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VII
.2. T
ABLES
71
Anotherinterestingfeatureofthearraypackageisthe
>{
decl
}
commandwhichcan
beusedbeforeacolumnspecifier. Itinsertsdecldirectlyinfrontofthecolumn. . For
examplelookattheinputbelow
\begin{center}
\begin{tabular}{|>{\bfseries}l|r|}
\hline
\multicolumn{1}{|m{1.5cm}|}{\centering Planet}
&\multicolumn{1}{m{2.3cm}|}%
{\centering Mean distance from sun \\ \ (km)}\\
\hline
Mercury & 58100000\\
Venus
& 108300000\\
Earth
& 150000000\\
Mars
& 228250000\\
Jupiter & 779500000\\
Saturn
& 1429000000\\
Uranus
& 2439000000\\
Neptune & 4504500000\\
Pluto
& 5903500000\\
\hline
\end{tabular}
\end{center}
whichproducestheoutput
Planet
Meandistance
fromsun
(km)
Mercury
58100000
Venus
108300000
Earth
150000000
Mars
228250000
Jupiter
779500000
Saturn
1429000000
Uranus
2439000000
Neptune
4504500000
Pluto
5903500000
Thearraypackagealsohasa
!
commandwhichworksjustlikethe
@
command,but
whchdoesnotsuppresstheintercolumnspace.
VII
.2.3. Themultirowpackage
Lookagainatthetablein68.Wouldn’titbeniceiftheentry“Planet”inthefirstcolumn
isverticallyalignedwiththecenterofthetworowsinthenextcolumnasbelow?
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72
VII
. R
OWS AND
C
OLUMNS
Planet
Distancefromsun
(millionkm)
Maximum
Minimum
Mercury
69.4
46.8
Venus
109.0
107.6
Earth
152.6
147.4
Mars
249.2
207.3
Jupiter
817.4
741.6
Saturn
1512.0
1346.0
Uranus
3011.0
2740.0
Neptune
4543.0
4466.0
Pluto
7346.0
4461.0
Thepackagemultirowiswhatweneedtodothispainlessly.Ithasacommand
\multirow{
num
}{
wd
}{
item
}
wherenumisthenumberofrowstobespanned,wdisthewidthofthiscolumnanditem
isthetextoftheiteminthiscolumn.Thiscanbeusedasinthefollowingexample
\begin{center}
\begin{tabular}{|l|r|r|}
\hline
\multirow{3}{1.5cm}{Planet}
& \multicolumn{2}{p{3.5cm}|}%
{\centering Distance from sun \\ (million n km)}\\
\cline{2-3}
& \multicolumn{1}{c|}{Maximum}
& \multicolumn{1}{c|}{Minimum}\\
\hline
Mercury & 69.4
& 46.8\\
Venus
& 109.0
& 107.6\\
Earth
& 152.6
& 147.4\\
Mars
& 249.2
& 207.3\\
Jupiter & 817.4
& 741.6\\
Saturn
& 1512.0 0 & & 1346.0\\
Uranus
& 3011.0 0 & & 2740.0\\
Neptune & 4543.0 0 & & 4466.0\\
Pluto
& 7346.0 0 & & 4461.0\\
\hline
\end{tabular}
\end{center}
Butthiscodedoesnotproducethetableabove,butonly
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VII
.2. T
ABLES
73
Planet
Distancefromsun
(millionkm)
Maximum
Minimum
Mercury
69.4
46.8
Venus
109.0
107.6
Earth
152.6
147.4
Mars
249.2
207.3
Jupiter
817.4
741.6
Saturn
1512.0
1346.0
Uranus
3011.0
2740.0
Neptune
4543.0
4466.0
Pluto
7346.0
4461.0
The troubleis thatthough h theentry “Planet”is s verticallycenteredinits s column, it
isnothorizontallycentered. Thehorizontalalignmentis s controlledbythecommand
\multirowsetup
andthisisbydefaultstto
\raggedright
.Soallthatisneededtogetthe
beautifultableseenatthebeginningofthissectionistoaddtheline
\renewcommand{\multirowsetup}{\centering}
atthebeginningofthecodeabove.
VII
.2.4.
tabbing
vs.
tabular
Let’stakeaquicklookattheprosandconsofthe
tabbing
and
tabular
environments.
• The
tabbing
environmentcanbetypesetonlyasaseparateparagraph,whilethe
tabular
environmentcanbeplacedanywhereintext,eveninsideMathematics.
• The
tabbing
environmentcanspanmultiplepages,butthe
tabular
environment
cannot.
tabbing
environmentscannotbenested,while
tabular
environmentscanbenested
toanynumberoflevels.
VII
.2.5. Multipagetables—Thepackagelongtable
Aswehavenoted,wecannotcreatetablespanningmorethanonepageusingthe
tabular
environment.ButthepackagelongtablebyDavidCarlislecandothisandithasquitea
fewothertricksalso.Tousethispackage,loaditasusualwiththecommand
\usepackage{longtable}
inthe preamble e andthentoproduce e a no-frills “longtable”justuse the commands
\begin{longtable} ... \end{longtable}
insteadofthe
\begin{tabular}... \end{tabular}
commands.Wecanusefootnotesandthe
\newpage
commandsinsidethe
longtable
en-
vironment.Ifthepackagearrayisalsoloaded,itsextrafeaturescanbeused.
Apartfromthis,thispackagehasprovisionstospecifyatthestartoftheinputthe
followingitems
• therowsthatshouldappearatthetopofthetable;theinputforthesetobetermi-
natedby
\endfirsthead
• therowsthatshouldappearineverypageafterthefirst,suchinputterminatedby
\endhead
• thoseatthebottomofeverypage,theinputterminatedby
\endfoot
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74
VII
. R
OWS AND
C
OLUMNS
• thoserowsattheveryendofthetable,terminatedby
\endlastfoot
Theseareillustratedinthe(long!)tablebelow.
ScienceandTechnologyintheTwentiethCentury
Year
Event
1900
MaxPlanckproposesquantumtheory
PublicationofSigmundFreud’sTheInterpretationofDreams
1901
Discoveryofprincipalbloodgroups
GuglielmoMarconitransmitswirelesssignalsacrosstheatlantic
1903
Wrightbrothersmaketheirfirstflight
1905
AlbertEinsteinpresentsSpecialTheoryofRelativity
1911
ErnestRutherfordproposestheoryofatomicstructure
1912
VictorHessdiscoverscosmicrays
1916
AlbertEinsteinpresentsgeneralTheoryofRelativity
1920
Radiobroadcastingbegins
1926
JohnLogieBairddemonstratestelevision
1928
AlexanderFlemingdiscoverspenicillin
1933
Discoveryofpolythene
1934
Discoveryofnuclearfission
1938
Discoveryofnylon
1940
Plutoniumobtainedbybombardmentofuranium
1942
Constructionoffirstnuclearreactor
1946
Constructionoffirstelectronicdigitalcomputer
1947
Firstsupersonicflight
Inventionofthetransistor
1951
Nuclearpowerstationsintroduced
1953
JamesWatsonandFrancisCrickshow
DNS
moleculestructure
1956
Contraceptivepillintroduced
1957
Launchofthefirstspacesatellite(Sputnik1)
1959
Firstphotographofthedarksideofthemoon(Luna3)
···
·········
···
·········
···
·········
···
·········
···
·········
···
·········
···
·········
···
·········
···
·········
···
·········
···
·········
···
·········
1961
YuriGagarinbecomesfirstmaninspace(Vostok1)
1966
Firstlunarsoftlanding(Luna9)
1967
Discoveryofpulsars
1968
Firstmannedlunarorbit(Apollo8)
1969
Firstmanonmoon(NeilArmstrong)
1972
Pocketcalculatorintroduced
continuedonthenextpage
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VII
.2. T
ABLES
75
ScienceandTechnologyintheTwentiethCentury(continued)
Year
Event
1974
First‘test-tubebabies’
1977
LaunchofVoyagermissionstoouterspce
1983
IBM
personalcomputerlaunched
1986
Hailey’scometintercepted
1997
Cloningof“Dolly”thesheep
2000
Decodingof90%ofhumangenomecompleted
Source:TheCambrigeFactfinder
Partofthecodetoproducethisisgivenbelow.
\renewcommand{\arraystretch}{1.2}
\begin{longtable}{|c|l|}
\multicolumn{2}{c}%
{\textbf{Science and d Technology y in the e Twentieth Century}}\\[5pt]
\hline
\multicolumn{1}{|c|}{\sffamily Year}
&\multicolumn{1}{|c|}{\sffamily Event}\\
\hline
\endfirsthead
\multicolumn{2}{c}%
{\textbf{Science and Technology in the Twentieth Century}
(\textit{continued})}\\[5pt]
\hline
\multicolumn{1}{|c|}{\sffamily Year}
&\multicolumn{1}{|c|}{\sffamily Event}\\
\hline
\endhead
\hline
\multicolumn{2}{r}{\small\itshape continued d on n the e next page}\\
\endfoot
\hline
\multicolumn{2}{r}{\small Source\,:\,\itshape The Cambrige Factfinder}
\endlastfoot
1900 & Max Planck proposes quantum theory\\
..............................................
2000 & Decoding of f 90\% of f human genome completed\\
\hline
\end{longtable}
VII
.2.6. Andthat’snotall!
Therearemanymorepackageswhichhelptoproducetablesofvariousrequirements.Be
suretocheckoutthepakagestabularx,delarray,dcolumnandhhline.
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76
TUTORIALVIII
TYPESETTINGMATHEMATICS
DonalKnuthcreatedT
E
XprimarilytotypesetMathematicsbeautifully.LAT
E
Xincludesall
thecapabilitiesofT
E
XinMathematicstypesetting,sometimeswitheasieruserinterfaces.
Thentherearepackageslikeamsmathwhichenhanceandrefinetheseinterfaces.
VIII
.1. T
HEBASICS
Amathematicalexpressionoccurringinrunningtext(calledin-textmath)isproducedby
enclosingitbetweendollarsigns.Thustoproduce
TheequationrepresentingastraightlineintheCartesianplaneisoftheformax+by+c=0,
wherea,b,careconstants.
wetype
The equation n representing
a straight t line in the Cartesian plane
is of the form $ax+by+c=0$, where e $a$, , $b$, $c$ are e constants.
Somecommentsareinorder. Firstnotethatthetextwithindollarsistypesetinitalic
(actuallymathitalic).Again,eventhoughwedidnotleaveanyspaceswithin
ax+by+c=0
,
T
E
Xleavesspacesoneithersideoftheadditionsignsandtheequalitysign.Ontheother
hand,evenifwetype
$ax + + by y + + c c = 0$
,theoutputwouldbethesame:ax+by+c=0.
Themoral?T
E
Xhasitsownspacingrulesinmathmode.
Toseeanotherinstanceofthis,changethelastpartofthecodeabovetoread
... where e $a, , b, , c$ are e constants.
Savessometyping,doesnotit?Butlookattheoutput.
TheequationrepresentingastraightlineintheCartesianplaneisoftheformax+by+c=0,
wherea,b,careconstants.
Doyouseethedifference? Therearenospacesafterthecommas,thoughwehadsuch
spacesintheoutput. SoT
E
Xswallowsspacesinmathmode(youcannotsavedollars
thatway!).
Incidentally, dollar signs areT
E
X wayofdistinguishingMathematicaltext. . L
A
T
E
X
hasotherwaysalsoofdoingit,using
\( ... \)
or
\begin{math} ... . \end{math}
.Thus
eitheroftheinputsshownbelowalsoproducesthesameoutputasabove.
The equation n representing a straight t line in n the Cartesian plane is of
the form \(ax+by+c=0\), where e \(a\), , \(b\), , \(c\) are constants.
The equation n representing a straight t line in n the Cartesian plane is
of the form \begin{math}ax+by+c=0\end{math}, where \begin{math} a
\end{math}, \begin{math} b \end{math}, \begin{math} } c c \end{math} are
constants.
77
78
VIII
. T
YPESETTING
M
ATHEMATICS
Nowsupposewewanttodisplaytheequationintheaboveoutputasin
TheequationrepresentingastraightlineintheCartesianplaneisoftheform
ax+by+c=0
wherea,b,careconstants.
Thiscanbedonebychangingtheinputasfollows:
The equation n representing a straight t line in n the Cartesian plane is
of the form
$$
ax+by+c=0
$$
where $a$, $b$, $c$ are e constants.
Again
$$ ... . $$
istheT
E
Xwayofproducingdisplayedmath.L
A
T
E
Xhastheconstructs
\[ ... \]
or
\begin{displaymath} ... . \end{displaymath}
alsotodothis.
VIII
.1.1. Superscriptsandsubscripts
Lookatthetextbelow
Intheseventeenthcentury,Fermatconjecturedthatifn>2,thentherearenointegersx,y,z
forwhich
x
n
+y
n
=z
n
.
Thiswasprovedin1994byAndrewWiles.
Thisisproducedbytheinput
In the seventeenth h century, , Fermat conjectured d that if f $n>2$, , then
there are no integers $x$, $y$, $z$ for which
$$
xˆn+yˆn=zˆn.
$$
This was s proved d in n 1994 by y Andrew w Wiles.
Thisshowsthatsuperscripts(mathematicianscallthemexponents)areproducedbythe
ˆ
symbol.Ifthesuperscriptismorethanonecharacterlong,wemustbecarefultogroup
thesecharactersproperly.Thustoproduce
Itiseasilyseenthat(x
m
)
n
=x
mn
.
wemusttype
It is easily seen that $(xˆm)ˆn=xˆ{mn}$.
Insteadof
$xˆ{mn}$
,ifwetype
$xˆmn$
weendupwith
x
m
n
insteadoftheintended
x
mn
intheoutput.
Wecanhavesuperscriptsofsuperscripts(andmathematiciansdoneedthem). For
example,
Numbersoftheform22
n
+1,wherenisanaturalnumber,arecalledFermatnumbers.
isproducedby
VIII
.1. T
HE BASICS
79
Numbers of the form $2ˆ{2ˆn}+1$, where $n$ is a natural number, are
called Fermat t numbers.
Notethegroupingofsuperscripts.(Whathappensifyoutype
$2ˆ2ˆn+1$
or
${2ˆ2}ˆn$
?)
Nowletusseehowsubscripts(mathematicianscallthemsubscripts)areproduced.
Toget
Thesequence(x
n
)definedby
x
1
=1, x
2
=1, x
n
=x
n−1
+x
n−2
(n>2)
iscalledtheFibonaccisequence.
wemusttype
The sequence e $(x_n)$ defined d by
$$
x_1=1,\quad x_2=1,\quad d x_n=x_{n-1}+x_{n-2}\;\;(n>2)
$$
is called the e Fibonacci sequence.
Thussubscriptsareproducedbythe
_
character.Notehowweinsertspacesbythe
\quad
command.(Thecommand
\;
inmathmodeproduceswhatisknownasa“thickspace”.)
Subscriptsofsubscriptscanbeproducedasinthecaseofsuperscripts(withappropriate
grouping).
Wecanalsohavesuperscriptsandsubscriptstogether.Thus
Ifthesequence(x
n
)convergestoa,thenthesequence(x2
n
)convergestoa2
isproducedby
If the sequence $(x_n)$ $ converges to $a$, then the e sequence
$(x_nˆ2)$ converges to $aˆ2$
Again,wemustbecarefulaboutthegrouping(orthelackofit)whentypesetting
superscriptsandsubscriptstogether.Thefollowinginputsandthecorrespondingoutputs
makethepoint.
$$
x_mˆn\qquad xˆn_m\qquad d {x_m}ˆn\qquad d {xˆn}_m
$$
x
n
m
x
n
m
x
m
n
x
n
m
(ThishastodowiththewayT
E
Xworks,producing“boxes”tofittheoutputcharacters.
Theboxforx
n
m
islike
x
n
m
whiletheboxforx
m
n
is
x
m
n
.
VIII
.1.2. Roots
Squarerootsareproducedbythe
\sqrt
argument.Thus
$\sqrt{2}$
produces
2. This
commandhasanoptionalargumenttoproduceotherroots.Thus
Whichisgreater
4
5or
5
4?
isproducedby
80
VIII
. T
YPESETTING
M
ATHEMATICS
Which is s greater r $\sqrt[4]{5}$ or r $\sqrt[5]{4}$?
Thehorizontallineabovetheroot(calledvinculumbymathematiciansofyore)elon-
gatestoaccommodatetheenclosedtext. Forexample,
$\sqrt{x+y}$
produces
x+y.
Also,youcanproducenestedrootsasin
Thesequence
2
2, 2
2
2−
2, 2
3
2−
2+
2, 2
4
2−
2+
2+
2+
2,...
convergetoπ.
bytyping
The sequence
$$
2\sqrt{2}\,,\quad 2ˆ2\sqrt{2-\sqrt{2}}\,,\quad d 2ˆ3
\sqrt{2-\sqrt{2+\sqrt{2}}}\,,\quad 2ˆ4\sqrt{2-
\sqrt{2+\sqrt{2+\sqrt{2+\sqrt{2}}}}}\,,\;\ldots
$$
converge to o $\pi$.
The
\ldots
commandaboveproduces...,thethreedotsindicatingindefinitecontin-
uation,calledellipsis(moreaboutthemlater).Thecommand
\,
producesa“thinspace”
(asopposedtoathickspaceproducedby
\;
,seenearlier). Whyallthisthinandthick
spacesintheaboveinput? Removethemandseethedifference. (Atastefullyapplied
thinspaceiswhatmakesamathematicalexpressiontypesetinT
E
Xreallybeautiful.)
Thesymbolπintheoutputproducedby
$\pi$
maybefamiliarfrom highschool
mathematics. ItisaGreekletternamed“pi”. . Mathematiciansoftenuselettersofthe
Greekalphabet((whichevenotherwiseisGreektomany)andamultitudeofothersym-
bolsintheirwork.AlistofavailablesymbolsinL
A
T
E
Xisgivenattheendofthischapter.
VIII
.1.3. Mathematicalsymbols
Inthelistattheendofthischapter,notethatcertainsymbolsaremarkedtobenotavail-
ableinnativeLAT
E
X,butonlyincertainpackages. Wewilldiscusssomesuchpackages
later. Anotherthingaboutthelististhattheyarecategorizedintoclassessuchas“Bi-
naryRelations”,“Operators”,“Functions”andsoon. Thisisnotmerelyamatterof
convenience.
WehavenotedthatT
E
Xleavessomeadditionalspacesaround“binaryoperators”
suchas+and−. Thesameistrueforanysymbolclassifiedasabinaryoperator. . For
example,considerthefollowing
Forrealnumbersxandy,defineanoperation◦by
xy=x+yxy
Thisoperationisassociative.
Fromthelistofsymbols,weseethat◦isproducedby
\circ
andthisisclassifiedasa
binaryoperator,sothatwecanproducethisby
For real numbers s $x$ and $y$, define e an n operation $\circ$ by
$$
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