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→Functions, symbols, special characters
For a little more semantics on these symbols, see the brief [http://www.math.upenn.edu/tex-stuff/cookbook.pdf TeX Cookbook].
For a little more semantics on these symbols, see the brief [http://www.math.upenn.edu/tex-stuff/cookbook.pdf TeX Cookbook].
== Larger expressions ==
=== Subscripts, superscripts, integrals ===
{| class="wikitable" border="1" cellspacing="0" cellpadding="4" style="border-collapse:collapse"
|-
! Feature !! Syntax !! How it looks rendered
|-
| Superscript
| <source lang="text" enclose="none">a^2</source> || <math>a^2</math>
|-
| Subscript
| <source lang="text" enclose="none">a_2</source> || <math>a_2</math>
|-
| rowspan="2"| Grouping
| <source lang="text" enclose="none">10^{30} a^{2+2}</source> || <math>10^{30} a^{2+2}</math>
|-
| <source lang="text" enclose="none">a_{i,j} b_{f'}</source> || <math>a_{i,j} b_{f'}</math>
|-
| rowspan="2"| Combining sub & super without and with horizontal separation
| <source lang="text" enclose="none">x_2^3</source> || <math>x_2^3</math>
|-
| <source lang="text" enclose="none">{x_2}^3</source> || <math>{x_2}^3 \,\!</math>
|-
| Super super
| <source lang="text" enclose="none">10^{10^{8}}</source> || <math>10^{10^{8}}</math>
|-
| rowspan="2"| Preceding and/or additional sub & super
| <source lang="text" enclose="none">\sideset{_1^2}{_3^4}\prod_a^b</source> || <math>\sideset{_1^2}{_3^4}\prod_a^b</math>
|-
| <source lang="text" enclose="none">{}_1^2\!\Omega_3^4</source> || <math>{}_1^2\!\Omega_3^4</math>
|-
| rowspan="4"| Stacking
| <source lang="text" enclose="none">\overset{\alpha}{\omega}</source> || <math>\overset{\alpha}{\omega}</math>
|-
| <source lang="text" enclose="none">\underset{\alpha}{\omega}</source> || <math>\underset{\alpha}{\omega}</math>
|-
| <source lang="text" enclose="none">\overset{\alpha}{\underset{\gamma}{\omega}}</source> || <math>\overset{\alpha}{\underset{\gamma}{\omega}}</math>
|-
| <source lang="text" enclose="none">\stackrel{\alpha}{\omega}</source> || <math>\stackrel{\alpha}{\omega}</math>
|-
| rowspan="2"| Derivatives
| <source lang="text" enclose="none">x', y'', f', f''</source> || <math>x', y'', f', f''</math>
|-
| <source lang="text" enclose="none">x^\prime, y^{\prime\prime}</source> || <math>x^\prime, y^{\prime\prime}</math>
|-
| Derivative dots
| <source lang="text" enclose="none">\dot{x}, \ddot{x}</source> || <math>\dot{x}, \ddot{x}</math>
|-
| rowspan="3"| Underlines, overlines, vectors
| <source lang="text" enclose="none">\hat a \ \bar b \ \vec c</source> || <math> \hat a \ \bar b \ \vec c</math>
|-
| <source lang="text" enclose="none">\overrightarrow{a b} \ \overleftarrow{c d} \ \widehat{d e f}</source> || <math> \overrightarrow{a b} \ \overleftarrow{c d} \ \widehat{d e f}</math>
|-
| <source lang="text" enclose="none">\overline{g h i} \ \underline{j k l}</source> || <math> \overline{g h i} \ \underline{j k l}</math>
|-
| Arc (workaround)
| <source lang="text" enclose="none">\overset{\frown} {AB}</source> || <math>\overset{\frown} {AB}</math>
|-
| Arrows
| <source lang="text" enclose="none"> A \xleftarrow{n+\mu-1} B \xrightarrow[T]{n\pm i-1} C</source> || <math> A \xleftarrow{n+\mu-1} B \xrightarrow[T]{n\pm i-1} C</math>
|-
| Overbraces
| <source lang="text" enclose="none">\overbrace{ 1+2+\cdots+100 }^{5050}</source> || <math>\overbrace{ 1+2+\cdots+100 }^{5050}</math>
|-
| Underbraces
| <source lang="text" enclose="none">\underbrace{ a+b+\cdots+z }_{26}</source> || <math>\underbrace{ a+b+\cdots+z }_{26}</math>
|-
| Sum
| <source lang="text" enclose="none">\sum_{k=1}^N k^2</source> || <math>\sum_{k=1}^N k^2</math>
|-
| Sum (force <source lang="text" enclose="none">\textstyle</source>)
| <source lang="text" enclose="none">\textstyle \sum_{k=1}^N k^2 </source> || <math>\textstyle \sum_{k=1}^N k^2</math>
|-
| Sum in a fraction (default <source lang="text" enclose="none">\textstyle</source>)
| <source lang="text" enclose="none">\frac{\sum_{k=1}^N k^2}{a}</source> || <math>\frac{\sum_{k=1}^N k^2}{a}</math>
|-
| Sum in a fraction (force <source lang="text" enclose="none">\displaystyle</source>)
| <source lang="text" enclose="none">\frac{\displaystyle \sum_{k=1}^N k^2}{a}</source> || <math>\frac{\displaystyle \sum_{k=1}^N k^2}{a}</math>
|-
| Sum in a fraction (alternative limits style)
| <source lang="text" enclose="none">\frac{\sum\limits^{^N}_{k=1} k^2}{a}</source> || <math>\frac{\sum\limits^{^N}_{k=1} k^2}{a}</math>
|-
| Product
| <source lang="text" enclose="none">\prod_{i=1}^N x_i</source> || <math>\prod_{i=1}^N x_i</math>
|-
| Product (force <source lang="text" enclose="none">\textstyle</source>)
| <source lang="text" enclose="none">\textstyle \prod_{i=1}^N x_i</source> || <math>\textstyle \prod_{i=1}^N x_i</math>
|-
| Coproduct
| <source lang="text" enclose="none">\coprod_{i=1}^N x_i</source> || <math>\coprod_{i=1}^N x_i</math>
|-
| Coproduct (force <source lang="text" enclose="none">\textstyle</source>)
| <source lang="text" enclose="none">\textstyle \coprod_{i=1}^N x_i</source> || <math>\textstyle \coprod_{i=1}^N x_i</math>
|-
| Limit
| <source lang="text" enclose="none">\lim_{n \to \infty}x_n</source> || <math>\lim_{n \to \infty}x_n</math>
|-
| Limit (force <source lang="text" enclose="none">\textstyle</source>)
| <source lang="text" enclose="none">\textstyle \lim_{n \to \infty}x_n</source> || <math>\textstyle \lim_{n \to \infty}x_n</math>
|-
| Integral
| <source lang="text" enclose="none">\int\limits_{1}^{3}\frac{e^3/x}{x^2}\, dx</source> || <math>\int\limits_{1}^{3}\frac{e^3/x}{x^2}\, dx</math>
|-
| Integral (alternative limits style)
| <source lang="text" enclose="none">\int_{1}^{3}\frac{e^3/x}{x^2}\, dx</source> || <math>\int_{1}^{3}\frac{e^3/x}{x^2}\, dx</math>
|-
| Integral (force <source lang="text" enclose="none">\textstyle</source>)
| <source lang="text" enclose="none">\textstyle \int\limits_{-N}^{N} e^x\, dx</source> || <math>\textstyle \int\limits_{-N}^{N} e^x\, dx</math>
|-
| Integral (force <source lang="text" enclose="none">\textstyle</source>, alternative limits style)
| <source lang="text" enclose="none">\textstyle \int_{-N}^{N} e^x\, dx</source> || <math>\textstyle \int_{-N}^{N} e^x\, dx</math>
|-
| Double integral
| <source lang="text" enclose="none">\iint\limits_D \, dx\,dy</source> || <math>\iint\limits_D \, dx\,dy</math>
|-
| Triple integral
| <source lang="text" enclose="none">\iiint\limits_E \, dx\,dy\,dz</source> || <math>\iiint\limits_E \, dx\,dy\,dz</math>
|-
| Quadruple integral
| <source lang="text" enclose="none">\iiiint\limits_F \, dx\,dy\,dz\,dt</source> || <math>\iiiint\limits_F \, dx\,dy\,dz\,dt</math>
|-
| Line or path integral
| <source lang="text" enclose="none">\int_{(x,y)\in C} x^3\, dx + 4y^2\, dy</source> || <math>\int_{(x,y)\in C} x^3\, dx + 4y^2\, dy</math>
|-
| Closed line or path integral
| <source lang="text" enclose="none">\oint_{(x,y)\in C} x^3\, dx + 4y^2\, dy</source> || <math>\oint_{(x,y)\in C} x^3\, dx + 4y^2\, dy</math>
|-
| Intersections
| <source lang="text" enclose="none">\bigcap_{i=_1}^n E_i</source> || <math>\bigcap_{i=_1}^n E_i</math>
|-
| Unions
| <source lang="text" enclose="none">\bigcup_{i=_1}^n E_i</source> || <math>\bigcup_{i=_1}^n E_i</math>
|}
=== Fractions, matrices, multilines ===
{| class="wikitable"
! Feature
! Syntax
! How it looks rendered
|-
| Fractions
| <source lang="text" enclose="none">\frac{2}{4}=0.5</source> or <source lang="text" enclose="none">{2 \over 4}=0.5</source>
| <math>\frac{2}{4}=0.5</math>
|-
| Small fractions
| <source lang="text" enclose="none">\tfrac{2}{4} = 0.5</source>
| <math>\tfrac{2}{4} = 0.5</math>
|-
| Large (normal) fractions
| <source lang="text" enclose="none">\dfrac{2}{4} = 0.5 \qquad \dfrac{2}{c + \dfrac{2}{d + \dfrac{2}{4}}} = a </source>
| <math>\dfrac{2}{4} = 0.5 \qquad \dfrac{2}{c + \dfrac{2}{d + \dfrac{2}{4}}} = a</math>
|-
| Large (nested) fractions
| <source lang="text" enclose="none">\cfrac{2}{c + \cfrac{2}{d + \cfrac{2}{4}}} = a</source>
| <math>\cfrac{2}{c + \cfrac{2}{d + \cfrac{2}{4}}} = a</math>
|-
| Cancellations in fractions<br>Note does not work with MathJax
| <source lang="text" enclose="none">\cfrac{x}{1 + \cfrac{\cancel{y}}{\cancel{y}}} = \cfrac{x}{2}</source>
| <math>\cfrac{x}{1 + \cfrac{\cancel{y}}{\cancel{y}}} = \cfrac{x}{2}</math>
|-
| Binomial coefficients
| <source lang="text" enclose="none">\binom{n}{k}</source>
| <math>\binom{n}{k}</math>
|-
| Small binomial coefficients
| <source lang="text" enclose="none">\tbinom{n}{k}</source>
| <math>\tbinom{n}{k}</math>
|-
| Large (normal) binomial coefficients
| <source lang="text" enclose="none">\dbinom{n}{k}</source>
| <math>\dbinom{n}{k}</math>
|-
| rowspan="7" | Matrices
| <source lang="latex">\begin{matrix}
x & y \\
z & v
\end{matrix}</source>
| <math>\begin{matrix}
x & y \\
z & v
\end{matrix}</math>
|-
| <source lang="latex">\begin{vmatrix}
x & y \\
z & v
\end{vmatrix}</source>
| <math>\begin{vmatrix}
x & y \\
z & v
\end{vmatrix}</math>
|-
| <source lang="latex">\begin{Vmatrix}
x & y \\
z & v
\end{Vmatrix}</source>
| <math>\begin{Vmatrix}
x & y \\
z & v
\end{Vmatrix}</math>
|-
| <source lang="latex">\begin{bmatrix}
0 & \cdots & 0 \\
\vdots & \ddots & \vdots \\
0 & \cdots & 0
\end{bmatrix}</source>
| <math>\begin{bmatrix}
0 & \cdots & 0 \\
\vdots & \ddots & \vdots \\
0 & \cdots & 0
\end{bmatrix} </math>
|-
| <source lang="latex">\begin{Bmatrix}
x & y \\
z & v
\end{Bmatrix}</source>
| <math>\begin{Bmatrix}
x & y \\
z & v
\end{Bmatrix}</math>
|-
| <source lang="latex">\begin{pmatrix}
x & y \\
z & v
\end{pmatrix}</source>
| <math>\begin{pmatrix}
x & y \\
z & v
\end{pmatrix}</math>
|-
| <source lang="latex">
\bigl( \begin{smallmatrix}
a&b\\ c&d
\end{smallmatrix} \bigr)
</source>
| <math>
\bigl( \begin{smallmatrix}
a&b\\ c&d
\end{smallmatrix} \bigr)
</math>
|-
| Case distinctions
| <source lang="latex">
f(n) =
\begin{cases}
n/2, & \text{if }n\text{ is even} \\
3n+1, & \text{if }n\text{ is odd}
\end{cases}</source>
| <math>f(n) =
\begin{cases}
n/2, & \text{if }n\text{ is even} \\
3n+1, & \text{if }n\text{ is odd}
\end{cases}</math>
|-
| rowspan="2" | Multiline equations
| <source lang="latex">
\begin{align}
f(x) & = (a+b)^2 \\
& = a^2+2ab+b^2 \\
\end{align}
</source>
| <math>
\begin{align}
f(x) & = (a+b)^2 \\
& = a^2+2ab+b^2 \\
\end{align}
</math>
|-
| <source lang="latex">
\begin{alignat}{2}
f(x) & = (a-b)^2 \\
& = a^2-2ab+b^2 \\
\end{alignat}
</source>
| <math>
\begin{alignat}{2}
f(x) & = (a-b)^2 \\
& = a^2-2ab+b^2 \\
\end{alignat}
</math>
|-
| Multiline equations <small>(must define number of columns used ({lcr}) (should not be used unless needed)</small>
| <source lang="latex">
\begin{array}{lcl}
z & = & a \\
f(x,y,z) & = & x + y + z
\end{array}</source>
| <math>\begin{array}{lcl}
z & = & a \\
f(x,y,z) & = & x + y + z
\end{array}</math>
|-
| Multiline equations (more)
| <source lang="latex">
\begin{array}{lcr}
z & = & a \\
f(x,y,z) & = & x + y + z
\end{array}</source>
| <math>\begin{array}{lcr}
z & = & a \\
f(x,y,z) & = & x + y + z
\end{array}</math>
|-
| Breaking up a long expression so that it wraps when necessary, at the expense of destroying correct spacing
| <source lang="latex">
f(x) =
\sum_{n=0}^\infty a_n x^n =
a_0+a_1x+a_2x^2+\cdots
</source>
| <math>f(x) =
\sum_{n=0}^\infty a_n x^n =
a_0 +a_1x+a_2x^2+\cdots</math>
|-
| Simultaneous equations
| <source lang="latex">\begin{cases}
3x + 5y + z \\
7x - 2y + 4z \\
-6x + 3y + 2z
\end{cases}</source>
| <math>\begin{cases}
3x + 5y + z \\
7x - 2y + 4z \\
-6x + 3y + 2z
\end{cases}</math>
|-
| Arrays
| <source lang="latex">
\begin{array}{|c|c||c|} a & b & S \\
\hline
0&0&1\\
0&1&1\\
1&0&1\\
1&1&0\\
\end{array}
</source>
| <math>
\begin{array}{|c|c||c|} a & b & S \\
\hline
0&0&1\\
0&1&1\\
1&0&1\\
1&1&0\\
\end{array}
</math>
|}
=== Parenthesizing big expressions, brackets, bars ===
{| class="wikitable"
! Feature !! Syntax !! How it looks rendered
|-
| Bad
| <source lang="text" enclose="none">( \frac{1}{2} )</source>
| <math>( \frac{1}{2} )</math>
|-
| Good
| <source lang="text" enclose="none">\left ( \frac{1}{2} \right )</source>
| <math>\left ( \frac{1}{2} \right )</math>
|}
You can use various delimiters with \left and \right:
{| class="wikitable"
! Feature
! Syntax
! How it looks rendered
|-
| Parentheses
| <source lang="text" enclose="none">\left ( \frac{a}{b} \right )</source>
| <math>\left ( \frac{a}{b} \right )</math>
|-
| Brackets
| <source lang="text" enclose="none">\left [ \frac{a}{b} \right ] \quad</source><br/> <source lang="text" enclose="none">\left \lbrack \frac{a}{b} \right \rbrack</source>
| <math>\left [ \frac{a}{b} \right ] \quad \left \lbrack \frac{a}{b} \right \rbrack</math>
|-
| Braces
| <source lang="text" enclose="none">\left \{ \frac{a}{b} \right \} \quad</source><br/> <source lang="text" enclose="none">\left \lbrace \frac{a}{b} \right \rbrace</source>
| <math>\left \{ \frac{a}{b} \right \} \quad \left \lbrace \frac{a}{b} \right \rbrace</math>
|-
| Angle brackets
| <source lang="text" enclose="none">\left \langle \frac{a}{b} \right \rangle</source>
| <math>\left \langle \frac{a}{b} \right \rangle</math>
|-
| Bars and double bars
| <source lang="text" enclose="none">\left | \frac{a}{b} \right \vert \quad</source><br/> <source lang="text" enclose="none">\left \Vert \frac{c}{d} \right \|</source>
| <math>\left | \frac{a}{b} \right \vert \quad \left \Vert \frac{c}{d} \right \|</math>
|-
| Floor and ceiling functions:
| <source lang="text" enclose="none">\left \lfloor \frac{a}{b} \right \rfloor \quad</source><br/> <source lang="text" enclose="none">\left \lceil \frac{c}{d} \right \rceil</source>
| <math>\left \lfloor \frac{a}{b} \right \rfloor \quad \left \lceil \frac{c}{d} \right \rceil</math>
|-
| Slashes and backslashes
| <source lang="text" enclose="none">\left / \frac{a}{b} \right \backslash</source>
| <math>\left / \frac{a}{b} \right \backslash</math>
|-
| Up, down, and up-down arrows
| <source lang="text" enclose="none">\left \uparrow \frac{a}{b} \right \downarrow \quad</source><br/> <source lang="text" enclose="none">\left \Uparrow \frac{a}{b} \right \Downarrow \quad</source><br/> <source lang="text" enclose="none">\left \updownarrow \frac{a}{b} \right \Updownarrow</source>
| <math>\left \uparrow \frac{a}{b} \right \downarrow \quad \left \Uparrow \frac{a}{b} \right \Downarrow \quad \left \updownarrow \frac{a}{b} \right \Updownarrow</math>
|-
| Delimiters can be mixed,<br>as long as \left and \right match
| <source lang="latex" enclose="none">\left [ 0,1 \right )</source><br/> <source lang="latex" enclose="none">\left \langle \psi \right |</source>
| <math>\left [ 0,1 \right )</math><br/> <math>\left \langle \psi \right |</math>
|-
| Use \left. and \right. if you<br/> do not want a delimiter to appear
| <source lang="text" enclose="none">\left . \frac{A}{B} \right \} \to X</source>
| <math>\left . \frac{A}{B} \right \} \to X</math>
|-
| rowspan="7" | Size of the delimiters (add "l" or "r" to indicate the side for proper spacing)
| <source lang="latex" enclose="none">( \bigl( \Bigl( \biggl( \Biggl( \dots \Biggr] \biggr] \Bigr] \bigr] ]</source>
| <math>( \bigl( \Bigl( \biggl( \Biggl( \dots \Biggr] \biggr] \Bigr] \bigr] ]</math>
|-
| <source lang="latex" enclose="none">\{ \bigl\{ \Bigl\{ \biggl\{ \Biggl\{ \dots</source><br/> <source lang="latex" enclose="none">\Biggr\rangle \biggr\rangle \Bigr\rangle \bigr\rangle \rangle</source>
| <math>\{ \bigl\{ \Bigl\{ \biggl\{ \Biggl\{ \dots \Biggr\rangle \biggr\rangle \Bigr\rangle \bigr\rangle \rangle</math>
|-
| <source lang="latex" enclose="none">\| \big\| \Big\| \bigg\| \Bigg\| \dots \Bigg| \bigg| \Big| \big| |</source>
| <math>\| \big\| \Big\| \bigg\| \Bigg\| \dots \Bigg| \bigg| \Big| \big| |</math>
|-
| <source lang="latex" enclose="none">\lfloor \bigl\lfloor \Bigl\lfloor \biggl\lfloor \Biggl\lfloor \dots</source><br/> <source lang="latex" enclose="none">\Biggr\rceil \biggr\rceil \Bigr\rceil \bigr\rceil \ceil</source>
| <math>\lfloor \bigl\lfloor \Bigl\lfloor \biggl\lfloor \Biggl\lfloor \dots \Biggr\rceil \biggr\rceil \Bigr\rceil \bigr\rceil \rceil</math>
|-
| <source lang="latex" enclose="none">\uparrow \big\uparrow \Big\uparrow \bigg\uparrow \Bigg\uparrow \dots</source><br/> <source lang="latex" enclose="none">\Bigg\Downarrow \bigg\Downarrow \Big\Downarrow \big\Downarrow \Downarrow</source>
| <math>\uparrow \big\uparrow \Big\uparrow \bigg\uparrow \Bigg\uparrow \dots \Bigg\Downarrow \bigg\Downarrow \Big\Downarrow \big\Downarrow \Downarrow</math>
|-
| <source lang="latex" enclose="none">\updownarrow \big\updownarrow \Big\updownarrow \bigg\updownarrow \Bigg\updownarrow \dots</source><br/> <source lang="latex" enclose="none">\Bigg\Updownarrow \bigg\Updownarrow \Big\Updownarrow \big\Updownarrow \Updownarrow</source>
| <math>\updownarrow \big\updownarrow \Big\updownarrow \bigg\updownarrow \Bigg\updownarrow \dots \Bigg\Updownarrow \bigg\Updownarrow \Big\Updownarrow \big\Updownarrow \Updownarrow</math>
|-
| <source lang="latex" enclose="none">/ \big/ \Big/ \bigg/ \Bigg/ \dots</source><br/> <source lang="latex" enclose="none">\Bigg\backslash \bigg\backslash \Big\backslash \big\backslash \backslash</source>
| <math>/ \big/ \Big/ \bigg/ \Bigg/ \dots \Bigg\backslash \bigg\backslash \Big\backslash \big\backslash \backslash</math>
|}
=== Equation numbering ===
The templates {{tl|NumBlk}} and {{tl|EquationRef}} can be used to number equations. The template {{tl|EquationNote}} can be used to refer to a numbered equation from surrounding text. For example, the following syntax:
: <code><nowiki>{{NumBlk|:|<math>x^2 + y^2 + z^2 = 1 \,</math>|{{EquationRef|1}}}}</nowiki></code>
produces the following result (note the equation number in the right margin):
{{NumBlk|:|<math>x^2 + y^2 + z^2 = 1 \,</math>|{{EquationRef|1}}}}
Later on, the text can refer to this equation by its number using syntax like this:
: <source lang="latex" enclose="none">As seen in equation ({{EquationNote|1}}), blah blah blah...</source>
The result looks like this:
: As seen in equation ({{EquationNote|1}}), blah blah blah...
Note that the equation number produced by {{tl|EquationNote}} is a link that the user can click to go immediately to the cited equation.