20 ESSENTIAL LATEX
A Mathematical symbols
\alpha _ \beta
_
\gamma
_
\delta
_ \epsilon
_
\varepsilon
_
\zeta
_
\eta
_ \theta
\vartheta
\iota
_
\kappa
_ \lambda
\mu
_
\nu
_
\xi
_ o
_
\pi
_
\varpi
_
\rho
_ \varrho
_
\sigma
_
\varsigma
_
\tau
_ \upsilon
_
\phi
_
\varphi
_
\chi
_ \psi
_
\omega
_ \Gamma
_
\Delta
\Theta
!
\Lambda
" \Xi
#
\Pi
$
\Sigma
%
\Upsilon
& \Phi
'
\Psi
(
\Omega
Table 1: Greek letters
) \pm
*
\cap
+
\diamond
,
\oplus
- \mp
.
\cup
/
\bigtriangleup
0
\ominus
1 \times
2
\uplus
3
\bigtriangledown
4
\otimes
5 \div
6
\sqcap
7
\triangleleft
8
\oslash
9 \ast
:
\sqcup
;
\triangleright
<
\odot
= \star
>
\vee
?
\lhd
@ A
\bigcirc
B \circ
C
\wedge
D
\rhd
@ E
\dagger
F \bullet
G
\setminus
H
\unlhd
@ I
\ddagger
J \cdot
K
\wr
L
\unrhd
@ M
\amalg
@
Not predefined in LATEX2
N
. Use the packages latexsym or amssymb
Table 2: Binary operation symbols
O \leq
P
\geq
Q
\equiv
RS
\models
T
\prec
U \succ
V
\sim
W
\perp
X
\preceq
Y
\succeq
Z \simeq
R
\mid
[
\ll
\
\gg
]
\asymp
^ \parallel
_
\subset
`
\supset
a
\approx
;b7
\bowtie
c \subseteq
d
\supseteq
VS
\cong
e
\Join
f
\sqsubset
g \sqsupset
Sh
\neq
i
\smile
j
\sqsubseteq
k
\sqsupseteq
S l
\doteq
m
\frown
n
\in
o
\ni
p
\propto
S
=
q
\vdash
r
\dashv
s
<
t
>
Table 3: Relation symbols
ESSENTIAL LATEX 21
_ \rmoustache _ _ \lmoustache _
\rgroup __ \lgroup
__
\arrowvert __
\Arrowvert __
\bracevert
Table 4: Large delimiters
_ \uparrow _ \Uparrow \downarrow \Downarrow _ \{ _ \} \updownarrow _ \Updownarrow _ \lfloor _ \rfloor _ \lceil _ \rceil _ \langle _ \rangle _ /
G
\backslash
R
| ^ \|
Table 5: Delimiters
_ \leftarrow ___ \longleftarrow _ \uparrow
_ \Leftarrow _ S
\Longleftarrow _ \Uparrow
_ \rightarrow ___ \longrightarrow \downarrow
_ \Rightarrow
S _ \Longrightarrow \Downarrow
_ \leftrightarrow ___ \longleftrightarrow \updownarrow
_ \Leftrightarrow _ _ \Longleftrightarrow _ \Updownarrow
!_ \mapsto !___ \longmapsto " \nearrow
_$# \hookleftarrow %_ \hookrightarrow & \searrow
' \leftharpoonup ( \rightharpoonup ) \swarrow
* \leftharpoondown + \rightharpoondown , \nwarrow
Table 6: Arrow symbols
l l l
\ldots J J J \cdots
...
\vdots
. . . \ddots - \aleph
. \prime / \forall 0 \infty 1 \hbar 2 \emptyset 3 \exists 4 \nabla 5 \surd 6 \Box
@ /
\triangle 7 \Diamond
@98 \imath : \jmath ; \ell < \neg = \top > \flat ? \natural @ \sharp A \wp
W
\bot B \clubsuit C \diamondsuit D \heartsuit E \spadesuit F \mho
@ G \Re H \Im I \angle J \partial
@
Not predefined in LATEX2
N
. Use the packages latexsym or amssymb
Table 7: Miscellaneous symbols
22 ESSENTIAL LATEX
\arccos \cos \csc \exp \ker \limsup \min \sinh
\arcsin \cosh \deg \gcd \lg \ln \Pr \sup
\arctan \cot \det \hom \lim \log \sec \tan
\arg \coth \dim \inf \liminf \max \sin \tanh
Table 8: Log-like symbols
_ \hat{a} _ _ \acute{a} __ \bar{a} __ \dot{a} __ \breve{a}
__ \check{a} __ \grave{a} __ \vec{a} _ \ddot{a} _ \tilde{a}
Table 9: Math mode accents
_ \sum
_
\prod
\coprod
_
\int
_
\oint
_ \bigcap
_
\bigcup
_
\bigsqcup
_
\bigvee
_
\bigwedge
_ \bigodot
_
\bigotimes
_
\bigoplus
_
\biguplus
Table 10: Variable-sized symbols
___ ___ \widetilde{abc}
___ __ \widehat{abc} _ _ _____ \overleftarrow{abc} __ _____ \overrightarrow{abc}
_____ \overline{abc} _____ \underline{abc}
_!__ ___"!_# \overbrace{abc} "!__#____!_
\underbrace{abc}
5 _____ \sqrt{abc}
$5
_____ \sqrt[n]{abc}
%'& f’
,.@)-0(+*/
\frac{abc}{xyz}
Table 11: LATEX math constructs
1 \hbar
1
\hslash
2
\vartriangle
3 \triangledown
4
\square
5
\lozenge
6 \circledS I \angle
7
\measuredangle
8 \nexists F \mho
9
\Finv
: \Game @
@ ;
\Bbbk
@ <
\backprime
= \varnothing
>
\blacktriangle
?
\blacktriangledown
@ \blacksquare
A
\blacklozenge
B
\bigstar
C \sphericalangle
D
\complement
E
\eth
F \diagup
@ G
\diagdown
@
@
Not defined in style amssymb, define using the LATEX2
N
\DeclareMathSymbol command
Table 12: AMS miscellaneous symbols
ESSENTIAL LATEX 23
\digamma
_
\varkappa
_
\beth
_
\daleth
_
\gimel
Table 13: AMS Greek and Hebrew
_ \ulcorner
_
\urcorner
_
\llcorner
_
\lrcorner
Table 14: AMS delimiters
__ \dashrightarrow
_ \dashleftarrow
_
\leftleftarrows
_ \leftrightarrows
_
\Lleftarrow
_
\twoheadleftarrow
_ \leftarrowtail
_
\looparrowleft
_
\leftrightharpoons
_ \curvearrowleft
_
\circlearrowleft
_
\Lsh
_ \upuparrows
_
\upharpoonleft
_
\downharpoonleft
_ \multimap
_
\leftrightsquigarrow
_
\rightrightarrows
_ \rightleftarrows
_
\rightrightarrows _ \rightleftarrows
\twoheadrightarrow
!
\rightarrowtail
"
\looparrowright
# \rightleftharpoons
$
\curvearrowright
%
\circlearrowright
& \Rsh
'
\downdownarrows
(
\upharpoonright
) \downharpoonright
*
\rightsquigarrow
Table 15: AMS arrows
+ \nleftarrow
,
\nrightarrow
-
\nLeftarrow
. \nRightarrow
/
\nleftrightarrow
0
\nLeftrightarrow
Table 16: AMS negated arrows
1 \dotplus
2
\smallsetminus
3
\Cap
4 \Cup
5
\barwedge
6
\veebar
7 \doublebarwedge
8
\boxminus
9
\boxtimes
: \boxdot
;
\boxplus
<
\divideontimes
= \ltimes
>
\rtimes
?
\leftthreetimes
@ \rightthreetimes
A
\curlywedge
B
\curlyvee
C \circleddash
D
\circledast
E
\circledcirc
F
\centerdot
G
\intercal
Table 17: AMS binary operators
24 ESSENTIAL LATEX
\leqq
_
\leqslant
_
\eqslantless
_ \lesssim
_
\lessapprox
_
\approxeq
_ \lessdot
_
\lll
_
\lessgtr
\lesseqgtr
\lesseqqgtr
_
\doteqdot
_ \risingdotseq
\fallingdotseq
_
\backsim
_ \backsimeq
_
\subseteqq
_
\Subset
f
\sqsubset
_
\preccurlyeq
_
\curlyeqprec
_ \precsim
_
\precapprox
_
\vartriangleleft
_ \trianglelefteq
_
\vDash
_
\Vvdash
_ \smallsmile
_
\smallfrown
_
\bumpeq
_ \Bumpeq
_
\geqq
_
\geqslant
\eqslantgtr
!
\gtrsim
"
\gtrapprox
# \gtrdot
$
\ggg
%
\gtrless
& \gtreqless
'
\gtreqqless
(
\eqcirc
) \circeq
*
\triangleq
+
\thicksim
, \thickapprox
-
\supseteqq
.
\Supset
g \sqsupset
/
\succcurlyeq
0
\curlyeqsucc
1 \succsim
2
\succapprox
3
\vartriangleright
4 \trianglerighteq
5
\Vdash
6
\shortmid
7 \shortparallel
8
\between
9
\pitchfork
: \varpropto
;
\blacktriangleleft
<
\therefore
= \backepsilon
>
\blacktriangleright
?
\because
Table 18: AMS binary relations
@ \nless
A
\nleq
B
\nleqslant
C \nleqq
D
\lneq
E
\lneqq
F \lvertneqq
G
\lnsim
H
\lnapprox
I \nprec
J
\npreceq
K
\precnsim
L \precnapprox
M
\nsim
N
\nshortmid
O \nmid
P
\nvdash
Q
\nvDash
R \ntriangleleft
S
\ntrianglelefteq
T
\nsubseteq
U \subsetneq
V
\varsubsetneq
W
\subsetneqq
X \varsubsetneqq
Y
\ngtr
Z
\ngeq
[ \ngeqslant
\
\ngeqq
]
\gneq
^ \gneqq
_
\gvertneqq
`
\gnsim
a \gnapprox
b
\nsucc
c
\nsucceq
d \succnsim
e
\succnapprox
f
\ncong
g \nshortparallel
h
\nparallel
Q
\nvDash
i \nVDash
j
\ntriangleright
k
\ntrianglerighteq
l \nsupseteq
m
\nsupseteqq
n
\supsetneq
o \varsupsetneq
p
\supsetneqq
q
\varsupsetneqq
Table 19: AMS negated binary relations
ESSENTIAL LATEX 25
B Horrible Mathematical Examples to Study
______ S 5 ___ __ ___ ,__________ (2)
\begin{equation}
\phi(t)=\frac{1}{\sqrt{2\pi}}
\intˆt_0 eˆ{-xˆ2/2} dx
\end{equation}
____ _____ __ _ _ _ "! $#% S __ _ !'& __( )+.*_1',)__-.12,/03*$
_ _"45__76 -l l l #%_8(3)
\begin{equation}
\prod_{j\geq 0}
\left(\sum_{k\geq 0}a_{jk} zˆk\right)
= \sum_{k\geq 0} zˆn
\left( \sum_{{k_0,k_1,\ldots\geq 0}
\atop{k_0+k_1+\ldots=n} }
a{_0k_0}a_{1k_1}\ldots \right)
\end{equation}
_9;:__S <>_ &=?_
@@ACB < style=""> _= 6
_;D _4__ _ED _4___F _ 6HIGG (4)
\begin{equation}
\pi(n) = \sum_{m=2}ˆ{n}
\left\lfloor \left(\sum_{k=1}ˆ{m-1}
\lfloor(m/k)/\lceil m/k\rceil
\rfloor \right)ˆ{-1}
\right\rfloor
\end{equation}
_ @__ __" JK # MLl l l L_MLON(__ _P" JQK # $Ll l l L_
" #__ SR 6?T+UVHT+W.X_Y _ (5)
\begin{equation}
\{\underbrace{%
\overbrace{\mathstrut a,\ldots,a}ˆ{k\ a’s},
\overbrace{\mathstrut b,\ldots,b}ˆ{l\ b’s}}
_{k+1\ \mathrm{elements}} \}
\end{equation}
WR " R[Z __ "\ _ _ R[Z _ _ & _ R]Z _ _ _^R[Z _ T
\begin{displaymath}
\mbox{W}ˆ+\
\begin{array}{l}
\nearrow\raise5pt\hbox{$\muˆ+ + \nu_{\mu}$}\\
\rightarrow \piˆ+ +\piˆ0 \\[5pt]
\rightarrow \kappaˆ+ +\piˆ0 \\
\searrow\lower5pt\hbox{$\mathrm{e}ˆ+
+\nu_{\scriptstyle\mathrm{e}}$}
\end{array}
\end{displaymath}
`_L_a_Scbed5fhg iii
`,.& , ` ,.& - ` ,& `-0& , ` -0& - ` -& `,& ` -& b iii
Scb
\begin{displaymath}
{F}(x,y)=0\quad\mathrm{and}\quad
\left|\begin{array}{ccc}
F_{xx}’’ & F_{xy}’’ & F_{x}’ \\
F_{yx}’’ & F_{yy}’’ & F_{y}’ \\
F_{x}’ & F_{y}’ & 0
\end{array} \right| =0
\end{displaymath}
26 ESSENTIAL LATEX
) iii
_6_ __ a6_ a_ !6_ ___6 D 6 : 6 ! _ _ D _ : _ iii ii
___6 DD _6 ii
_Zii
D: 66 :_66 ii
_Zii
D: __ :___ ii
_
\begin{displaymath}
\frac{\pm
\left|\begin{array}{ccc}
x_1-x_2 & y_1-y_2 & z_1-z_2 \\
l_1 & m_1 & n_1 \\
l_2 & m_2 & n_2
\end{array}\right|}{
\sqrt{\left|\begin{array}{cc}l_1&m_1\\
l_2&m_2\end{array}\right|ˆ2
+ \left|\begin{array}{cc}m_1&n_1\\
n_1&l_1\end{array}\right|ˆ2
+ \left|\begin{array}{cc}m_2&n_2\\
n_2&l_2\end{array}\right|ˆ2}}
\end{displaymath}
____ __ L__ __ L_ L__ S __ _ _ _ 1@A__ ___ _ _ _ __ _
_ ________ &____ ____
___ ____ _ Z _ ___ _____ _ _ _ _ (6)
Z __ __ Z _ __ _ _
___ ____ _ Z _ ___ ____&__ _ _ _ _ _ _ _ Z _ &__ __ __ _
GI \newcommand{\CA}{C_{\rm A}} \newcommand{\CV}{C_{\rm V}}
\newcommand{\CPA}{{C’}_{\rm A}} \newcommand{\CPV}{{C’}_{\rm V}}
\newcommand{\GZ}{\Gammaˆ2_{\rm Z}}
\newcommand{\MZ}{Mˆ2_{\rm Z}} \newcommand{\MZs}{{(s-Mˆ2_{\rm Z})}}
\newcommand{\BE}{\left\{\frac{\displaystyle 3-\betaˆ2}{\displaystyle 2}\right\}}
\begin{eqnarray}
\sigmaˆf_0(Q,T_{3R},\beta,s) & = &
\frac{4\pi\alphaˆ2}{3s}\beta \times
\left[ \frac{Qˆ2 \BE - 2Q \CV \CPV s \MZs}{\MZsˆ2 + \MZ \GZ \BE}
\right. \nonumber \\[-3mm]
& & \\[-3mm]
& + &
\left.\frac{(\CVˆ2 + \CAˆ2) sˆ2}%
{\MZsˆ2+\MZ\GZ\left\{\CPVˆ2 \BE+\CPAˆ2 \{\betaˆ2\}\right\}}
\right] \nonumber
\end{eqnarray}
Bibliography
1 Leslie Lamport. LATEX—A Document Preparation System—User’s Guide and Reference Manual.
Addison-Wesley, Reading, MA, USA, 1985.
2 Donald E. Knuth. The TEXbook, volume A of Computers and Typesetting. Addison-Wesley,
Reading, MA, USA, 1986.
3 Michel Goossens, Frank Mittelbach and Alexander Samarin. The LATEX Companion Addison-
Wesley, Reading, MA, USA, 1993.
No comments:
Post a Comment