Help:TeX markup

Wikibooks uses TeX markup for mathematical formulas. It generates either PNG images or simple HTML markup, depending on user prefs 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 in between the corresponding inequality signs, where the ellipse are <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).

Discussion, bug reports and feature requests should go to the Wikitech-l mailing list or to Wikibooks:TeX requests.

For style issues regarding the typesetting of math, see the mathematics WikiProject. In particular, please avoid using this feature as part of a line of regular text, as the formulas don't align properly and the font is too large.

Regarding color, notice that this page is a special page (its name begins with "Wikibooks:") and has therefore a yellow background. Normal Wikibooks pages are white, just like the formulas, so don't worry. (this isn't true yet...)

Note: Math formulas using <math> ... </math> having special characters (with a \ at the start) in them are displayed in a larger font than math formulas without special characters in them. Because of this, multi-equation mathematical discussions could have an inconsistent mixture of large font and small font equations. In order to keep the font size consistent, one can put at least one special character in every equation, even if a special character is not needed otherwise, so that all the equations will be shown in the larger font. To do this with an equation that otherwise doesn't need a special character, insert   \,   right before </math>.    \, (backslash, comma) stands for a small space, which can be placed at the end of an equation with no visible effect except to enlarge the font size.

Special characters

Feature	Syntax	How it looks rendered
std. functions (good)	\sin x + \ln y +\operatorname{sgn} z	$\sin x+\ln y+\mathrm{sgn}z$
std. functions (wrong)	sin x + ln y + sgn z	$sinx+lny+sgnz$
Derivatives	\nabla \partial dx	$\mathrm{\nabla }\partial dx$
Sets	\forall x\not\in\empty\subseteq A\cap B\cup \exists \{x,y\} \times C	$\mathrm{\forall }x\in ̸\mathrm{\varnothing }\subseteq A\cap B\cup \mathrm{\exists }\{x,y\}\times C$
Logic	p\wedge \bar{q} \rightarrow p\vee \bar{q} \Rightarrow \Leftrightarrow	$p\wedge \overline{q}\to p\vee \overline{q}\Rightarrow \iff$
Root	\sqrt{2}\approx 1.4	$\sqrt{2}\approx 1.4$
	\sqrt[n]{x}	$\sqrt[n]{x}$
Relations	\sim \simeq \cong \le \ge \equiv \approx \ne	$\sim \simeq \cong \le \ge \equiv \approx \ne$
Geometric	\angle \perp \[pipe]	$\mathrm{\angle }\perp \Vert$
Special	\oplus \otimes \pm \mp \hbar \dagger \ddagger \star \circ \cdot \bullet \infty	$\oplus \otimes \pm \mp \hslash †‡\star \circ \cdot \bullet \mathrm{\infty }$

Subscripts, superscripts

Feature	Syntax	How it looks rendered
Superscript	a^2	$a^2$
Subscript	a_2	$a_2$
Accent	\dot{x}, \ddot{x}, \hat{x}, \bar{x}, \vec{x}, \tilde{x}	$\dot{x},\ddot{x},\hat{x},\overline{x},\overrightarrow{x},\tilde{x}$
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'	$x^{\prime }$
Derivative (wrong in HTML)	x^\prime	$x^{\prime }$
Derivative (wrong in PNG)	x\prime	$x\prime$
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	$\underset{n\to \mathrm{\infty }}{\lim }{x}_n$
Integral	\int_{-N}^{N} e^x\, dx	$\underset{-N}{\overset{N}{\int }}{e}^{x}dx$
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}	$(\genfrac{}{}{0ex}{}{n}{k})$
Matrices	\begin{pmatrix} x & y \\ z & v \end{pmatrix}	$\left(\begin{array}{cc}x& y\\ z& v\end{array}\right)$
	\begin{bmatrix} 0 & \cdots & 0 \\ \vdots & \ddots & \vdots \\ 0 & \cdots & 0\end{bmatrix}	$\left[\begin{array}{ccc}0& \cdots & 0\\ ⋮& \ddots & ⋮\\ 0& \cdots & 0\end{array}\right]$
	\begin{Bmatrix} x & y \\ z & v \end{Bmatrix}	$\left\{\begin{array}{cc}x& y\\ z& v\end{array}\right\}$
	\begin{vmatrix} x & y \\ z & v \end{vmatrix}	$\left|\begin{array}{cc}x& y\\ z& v\end{array}\right|$
	\begin{Vmatrix} x & y \\ z & v \end{Vmatrix}	$\Vert \begin{array}{cc}x& y\\ z& v\end{array}\Vert$
	\begin{matrix} x & y \\ z & v \end{matrix}	$\begin{array}{cc}x& y\\ z& v\end{array}$
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.	$f(n)=\{\begin{array}{cc}n/2,& \text{if }n\text{ is even}\\ 3n+1,& \text{if }n\text{ is odd}\end{array}$
Multiline equations	\begin{matrix}f(n+1)&=& (n+1)^2 \\ \ & =& n^2 + 2n + 1\end{matrix}	$\begin{array}{ccc}f(n+1)& =& (n+1{)}^2\\ & =& n^2+2n+1\end{array}$

Fonts

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

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	$⟨A⟩$
Bars	A \right|	$\left|A\right|$
Use \left. and \right. if you don't want a delimiter to appear:	\left. {A \over B} \right\} \to X	$\frac{A}{B}\}\to X$

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	$ab$
quad space	a \quad b	$ab$
text space	a\ b	$ab$
large space	a\;b	$ab$
medium space	a\>b	[not supported]
small space	a\,b	$ab$
no space	ab	$ab$
negative space	a\!b	$ab$

See also:

• Large tutorial at Meta
• Proposed GNU LilyPond support
• Category:RenderPNG

External Links

• A PDF document introducing TeX -- see page 39 onwards for a good introduction to the maths side of things: http://www.ctan.org/tex-archive/info/gentle/gentle.pdf
• Complete reference list of symbols: http://wso.williams.edu/how/lshort2e/node61.html
• Can't remember but I put it here so it must be ok ;-) http://www.ams.org/tex/amslatex.html
• A set of public domain fixed-size math symbol bitmaps: http://us.metamath.org/symbols/symbols.html