3.10 List of Mathematical Symbols
77
Table 3.5: BIG Operators.
\sum
\bigcup
\bigvee
\prod
\bigcap
\bigwedge
\coprod
\bigsqcup
\biguplus
\int
\oint
\bigodot
\bigoplus
\bigotimes
Table 3.6: Arrows.
\leftarrow or \gets
←−
\longleftarrow
\rightarrow or \to
−→
\longrightarrow
\leftrightarrow
←→
\longleftrightarrow
\Leftarrow
⇐=
\Longleftarrow
\Rightarrow
=⇒
\Longrightarrow
\Leftrightarrow
⇐⇒
\Longleftrightarrow
→
\mapsto
−→
\longmapsto
← \hookleftarrow
→
\hookrightarrow
\leftharpoonup
\rightharpoonup
\leftharpoondown
\rightharpoondown
\rightleftharpoons
⇐⇒
\iff (bigger spaces)
\uparrow
\downarrow
\updownarrow
\Uparrow
\Downarrow
\Updownarrow
\nearrow
\searrow
\swarrow
\nwarrow
;
\leadsto
a
a
Use the latexsym package to access this symbol
Table 3.7: Arrows as Accents.
−−→
AB
\overrightarrow{AB}
AB
−−→
\underrightarrow{AB}
←−−
AB
\overleftarrow{AB}
AB
←−−
\underleftarrow{AB}
←→
AB
\overleftrightarrow{AB}
AB
←→
\underleftrightarrow{AB}
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78
Typesetting Mathematical Formulae
Table 3.8: Delimiters.
( (
) )
↑ \uparrow
[ [ or \lbrack
] ] or \rbrack
↓ \downarrow
{ \{ or \lbrace } \} or \rbrace  \updownarrow
 \langle
 \rangle
⇑ \Uparrow
| | or \vert
 \| or \Vert
⇓ \Downarrow
/ /
\ \backslash
 \Updownarrow
 \lfloor
 \rfloor
 \rceil
 \lceil
Table 3.9: Large Delimiters.
\lgroup
\rgroup
\lmoustache
\arrowvert
\Arrowvert
\bracevert
\rmoustache
Table 3.10: Miscellaneous Symbols.
... \dots
··· \cdots
.
.
. \vdots
.
.
.
\ddots
~
\hbar
ı
\imath
 \jmath
\ell
\Re
\Im
\aleph
\wp
\forall
\exists
f
\mho
a
\partial
\prime
\emptyset
\infty
\nabla
\triangle
2
\Box
a
3
\Diamond
a
\bot
\top
\
\angle
\surd
\diamondsuit
\heartsuit
\clubsuit
\spadesuit
¬
\neg or \lnot
\flat
 \natural
\sharp
a
Use the latexsym package to access this symbol
Table 3.11: Non-Mathematical Symbols.
These symbols can also be used in text mode.
† \dag
§ \S
©
\copyright
®
\textregistered
‡ \ddag
¶ \P
£
\pounds
%
\%
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3.10 List of Mathematical Symbols
79
Table 3.12: A
M
SDelimiters.
p \ulcorner
q \urcorner
x \llcorner
y \lrcorner
| \lvert
| \rvert
 \lVert
 \rVert
Table 3.13: A
M
SGreek and Hebrew.
z
\digamma
{
\varkappa
i \beth
j \gimel
k
\daleth
Table 3.14: Math Alphabets.
See Table6.4 on125 for other math fonts.
Example
Command
Required package
ABCDEabcde1234
\mathrm{ABCDE abcde 1234}
ABCDEabcde1234
\mathit{ABCDE abcde 1234}
ABCDEabcde \mathnormal{ABCDE abcde 1234}
ABCDE
\mathcal{ABCDE abcde 1234}
ABCDE
\mathscr{ABCDE abcde 1234}
mathrsfs
ABCDEabcde1234
\mathfrak{ABCDE abcde 1234}
amsfonts or amssymb
ABCDEa1234
\mathbb{ABCDE abcde 1234}
amsfonts or amssymb
Table 3.15: A
M
SBinary Operators.
u
\dotplus
 \centerdot
n
\ltimes
o
\rtimes
>
\divideontimes
d
\doublecup
e
\doublecap
r
\smallsetminus
Y
\veebar
Z
\barwedge
[
\doublebarwedge
\boxplus
\boxminus
\circleddash
\boxtimes
\boxdot
}
\circledcirc
|
\intercal
~
\circledast
i
\rightthreetimes
g
\curlyvee
f
\curlywedge
h
\leftthreetimes
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80
Typesetting Mathematical Formulae
Table 3.16: A
M
SBinary Relations.
l
\lessdot
m
\gtrdot
+
\doteqdot
6
\leqslant
>
\geqslant
:
\risingdotseq
0
\eqslantless
1
\eqslantgtr
;
\fallingdotseq
5
\leqq
=
\geqq
P
\eqcirc
n
\lll or \llless
o
\ggg
$
\circeq
.
\lesssim
&
\gtrsim
,
\triangleq
/
\lessapprox
\gtrapprox
l
\bumpeq
7
\lessgtr
?
\gtrless
m
\Bumpeq
Q
\lesseqgtr
R
\gtreqless
s
\thicksim
S
\lesseqqgtr
T
\gtreqqless
t
\thickapprox
4
\preccurlyeq
<
\succcurlyeq
u
\approxeq
2
\curlyeqprec
3
\curlyeqsucc
v
\backsim
-
\precsim
%
\succsim
w
\backsimeq
w
\precapprox
v
\succapprox
\vDash
j
\subseteqq
k
\supseteqq
\Vdash
q
\shortparallel
c
\Supset
\Vvdash
J
\blacktriangleleft
A
\sqsupset
 \backepsilon
B
\vartriangleright
*
\because
_
\varpropto
I
\blacktriangleright
b
\Subset
G
\between
D
\trianglerighteq
a
\smallfrown
t
\pitchfork
C
\vartriangleleft
p
\shortmid
\smallsmile
E
\trianglelefteq
)
\therefore
@
\sqsubset
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3.10 List of Mathematical Symbols
81
Table 3.17: A
M
SArrows.
L99 \dashleftarrow
99K \dashrightarrow
\leftleftarrows
\rightrightarrows
\leftrightarrows
\rightleftarrows
W
\Lleftarrow
V
\Rrightarrow
\twoheadleftarrow
\twoheadrightarrow
\leftarrowtail
\rightarrowtail
\leftrightharpoons
\rightleftharpoons
\Lsh
\Rsh
"
\looparrowleft
#
\looparrowright
x
\curvearrowleft
y
\curvearrowright
 
\circlearrowleft
\circlearrowright
(
\multimap
\upuparrows
\downdownarrows
\upharpoonleft
\upharpoonright
\downharpoonright
\rightsquigarrow
!
\leftrightsquigarrow
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82
Typesetting Mathematical Formulae
Table 3.18: A
M
SNegated Binary Relations and Arrows.
\nless
\ngtr
&
\varsubsetneqq
\lneq
\gneq
\varsupsetneqq
\nleq
\ngeq
"
\nsubseteqq
\nleqslant
\ngeqslant
#
\nsupseteqq
\lneqq
 
\gneqq
- \nmid
\lvertneqq
\gvertneqq
,
\nparallel
\nleqq
\ngeqq
. \nshortmid
\lnsim
\gnsim
/
\nshortparallel
\lnapprox
\gnapprox
\nsim
\nprec
\nsucc
\ncong
\npreceq
\nsucceq
0
\nvdash
\precneqq
\succneqq
2
\nvDash
\precnsim
\succnsim
1
\nVdash
\precnapprox
\succnapprox
3
\nVDash
(
\subsetneq
)
\supsetneq
6
\ntriangleleft
\varsubsetneq
!
\varsupsetneq
7
\ntriangleright
*
\nsubseteq
+
\nsupseteq
5
\ntrianglelefteq
$
\subsetneqq
%
\supsetneqq
4
\ntrianglerighteq
8
\nleftarrow
9
\nrightarrow
=
\nleftrightarrow
:
\nLeftarrow
;
\nRightarrow
<
\nLeftrightarrow
Table 3.19: A
M
SMiscellaneous.
~
\hbar
}
\hslash
|
\Bbbk
\square
\blacksquare
s
\circledS
M
\vartriangle
N
\blacktriangle
{
\complement
O
\triangledown
H
\blacktriangledown
a
\Game
\lozenge
\blacklozenge
F
\bigstar
\
\angle
]
\measuredangle
\diagup
\diagdown
8 \backprime
@
\nexists
\Finv
?
\varnothing
g
\eth
^
\sphericalangle
f
\mho
Chapter 4
Specialities
When putting together a large document, L
A
T
E
Xwill help with some special
features like index generation, bibliography management, and other things. A
much more complete description of specialities and enhancements possible with
LAT
E
Xcan be found in the LAT
E
XManual [1] and The LAT
E
XCompanion [3].
4.1 Including Encapsulated PostScript
L
A
T
E
X provides the basic facilities to work with floating bodies, such as
images or graphics, with the figure and table environments.
There are several ways to generate the actual graphics with basic LAT
E
X
or a L
A
T
E
Xextension package, a few of them are described in chapter5.
Please refer to The LAT
E
XCompanion [3] and the LAT
E
XManual [1] for more
information on that subject.
Amuch easier way to get graphics into a document is to generate them
with a specialised software package
1
and then include the finished graphics
in the document. Here again, L
A
T
E
Xpackages offer many ways to do this,
but this introduction will only discuss the use of Encapsulated PostScript
(EPS) graphics, because it is quite easy to do and widely used. In order
to use pictures in the EPS format, you must have a PostScript printer
2
available for output.
Agood set of commands for inclusion of graphics is provided in the
graphicx package by D. P. Carlisle. It is part of a whole family of packages
called the “graphics” bundle.
3
When working on a system with a PostScript printer available for
output and with the graphicx package installed, use the following step by
1
Such as XFig, Gnuplot, Gimp, Xara X ...
2AnotherpossibilitytooutputPostScriptistheGhostScriptprogram
available
from CTAN://support/ghostscript. Windows and OS/2 users might want to look for
GSview.
3
CTAN://pkg/graphics
84
Specialities
step guide to include a picture into your document:
1. Export the picture from your graphics program in EPS format.
4
2. Load the graphicx package in the preamble of the input file with
\usepackage[driver]{graphicx}
where driver is the name of your “dvi to PostScript” converter
program. The most widely used program is calleddvips. The name of
the driver is required, because there is no standard on how graphics
are included in T
E
X. Knowing the name of the driver, the graphicx
package can choose the correct method to insert information about the
graphics into the.dvi file, so that the printer understands it and can
correctly include the .eps file.
3. Use the command
\includegraphics[key=value, ...]{file}
to include file into your document. The optional parameter accepts a
comma separated list of keys and associated values. The keys can be
used to alter the width, height and rotation of the included graphic.
Table4.1 lists the most important keys.
Table 4.1: Key Names for graphicx Package.
width
scale graphic to the specified width
height scale graphic to the specified height
angle
rotate graphic counterclockwise
scale
scale graphic
4
If your software cannot export into EPS format, you can try to install a PostScript
printer driver (such as an Apple LaserWriter, for example) and then print to a file with
this driver. With some luck this file will be in EPS format. Note that an EPS must not
contain more than one page. Some printer drivers can be explicitly configured to produce
EPS format.
4.2 Bibliography
85
The following example code may help to clarify things:
\begin{figure}
\centering
\includegraphics[angle=90,
width=0.5\textwidth]{test}
\caption{This is a test.}
\end{figure}
It includes the graphic stored in the file test.eps. The graphic is first
rotated by an angle of 90 degrees and then scaled to the final width of 0.5
times the width of a standard paragraph. The aspect ratio is 1.0, because
no special height is specified. The width and height parameters can also be
specified in absolute dimensions. Refer to Table6.5 on page130 for more
information. If you want to know more about this topic, make sure to read
[9] and [13].
4.2 Bibliography
Produce a bibliography with thethebibliography environment. Each entry
starts with
\bibitem[label]{marker}
The marker is then used to cite the book, article or paper within the
document.
\cite{marker}
If you do not use the label option, the entries will get enumerated auto-
matically. The parameter after the\begin{thebibliography} command
defines how much space to reserve for the number of labels. In the example
below,{99} tells L
A
T
E
Xto expect that none of the bibliography item numbers
will be wider than the number 99.
Partl~\cite{pa} has
proposed that \ldots
\begin{thebibliography}{99}
\bibitem{pa} H.~Partl:
\emph{German \TeX},
TUGboat Volume~9, Issue~1 (1988)
\end{thebibliography}
Partl [1] has proposed that ...
Bibliography
[1] H. Partl: : German n T
E
X, TUGboat
Volume 9, Issue 1 (1988)
86
Specialities
For larger projects, you might want to check out the BibT
E
Xprogram.
BibT
E
Xis included with most T
E
Xdistributions. It allows you to maintain
abibliographic database and then extract the references relevant to things
you cited in your paper. The visual presentation of BibT
E
X-generated
bibliographies is based on a style-sheets concept that allows you to create
bibliographies following a wide range of established designs.
4.3 Indexing
Avery useful feature of many books is their index. With L
A
T
E
Xand the
support programmakeindex,
5
an index can be generated quite easily. This
introduction will only explain the basic index generation commands. For a
more in-depth view, please refer to The LAT
E
XCompanion [3].
To enable their indexing feature of L
A
T
E
X, the makeidx package must be
loaded in the preamble with
\usepackage{makeidx}
and the special indexing commands must be enabled by putting the
\makeindex
command in the preamble.
The content of the index is specified with
\index{key@formatted_entry}
commands, where formatted_entry will appear in the index and key will be
used for sorting. The formatted_entry is optional. If it is missing the key
will be used. You enter the index commands at the points in the text that
you want the final index entries to point to. Table4.2 explains the syntax
with several examples.
When the input file is processed with L
A
T
E
X, each\index command
writes an appropriate index entry, together with the current page number,
to a special file. The file has the same name as the L
A
T
E
Xinput file, but a
different extension (.idx). This.idx file can then be processed with the
makeindex program:
makeindex filename
Themakeindex program generates a sorted index with the same base file
name, but this time with the extension.ind. If now the L
A
T
E
Xinput file is
5
On systems not necessarily supportingfilenames longer than 8 characters, the program
may be called makeidx.
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