; TeX output 1995.07.11:1814ARrҠ.3{G ptmr7tEssentialQLyy#3{ ptmr7tATSEyX++^ZJonW BarbrickwithadditionsbyDa“vidCarlisle,MichelGoossens,SebastianRahtz,AdrianClark%d)January1994(W4e9Vff phvb7tContents:5ߌ ptmb7t1Introduction) b> cmmi10::::::::::::::::::::::::::::::::::::::p12HogwDoesLff>ߌ ptmb7tA;TU>NEXW@ork?呍::::::::::::::::::::::::::::::::,13ASampleLffA;TU>NEXFilex::::::::::::::::::::::::::::::::::*21SimpleText,a:::::::::::::::::::::::::::::::::::::::sn44DocumentClassesandOptionsT::::::::::::::::::::::::::::5b55EnvironmentsN::::::::::::::::::::::::::::::::::::::66TBypeStyles1:::::::::::::::::::::::::::::::::::::::x77SectioningCommandsandTablesofContentsFݍ::::::::::::::::::::88ProducingSpecialSymbolsn䍑::::::::::::::::::::::::::::::99Titles::::::::::::::::::::::::::::::::::::::::::*910TabularMaterialFa::::::::::::::::::::::::::::::::::::n1011TablesandFigures:::::::::::::::::::::::::::::::::::1112Cross-ReferencesandCitations'썑::::::::::::::::::::::::::::n1113MathematicalTBypesetting졍:::::::::::::::::::::::::::::::31314Whatabout$'Gs?Ӎ::::::::::::::::::::::::::::::::::::A1415Letters\R:::::::::::::::::::::::::::::::::::::::::`1516ErrorsdH:::::::::::::::::::::::::::::::::::::::::: U1617AFinalReminderZ:::::::::::::::::::::::::::::::::::18AMathematicalsymbols4:::::::::::::::::::::::::::::::::A19BHorribleMathematicalExamplestoStudym::::::::::::::::::::::z24ҍ3{ ptmr7t1*ARrҍ21NS ptmrc7tNEssentialL`ffOS ptmrc7tOAMNTU>?EfX.{Bibliograph٠y::::::::::::::::::::::::::::::::::::::::N25 hListofTab$lesw1&Greekletters.....................................19 Db2&Binaryoperationsymbols+3..............................193&Relationsymbols㍍..................................194&Largedelimiters[󍍑...................................205&DelimitersG......................................206&ArrowsymbolsO...................................207&Miscellaneoussymbolsc...............................208&Log-likgesymbolsQ..................................219&Mathmodeaccents=).................................2110&Variable-sizedsymbols...............................2111&Lff?3{ ptmr7tA;TU>?E1fXmathconstructs\................................2112&AMSmiscellaneoussymbols4............................2113&AMSGreekandHebrew..............................2214&AMSdelimitersK...................................2215&AMSarrowsv.....................................2216&AMSne٠g7atedarrows................................2217&AMSbinaryoperators................................2218&AMSbinaryrelations................................2319&AMSne٠g7atedbinaryrelations<...........................231hIntrJoductionlCThisEdocumentisanattempttogiv٠eyouallthe@Kj ptmri7t@essentialGinformationthatyouwillneedinor- der6KtousetheLffA;TU>?E1fXdocumentpreparationsystem[1].^1.wXOnlybasicfeaturesareco٠vered,cand6Kavast-amountofdetailhasbeenomitted.^MInadocumentofthissizeitisnotpossibletoincludeev٠erythingthatyoumightneedtoknowY,Gandifyouintendtomakgee٠xtensiveuseoftheprogramyougzshouldrefertoamorecompletereference.LKAttemptingtoproducecomple٠xdocumentsusingonly|theinformationfoundbelowwillrequiremuchmorewgorkthanitshould,}Yandwillprobablyproducealessthansatisfgactoryresult. 8ThemainreferenceforLffA;TU>?E1fXis@TheLffCKj ptmri7tCA-S@TU>4xEXUser'sguideandReferGenceManual냻byLeslieLamport[1].DThisPcontainsalltheinformationthatyouwillev٠erneedtoknowabouttheprogram,andyouwillneedaccesstoacopgyifyouaretouseLffA;TU>?E1fXseriouslyY.BothYtheManualandthisdocumentavoidYmentioningan٠ythingthatdependsontheparticularcomputer>systemthatyouareusing.2ThisisbecauseLffA;TU>?E1fXisavailableonanumberofsystemsandthe٠yalldi erinonewgayoranothers8.ZInstead,theybothrefertoa@localguidefortheirpartic-ularsystem. h2hHoȽwDoesLفKe9V phvb7tKAFTyԒEgyXW"ork?lCIn?E1fX,kTyougeneratea lecontainingboththete٠xtthatyouwishtotypesetandinstructionsZtotellLffA;TU>?E1fXhowyouwgantittoappears8.Ygouwillnormallycreatethis leusingyoursystem's8s6te٠xteditor.;Ygoucangiv٠ethe leanynameyoulikge,Dbutitshouldend\L0 pcrr7tL.tex"toidentifytheϋ le's8scontents.CYgouthengetLffA;TU>?E1fXtoprocessthe le,nanditcreatesanew leoftypesetting Vff֟ 荍 h-:B3{ ptmr7tB1fhA3{ ptmr7tAFMor`thosereaderswhoha vesomefamiliaritywithLBA@ATEX,thisdocumentassumestheLBAATEX302&2cmmi8"{AreleaseofJanuary1994 orlatergARrҍNEssentialL`ffOAMNTU>?EfX13.{commands;;this/hasthesamenameasyour lebutthe\L.tex"endingisreplacedby\L.dvi". ThisTstandsfor`LDeLviceLIndependent'and,asthenameimplies,this lecanbeusedtocreateoutputonarangeofprintingdevices.TxYgour@localguidewillgointomoredetail. 卑Rather/thanencourageyoutodictatee٠xactlyhowyourdocumentshouldbelaidout,[LffA;TU>?E1fXinstructions`Iallowyoutodescribeits@loggicalstructurGe.IF٠orexample,fyoucanthinkofaquotationembeddedIwithinyourte٠xtasanelementofthislogicalstructure:youwgouldnormallyexpecta3quotationtobedisplayedinarecognizablestyletosetito fromtherestofthete٠xt.otA3{hu-manmtypesetterwgouldrecognizethequotationandhandleitaccordinglyY,q~butsinceLffA;TU>?E1fXisonlyacomputerprogramitrequiresyourhelp.wkTherearethereforeLffA;TU>?E1fXcommandsthatallowyoutoidentifyquotationsandconsequentlyallowLffA;TU>?E1fXtotypesetthemcorrectlyY.Fundamental:toLffA;TU>?E1fXistheideaofa@documentclassthatdeterminese٠xactlyhowadocumentwillsbeformatted.-LffA;TU>?E1fXpro٠videsstandarddocumentclassesthatdescribehowcommonlogicalstructures(suchasquotations)shouldbeformatted.f.Ygoumayhav٠etosupplementthesestylesbyspecifying+theformattingoflogicalstructurespeculiartoyourdocument, suchasmathematicalformulae.DYgouQ\canalsomodifythestandarddocumentclassesorev٠encreateanentirelynewone,thoughyoushouldknowthebasicprinciplesoftypographicaldesignbeforecreatingaradicallynewstyle.Thereȁareanumberofgoodreasonsforconcentratingonthelogicalstructureratherthanontheq:appearanceofadocument.ODoingsoprev٠entsyoufrommakingelementarytypographicaler-rorsl inthemistakgenbeliefthatthe٠yimprovethestheticsofadocument|youshouldrememberthattheprimaryfunctionofdocumentdesignistomakgedocumentseasiertoread,C notprettiers8.It!isalsomore e٠xible,sinceyouneedonlyalterthede nitionofthequotationstyletochangethefappearanceof@allthequotationsinadocument.^Mostimportantofall,@logicaldesignencour-agestbetterwriting.PAtvisualsystemmakgesiteasiertocreatevisuale ectsratherthanacoherentstructure;logical=designencouragesyoutoconcentrateonyourwritingandmakgesithardertouseformattingasasubstituteforgoodwriting.$捍3hASampleLفKAFTyԒEgyXFileIHav٠ealookattheexampleLffA;TU>?E1fX leinFigure1.Itisaslightlymodi edcopgyofthestandardLffA;TU>?E1fXjRe٠xample leLsmall.tex9jR.nYgourlocalguidewilltellyouhowyoucanmakgeyourowncopgy+ofthis le.Thelinenumbersdowntheleft-handsidearenotpartofthe le,buthav٠ebeenaddedtomakgeiteasiertorefertovariousportions.ڎAlsohav٠ealookatFigure2whichshows,moreorless,theresultofprocessingthis le.k捍Rl phvr7tR3.1RunningUT`ext>JMostsdocumentsconsistalmostentirelyofrunningte٠xt|wgordsformedintosentences,Pwhichare[Finturnformedintoparagraphs|andthee٠xample leisnoexception.KDescribingrunningte٠xtposesnoproblems,youjusttypeitinnaturallyY.wIntheoutputthatitproduces,LffA;TU>?E1fXwill lllines'andadjustthespacingbetweenwgordstogiv٠etidyleftandrightmargins._Thespacinganddistributionˠofthewgordsinyourinput lewillhav٠enoe ectatallontheeventualoutput.7YAnynumberGofspacesinyourinput learetreatedasasinglespacebyLffA;TU>?E1fX.LItalsore٠g7ardstheendofULeachlineasaspacebetweenwgords(seelines15{17).F?E1fXIreserv٠esanumberofthelesscommonkgeyboardcharactersforitsownuse.UThetencharactersʍL# $%&~_^\{}shouldnotappearaspartofyourte٠xt|iftheydo,LffA;TU>?E1fXwillgetconfused.DARrҍ41NEssentialL`ffOAMNTU>?EfX.q?ffQ0 pcrr7tQ1:%SMALL.TEX--Released5July1985 ff2:%USETHISFILEASAMODELFORMAKINGYOUROWNLaTeXff3:%INPUTFILE.EVERYTHINGTOTHERIGHTOFA %ISffAff4:%REMARKTO YOUANDISIGNOREDBYLaTeX.ff5:%ff6:%WARNING! DONOTTYPEANYOFTHEFOLLOWING10CHARACTERSff7:%EXCEPTASDIRECTED:+30&32$#%_{}^~\ff8:ff9:\documentclass[11pt]{article}%YOURINPUTFILEMUSTCONTAIN10:ff\begin{document}F3.%THESETWOLINESPLUS11:%ffTHE\endCOMMANDATTHEEND12:13:ff\section{SimpleText}%THISCOMMANDMAKESASECTIONTITLE.14:15:ffWordsareseparatedbyoneormore fdspaces. Paragraphsare16:separatedffbyoneormoreblanklines. Theoutputisnotaffected17:ffbyaddingextraspacesorextrablanklinestotheinputfile.18:19:20:ffDoublequotesaretypedlikethis:``quotedtext''.21:ffSinglequotesaretypedlikethis:`single-quotedtext'.22:23:ffLongdashesaretypedasthreedashcharacters---likethis.24:25:ffItalictextistypedlikethis:\emph{thisisitalictext}.26:ffBold32textistypedlikethis:\textbf{thisis boldtext}.27:28:ff\subsection{AWarningorTwo}+30%THISMAKESASUBSECTIONTITLE.29:30:ffIfyougettoomuchspaceafteramid-sentenceperiod---abbreviations31:fflikeetc.\arethecommonculprits)---thentypeabackslashfollowedby32:ffaspaceaftertheperiod,asinthissentence.33:34:ffRemember,don'ttypethe10specialcharacters(suchasdollarsignand35:ffbackslash)exceptasdirected! Thefollowingsevenareprintedby36:fftypingabackslashinfrontofthem: \$\&\#\%\_\{and\}.37:ffThemanualtellshowtomakeothersymbols.38:39:ff\end{document}k%THEINPUTFILEENDSLIKETHISFigure1:TxASampleLffA;TU>?E1fXFileXARrҍNEssentialL`ffOAMNTU>?EfX15. wuэ1hSimpleT"eȽxtW37ordsL areseparatedbyoneormorespaces.C'P٠aragraphsareseparatedbyoneormoreblanklines. Theoutputisnota ectedbyaddinge٠xtraspacesorextrablanklinestotheinput le.Double5quotesaretypedlikgethis:2\quotedte٠xt".Singlequotesaretypedlikethis:2`single-quotedte٠xt'.Longdashesaretypedasthreedashcharacters|likgethis.Italicte٠xtistypedlikgethis:Tx@thisisitalictext.Boldte٠xtistypedlikgethis:thisisboldtext._R1.1AUW&arLningorT`wIoIfyougettoomuchspaceafteramid-sentenceperiod|abbreviationslikgeetc.arethecommonculprits)|thentypeabackslashfollowedbyaspaceaftertheperiod,asinthissentence.Remember,rTdon'tntypethe10specialcharacters(suchasdollarsignandbackslash)e٠xceptasdirected!Thepfollowingsev٠enareprintedbytypingabackslashinfrontofthem:X$&#%ff z !", cmsy10fandg.TxThemanualtellshowtomakgeothersymbols.ZNFigure2:TxTheResultofProcessingtheSampleFileR3.2L+Sl phvr7tSA7LRT#SEXUCommandsԉThereRareanumberofwgordsinthe lethatstartwith`L\'(seelines9,10and13).uTheseare LffA;TU>?E1fX@commandsandthe٠ydescribethestructureofyourdocument.Thereareseveralthingsthatyoushouldrealizeaboutthesecommands:ꍍAllLffA;TU>?E1fXcommandsconsistofa`L\'followedbyoneormorecharacters.s򍍍LffA;TU>?E1fXbcommandsshouldbetypedusingthecorrectmixtureofupper-andlower-caselet-ters.TxL\BEGINandL\Beginare@notthesameasL\begin.Someucommandsareplacedwithinyourte٠xt.3Theseareusedtoswitchthings,blikgedif-ferent Itypestyles,0onando .STheL\smallcommandisusedlikgethistoemphasizete٠xt,normally%bychangingtoan@italictypestyle(seeline25).F=Thecommandandthete٠xtarealgwaysO'enclosedbetween`L{'and`L}'|the`L{\em'turnsthee ectonandandthe`L}'turnsitzo .RAllthetypefgace-changingswitcheslikethishav٠eacorresponding@command߻withanargument|allthepossibilitiesareshownonpage7.ThereareothercommandsthatlooklikgeꍑGL\command{text}InQthiscase,%Ltext viscalledthe\argument"ofthecommand.kTheL\sectioncommandishlikgethis(seeline13).qSometimesyouhav٠etousecurlybrackets`L{}'toenclosetheargument,sometimessquarebrackgets`L[]',andsometimesboth.Thereismethodbehindthis?apparentmadness,obutforthetimebeingyoushouldbesuretocopgythecommandse٠xactlyasgiven.s򍍍Whenacommand's8snameismadeupentirelyofletters, dyoumustmakgesurethattheendofthecommandismarkgedbysomethingthatisn'taletters8. Thisisusuallyeithertheopen-ingbrackgetaroundthecommand's8sargument,oraspace.Whenit'saspace,thatspaceisalgwaysignoredbyLffA;TU>?E1fX.TxW37eshallseelaterthatthiscansometimesbeaproblem.`]ARrҍ61NEssentialL`ffOAMNTU>?EfX.{R3.3Ov3erIallUStr. ucturexThere_"aresomeLffA;TU>?E1fXcommandsthatmustappearinev٠erydocument.ITheactualtextofthedoc- umentalgwaysstartswithaL\begin{document}commandandendswithanL\end{document}command{(seelines10and39).SAn٠ythingthatcomesaftertheL\end{document}commandisignored.3Ev٠erythingthatcomesbeforetheL\begin{document}commandiscalledthe@prGeam-ble.TxThepreambleshouldcontainonlyLffA;TU>?E1fXcommandstodescribethedocument's8sstyle. . One;commandthatmustappearinthepreambleistheL\documentclasscommand(seeline9).џThiscommandspeci estheo٠verallstyleforthedocument.Oure٠xample leisasimpletechnicalkdocumentandusestheLarticlestyle,modi edtoprintinelev٠en-pointfonts.TThereareotherstylesthatyoucanuse,asyouwilldisco٠verinSection4.]3R3.4OtherUThingstoLookAtLffA;TU>?E1fXd(canprintbothopeningandclosingquotecharacters,2andcanmanageeitheroftheseei-ther%singleordouble.T37odothis,.itusesthetwgoquotecharactersfromyourke٠yboard:L`(whichsometimesyresemblesagrav٠eaccentorback-quote)andL'(apostrophe).~Ygoutypethesecharac-ters@onceforsinglequote(seeline21),q.andtwicefordoublequotes(seeline20).LThedoublequotecharacteritselfL"isalmostnev٠erused. . LffA;TU>?E1fXCcanproducethreedi erentkindsofdashes.BAlongdash,Tforuseasapunctuationsymbol,?E1fXspecialsymbolsinyourf^te٠xt.Sevenofthemcanbeprintedbymakingthemintocommandsbyproceedingthembybackslash(seeline36).Theremainingthreesymbolscanbeproducedbymoreadvancedcommands,ascansymbolsthatdonotappearonyourkge٠yboardsuchasy,z,x,@$,Gc ,]and|.ItissometimesusefultoincludecommentsinaLffA;TU>?E1fX le,_toremindyouofwhatyouhav٠edoneorwh7yyoudidit.Ev٠erythingtotherightofaL%-signisignoredbyLffA;TU>?E1fX,Ӎandsoitcanbeusedtointroduceacomment. }34hDocumentClassesandOptionsWwTherearefourstandarddocumentclassesavailableinLffA;TU>?E1fX:T0 pcrb7tTarticle/intendedforshortdocumentsandarticlesforpublication.GArticlesdonothav٠echap-ters,yIandwwhenL\maketitleisusedtogenerateatitle(seeSection9),thetitleappearsatthetopofthe rstpageratherthanonapageofitsown.\Treport)intended+forlongertechnicaldocuments.ItissimilartoLarticle,e٠xceptthatitcon-tainschaptersandthetitleappearsonapageofitsown.Tbookintendedasabasisforbookpublication.q5P٠agelayoutisadjustedassumingthattheoutputwillev٠entuallybeusedtoprintonbothsidesofthepapers8.Tletter)intendedeZforproducingpersonalletters.Thisstylewillallowyoutoproducealltheelementsofawelllaidoutletter:Txaddresses,date,signature,etc..Theseastandardstylescanbemodi edbyanumberof@options.3The٠yappearinsquarebrackgetsaftertheL\documentclasscommand.wOnlyoneclasscanbeusedinadocumentbutyoucanhav٠emorethanoneoption,inwhichcasetheirnamesshouldbeseparatedbycommas.Thestandardoptionsare:T11ptprintsthedocumentusingelev٠en-pointtypefortherunningtextratherthattheten-pointtypenormallyused.TxElev٠en-pointtypeisabouttenpercentlargerthanten-point.owARrҍNEssentialL`ffOAMNTU>?EfX17.{T12ptprintsUthedocumentusingtwelv٠e-pointtypefortherunningtextratherthantheten-point typenormallyused.TxT37welv٠e-pointtypeisabouttwentypercentlargerthanten-point.Ttwoside/causesdocumentsinthearticleorreportstylestobeformattedforprintingonbothsidesofthepapers8.TxThisisthedefgaultforthebookstyle.Ttwocolumn;producestwgocolumnsofte٠xtoneachpage.Ttitlepage;causes|theL\maketitlecommandtogenerateatitleonaseparatepagefordoc-uments+intheLarticle0Vstyle.VA+Sseparatepageisalgways+usedinboththeLreport*VandLbook3styles.Thereo?E1fXwgasjWdesignedinAmericawherethestandardpaperisshorterandslightlywiderthanA4;qwithoutthisoptionyouwill ndthatyouroutputlooksalittlestrange.)۷5hEnlvirJonmentsW37ezmentionedearliertheideaofidentifyingaquotationtoLffA;TU>?E1fXsothatitcouldarrangetotype-setitcorrectlyY.1~T37odothisyouenclosethequotationbetweenthecommandsL\begin{quotation}andPL\end{quotation}.iThisisane٠xampleofaLffA;TU>?E1fXconstructioncalledan@environment.Anumberofspeciale ectsareobtainedbyputtingte٠xtintoparticularenvironments.R5.1QuotationsTherearetwgoenvironmentsforquotations:Lquote$FandLquotation8.FLquote$6isusedeitherforashortquotationorforasequenceofshortquotationsseparatedbyblanklines:oWUSpresidentshav٠ebeenknownfortheirpith7yremarks:Thebuckstopshere.Iamnotacrook.ҍQUSffpresidentshavebeenknownfor ҍtheirffpithyremarks:ҍ\begin{quote}ҍTheffbuckstopshere.ҍIffamnotacrook.ҍ\end{quote}]UsebtheLquotation<,environmentforquotationsthatconsistofmorethanoneparagraph.P٠aragraphsintheinputareseparatedbyblanklinesasusual:Hereissomeadvicetoremember:(EnvironmentsJformakingquotationscanbeusedforotherthingsaswell.(Man٠y~Kproblemscanbesolvedbynovelap-plicationsofe٠xistingenvironments.ҍQHereffissomeadvicetoremember: ҍ\begin{quotation}ҍEnvironmentsffformakingquotationsҍcanffbeusedforotherthingsaswell.ҍManyffproblemscanbesolvedbyҍnovelffapplicationsofexistingҍenvironments.ҍ\end{quotation}zR5.2Center. ingUandFlushingTLe٠xt canbecentredonthepagebyputtingitwithintheLcenter)@environment,)anditwillappear ushLag7ainsttheleftorrightmarginsifitisplacedwithintheLflushleft:8orLflushright@8en-vironments.NNoticeo thespellingofLcenter&o |unfortunatelyLffA;TU>?E1fXdoesn'tunderstandtheBritishEnglishspelling.qARrҍ81NEssentialL`ffOAMNTU>?EfX.{TLe٠xtZwithintheseenvironmentswillbeformattedinthenormalwgay;ginparticular,btheendsof the~linesthatyoutypearere٠g7ardedasspaces.ST37oindicateanewline,~myoutypetheL\\command.F٠orexample:u"䍑^onetwgothreeqfourr{ v٠eҍQ\begin{center} ҍoneҍtwoҍthreeff\\ҍfourff\\ҍfiveҍ\end{center}tR5.3ListsBThereRarethreeenvironmentsforconstructinglists.̞Ineachone,eeachnewitemisbe٠gunwithanXL\itemcommand.GIntheLitemize0environment,+thestartofeachitemisgiv٠enamarkger,while,jin"theLenumerate;Denvironment,eachitemismarkgedbyanumbers8./Theseenvironmentscanfbenestedwithineachother,kinwhichcasetheamountofindentationusedandthemarkgerareadjustedaccordingly:䍍ItemizedlistsarehandyY.Howev٠er,don'tforget"1./The`item'command."2./The`end'command.ҍQ\begin{itemize} ҍ\itemffItemizedlistsarehandy.ҍ\itemffHowever,don'tforgetY\begin{enumerate}Y\itemffThe`item'command.Y\itemffThe`end'command.Y\end{enumerate}ҍ\end{itemize}sThethirdlist-makingenvironmentisLdescriptionD. 9InaLdescriptionG{,youspecifytheitemlabelsinsidesquarebrackgetsaftertheL\itemcommand.TxF٠orexample:Threeanimalsthatyoushouldknowaboutare:gnatлAsmallanimalthatcausesnoendoftrouble.gnuAlargeanimalthatcausesnoendoftrouble.armadillo.eAmedium-sizedanimal.ҍQThreeffanimalsthatyoushould ҍknowffaboutare:ҍ\begin{description}Y\item[gnat]ffAsmallanimalthatcausesl%noffendoftrouble.Y\item[gnu]ffAlargeanimalthatcausesl%noffendoftrouble.Y\item[armadillo]ffAmedium-sizedanimal.ҍ\end{description}~R5.4V BerbatimUOutputBSometimesyouwillwganttoincludete٠xtexactlyasitappearsonaterminalscreen.hForexample,youmightwganttoincludepartofacomputerprogram.FNotonlydoyouwantLffA;TU>?E1fXtostopplayingaroundwiththelayoutofyourte٠xt,youalsowganttobeabletotypeallthecharacterson ARrҍNEssentialL`ffOAMNTU>?EfX19.{yourkge٠yboardwithoutconfusingLffA;TU>?E1fX.TxTheLverbatim5environmenthasthise ect: Thesectionofprograminquestionis:L{thisfinds%a&%b} fori:=1to27dobegintable[i]:=fn(i);process(i)end;ҍQTheffsectionofprogramin ҍquestionffis:ҍ\begin{verbatim}ҍ{ffthisfinds%a&%b}ҍforffi:=1to27dobegintable[i]ff:=fn(i);process(i)end;ҍ\end{verbatim}h6hT"ypeStyles^)W37ehav٠ealreadycomeacrosstheL\emphcommandforchangingthetypefgacetoemphasis._kHere isafulllistoftheavailabletypefgacechangingcommands:Wd@CommanduorE ectL\textrm{...}u{\rmfamily...}TLe٠xtissetinromanfgamilyL\textsf{...}u{\sffamily...}TLe٠xtissetinUl phvr7tUsansǧser&_iffgamilyL\texttt{...}u{\ttfamily...}TLe٠xtissetinLtypewriterfgamilyL\textmd{...}u{\mdseries...}TLe٠xtissetinmediumseriesL\textbf{...}u{\bfseries...}TLe٠xtissetinboldseriesL\textup{...}u{\upshape...}TLe٠xtissetinuprightshapeL\textit{...}u{\itshape...}TLe٠xtissetin@italicshapeL\textsl{...}u{\slshape...}TLe٠xtissetinM3{ ptmro7tMslantedлshapeL\textsc{...}u{\scshape...}TLe٠xtissetinNsmallcapsshapeL\emph{...}u{\em...}TLe٠xtisset@emphasizedL\textnormal{..}u{\normalfont..}TLe٠xtissetinthedocumentfontWύRememberthatthedeclarationv٠ersions(secondcolumn)areused@insideapairofbracestolimittheamountofte٠xtthattheya ect.mItisrecommendedthatyouusethecommands( rstcolumn)Fwithaparameterofthete٠xttotypesetdi erentlyY.A-Inadditiontothetypefgacecommands,thereareasetofcommandsthatalterthesizeofthetype.TxThesecommandsare:, W3{ ptmr7tWtinylscriptsizeeAfootnotesizeP3{ ptmr7tPsmall]normalsize larȹge 23{ff ptmr7tLargeLARGEQX3{q ptmr7tXhuge/\V3{H ptmr7tVHugeҍQ\tinyfftiny ҍ\scriptsizeffscriptsizeҍ\footnotesizefffootnotesizeҍ\smallffsmallҍ\normalsizeffnormalsizeҍ\largefflargeҍ\LargeffLargeҍ\LARGEffLARGEҍ\hugeffhugeҍ\HugeffHuge YARrҍ10,NEssentialL`ffOAMNTU>?EfX.`7hSectioningCommandsandTab$lesofContentsTLechnicalJdocuments,6likgethisone,areoftendividedintosections. WEachsectionhasaheading containing5atitleandanumberforeasyreference.LffA;TU>?E1fXhasaseriesofcommandsthatwillallowvWyoutoidentifydi erentsortsofsections.7}Onceyouhav٠edonethis,LffA;TU>?E1fXtakgesontheresponsibilityoflayingoutthetitleandofpro٠vidingthenumbers. mThecommandsthatyoucanuseare:ڍL\chapter&\subsection-\paragraph\section&\subsubsection\subparagraphThenamingoftheselasttwgoisratherunfortunate,sincethe٠ydonotreallyhaveanythingtodowith`paragraphs'inthenormalsenseofthewgord:Ethe٠yarejustlowerlev٠elsofsection.+Inmostdocumentastyles,headingsmadewithL\paragraphandL\subparagrapharenotnumbered.L\chapterisnotavailableindocumentstyleLarticle,. IThecommandsshouldbeusedintheordergiv٠en,sincesectionsarenumberedwithinchapters,subsectionswithinsections,etc.. mA sev٠enth sectioningcommand,=L\part,is alsoavailable.T'Itsuseisalgways optional,=anditisusedwtodividealargedocumentintoseriesofparts.Itdoesnotalterthenumberingusedforan٠yoftheothercommands.IncludingthecommandL\tableofcontentsinyourdocumentwillcauseacontentslistto2beincluded,B\containinginformationcollectedfromthevarioussectioningcommands.:Ygouwillnotice&thateachtimeyourdocumentisrunthroughLffA;TU>?E1fXthetableofcontentsisalgways&madeupZUoftheheadingsfromthe@prGe٠vioustimeyouranLffA;TU>?E1fXonit.xThisisbecauseLffATU>?E1fXcollectsinformationryforthetableasitprocessesthedocument,u.andthenincludesitthene٠xttimeitisrun.ThisjcansometimesmeanthatthedocumenthastobeprocessedthroughLffA;TU>?E1fX@twicetogetacorrecttableofcontents."T8hPrJoducingSpecialSymbolsYgouqcanincludeinyourLffA;TU>?E1fXdocumentawiderangeofsymbolsthatdonotappearonyourkge٠yboard.TxForastart,youcanaddanaccenttoan٠yletter:)卍b߀fffd ffğYfdoffL\`{o} ffB3~AoWL\~{o}  ff332o32L\v{o} ff fffdoffL\c{o} ffB3AoWL\'{o}  ff332o32L\={o} ff ffğY}fdoffL\H{o} ffA̻oA?C .WL\d{o}  ff3^32o32L\^{o} ff ffğY_fdoffL\.{o} ffAհlA̻ooWL\t{oo} ff32o%#32L\b{o} ff ffğYfdoffL\"{o} ffB3AoWL\u{o}  ff32 ffff($Sev٠eralothersymbolsareavailableandaregeneratedusingthefollowingcommands:ڍyzL\dag0xxL\S?G׻c< UAL\copyrightzzL\ddag*{L\P<@$AL\poundsL\oe62qL\OEjL\AE C2qL\AE5p36aL\aarAL\AAAL\o<L\ONL\l2CL\E<AL\ss6>L?`<L!`<.@..AL\ldots$LffA;TU>?E1fXL\LaTeXThere/VisalsoaL\todaycommandthatprintsthecurrentdate.9Whenyouusethesecommandsre-memberPthatLffA;TU>?E1fXwillignorean٠yspacesthatfollowthem,Zasothatyoucantype`L\pounds20'toget`@$20'.1~Howev٠er,,ifyoutype`L\LaTeXiswonderful'youwillget`LffA;TU>?E1fXiswgonderful'|noticethelackofspaceafterLffA;TU>?E1fX.cxT37oo٠vercomethisproblemyoucanfollowan٠yofthesecom- ARrҍNEssentialL`ffOAMNTU>?EfX,11.{mandsrbyapairofemptybracesandthenan٠yspacesthatyouwishtoinclude,ߎandyouwillsee thatL\LaTeX{}reallyiswonderful!(LffA;TU>?E1fXreallyiswgonderful!). +0FinallyY,kLffA;TU>?E1fXˉ`math'mode,normallyusedtolayoutmathematicalformulae,giv٠esaccesstoanev٠enlargerrangeofsymbols,2includingtheupperandlowercasegreekmathematicalalphabet,calligraphictletters,vmathematicaloperatorsandrelations,arrowsandawholelotmore.PThiswillbediscussedinSection13. m9hTitlesR Mostdocumentshav٠eatitle.CT37otitleaLffA;TU>?E1fXdocument,youincludethefollowingcommandsinyourdocument,usuallyjustafterL\begin{document}. `Y0 pcrr7tY\title{requiredtitle} \author{requiredauthor}\date{requireddate}\maketitleV`IfEtherearesev٠eralauthors,QrthentheirnamesshouldbeseparatedbyL\andintheL\authorcom- mand;bthe٠ycanalsobeseparatedbyL\\ifyouwgantthemtobecentredondi erentlines.=IftheL\datecommandisleftout,thenthecurrentdatewillbeprinted.#sj>L\title{Essential\LaTeX}\author{JonWarbrick\andANOther}\date{14thFebruary1988}\maketitleSٍ@EssentialLffA;TU>?E1fXCJW37arbrick ANOtheriB14thFebruary1988#{The?e٠xactappearanceofthetitlevariesdependingonthedocumentstyle.?IntheLreport(andLbookustyles,wGtheutitleappearsonapageofitsown.PIntheLarticle.2style,itnormallyappearsatthetopofthe rstpage;usetheclassoptionLtitlepage;toalterthis(seeSection4).10iTabJularMaterialR BecausezLffA;TU>?E1fXwillalmostalgwayszconv٠ertasequenceofspacesintoasinglespace,Xitcanberatherdiculttolayouttables.TxSeewhathappensinthise٠xampleV`IncomeExpenditureResult20s0d19s11dhappiness20s0d20s1dmiseryҍQ\begin{flushleft} ҍIncome ExpenditureffResult\\ҍ20sff0d 19s11dhappiness\\ҍ20sff0d 20s1d fdmiseryҍ\end{flushleft}KHmTheטLtabbing/0environmentטo٠vercomesthisproblem.[@Withinit,~yousettab-stopsandtabtothem-muchasyouwgoulddoonatypewriters8.]T37ab-stopsaresetwiththeL\=command,Yλcommandmo٠vestothene٠xtstop.tTheL\\commandisusedtoseparateeachline.AlinethatendsinL\killproducesnooutput,andcanbeusedtosettab-stops:fdIncomeExpenditureResult20s0d19s11d^Happiness20s0d20s1d^MiserydQ\begin{tabbing} dIncomeff\=Expenditure\=%\killdIncomeff\>Expenditure\>Result\\d20sff0d\>19s11d\>Happiness \\d20sff0d\>20s1d \>Miseryd\end{tabbing} sARrҍ12,NEssentialL`ffOAMNTU>?EfX.{Unlikge)atypewriter's8stabke٠yY,9ttheL\>commandalwaysmo٠ves)tothene٠xttab-stopinse- quence,hnev٠en9ifthismeansmovingtotheleft.LThiscancausetexttobeoverwritteniftheg7apbetweentwgotab-stopsistoosmall.Ifyouhav٠emoresophisticatedtabularwgork,youwillneedtheLtabular/environment.z Thisdi ersfromLtabbing/inthatyouneednotwgorryaboutwidthsofcolumns|LffA;TU>?E1fXwilllookatthe-wholetableandseehowwidecolumnsneedtobetocopewiththewidestentriesinthem.Ygoulmust,&howev٠er,telllLffA;TU>?E1fXhowman٠ycolumnsthereareandhowyouwishtolaythemout.Ygoudothisbysupplyinga@templateafterL\begin{tabular}withaletterforeachcolumn:卍dhLlzmeansthecolumnwillbeleftjusti edhLrzmeansthecolumnwillberightjusti edhLczmeansthecolumnwillbecentredItemsǪwithinarowareseparatedbythe&character(nowyouknowwh7yitistreatedspecially),andtherowisended,asbefore,withL\\.9Asimpletablewiththreecolumnsandtwgorowslookslikge:1d@Name8TVAggeSǎHeightSebastian=Dž45SDž195cmMathewBDž1XDž68cmҍQ\begin{tabular}{lrr} ҍ\emffName&\emAge&\emHeight\\ҍSebastianff&45&195cm0\\ҍMathew&ff1&68cmҍ\end{tabular}HVariousotherbellsandwhistlescanbeusedtomakgethelayoutnicer:/ 1.YgoucanputL\hlinebetweenrowstodra٠walineacrossthetable./ 2.T37ypeaL|inthetemplatewhereyouwgantav٠erticalbardownev٠eryrowofthetable. 3.Ygou)canspecifythatacolumnisofa x٠edwidthwithtext owingwithinitbyusingthe symbolLpinthetemplate,followedbyawidthbetweenL{andL}.Thewidthcanbegiv٠eninan٠yof`cm',`mm'or`in'(butnot`inches'!)./Thus,amoresophisticatedtablemightlooklikgethis:QL̍fffd fffd@Group9G ff_dTBype ffhSherds ffff fffdGroups1{9$ ff_dGre٠ywgares ff(218 ff $fffdGroups40{44$ff_dBlackaz(mostly_d`black/bur-_dnished')wgares$ff(116$ff$fffdGroups61{67ff_dBu -red-orange_dwgaresffš(46fffffdGroups81{85ff_dColour-coated_d newgaresffš(67fffffdGroups91{2,93{4ff_dMortaria0and_dmiscellaneousffš(35ff fffdGroup96,С ff_dSamian ffš(56 fffffd ffX ff ff(538 ffffҍQ\begin{tabular}{|l|p{1in}|r|} \hline ҍ\emffGroup&\emType&Sherds \\\hlineҍGroupsff1--932&Greywares&218\\ҍGroupsff40--44&Black(mostlyҍ`blackffburnished') wares&116\\ҍGroupsff61--67&Buff-red-orangeҍwaresff&46f\\ҍGroupsff81--85&Colour-coatedҍfineffwares&67K\\ҍGroupsff91--2,93--4&Mortariaҍandffmiscellaneous&35%\\ҍGroupff96&Samian&56+30\\\hline8&&538|3*\\\hlineҍ\end{tabular}bNotethatline-endingsinwhatyoutypearenotimportant;rowsendonlywhenaL\\isfound."?11iTab$lesandFiguresWhenyoulayoutsomete٠xtandnumbersinatable,itisalmostalgwaysintendedthatthewholeunitzstaystogether,!notbreakingo٠verzapage.Whatdoyoudowhenyouareatthebottomofa ARrҍNEssentialL`ffOAMNTU>?EfX,13.{pagewithnotenoughspaceleft?(SimilarlyY,vwhatdoyoudowhenyouwganttoleav٠espacefora photograph-tobepastedin?9!Whenyouaretypingthete٠xt,>cyoudonotknowwhereLffA;TU>?E1fXwillstartaԵnewpage,soitisoftenv٠erydiculttoleavespacejustwhereyouwgant.RLffA;TU>?E1fXsolvesthisbyasystemof` oats',+objectsthatwillbeplacedinanicepositiononthepage,butnotnecessarilye٠xactly?whereyouputitinyour le.a5Theywilloftenbeplacedatthebottomofthecurrentpage,oroatthetopofthene٠xt,soronapagebythemselves,siftheyneedthatmuchspace.OLffA;TU>?E1fXletsyouspecifytwgosortsof oat,_namely@tablesand@ gurGes;?ineachofthemyoucanspecifyacaption.The@followingshowshowyouwgouldsetupspacefora gureinwhichyouwantedtoleav٠e3inchesofspace,followedbyacaption: L\begin{figure} \vspace{3in} \caption{APhotographofmySubject} \end{figure}pFiguresA]andtablesareautomaticallynumbered,Mlikgesections;V>justasL\tableofcontentslistsyoursections,,subsections,etc.withtheirpagenumbers,L\listoffiguresandL\listoftableswilllistthe guresandtableswiththeircaptions. 12iCrJoss-Ref$erencesandCitationskOneofthemostusefulthingsLffA;TU>?E1fXcandoforyouistotoautomaticallygenerateasection,page,={ gure,table,orequationnumberinacross-reference.9F٠orexample,={torefertoSection4ofthisreport(ondocumentstyles)andFigure2(theoutputofprocessingLsample.tex>)inthissentence,thecommandsusedwere:LtorefertoSection~\ref{sec:styles}ofthisreport(ondocumentstyles)andFigure~\ref{fig:result}(theoutputofprocessingpYgouwillseethattheL\refcommandinsertedthecross-referencesnumberintotheprinteddoc-ument.TxTheL~simplyinsertsaspacewhileprohibitingLffA;TU>?E1fXfrombreakingaline. 8_Ofcourse,torefertoacross-reference,theremustbeanindicationintheLffA;TU>?E1fXinput leofthe!pointbeingreferredto.7ThisisdoneviatheL\labelcommand.Thelabelforasectionismostconv٠enientlydoneimmediatelyafterthesectionheading,asin:L\section{DocumentClassesandOptions}\label{sec:styles}pandthatfora gureortableinorimmediatelyfollowingtheL\captioncommand:L\caption{TheResultofProcessingtheSampleFile}\label{fig:result}pAn٠ytextmaybeusedinL\labelandL\refcommands,thoughtheconventionimpledaboveisa?goodonetofollowY.GP٠agereferencesuseL\labelinthesamewgay,obutarereferredtousingL\pagerefinsteadofL\ref. 8_IndmuchthesamewgaythatyoucanrefertootherpartsofyourdocumentfromtheLffA;TU>?E1fX lesymbolicallyY,~iyouKmayciteotherdocuments. T37odothis,youincludetheL\citecommandinyourte٠xt,asinLThebookbyLamport\cite{Lamport-LaTeX}istheprincipalreferenceworkon\LaTeX.pTheɃargumenttotheL\citecommand,knownasthe@citationkge7y,isusedtouniquelyidentifyapaper,book,orotherdocumentthathasbeendescribedina@biblioggr٠aphicdatabase. 8_HavingVtcitedotherwgorkfromyourdocument,^youcangeneratealistofreferencesbyinclud-ingthecommandszARrҍ14,NEssentialL`ffOAMNTU>?EfX.{L\bibliographystyle{plain} \bibliography{mybib1,mybib2}ҍwhereuyouwgantthelisttoappears8.QTheL\bibliographystylecommandtellsLffA;TU>?E1fXhowyouwgantthecitationstoappear,thestandardonesbeing:Tplain#CitationsYaresortedalphabeticallyinthelist,witheachentrybeingassignedanumber;entriesinthete٠xtareindicatedinsquarebrackgets.Tunsrt#CitationsCareorderedinthereferencelistintheorderoftheir rstappearanceandas-signedanumber;entriesinthete٠xtareindicatedinsquarebrackgets.Talpha#Citationsqaresortedalphabeticallyinthelistbuthav٠elabelslikge\Lam86"insteadofanumber;thesamelabelappearsinthete٠xtinsquarebrackgets.Tabbrev)CitationsaresimilartoLalpha#butaremorecompact(e.g.,byabbreviatingmonthandjournalnames).ThehsargumentoftheL\bibliographycommandisacomma-separatedlistof lenames,which6shouldendinL.bibm(i.e.,Lmybib1.bib@mandLmybib2.bibinthee٠xampleabove).<These les7containthee٠xpandedreferencesreferredtobytheL\citecommands.A0fulldescriptionofthe,:formatoftheseL.bibXt lesandhowthecitationsareconv٠ertedtoaLffA;TU>?E1fX-compatibleformare׭be٠yondthescopeofthis(introductory)guide;detailsaregiveninAppendixBחofLamport's8sbook./13iMathematicalT"ypesettingR13.1#ZMath,UDisplay-mathandEquation%Mathematics+istreatedbyTU>?E1fXcompletelydi erentlyfromordinaryte٠xt.Therearetwgospecial@modesformathematics,knownas@mathmodeand@displaymathmode.鍑MathmodecommandsaresurroundedbyL\(.@..L\)orbyL$.@..L$.эSomeomathematicssetinlineK`y cmr102v3ac=6.$Noteothatspacesintheinput leareignoredinmathmode.ҍQSomeffmathematicssetinline ҍ\(ff2\times3=326\).ҍNoteffthatspacesintheinputfileҍareffignoredinmathmode.IDisplaymathmodecommandsaresurroundedbyL\[.@..L\].Alargerequationtobedisplayedonalinebyitself.ɍQf(x)= O!cmsy71 u cmex10X t 0ercmmi7iٓRcmr7=0<$f^(i) ݲ(x)wfe n (֍ i/i!ҍQAfflargerequationtobedisplayedonalinebyitself. ҍ\[fff(x)=\sum_{i=0}^{\infty}\frac{f^{(i)}(x)}{i!}\]VThereisavariantofdisplaymathmode,theLequation5environment,whichautomaticallygen- ARrҍNEssentialL`ffOAMNTU>?EfX,15.{eratesanequationnumbers8.j/S^d;a1Jb2 ;a0Jb1Tc^]^dj2y0 j1y3^7=^d#4#6 #1#3(#^)(1)ҍQ\begin{equation} ҍ\left(\begin{array}{cc}ҍ1ff&2\\0&1ҍ\end{array}\right)ҍ\left(\begin{array}{cc}ҍ2ff&0\\1&3ҍ\end{array}\right)ҍ=ҍ\left(\begin{array}{cc}ҍ4ff&6\\1&3ҍ\end{array}\right)ҍ\end{equation}L6Theseshorte٠xamplesshowthemaintypesofcommandsavailableinmathmode.źAvfew thingstonoteare: 1.SubscriptsandsuperscriptsareproducedwithL_andL^,asinLx_{1}=p^{2}forx1'=p^2|s.j 2.FractionsareproducedbytheL\fraccommand:TxL\(\frac{a+b}{c}\)giv٠es 3a+b3&fe D5c䪻. 3.Variouscommandsgiv٠enamestomathematicalsymbols: L\infty\Rightarrow\surd\bigotimesgenerate10)fpUGN 4.ArraysareproducedbytheLarray#6environment.|HThisisidenticaltotheLtabular/6envi-ronmentXdescribedinSection10e٠xceptthattheentriesaretypesetinmathmodeinsteadofLRmode.NotethattheLarray#3environmentdoesnotputbrackgetsarroundthearrayY,=soitcanqwalsobeusedforsettingdeterminants|orev٠ensetsofequationsinwhichyouwgantthecolumnstolineup. 5.ThecommandsL\leftandL\rightproducedelimitersthatgrowaslargeasneeded.The٠y?canbeusedwithavarietyofsymbols,Oe.g.,L\left(?\left\{\left|.5Thefullsetofthesedelimitersisshownintables5and4belowY.EIR13.2#ZSpacing؄AllVspacesintheinput leareignoredinmathmode.ؽSometimesyoumaywganttoadjustthespacing;useoneofthefollowingcommandstoachiev٠ethis.dj L\,thinspaceК?E1fXneedssomehelpwithspacingisj<īRR UVz?dxdy[::īR RUNzpdxdyҍQ\(\int\!\!\intffz\,dxdy..\int\intzdxdy\)'wR13.3#ZChangingUFontsinMathModeTheGdefgaultmathmodefontismathital2`ic.AThisshouldnotbeconfusedwithordinary@textitalic.The5fontfor`ordinary'letterscanbechangedwiththeusualcommands,DL\emph,L\textbf,etc..NotethatlowercaseGreekletters(L\alpha,etc.)arere٠g7ardedasmathematicalsymbols(whichmeansthatthe٠ymustbetypedinmathmode)andarenota ectedbythesecommands.)ARrҍ16,NEssentialL`ffOAMNTU>?EfX.{L\mathbf8producesboldfaceromanletters.gIfyouwishtohav٠e]DF cmmib10]boldfacemathitalic letters,dRand6boldfgaceGreeklettersandmathematicalsymbols,usetheL\boldmathcommand@beforGegoingintomathmode.TxThischangesthedefgaultmathfontstobold. pqǍx⚲=2>s)x'6:28aZ"V cmbx10Zx=2)x'6:28a]xQhZ=2]9`Ɍ cmbsy10`)]x`'Z6]:Z28ҍQ\(ffx=2\pi\Rightarrowx\simeq6.28\) ҍ\(\mathbf{x}ff=2\pi\Rightarrowx\simeq6.28\)ҍ{\boldmathff\(x=\mathbf{2}\pi\Rightarrowx98\simeq{\mathbf{6.28}}K\)}@=bThere3isalsoacalligraphicfontforuppercaseletters;LtheseareproducedbytheL\mathcalcommand:TFhҍQ\(ff\mathcal{F}\)&z14iWhatabout$'"s? ۍIf-&youhav٠econvertedtoLffA;TU>?E1fXfromplainorAU>?M S-TU>?EX,Xpyouwillprobablybewgonderingwh7ytherehasbeennomentionof$and$$. In'thesesystemsmathmodeissurroundedbyL$'s8sanddisplaymathmodeissurroundedbyL$$.xThis&hascertaindra٠wbacksovertheLffA;TU>?E1fXsystemasitisdicultforyourtexteditortomatch L$'s8sasitishardtotellwhichonesarestartingmathmodeandwhichareendingit.TU>?E1fXwillalsogetconfusedifyoumissa$out.The(incorrect)input(Llet(a,b,c)$beaPythagoreantriple,i.e.\threeintegerssuchthat$a^{2}+b^{2}=c^{2}$. pproducestheslightlymysteriouserrormessageL!Missing$inserted.`$r^l.56...triple,i.e.\threeintegerssuchthat$a^,{2}+b^{2}=c^{2}$? pNotethatitreportsthewrongerrorandinthewrongplace,theuseoftheL^commandoutofmath-mode.]sTU>?E1fXhastypeset`bea.@..msuch-that'inmathmodeand@exitedrmathmodeattheL$after`suchthat'.IfyouhadmadetheequivalentLffA;TU>?E1fXerror,LffATU>?E1fXhasabetterideaofwhatyouindended:Llet(a,b,c)\)beaPythagoreantriple,i.e.\threeintegerssuchthat\(a^{2}+b^{2}=c^{2}\) pTheerrormessagemaystillbeunintellig7able,Dbutatleastitreportstheerrorintherightplace,you hav٠eusedL\)toendmathmodewhenyouwerenotinmathmode(asyouomittedtheL\(whichshouldhav٠ebeenbeforetheL(a,b,c)).LLaTeXerror. SeeLaTeXmanualforexplanation.TType Hforimmediatehelp.!Badmathenvironmentdelimiter.\@latexerr...forimmediatehelp.}\errmessage{#1}ޠARrҍNEssentialL`ffOAMNTU>?EfX,17.{L\)...ifinner$\else\@badmath\fi\else\@badmath ,\fil.56let(a,b,c)\)rbeaPythagoreantriple,i.e.\threeintegerssuchthat\...?T\Thesingledollarissometimesusefulforsmallsectionsofmath.T\TLetGbeap-groupҍQLetff$G$bea$p$-groupčThedoubledollaris@notalgwaysequivalenttoL\[...\],andsoshouldnotbeusedifyouwgantFEyourLffA;TU>?E1fX letobecompatiblewithdi erentstylesandoptions(trythe@ eqnclassoption).GR14.1#ZSymbols#ThefollowingtablesshowmostofthesymbolsavailablefromthestandardLffA;TU>?E1fXsymbolfonts.Ne٠g7ationsoftherelationalsymbolscanbemadewiththeL\notcommand:ǍG6HҍQ$Gff\not\equivH$čIn3theappendixwehav٠ebroughttogetherasetoftablesregroupingallstandardLffA;TU>?E1fXsym-bols(tables1to11.2T37ables13to612showsupplementaryAU>?M S-TU>?E1fXsymbols,ܢwhichareavail-ablewhenyouspecifytheLamssymbpackage. g15iLetterȽsP"ProducingkglettersissimplewithLffA;TU>?E1fX.T37odothisyouusethedocumentstyleLletter.Ygoucanmakgean٠ynumberofletterswithasingleinput le.zQYgournameandaddress,whicharelikelyto$(bethesameforallletters,M3aregiv٠enonceatthetopofthe le.@EachletterisproducedbyaLlettersenvironment,Phavingthenameandaddressoftherecipientasitsargument.Theletteritselfbe٠ginswithanL\openingcommandtogeneratethesalutation. *.TheletterendswithaL\closingcommand.YgoucanusethecommandsL\enclandL\ccto_generatelistsofenclosuresandpeopletowhomyouaresendingcopies.mAn٠ytextthatfollowsthe=L\closingmustbeproceededbyaL\pscommand.>,Thiscommandproducesnote٠xt|you'gllhav٠etotype\P.S.L"yourself|butisneededtoformattheadditionalte٠xtcorrectlyY.Ane٠xamplewillmakgethisclearer: \Y\documentstyle{letter} \begin{document}\address{1234AvenueoftheArmadillos\\D37GnuYork,G.Y.56789}\signature{R.(Ma)Dillo\\DirectorofCuisine}\begin{letter}{G.NathenielPicking\\aAcmeExterminators\\aIllinois}\opening{DearNat,}I'mafraidthatthearmadilloproblemisstillwithus.Idideverything......andIhopethatyoucangetridofthenasty ARrҍ18,NEssentialL`ffOAMNTU>?EfX.{Ybeaststhistime. \closing{BestRegards,}\cc{JimmyCarter\\RichardM.Nixon}\end{letter}\end{document} o16iErrJorȽsR㍻When7youcreateanewinput leforLffA;TU>?E1fX,youwillprobablymakgemistakes.3Ev٠erybodydoes, andQit's8snothingtobewgorriedabout.ɉAswithmostcomputerprograms,therearetwosortsofmistakge/thatyoucanmake:thosethatLffA;TU>?E1fXnoticesandthosethatitdoesn't.cT37otakearathersilly.e٠xample,YsinceLffA;TU>?E1fXdoesn'tunderstandwhatyouaretyping,itisn'tgoingtobewgorriedifyoumis-spellsomeofthewgordsinyourte٠xt;youwilljusthavetoaccuratelyproof-readyourprintedTZoutput.хOntheotherhand,pifyoumis-spelloneoftheenvironmentnamesinyour lethenLffA;TU>?E1fXwgon'tknowwhatyouwantittodo. +Whenthissortofthinghappens,LffA;TU>?E1fXprintsanerrormessageonyourterminalscreenandthenstopsandwgaitsforyoutotakesomeaction.uTheerrormessagesthatitproducesmayseemuser-unfriendly\andnotalittlefrighteningat rst.Nev٠ertheless,sifyouknowwheretolookthe٠ywillprobablytellyouwheretheerrorisandwhatwentwrong.Consider0whatwgouldhappenifyoumistypedL\begin{itemize}asL\begin{itemie}.WhenLffA;TU>?E1fXprocessesthisinstruction,itdisplaysthefollowingonyourterminal: BYLaTeXerror. SeeLaTeXmanualforexplanation. \38Type Hforimmediatehelp.!Environmentitemieundefined.\@latexerr...forimmediatehelp.}\errmessage{#1} \endgroupl.140\begin{itemie}?WBAftertypingthe`?'TxLffA;TU>?E1fXstopsandwgaitsforyoutotellitwhattodo.The rsttwgolinesofthemessagejusttellyouthattheerrorwasdetectedbyLffA;TU>?E1fX.AThe third line,0Ztheonethatstarts`!'isthe@errorindicator.Ittellsyouwhattheproblemis,0Zthoughuntil6youhav٠ehadsomeexperienceofLffA;TU>?E1fXthismaynotmeanalottoyou.xInthiscaseitisjust^tellingyouthatitdoesn'trecogniseanenvironmentcalledLitemie&^. Thene٠xttwgolinestellyouwhatLffA;TU>?E1fXwgasdoingwhenitfoundtheerror;the٠yareirrelevantatthemomentandcanbeignored.KThefL nallineiscalledthe@errorlocator,kpandisacopgyofthelineinyour lethatcausedthe4kproblem.qItstartswithalinenumbertohelpyouto nditinyour le.Iftheerrorwgasinthemiddleofaline,itwillbeshownbrokgenatthepointwhereLffA;TU>?E1fXrealizedthattherewasanerrors8.Aswithallcomputerprograms,3LffA;TU>?E1fXcansometimespassthepointwheretherealerrorwgasbeforedisco٠veringthatsomethingiswrong,butitdoesn'tusuallygetv٠eryfars8.Atwthispointyoucoulddosev٠eralthings.QIfyouknewenoughaboutLffA;TU>?E1fXyoumightbeabletoR xtheproblem,[oryoucouldtype`LX'andpressthereturnkge٠ytostopLffA;TU>?E1fXrunningwhileyougoEandcorrecttheerrors8.fGThebestthingtodo,howev٠er,isEjusttopressthereturnkge٠yY.fGThiswillallow'pLffA;TU>?E1fXtogoonrunningasifnothinghadhappened.JIfyouhav٠emadeonemistakge,QLthenyou!hav٠eprobablymadeseveralandyoumayaswelltryto ndthemallinonego.:It's8smuchmoreecienttodoitthiswgaythantorunLffA;TU>?E1fXo٠verando٠verag7ain xingoneerroratatime.Don'twgorryaboutrememberingwhattheerrorswere|acopyofalltheerrormessagesisbeingsav٠edina@logg lesothatyoucanlookatthemafterwards.'Seeyour@localguideto ndoutwhatthis leiscalled.Ifyoulookatthelinethatcausedtheerror,it's8snormallyob٠viouswhattheproblemwgas.EIfyouycan'twgorkoutwhatyourproblemis,lookatthehintsbelowand,ifthe٠ydon'thelp,consultARrҍNEssentialL`ffOAMNTU>?EfX,19.{Chapter6ofLamport's8sbook:itcontainsalistofalloftheerrormessagesthatyouarelikgelyto encounter,togetherwithsomesuggestionsastowhatmayhav٠ecausedthem.Someofthemostcommonmistakgesthatcauseerrorsare:oAmis-speltcommandorenvironmentname.*ލImproperlymatched`L{'and`L}'|rememberthatthe٠yshouldalgwayscomeinpairs.Tgrying"touseoneofthetenspecialcharactersL#$%&_{}~^"andL\asanordi- naryprintingsymbol.AmissingL\endcommand.Amissingcommandargument(that's8sthebitenclosedin'L{'and`L}').A single)errorcangetLffA;TU>?E1fXsoconfusedthatitreportsaseriesofspuriouserrorsasaresult.If youf_hav٠eanerrorthatyouunderstand,kfollowedbyaseriesthatyoudon't,thentrycorrectingthe rsterror|therestmayvanishasifbymagic.SometimesLffA;TU>?E1fXmaywriteaL*andstopwithoutanerrormessage.@ThisisnormallycausedbyKamissingL\end{document}command,~thoughothererrorscancauseit.IfthishappenstypeL\stopandpressthereturnkge٠yY.FinallyY,>LffA;TU>?E1fXwillsometimesprint@warningmessages.#The٠yreportproblemsthatwerenotbad6~enoughtocauseLffA;TU>?E1fXtostopprocessing,dbutnev٠erthelessmayrequireinvestig7ation.wThemostcommonproblemsare`o٠verfull'and`underfull'linesofte٠xt.TxAmessagelikge: oYOverfull\hbox(10.58649pttoowide)inparagraphatlines172--175 []\tenrmMathematicalfor-mu-lasmaybedis-played.Adis-playedindicates`uthatLffA;TU>?E1fXcouldnot 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ne,?E1fXtoproduceawiderangeofdocuments.O!ButthisdocumenthasonlyscratchedthesurfgaceofthethingsthatLffA;TU>?E1fXcando.Thisentiredocumentwasitselfproducedwith?E1fX(withnostickingthingsinorclev٠eruseofaphotocopier)andev٠enithasn'tusedalltheJfeaturesthatitcould.&VFromthisyoumaygetsomefeelingforthepowerthatLffA;TU>?E1fXputsatyourdisposal.Please~rememberwhatwgassaidintheintroduction:suifyou@dohav٠eacomplexdocumenttoproducethen@goandrGeadLamport'sbook.2}Ygouwillbewgastingyourtimeifyourelyonlyonwhatyou=hav٠ereadhere./Onceyouhav٠eusedLffA;TU>?E1fXforsometime,youmightwganttoknowhowtousetheman٠ystyle leextensions,iwhichhavebeendevelopedtoaidLffA;TU>?E1fXuserstotypesettheirdocuments.gVThis۟andmuchelse(likgehowtouse@MakeIndex,forgeneratingindices,orBNib32TU>&dE1fX,formanagingyourbibliographies)isco٠veredin@TheLffCA-S@TU>4xE1fXCompanion[3].ZFinallythe 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~L\hbar}HL\hslashHML\vartriangle  OL\triangledownHL\squareHL\lozenge sL\circledS\HL\angleH]L\measuredangle @L\nexistsfHL\mhoH`L\Finv^a aL\Game^a|HL\Bbbk^aH8L\backprime ?L\varnothingNHL\blacktriangleHHL\blacktriangledown L\blacksquareHL\blacklozengeHFL\bigstar ^L\sphericalangle{HL\complementHgL\eth L\diagup^aHL\diagdown^a ^a{PNot@de nedinstyleQamssymbP,de neusingtheLBAPTfEߨXY2e"#AoQ\DeclareMathSymbolPcommandRQ䍍rʻT37able12:TxAMSmiscellaneoussymbolsYARrҍNEssentialL`ffOAMNTU>?EfX,23.S/Ldz%ɩL\digammaaɩ{tqL\varkappaqiɆL\bethk0L\daleth<0jLL\gimel{PT37able13:TxAMSGreekandHebrew5 Ld!Rp2RL\ulcornertRqRL\urcornerRxRL\llcornerRy+RL\lrcornerT37able14:TxAMSdelimiterschEd99K!L\dashrightarrowL99L\dashleftarrow8NL\leftleftarrows !L\leftrightarrowsWL\Lleftarrow8NL\twoheadleftarrow!L\leftarrowtail"L\looparrowleft8 NL\leftrightharpoonsx!L\curvearrowleft L\circlearrowleft8NL\Lsh!L\upuparrowsL\upharpoonleft8NL\downharpoonleft(!L\multimap!L\leftrightsquigarrow8NL\rightrightarrows!L\rightleftarrowsL\rightrightarrows8NL\rightleftarrows!L\twoheadrightarrowL\rightarrowtail8#NL\looparrowright !L\rightleftharpoonsyL\curvearrowright8NL\circlearrowright!L\RshL\downdownarrows8NL\upharpoonright!L\downharpoonright L\rightsquigarrowWQ䍍wǻT37able15:TxAMSarrowsCr܃䍍dR8&RL\nleftarrowzR9RL\nrightarrowR:RL\nLeftarrow R;&RL\nRightarrowzR=RL\nleftrightarrowR<RL\nLeftrightarrow!Q䍍ĘT37able16:TxAMSne٠g7atedarrowsr䍍du$nL\dotplusnr6L\smallsetminus6e:L\Cap d$nL\CupnZ6L\barwedge6Y:L\veebar[$nL\doublebarwedgen 6L\boxminus6:L\boxtimes$nL\boxdotn6L\boxplus6>:L\divideontimesn$nL\ltimesno6L\rtimes6h:L\leftthreetimesi$nL\rightthreetimesnf6L\curlywedge6g:L\curlyvee$nL\circleddashn~6L\circledast6}:L\circledcirc$nL\centerdotn|6L\intercalEQ䍍QlT37able17:TxAMSbinaryoperatorsgARrҍ24,NEssentialL`ffOAMNTU>?EfX.S(ލ~݆5L\leqq6vL\leqslantv02L\eqslantless .L\lesssim/vL\lessapproxvu2L\approxeqlL\lessdotnvL\lllv72L\lessgtr lQL\lesseqgtrSvL\lesseqqgtrv+2L\doteqdot 9:L\risingdotseq;vL\fallingdotseqvv2L\backsimwL\backsimeqjvL\subseteqqvb2L\Subset@L\sqsubset4vL\preccurlyeqv22L\curlyeqprec-L\precsimwvL\precapproxvC2L\vartriangleleftEL\trianglelefteqvL\vDashv2L\Vvdash`L\smallsmileavL\smallfrownvl2L\bumpeqmL\Bumpeq=vL\geqqv>2L\geqslant1L\eqslantgtr&vL\gtrsimv'2L\gtrapproxmL\gtrdotovL\gggv?2L\gtrlessRL\gtreqlessTvL\gtreqqlessvP2L\eqcirc $L\circeq,vL\triangleqvs2L\thicksimtL\thickapproxkvL\supseteqqvc2L\SupsetAL\sqsupset<vL\succcurlyeqv32L\curlyeqsucc%L\succsimvvL\succapproxvB2L\vartrianglerightDL\trianglerighteq vL\Vdashvp2L\shortmidqL\shortparallelGvL\betweenvt2L\pitchfork_L\varproptoJvL\blacktriangleleftv)2L\thereforeL\backepsilonIvL\blacktrianglerightv*2L\becauseZT37able18:TxAMSbinaryrelations>~nL\nlessn6L\nleq6 :L\nleqslant ˏnL\nleqqn 6L\lneq6:L\lneqq WnL\lvertneqqn6L\lnsim6:L\lnapprox nL\nprecn6L\npreceq6:L\precnsimnL\precnapproxn6L\nsim6.:L\nshortmid-nL\nmidn06L\nvdash62:L\nvDash6nL\ntriangleleftn56L\ntrianglelefteq6*:L\nsubseteq(nL\subsetneqn 6L\varsubsetneq6$:L\subsetneqq&nL\varsubsetneqqn6L\ngtr6:L\ngeq nL\ngeqslantn6L\ngeqq6 :L\gneq W nL\gneqqn6L\gvertneqq6:L\gnsimnL\gnapproxn6L\nsucc6:L\nsucceqnL\succnsimn6L\succnapprox6:L\ncong/nL\nshortparalleln,6L\nparallel62:L\nvDash3nL\nVDashn76L\ntriangleright64:L\ntrianglerighteq+nL\nsupseteqn#6L\nsupseteqq6):L\supsetneq!nL\varsupsetneqn%6L\supsetneqq6':L\varsupsetneqq|ʍqһT37able19:TxAMSne٠g7atedbinaryrelationsq_ARrҍNEssentialL`ffOAMNTU>?EfX,25.`BHorrib$leMathematicalExamplestoStudȽyqЍC(t)=<$ ,1Kwfedv EPpUWPfe E2ra0|sk0-a1k1N:::X010Cfi0AK)(3)ҍQ\begin{equation} Y\prod_{j\geqff0}Y\left(\sum_{k\geqff0}a_{jk}z^k\right)ҍ=ff\sum_{k\geq0}z^nY\left(ff\sum_{{k_0,k_1,\ldots\geq0}3҉\atop{k_0+k_1+\ldots=n}})a{_0k_0}a_{1k_1}\ldots \right)ҍ\end{equation}lƍ M[ٲ(n)=ꨴn *X m=2^6^6^6fi^4U \ $?m1 %YX 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ҍ{F}(x,y)=0\quad\mathrm{and}\quad8\left|\begin{array}{ccc}YF_{xx}''ff&F_{xy}''&F_{x}'\\YF_{yx}''ff&F_{yy}''&F_{y}'\\YF_{x}'32&ffF_{y}'&0#W\end{array} fd\right|ff=0ҍ\end{displaymath}]ARrҍ26,NEssentialL`ffOAMNTU>?EfX.{2z왒3˧      d x1S8x24y1S8y2]z1S8z2 յl1=}m1g޵n1յl2=}m2g޵n2ͫ      Jfe%ʍn/s n/fe%э  dUUl1͢m1 UUl2͢m2,̫ , , , /g!ڱ26t+8 8 8 8 d 5m1!_n1 ĵn1#Tl11Ol 1Ol 1Ol 1Ol 4ڱ2;Z+8 8 8 8 d 5m2!_n2 ĵn2#Tl21Ol 1Ol 1Ol 1Ol 4ڱ2ҍQ\begin{displaymath} ҍ\frac{\pmҍ\left|\begin{array}{ccc}ҍx_1-x_2 &ffy_1-y_2&z_1-z_2\\ҍl_1 fd&ffm_1&n_1\\ҍl_2 fd&ffm_2&n_2ҍ\end{array}\right|}{ҍ\sqrt{\left|\begin{array}{cc}l_1&m_1\\ҍl_2&m_2\end{array}\right|^2ҍ+\left|\begin{array}{cc}m_1&n_1\\ҍn_1&l_1\end{array}\right|^2ҍ+\left|\begin{array}{cc}m_2&n_2\\ҍn_2&l_2\end{array}\right|^2}}ҍ\end{displaymath}ZV&q!1ɍ[ٴfxݍ0(Q;T3R յ; ;s)oh=<$bY4[ z^2bYwfe (֍%W3s; V828686fi84򙖍 Q^2'^O38 2Ofen, r72+^5Ѹ82QCVC^0-V]s(sM^2ٔZ)  fec6ز(s8M:2ٔZ)5D24xE1fX|A2DocumentPrGepar٠ationSystem|User'sGuideandReferenceMan- 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