Elevator Lady Inc.

Now with more awesome.

 

Common expressions

What follows in this and next sections is but a very concise collection of most common and useful symbols available in LaTeX (and hence Aurora). It is primarily based on the material of:

If you cannot find some symbol here or in the documents above, The Comprehensive LaTeX Symbol List the reference to over 3300 symbols that can be used in LaTeX (and thus, again, Aurora)—will most definitely have whatever it is you need.

Aurora’s default preamble includes both amsmath and amssymb; therefore, the examples below use symbols and commands from these packages indiscriminately. All these examples should be used in math mode unless noted otherwise.

Operations

square root

\sqrt{x+\sqrt{y}}

higher order roots

\sqrt[mn]{x+y} \quad \sqrt[3]{2}

root sign

\surd[x+y]

fractions

\frac{a+b}{x+\log\frac{Y}{Z}}

force large (display) fraction

\frac{a+b}{x+\log\dfrac{Y}{Z}}

continued fraction

1+\cfrac{2}{

  3+\cfrac{4}{

    5+\cfrac{6}{7+\dotsb}}} =

\frac{1}{\sqrt e - 1}

binomial

\binom{n+1}{k}

prime

y'' + y' + y = u

“mod”

\begin{array}{l}

  a\bmod n=b \\

  a\equiv b\pmod n \\

  a\equiv b\mod n \\

  a\equiv b\pod n

\end{array}

Subscripts and superscripts

subscripts

x_1, x_2 \quad a_{ij}

superscripts

x^y \quad e^{2j\pi t} \quad

a_{ij}^2

multilevel subscripts

\sum_{\substack{

      1 \le m \le N, \\

      m\text{ odd}}} P(m)

nested sub/superscripts

a_{b_j} \quad e^{x^2}

sub- and superscripts before the symbol

{}_n C_k

subscripts and superscripts for large symbols

\sideset{^a_b}{'_c}\sum

 

Sums, integrals, and products

sum

\sum_{i=1}^{+\infty}

product

\prod_{\alpha \in U}

integral

\int_{x_0}^{x_1}

contour integral

\oint_C

double and triple integrals

\iint_S \quad \iiint_S

even more integrals

\iiiint_S \quad \idotsint_S

integrals with alternative limit placement

\int\limits_\alpha^\beta \quad

\iint\limits_S

unions and intersections

\bigcup_{\alpha\in S} \quad

\bigcap_{V\in\mathfrak{V}}

direct sums, co-products, and so on

\bigodot \quad \bigoplus

\bigotimes \quad \bigsqcup

\biguplus \quad \coprod

\bigvee \quad \bigwedge

Brackets

pairing brackets

( \; ), [ \; ], \{ \; \}

\lvert\;\rvert, \lVert\;\rVert

\lceil\;\rceil, \lfloor\;\rfloor

\langle\;\rangle

Aurora also defines the following two commands in its default preamble:

absolute value

\abs{u(t)}

norm

\norm{\hat{G}}_\infty

To make the brackets scale to the size of the enclosed expression, use \left and \right commands:

\left
\right

\left(

  \sum_{i=1}^{n} e^{2\pi j i^2}

\right)

plain

( \sum_{i=1}^{n} e^{2\pi j i^2} )

Alternatively, the bracket size can be specified explicitly using the following commands:

\Biggl \biggl \Bigl \bigl( \quad

\Biggr\} \biggr\} \Bigr\} \bigr\}

This may be necessary when \left and \right commands create delimiters that are visually too large:

\left
\right

\left[ \sum_j

      \left|\sum_i x_{ij}\right|^2

\right]^{1/2}

manually-sized

\biggl[ \sum_j

      \Bigl|\sum_i x_{ij}\Bigr|^2

\biggr]^{1/2}

or when \left and \right create brackets of the same size in nested expressions:

\left
\right

O\left(\left(

    m^2+n^2\right)\log n\right)

manually-sized

O\bigl((m^2+n^2)\log n\bigr)

Multiline formulas and piecewise functions

piecewise functions/cases

a_k = \begin{cases}

  k & \text{for $k \le n/2$} \\

  n & \text{for $k=n/2$} \\

  k-1 & \text{otherwise}

\end{cases}

multiline equations (aligned at &)

\begin{split}\tan^2 x

  &= \sin^2 x/\cos^2 x \\

  &= 1/\cos^2 x - 1

\end{split}

systems of equations

\left\{\begin{array}{l}

  ax+by=r_1 \\

  cx+dy=r_2

\end{array}\right.

Arrows

implication

x^2=4 \implies x=\pm 2

“if and only if”

x^2=4 \iff x=\pm 2

“tends to”

x\to+\infty

“gets”

A\gets B+C

sizable single horizontal arrows

A\xleftarrow{\rm today}B

B\xrightarrow{\rm tomorrow}C

C \xrightarrow

    [\text{(except Fridays)}]

    {\text{every day}} D

sizable single vertical arrows

\left\uparrow\sum \right\downarrow \;

\Big\updownarrow

sizable double vertical arrows

\left\Uparrow\sum \right\Downarrow \;

\Big\Updownarrow

A large collection of arrows can be found in the symbols section.

Over- and underbraces and other embellishments

overline

\overline{A+B}

underline

\underline{A+B}

hat

\widehat{A+B}

tilde

\widetilde{A+B}

vector markers

\overrightarrow{AB} \text{ and }

\overleftarrow{BA}

overbrace

\overbrace{x_1+x_2+\cdots+x_k}^

      {k \text{ in total}}

underbrace

m^n=\underbrace{m\cdot m\cdots m}_{n}

affixing arbitrary symbols

x\overset{?}{\ge}y

Function names

To get correct font and spacing around the names of mathematical functions, prefix the function name with \. For example, writing cos 2\pi\alpha gives (incorrect), whereas \cos 2\pi\alpha gives (correct). Full list of function names defined in LaTeX is given below:

\arccos

\exp

\log

\arcsin

\gcd

\max

\arctan

\hom

\min

\arg

\inf

\Pr

\cos

\injlim

\projlim

\cosh

\varinjlim

\varprojlim

\cot

\ker

\sec

\coth

\lg

\sin

\csc

\lim

\sinh

\deg

\liminf

\sup

\det

\varliminf

\tan

\dim

\limsup

\tanh

\ln

\varlimsup

 

To declare additional function names that behave like the ones above, use the \DeclareMathOperator command in the preamble: \DeclareMathOperator{\rank}{rank}, after which \rank A will produce . Alternatively, using \operatorname{rank} A inline will also produce .

Matrices

matrix (square-bracketed)

\begin{bmatrix}

      \lambda \\

      1 & \lambda \\

      & \ddots & \ddots \\

      & & 1 & \lambda

\end{bmatrix}_{n\times n}

alternative delimiters

\begin{pmatrix}a\\b\\c\end{pmatrix},

\begin{Bmatrix}a\\b\\c\end{Bmatrix},

\begin{vmatrix}a\\b\\c\end{vmatrix},

\begin{Vmatrix}a\\b\\c\end{Vmatrix},

\begin{matrix}a\\b\\c\end{matrix}

inline matrices

(\begin{smallmatrix}1 && 2 \\

3 && 4\end{smallmatrix})

Punctuation

dots between commas

x_1, x_2, \dotsc, x_n

dots between binary operations

x_1 + x_2 + \dotsb + x_n

dots between integrals

\int\dotsi\int

dots between multiplication signs

x(x+1)\dotsm(x+n)

colon (meaning “such that” or when defining domains)

f\colon \mathbb{N}\to\mathbb{R}

vertical and diagonal

\vdots \quad \ddots

Fonts

Normally, everything typed in math mode is considered to be a part of the formula and is typeset as such—spaces are ignored, most symbols come out in medium-weight italics, and so on. If you want to use a different mathematical font or to enter a few words of regular text in math mode like in the piecewise example above, the following commands can help:

normal text

x+\frac{1}{x} \ge 2

\text{ for all $x>0$}

(note that this is one of the rare cases when spaces matter in LaTeX; also note that you can switch back to math mode in \text)

bold text, upright

\textbf{I am Jack's bold text.}

bold math, upright

AB\mathbf{CD}EF

bold math, italic

AB\boldsymbol{C}\boldsymbol{D}EF

“poor man’s bold”

AB\pmb{C}\pmb{D}EF

(overlays several copies of a symbol with slight offsets on top of each other)

calligraphic
(uppercase Latin letters only)

\begin{array}{c}

\mathcal{ABCDEFGHIJKLM} \\

\mathcal{NOPQRTSUVWXYZ}\end{array}

blackboard bold (uppercase Latin letters only)

\begin{array}{c}

\mathbb{ABCDEFGHIJKLM} \\

\mathbb{NOPQRTSUVWXYZ}\end{array}

Fraktur
(Latin letters and digits only)

\begin{array}{c}

\mathfrak{ABCDEFGHIJKLM} \\

\mathfrak{NOPQRTSUVWXYZ} \\

\mathfrak{abcdefghijklm} \\

\mathfrak{nopqrtsuvwxyz} \\

\mathfrak{0123456789}\end{array}

sans-serif font

\begin{array}{c}

\mathsf{ABCDEFGHIJKLM} \\

\mathsf{NOPQRTSUVWXYZ} \\

\mathsf{abcdefghijklm} \\

\mathsf{nopqrtsuvwxyz} \\

\mathsf{0123456789}\end{array}

typewriter

\begin{array}{c}

\mathtt{ABCDEFGHIJKLM} \\

\mathtt{NOPQRTSUVWXYZ} \\

\mathtt{abcdefghijklm} \\

\mathtt{nopqrtsuvwxyz} \\

\mathtt{0123456789}\end{array}

Spacing

The following commands can be used to fine-tune spacing in math mode:

default (none)

x y

quad (width of )

x\quad y

 quad

x\,y

 quad

x\:y

 quad

x\;y

 quad

x\ y

double quad

x\qquad y

ve  quad

x\!y

custom spacing
(1 mu =  quad)

x\mspace{-19mu}y

virtual space

\Gamma_{ij}^{\phantom{ij}k}