# Help:Math markup

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MediaWiki uses LaTeX markup to render mathematical formulas. It generates either PNG images or simple HTML markup, depending on user preferences and the complexity of the expression. Alternatively, if you are using an advanced browser like Mozilla or Mozilla Firefox, MediaWiki can generate enhanced HTML or even MathML in most cases.

Math markup goes inside $...$ 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).

Note that PNG images use font sizes and types independent of browser settings. Therefore, in most cases these deviate from what HTML renders (the latter does depend on browser settings). Please avoid using TeX markup as part of a line of regular text, as the formulas don't align properly and the font size, as said, usually does not match. Additionally, the background color of the PNG images cannot be changed by the user.

Following are some selected examples of math markup that can be used in Memory Alpha articles. For more detailed information, see Displaying a formula on Wikipedia.

## Special characters Edit

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 $sin x + ln y + sgn z\,$
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 $\sqrt{2}\approx 1.4$
\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

$\leftarrow\ \rightarrow\ \leftrightarrow$
$\longleftarrow\ \longrightarrow$
$\mapsto\ \longmapsto$
$\nearrow\ \searrow\ \swarrow\ \nwarrow$
$\uparrow\ \downarrow\ \updownarrow$

\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

$\oplus \otimes \pm \mp \hbar \dagger \ddagger \star \circ \cdot \times \bullet\ \infty$
$\ell \mho \Finv \Re \Im \wp \complement \diamondsuit \heartsuit \clubsuit \spadesuit \Game \flat \natural \sharp$

## Subscripts and superscripts Edit

Feature Syntax How it looks rendered
Superscript a^2 $a^2$
Subscript a_2 $a_2$
Grouping a^{2+2} $a^{2+2}$
a_{i,j} $a_{i,j}$
Combining sub & super x_2^3 $x_2^3$
Derivative (good) x' $x'$
Derivative (wrong in HTML) x^\prime $x^\prime$
Derivative (wrong in PNG) x\prime $x\prime$
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 $\int_{-N}^{N} e^x\, dx$
Line Integral \oint_{C} x^3\, dx + 4y^2\, dy $\oint_{C} x^3\, dx + 4y^2\, dy$

## Fractions, matrices and multilines Edit

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} $\begin{pmatrix} x & y \\ z & v \end{pmatrix}$
\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{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{matrix} x & y \\ z & v \end{matrix} $\begin{matrix} x & y \\ z & v \end{matrix}$
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 Edit

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 Edit

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 Edit

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 $a\!b$

## Forced PNG rendering Edit

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 and negative space, which cancel out) somewhere inside the math tags (probably at the end).

This could be useful to keep the rendering of formulas in a proof consistent, for example, or to fix formulas that render incorrectly in HTML (x prime, or a^{2+2}), 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} \,\! $a^{2+2} \,\!$
\int_{-N}^{N} e^x\, dx $\int_{-N}^{N} e^x\, dx$
\int_{-N}^{N} e^x\, dx \,\! $\int_{-N}^{N} e^x\, dx \,\!$

This has been tested with most of the formulas 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.-->