Aurora_ Short introduction to LaTeX symbols and commands.pdf

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10/7/13 Aurora: Short introduction to LaTeX symbols and commands

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Common expressionsWhat 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:

(Not so) short introduction to LaTeX ,

Short Math Guide for LaTeX , and the

TeX Reference Card .

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.

Auroras default preamble includes both amsmathand 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}{\sqrte - 1}

binomial \binom{n+1}{k}

prime y'' + y' + y = u

mod

\begin{array}{l}

a\bmodn=b \\

a\equivb\pmodn \\

a\equivb\modn \\

a\equivb\podn

\end{array}

Subscripts and superscripts

subscripts x_1, x_2\quada_{ij}

superscriptsx^y \quade^{2j\pit}\quad

a_{ij}^2

multilevel

subscripts

\sum_{\substack{

1\lem \leN, \\

m\text odd P m

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nested

sub/superscriptsa_{b_j}\quade^{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\inU}

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 andintersections

\bigcup_{\alpha\inS}\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 a lso de fines 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 s ize of the enclosed expression, use \leftand \rightcommands:

\left

\right

\left(

\sum_{i=1}^{n}e^{2\pij i^2}

\right)

plain( \sum_{i=1}^{n}e^{2\pij i^2})


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

\Biggl( \biggl( \Bigl( \bigl( \quad

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

This may be necessa ry when \leftand \rightcommands 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 \leftand \rightcreate brackets of the same size in nested expressions:

\left

\right

O\left(\left(

m2+n^2\right)\logn\right)

manually-sized O\bigl((m^2+n^2)\logn\bigr)

Multiline formulas and piecewise functions

piecewise

functions/cases

a_k = \begin{cases}

k &\text{for $k \len/2$}\\

n &\text{for $k=n/2$}\\

k-1&\text{otherwise}

\end{cases}

multiline

equations

(aligned at &)

\begin{split}\tan^2x

&= \sin^2x/\cos^2x \\

&= 1/\cos^2x - 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\impliesx=\pm2

if and only if x^2=4\iffx=\pm2

tends to x\to+\infty

gets A\getsB+C

sizable single

horizontal arrows

A\xleftarrow{\rmtoday}B

B\xrightarrow{\rmtomorrow}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
http://elevatorlady.ca/doc/refcard/symbols.html


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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\cdotm\cdotsm}_{n}

affixing arbitrary

symbolsx\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\alphagives (incorrect), whe reas \cos2\pi\alphagives (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 \rankAwill produce .

Alternatively, using \operatorname{rank}Ainline will also produce .

Matrices

matrix (square-

bracketed)

\begin{bmatrix}

\lambda\\

1&\lambda\\

&\ddots&\ddots\\

&&1&\lambda

\end{bmatrix}_{n\timesn}

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


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dots between

commasx_1, x_2, \dotsc, x_n

dots between

binary operationsx_1+ x_2+ \dotsb+ x_n

dots between

integrals

\int\dotsi\int

dots between

multiplication signsx(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 suchspaces

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 exampleabove, the

following commands can help:

normal text

x+\frac{1}{x}\ge2

\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 mans 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}
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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\quady

quad x\,y

quad x\:y

quad x\;y

quad x\y

double quad x\qquady

ve quad x\!y

custom spacing

(1 mu = quad)x\mspace{-19mu}y

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

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