Aurora_ Short introduction to LaTeX symbols and commands.pdf
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Transcript of Aurora_ Short introduction to LaTeX symbols and commands.pdf
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8/14/2019 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
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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}