approx \ \neq }
Geometric	\Diamond \Box \triangle \angle \perp \mid \nmid \\| 45^\circ	$\Diamond \Box \triangle \angle \perp \mid \nmid \\| 45^\circ$ {\displaystyle \Diamond \Box \triangle \angle \perp \mid \nmid \\|45^{\circ }}
Arrows	\leftarrow \rightarrow \leftrightarrow \longleftarrow \longrightarrow \mapsto \longmapsto \nearrow \searrow \swarrow \nwarrow \uparrow \downarrow \updownarrow	$\leftarrow\ \rightarrow\ \leftrightarrow$ {\displaystyle \leftarrow \ \rightarrow \ \leftrightarrow } $\longleftarrow\ \longrightarrow$ {\displaystyle \longleftarrow \ \longrightarrow } $\mapsto\ \longmapsto$ {\displaystyle \mapsto \ \longmapsto } $\nearrow\ \searrow\ \swarrow\ \nwarrow$ {\displaystyle \nearrow \ \searrow \ \swarrow \ \nwarrow } $\uparrow\ \downarrow\ \updownarrow$ {\displaystyle \uparrow \ \downarrow \ \updownarrow }
Arrows	\Leftarrow \Rightarrow \Leftrightarrow \Longleftarrow \Longrightarrow \Longleftrightarrow \Uparrow \Downarrow \Updownarrow	$\Leftarrow\ \Rightarrow\ \Leftrightarrow$ {\displaystyle \Leftarrow \ \Rightarrow \ \Leftrightarrow } $\Longleftarrow\ \Longrightarrow\ \Longleftrightarrow$ {\displaystyle \Longleftarrow \ \Longrightarrow \ \Longleftrightarrow } $\Uparrow\ \Downarrow\ \Updownarrow$ {\displaystyle \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	${\displaystyle \oplus \otimes \pm \mp \hbar \dagger \ddagger \star \circ \cdot \times \bullet\ \infty}$ {\displaystyle \oplus \otimes \pm \mp \hbar \dagger \ddagger \star \circ \cdot \times \bullet \ \infty } $\ell \mho \Finv \Re \Im \wp \complement \diamondsuit \heartsuit \clubsuit \spadesuit \Game \flat \natural \sharp$ {\displaystyle \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	$a^2$ {\displaystyle a^{2}}
Subscript	a_2	$a_2$ {\displaystyle a_{2}}
Grouping	a^{2+2}	$a^{2+2}$ {\displaystyle a^{2+2}}
Grouping	a_{i,j}	$a_{i,j}$ {\displaystyle a_{i,j}}
Combining sub & super	x_2^3	$x_2^3$ {\displaystyle x_{2}^{3}}
Derivative (good)	x'	$x'$ {\displaystyle x'}
Underlines and overlines	\hat a \bar b \vec c \widehat {d e f} \overline {g h i} \underline {j k l}	$\hat a \ \bar b \ \vec c \ \widehat {d e f} \ \overline {g h i} \ \underline {j k l}$ {\displaystyle {\hat {a}}\ {\bar {b}}\ {\vec {c}}\ {\widehat {def}}\ {\overline {ghi}}\ {\underline {jkl}}}
Arrows	A \xleftarrow{n+\mu-1} B \xrightarrow[T]{n\pm i-1} C	$A \xleftarrow{n+\mu-1} B \xrightarrow[T]{n\pm i-1} C$ {\displaystyle A\xleftarrow {n+\mu -1} B{\xrightarrow[{T}]{n\pm i-1}}C}
Overbraces	\overbrace{ 1+2+\cdots+100 }^{5050}	$\overbrace{ 1+2+\cdots+100 }^{5050}$ {\displaystyle \overbrace {1+2+\cdots +100} ^{5050}}
Underbraces	\underbrace{ a+b+\cdots+z }_{26}	$\underbrace{ a+b+\cdots+z }_{26}$ {\displaystyle \underbrace {a+b+\cdots +z} _{26}}
Sum	\sum_{k=1}^N k^2	$\sum_{k=1}^N k^2$ {\displaystyle \sum _{k=1}^{N}k^{2}}
Product	\prod_{i=1}^N x_i	$\prod_{i=1}^N x_i$ {\displaystyle \prod _{i=1}^{N}x_{i}}
Limit	\lim_{n \to \infty}x_n	$\lim_{n\to\infty}x_n$ {\displaystyle \lim _{n\to \infty }x_{n}}
Integral	\int_{-N}^{N} e^x,円 dx	${\displaystyle \int_{-N}^{N} e^x,円 dx }$ {\displaystyle \int _{-N}^{N}e^{x},円dx}
Line Integral	\oint_{C} x^3,円 dx + 4y^2,円 dy	$\oint_{C} x^3,円 dx + 4y^2,円 dy$ {\displaystyle \oint _{C}x^{3},円dx+4y^{2},円dy}

Fractions, matrices, and multilines[ ]

Feature	Syntax	How it looks rendered
Fractions	\frac{2}{4} or {2 \over 4}	$\frac{2}{4}$ {\displaystyle {\frac {2}{4}}}
Binomial coefficients	{n \choose k}	${n \choose k}$ {\displaystyle {n \choose k}}
Matrices	\begin{pmatrix} x & y \\ z & v \end{pmatrix}	${\displaystyle \begin{pmatrix} x & y \\ z & v \end{pmatrix}}$ {\displaystyle {\begin{pmatrix}x&y\\z&v\end{pmatrix}}}
	\begin{bmatrix} 0 & \cdots & 0 \\ \vdots & \ddots & \vdots \\ 0 & \cdots & 0\end{bmatrix}	${\displaystyle \begin{bmatrix} 0 & \cdots & 0 \\ \vdots & \ddots & \vdots \\ 0 & \cdots & 0\end{bmatrix} }$ {\displaystyle {\begin{bmatrix}0&\cdots &0\\\vdots &\ddots &\vdots \0円&\cdots &0\end{bmatrix}}}
	\begin{Bmatrix} x & y \\ z & v \end{Bmatrix}	${\displaystyle \begin{Bmatrix} x & y \\ z & v \end{Bmatrix}}$ {\displaystyle {\begin{Bmatrix}x&y\\z&v\end{Bmatrix}}}
	\begin{vmatrix} x & y \\ z & v \end{vmatrix}	${\displaystyle \begin{vmatrix} x & y \\ z & v \end{vmatrix}}$ {\displaystyle {\begin{vmatrix}x&y\\z&v\end{vmatrix}}}
	\begin{Vmatrix} x & y \\ z & v \end{Vmatrix}	${\displaystyle \begin{Vmatrix} x & y \\ z & v \end{Vmatrix}}$ {\displaystyle {\begin{Vmatrix}x&y\\z&v\end{Vmatrix}}}
	\begin{matrix} x & y \\ z & v \end{matrix}	${\displaystyle \begin{matrix} x & y \\ z & v \end{matrix}}$ {\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.	$f(n) = \left \{ \begin{matrix} n/2, & \mbox{if }n\mbox{ is even} \\ 3n+1, & \mbox{if }n\mbox{ is odd} \end{matrix} \right.$ {\displaystyle f(n)=\left\{{\begin{matrix}n/2,&{\mbox{if }}n{\mbox{ is even}}\3円n+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}	$\begin{matrix}f(n+1)&=& (n+1)^2 \\ \ & =& n^2 + 2n + 1\end{matrix}$ {\displaystyle {\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	$\alpha\ \beta\ \gamma\ \Gamma\ \phi\ \Phi\ \Psi\ \tau\ \Omega$ {\displaystyle \alpha \ \beta \ \gamma \ \Gamma \ \phi \ \Phi \ \Psi \ \tau \ \Omega }
Blackboard bold	x\in\mathbb{R}\sub\mathbb{C}	$x\in\mathbb{R}\subset\mathbb{C}$ {\displaystyle x\in \mathbb {R} \subset \mathbb {C} }
Boldface (vectors)	\mathbf{x}\cdot\mathbf{y} = 0	$\mathbf{x}\cdot\mathbf{y} = 0$ {\displaystyle \mathbf {x} \cdot \mathbf {y} =0}
Boldface (Greek)	\boldsymbol{\alpha} + \boldsymbol{\beta} + \boldsymbol{\gamma}	$\boldsymbol{\alpha} + \boldsymbol{\beta} + \boldsymbol{\gamma}$ {\displaystyle {\boldsymbol {\alpha }}+{\boldsymbol {\beta }}+{\boldsymbol {\gamma }}}
Fraktur typeface	\mathfrak{a} \mathfrak{B}	$\mathfrak{a} \mathfrak{B}$ {\displaystyle {\mathfrak {a}}{\mathfrak {B}}}
Script	\mathcal{ABC}	$\mathcal{ABC}$ {\displaystyle {\mathcal {ABC}}}
Hebrew	\aleph \beth \gimel \daleth	$\aleph\ \beth\ \gimel\ \daleth$ {\displaystyle \aleph \ \beth \ \gimel \ \daleth }
Non-italicized characters	\mbox{abc}	$\mbox{abc}$ {\displaystyle {\mbox{abc}}}
Mixed italics (bad)	\mbox{if} n \mbox{is even}	$\mbox{if} n \mbox{is even}$ {\displaystyle {\mbox{if}}n{\mbox{is even}}}
Mixed italics (good)	\mbox{if }n\mbox{ is even}	$\mbox{if }n\mbox{ is even}$ {\displaystyle {\mbox{if }}n{\mbox{ is even}}}

Parenthesizing big expressions[ ]

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

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

Feature	Syntax	How it looks rendered
Parentheses	\left ( A \right )	$\left ( A \right )$ {\displaystyle \left(A\right)}
Brackets	\left [ A \right ]	$\left [ A \right ]$ {\displaystyle \left[A\right]}
Braces	\left \{ A \right \}	$\left \{ A \right \}$ {\displaystyle \left\{A\right\}}
Angle brackets	\left \langle A \right \rangle	$\left \langle A \right \rangle$ {\displaystyle \left\langle A\right\rangle }
Bars and double bars	\left \| A \right \| and \left \\| B \right \\|	$\left \| A \right \| and \left \\| B \right \\|$ {\displaystyle \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 \|	$\left [ 0,1 \right )$ {\displaystyle \left[0,1\right)} $\left \langle \psi \right \|$ {\displaystyle \left\langle \psi \right\|}
Use \left. and \right. if you don't want a delimiter to appear	\left . \frac{A}{B} \right \} \to X	$\left . \frac{A}{B} \right \} \to X$ {\displaystyle \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	$a \qquad b$ {\displaystyle a\qquad b}
quad space	a \quad b	$a \quad b$ {\displaystyle a\quad b}
text space	a\ b	$a\ b$ {\displaystyle a\ b}
large space	a\;b	$a\;b$ {\displaystyle a\;b}
medium space	a\>b	[not supported]
small space	a,円b	$a,円b$ {\displaystyle a,円b}
no space	ab	$ab,円$ {\displaystyle ab,円}
negative space	a\!b	$a\!b$ {\displaystyle 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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