; TeX output 1996.03.24:1728|gT8ႍ NH cmbx12The T{NotSoShortiCIn8tro duction T{toL(ՍpNq cmbx12AX=TUdE 5X22cDFH cmmib10" .hWK1@ff cmti12Or @LJ@': cmti10@ATwEZWX2ein69minutes򍍟s536U"V 3 cmbx10Ubty2T\obiasOetikeregHubYert2Ptartl,IreneHynaandElisabethScthlegl31(HK`y 3 cmr10Veersionf2.2-Beta,25thJan!uary,1996܎*|퍍냍FUiiFzffhg3"WBAacmr6BThisbdo1cumen9tis\publicdomain".GItmayb1eprintedanddistributedfreeofchargeinitsoriginalformF(includingthelistofauthors).##Ifitisc9hangedorifpartsofitareusedwithinanotherdo1cument,)thentheauthorFlistm9ustincludealltheoriginalauthorsANDpthatauthor(thoseauthors)whohas(have)madethechanges.FWhenthisdo1cumen9tisusedcommerciallyj,theGNUcopyleftapplies.v|퍍냎g3"Thank T{y8ou!5Muc!hJofthematerialusedinthisintroMductioncomesfromanAustrian in!troMductionftoLA|{Ycmr8AAGT,[wEB X2.09writteninGermanby:1`HubMertfP!artl 5C b> 3 cmmi10C;`@Zentr}'alerInformatikdienstderUniversitatf urBodenkulturWien1`IrenefHyna 5C;`@Bundesministeriumf urWissenschaftundF;orschungWien1`ElisabMethfSc!hlegl 5C;`@inGr}'azP'Ifry!ouareinterestedintheGermandoMcumentyoucan ndaversionupMdatedforLAAGT,[wEB Xv2zC".۹b!yJforgKnappenatVThepicturewill1`onlyNbMeaframew!ork,Ɇbutitwillenableyoutointegratetheinformation1`pro!videdfintheotherchaptersintothebigpicture.čUChapter22S۹goMes#in!tothedetailsoftypMesettingyourdoMcuments.qItexplains1`most#oftheessen!tialLAAGT,[wEB Xcommandsandenvironments.Afterread-1`ingfthisc!hapteryouwillbMeabletowriteyour rstdoMcuments.UChapter23S۹explains ho!wtotypMesetformulaewithLAAGT,[wEB X.jAgainalotofex-1`ampleshelpy!outounderstandhowtouseoneofLAAGT,[wEB Xmainstrengths.1`A!t5Ltheendofthischapteryou ndtables,Klistingallthemathematical1`sym!bMolsfavdDailableinLAAGT,[wEB X.UChapter24S۹addsyinsomebitsandbMobsaboutLAAGT,[wEB Xwhic!harenotessential,1`butOv!eryhandye.Amongotherthingsyouwilllearnhowtoinclude1`eps(graphicsin!toyourdoMcumentsorhowtoaddanindextoyour1`publication.v |퍍냍FUviPrefaceFzffhg3"FItr4isimpMortan!ttoreadthechaptersinsequentialorder.AHThebMookr4isnot Fthat5bigafterall.XMak!esuretocarefullyreadtheexamples,LYbMecauseagreatFpart,oftheinformationiscon!tainedinthevdDariousexamplesyouwill ndallFthroughfoutthebMook.FIfy!ouneedtogetholdofanyLAAGT,[wEB Xrelatedmaterial,havealoMokinoneofFtheVCTANftparc!hives.FeortheUSitisatVftp.shsu.edu,forGerman!yitisFVftp.dante.deandfortheUKitisVftp.tex.ac.uk.>Ify!ouarenotinoneFoffthesecoun!tries,choMosethearchiveclosesttoyou.FIf y!ouhaveideasforsomethingtobMeadded,qremovedoralteredinthisFdoMcumen!t,pleaseletmeknow.xTIamespMeciallyinterestedinfeedbackfromFLAAGT,[wEB Xno!vicesabMoutwhichbitsofthisintroareeasytounderstandandFwhic!hfcouldbMeexplainedbetter.$a`TeobiasfOetik!er 5C k`@Dep}'artmentofElectricalEngineering,a`SwissF;e}'deralInstituteofT;echnologyFThefcurren!tversionofthisdoMcumentwillbMeavdDailableonFVCTAN:/tex-archive/info/lshortvd|퍍냎g덑Con8tentsA2aUThank2ytou!^iii2aPreface8sv1&lThings2Y\ouNeedtoKnotw*1 򍍑&lϹ1.1?1ThefNameoftheGameq.=....................a1?11.1.1brT,[wEB X+q.=...........................a1?11.1.2brLAAGT,[wEB Xf.=..........................a1&l1.2?1BasicsB̍.=..............................a2?11.2.1brAuthor,fBoMokDesigner,andT!ypesetter򍍑.=.......a2?11.2.2brLa!youtfDesign.=.....................a2?11.2.3brAdvdDan!tagesfandDisadvan!tages#.=............a3&l1.3?1LAAGT,[wEB XfInputFiles$.=........................a4?11.3.1brSpaces^.=..........................a4?11.3.2brSpMecialfCharactersp7.=...................a4?11.3.3brLAAGT,[wEB XfCommandsn.=...................a5?11.3.4brCommen!ts=ύ.=........................a5&l1.4?1InputfFileStructure;.=......................a6&l1.5?1ThefLa!youtoftheDoMcumentZ.=.................a7?11.5.1brDoMcumen!tfClasses.=...................a7?11.5.2brP!ackdDagesꍍ.=.........................a7?11.5.3brP!agefStyles.=.......................11&l1.6?1BigfProjects/K.=...........................112aU2&lTtypYesetting2T\extC13&lϹ2.1?1LinebreakingfandP!agebreakingW͍.=................13?12.1.1brJusti edfP!aragraphs.=..................13?12.1.2brHyphenation.=......................14&l2.2?1SpMecialfCharactersandSym!bols-.=................15?12.2.1brQuotationfMarks򯍍.=....................15?12.2.2brDashesfandHyphensfz.=..................15?12.2.3brEllipsisf(.3..)_Ǎ.=......................16?12.2.4brLigaturesrI.=........................16v!|퍍냍FUviiifwCONTENTSFzffhg3"o12.2.5rAccen!tsfandSpMecialCharacters񀍍.=............16 Vl2.3o1In!ternationalfLanguageSuppMortt.=................17Vl2.4o1ThefSpacebMet!weenfWeordsf.=...................18Vl2.5o1Titles,fChapters,andSections].=.................18Vl2.6o1CrossfReferences5.=........................20Vl2.7o1FeoMotnotesRO.=............................20Vl2.8o1EmphasizedfWeords.=.......................21Vl2.9o1En!vironmentsۇ.=..........................21o12.9.1rItemise,fEn!umerate,andDescription.=.........21o12.9.2rFlushleft,fFlushrigh!t,andCentervˍ.=...........22o12.9.3rQuote,fQuotation,andVeerseፍ.=.............22o12.9.4rPrin!tingfVeerbatim,.=...................23o12.9.5rTeabular#.=.........................24Vl2.10o1FloatingfBoMdies .=.........................26Vl2.11o1AddingfNewCommandsandEn!vironments.=.........28o12.11.1rNewfCommands.=....................28o12.11.2rNewfEn!vironments˽.=...................29ύFU3VlTtypYesetting2MathematicalF\ormulae=p31VlϹ3.1o1GeneralW1.=.............................31Vl3.2o1GroupingfinMathMoMdeb.=....................33Vl3.3o1BuildingfBloMc!ksofaMathematicalFeormulax.=.........33Vl3.4o1MathfSpacing~.=..........................36Vl3.5o1VeerticallyfAlignedMaterialf.=..................37Vl3.6o1MathfFeon!tSizev.=.........................38Vl3.7o1DescribingfVeariables2.=......................39Vl3.8o1Theorems,fLa!ws,.3..ւ.=......................40Vl3.9o1Boldfsym!bMols΍.=..........................41Vl3.10o1ListfofMathematicalSym!bMols.=.................42FU4VlSpYecialities J49VlϹ4.1o1Feon!tsfandSizesot.=.........................49Vl4.2o1Spacingrr.=.............................51o14.2.1rLinefSpacing.=......................51o14.2.2rP!aragraphfFeormatingz.=.................51o14.2.3rHorizon!talfSpace9.=....................52o14.2.4rVeerticalfSpace{鍍.=.....................53Vl4.3o1P!agefLayout퍍.=...........................53Vl4.4o1Bibliograph!y.=..........................55Vl4.5o1Indexing0O.=.............................56Vl4.6o1IncludingfEPSGraphicst%.=....................57v >|퍍냎g3"List T{ofFigures5&lϹ1.1?1AfMinimalLAAGT,[wEB XFile.=.....................a6 &l1.2?1ExamplefofaRealisticJournalArticleX.=............a7&l4.1?1P!agefLayoutParameters.=....................54v g |g j|퍍냎g3"List T{ofTables5&lϹ1.1?1DoMcumen!tfClasses󍍑.=.......................a8 &l1.2?1DoMcumen!tfClassOptionsȍ.=....................a8&l1.3?1SomefoftheP!ackdDagesfDistributedwithLAAGT,[wEB Xr*.=........10&l1.4?1ThefPrede nedP!ageStylesofLAAGT,[wEB X4.=.............11&l2.1?1Accen!tsfandSpMecialCharacters͍.=................17&l2.2?1FloatfPlacingP!ermissions_.=...................26&l3.1?1MathfMoMdeAccen!tsˍ.=......................42&l3.2?1Lo!wercasefGreekLetters͍.=....................42&l3.3?1UppMercasefGreekLettersqB.=....................42&l3.4?1BinaryfRelationsqS.=........................43&l3.5?1BinaryfOpMerators0%.=........................43&l3.6?1BIGfOpMerators獍.=.........................44&l3.7?1Arro!wsټ.=..............................44&l3.8?1Delimitersۖ.=............................44&l3.9?1LargefDelimitersS%.=........................44&l3.10?1MiscellaneousfSym!bMols.=.....................45&l3.11?1Non-MathematicalfSym!bMolsAv.=..................45&l3.12?1AMSfDelimitersl.=.........................45&l3.13?1AMSfGreekandHebrew.=....................45&l3.14?1AMSfBinaryRelationsL.=.....................46&l3.15?1AMSfArro!ws򍍑.=..........................46&l3.16?1AMSfNegatedBinaryRelationsandArro!ws0.=.........47&l3.17?1AMSfBinaryOpMeratorsE[.=....................47&l3.18?1AMSfMiscellaneous'a.=.......................48&l3.19?1MathfAlphabMets .=........................48&l4.1?1Feon!tst.=...............................50&l4.2?1Feon!tfsizesB.=............................50&l4.3?1Mathffon!ts%.=...........................50&l4.4?1T,[wEB XfUnits ύ.=............................53&l4.5?1IndexfKeySyn!taxExamplesڍ.=..................57&l4.6?1KeyfNamesforWm#R 3 cmss10WgraphicxP!ackdDagek0.=...............58v j|g|퍍냎g!Chapter 12_Things T{YouNeedtoKno8w6WInthe rstpa!rtofthischapteryouwillgetashortoverviewabMoutthephilosophy andU"histo!ryofL󏍑Xs6cmss8XAWT,nEXpXv2zC")*W.ThesecondpartofthechapterfoMcusesonthebasicstructures >ofaL󏍑XAWT,nEXpXdoMcument.eAfterreadingthischaptery!oushouldhavearough3kno!wledgeofhowL󏍑XAWT,nEXpXworks.Whenreadingon,W#thiswillhelpyoutointegratefallthenewinfo!rmationintothebigpicture.1,YNff cmbx12Y1.1:cTheffNameoftheGame[N cmbx12[1.1.1?@TESX{ T,[wEB XLisacomputerprogramb!yDonaldE.Knuth[2y].ItisaimedattypMeset-tingftextandmathematicalform!ulae.'T,[wEB X ispronounced\Teec!h,"35witha\ch"asintheGermanword\Ach"orfinScottish\LoMc!h."InanVASCIIenvironmentT,[wEB XbMecomesVTeX."[1.1.2?@LAl#b2@cmbx8bA~/[TESXLAAGT,[wEB Xisamacropac!kdDagewhichenablesauthorstotypMesetandprinttheirw!ork'ExXintoTU>'ExXniciansandUUTU>'ExXpGerts.T*oGdayUUisMarch24,1996.:qI?readthatKnuthdividesthe people?workingwith\TeX{}into\TeX{}nicians?and\TeXperts.\\Today?is\today.@č'Somecommandsneedaparameterwhic!hhastobMegivenbMetweencurlybracesV{}afterthecommandname.bSomecommandssuppMortoptionalparameterszwhic!hareaddedafterthecommandnameinsquarebracketsV[].The\nextexampleusessomeLAAGT,[wEB Xcommands.Don'tw!orryabMoutthem,theyfwillbMeexplainedlater.Y*ouUUcanrp0J cmsl10rleanonme!qYou?can\textsl{lean}onme!* Please,`start'anewlinerighthere! ThankUUyou!:qPlease,?startanewline right?here!\linebreak[3]Thank?you!G [1.3.4?@CommentsWhen"LAAGT,[wEB Xencoun!tersaV%characterwhileproMcessinganinput le,B itig-noresAtherestofthepresen!tline.|Thisisusefulforaddingnotestotheinput le,fwhic!hwillnotshowupintheprintedversion.v|퍍냍FU6pThings2Y\ouNeedtoKnotwFzffhg3"FThisUUisanexample.qThis?isan%stupid %?Better:instructive<----example.L⍍FY1.4jcInputffFileStructure>FWhenHLAAGT,[wEB Xv2zC"/KproMcessesHaninput leitexpectsittofollo!wacertainstruc- Fture.Th!usfeveryinput lemuststartwiththecommand܍a`V\documentclass{...}ۍFThis1spMeci eswhatsortofdocumen!tyouintendtowrite.=Afterthat,TNyouFcanincludecommandswhic!hin uencethestyleofthewholedoMcumentorFy!ou:canloadpackdDageswhichaddnewfeaturestotheLAAGT,[wEB Xsystem.TeoloadFsuc!hfapackdDageyouusethecommanda`V\usepackage{...}ۍWWhen%vallthesetupw!orkisdoneA3,E:youstartthebMody%vofthetextwithFthefcommanda`V\begin{document}WNo!w_zyouenterthetextmixedwithsomeusefulLAAGT,[wEB Xcommands. At FthefendofthedoMcumen!tyouaddthea`V\end{document}ۍFcommand, whic!hZtellsLAAGT,[wEB Xtocallitadaye.AnythingwhichfollowsthisFcommandfwillbMeignoredb!yLAAGT,[wEB X.jjWFigure]1.1sho!wsthecontentsofaminimalLAAGT,[wEB Xv2zC".9 le.A4slightlymoreFcomplicatedfinput leisgiv!eninFigure1.2.F ʹffp L͍ {-=B3acTheTareabAet9weenTsߤN cmtt9s\documentclasscands\begine cmsy9efsdocumentegRciscalledvj cmti9vpreamblec.yK~5^I#ffn V\documentclass{article}\begin{document}Smallisbeautiful.\end{document}ffn;Tc7Figuref1.1:AMinimalLAAGT,[wEB XFilev˷|퍍냍U1.52TheLatyout2oftheDoYcumenttw,7zffhg3"Y1.5:cTheffLayoutoftheDos3cumentk[1.5.1?@Do`cumentClassesyThe rstinformationLAAGT,[wEB Xneedstokno!wwhenproMcessinganinput leis the}t!ypMeofdocumen!ttheauthorwantstocreate.PThisisspMeci edwiththeV\documentclassfcommand.Z1ff ͤ ff͟fdq\documentclass[@options!q]{@classq} ffffmHereŔclassspMeci esthet!ypeofdocumen!ttobecreated.;gTeable1.1liststhedoMcumen!tclassesexplainedinthisintroMduction.]`TheLAAGT,[wEB Xv2zC"0\Mdistributionpro!videsadditionalclassesforotherdoMcumentsincludinglettersandslides.TheoptionsparametercustomisesthebMeha!viourofthedocumen!tclass.hTheoptions\ha!vetobMeseparatedbycommas.InTeable1.2themostcommonoptionsfforthestandarddoMcumen!tclassesarelisted. s'Example:Anfinput leforaLAAGT,[wEB XdoMcumen!tcouldstartwiththeline1`V\documentclass[11pt,twoside,a4paper]{article}itinstructsLAAGT,[wEB Xtot!ypMesetthedocumen!tasanarticleľwithabasefontsizeof;elevenSppointsSandtoproMduceala!yout;suitablefordoublesidepd9prin!tingonfa4ppaper.h[1.5.2?@Pack@agesWhilen(writingy!ourdoMcument,youwillprobably ndthattherearesomeareas?wherebasicLAAGT,[wEB Xcannotsolv!eyourproblem.iIfyouwanttoinclude;f;yff V\documentclass[a4paper,11pt]{article}\usepackage{latexsym}\author{H.~Partl}\title{Minimalism}\frenchspacing\begin{document}\maketitle\tableofcontents\section{Start}Wellandherebeginsmylovelyarticle.\section{End}\ldots{}andhereitends.\end{document}ffxĉQ+Figuref1.2:ExampleofaRealisticJournalArticlevg|퍍냍FU8pThings2Y\ouNeedtoKnotwFzffhgXke{Teablef1.1:DoMcumen!tClassesMeOH̉ffUnݟVarticle-@for.articlesinscien!ti cjournals,Ppresentations,short.repMorts, `programfdoMcumen!tation,invitations,.3..Vreport'forRlongerrepMortscon!tainingseveralchapters,VsmallbMooks,PhD`theses,f.3..VbookxBforfrealbMooksVslide"7forfslides.Theclassusesbigsansserifletters. ЉffUnݎ*.&荍\Teablef1.2:DoMcumen!tClassOptionsፍOHN͖ffUnݟV10pt,fV11pt,V12ptbSetsfthesizeofthemainfon!tforthedoMcument.If `nofoptionisspMeci ed,V10ptisassumed.Va4paper,fVletterpaper,.3..De nesfthepapMersize.Thedefaultsize`isfVletterpaper.Besidesthat,Va5paper,Vb5paper,`Vexecutivepaper,fandVlegalpapercanbMespeci ed.Vfleqn-+!T!ypMesetsfdisplayedformulaeleft-alignedinsteadofcentred.Vleqno-+!Placesfthen!umbMeringfofform!ulaeonthelefthandside`insteadfoftherigh!t.Vtitlepage,fVnotitlepage(SpMeci esfwhetheranewpageshouldbe`startedfafterthedoMcumen!ttitleornot.TheVarticleclassdoes`notfstartanewpageb!ydefault,whileVreportandVbookdo.VtwocolumnD)ɹInstructsLAAGT,[wEB Xtot!ypMesetthedocumen!tintwocolumns.Vtwoside,onesidelgoSpMeci esfwhetherdoubleorsinglesidedoutput`shouldfbMegenerated.TheclassesVarticleandVreportaresingle`sidedfandtheVbookclassisdoublesidedb!ydefault.Vopenright,openanywùMak!esfchaptersbMegineitheronlyonright`handfpagesoronthenextpagea!vdDailable.ThisdoMesnotwork`withftheVarticleclass,asitdoMesnotkno!waboutc!hapters.The`Vreport~׹classb!ydefaultstartschaptersonthenextpageavdDailable`andftheVbookclassstartsthemonrigh!thandpages. ЉffUnݎv |퍍냍U1.52TheLatyout2oftheDoYcumenttw,9zffhg3"graphics,colouredtextorsourcecoMdefroma lein!toyourdoMcument,you needtoenhancethecapabilitiesofLAAGT,[wEB X.USuc!henhancementsarecalledpac!kdDages.Packagesfareactivatedwiththe1ff ͤ ff͟fdq\usepackage[@options!q]{@p}'ackage[q} ffff`command.FWhereppackage@isthenameofthepac!kdDageandoptions巹isalistofk!eywords5whichtriggerspMecialfeaturesinthepackdDage.xSomepackdDagescomewiththeLAAGT,[wEB Xv2zC"2 basedistribution(SeeTeable1.3).Othersarepro!videdseparatelye. dYouma!y ndmoreinformationonthepackdDagesinstalledaty!oursiteinyourLpocalMGuide\[4y].TheprimesourceforinformationabMoutLAAGT,[wEB XPisTheLnoAT"R[wE)XComppanion[[3y].aItPcon!tainsdescriptionsofhundredsofўpac!kdDagesalongwithinformationofhowtowriteyourownextensionstoLAAGT,[wEB Xv2zC">.v i|퍍냍FU10pThings2Y\ouNeedtoKnotwFzffhgbNsTeablef1.3:SomeoftheP!ackdDagesfDistributedwithLAAGT,[wEB Xh]2Yىff8VdocAllo!wsfthedoMcumentationofLAAGT,[wEB Xprograms. `DescribMedfinVdoc.dtxoaandinTheLnoAT"R[wE)XComppanion}q[3y].Vexscale-@Pro!videsfscaledversionsofthemathsextensionfont.`DescribMedfinVltexscale.dtx.Vfontenc-@SpMeci esfwhic!hfontencoMdingLAAGT,[wEB Xshoulduse.`DescribMedfinVltoutenc.dtx.Vifthen'Pro!videsfcommandsoftheform``if.3..thenfdo...otherwisedo....'`DescribMedfinVifthen.dtxandTheLnoAT"R[wE)XComppanion}q[3y].Vlatexsym3vTeoaccesstheLAAGT,[wEB Xsym!bMolfont,youshouldusethe`Vlatexsympac!kdDage.DescribMedinVlatexsym.dtxandinThe`LnoAT"R[wE)XComppanion}q[3y]Vmakeidx-@Pro!vides)commandsforproMducingindexes.bDescribedin`sectionf4.5andinTheLnoAT"R[wE)XComppanion}q[3y].Vsyntonly3vProMcessesfadocumen!twithouttypMesettingit.`DescribMedTRinVsyntonly.dtxandinTheaLnoAT"R[wE)XComppan-`ion}q[3y].Thisfisusefulforquic!kerrorchecking.Vinputenc3vAllo!wsthespMeci cationofaninputencodingsuc!has`ASCIMI,~ISOwLatin-1,ISOLatin-2,437/850~IBMcoMdepages,`AppleMacin!tosh,"Next,ANSI-Windowsoruser-de nedone.`DescribMedfinVinputenc.dtx. gff8ffff}0 L͍ -=yt}\cmti7yaacThis½ leshouldbAeinstalledony9oursystem,andyoushouldbAeableto getasdvic leb9ytypingΕslatexdoc.dtxc.Thesameistrueforalltheother lesmen9tionedTinthistable.v H|퍍냍U1.62BigProjectsqhX11zffhg3"[1.5.3?@PageStylesALAAGT,[wEB XYsuppMortsthreeprede nedheader/footercom!binations|so-calledpage st!yles.Thefstyleyparameterofthe$1ff_,D ͤ ff͟fdq\pagestyle{@style[q} ffff_,D {commandde neswhic!honetouse.Teable1.4liststheprede nedpagestyles.rX/jTeablef1.4:ThePrede nedP!ageStylesofLAAGT,[wEB XKhHY݉ffUnݟVplain"7prin!ts thepagenumbMersonthebottomofthepageinthemiddle`offthefoMoter.Thisisthedefaultpagest!yle.Vheadings3vprin!tsjthecurrentchapterheadingandthepagenumbMerin`theheaderoneac!hpagewhilethefoMoterremainsemptye.(Thisis`thefst!yleusedinthisdoMcument)Vempty"7setsfbMoththeheaderandthefootertobeempt!ye. gffUnݎox'ItxispMossibletoc!hangethepagestyleofthecurrentpagewiththecom-mand1fft,8 ͤ ff͟fdq\thispagestyle{@style[q} fffft,8 {'InErThe}NotethatLAAGT,[wEB XwillstartanewpagebMeforeprocessingthematerialfinputfrom lename.'TheCsecondcommandcanbMeusedinthepream!ble.uItallowsyoutov |퍍냍FU12pThings2Y\ouNeedtoKnotwFzffhg3"FinstructfLAAGT,[wEB XtoonlyinputsomeoftheV\included les.čF1ffi ͤ ff͟fdq\includeonly{@ lename[q,@ lenameq,...q} ffffi`WAfter@thiscommandisexecutedinthepream!bleofthedoMcument.{Only FV\includeڹcommandsforthe lenameswhic!harelistedintheargumentofFtheV\includeonlycommandwillbMeexecuted.@Notethattherem!ustbenoFspacefbMet!weenthe lenameandthecomma.WThe!5V\includecommandstartst!ypMesettingtheincludedtextonanewFpage.\Thisishelpfulwheny!ouuseV\includeonly,XbMecausethepagebreaksFwillnotmo!ve,7evenwhensomeincluded lesatommited.:?SometimesthisFmigh!tfnotbMedesirable.Inthiscase,youcanusetheF1ff[ ) ͤ ff͟fdq\input{@ lename[q} ffff[ )Wcommand.Itdsimplyincludesthe lespMeci ed.No ash!ysuits,nostringsFattac!hed.v |퍍냎g-Chapter 22yT8yp esetting T{Text6WAfterreadingthep!reviouschapteryoushouldknowabMoutthebasicstu from whichaL󏍑XAWT,nEXpXv2zC",WdoMcumentismade.+InthischapterIpwill llintheremainingstructurefy!ouwillneedtoknowinordertoproMducerealworldmaterial.1QY2.1:cLinebreakingffandPagebreaking[2.1.1?@Justi edParagraphsOften bMooksaret!ypesetwitheac!hlinehavingthesamelength.LAAGT,[wEB Xinsertsthe!necessarylinebreaksandspacesbMet!ween!wordsbyoptimisingthecon-ten!ts$ofawholeparagraph.Ifnecessaryitalsohyphenateswordsthatwouldnot tcomfortablyonaline.Ho!wtheparagraphsaretypMesetdependsonthedoMcumen!tclass.Normallythe rstlineofaparagraphisindentedandthereGisnoadditionalspacebMet!weenGtwoparagraphs.}Refertosection4.2.2forfmoreinformation.'InfspMecialcasesitmigh!tbenecessarytoorderLAAGT,[wEB Xtobreakaline:41ffP8 ͤ ff͟fdq\\UUorq\newline ffffP8nstartfanewlinewithoutstartinganewparagraph.%ԍ1ff ͤ ff͟fdq\\* ffffadditionallyfprohibitsapagebreakaftertheforcedlinebreak.1ff5 ͤ ff͟fdq\newpage ffff5莎startsfanewpage.vԠ|퍍냍FU14OHTtypYesetting2T\extFzffhg3"F1ffY ͤ ff͟fdq\linebreak[@ncq],UUq\nolinebreak[@nq],q\pagebreak[@nq]andq\nopagebreak[@nq]͡ ffffYFdof;whattheirnamessa!ye.yTheyenabletheauthortoin uencetheiractions, Fwith7theoptionalargumen!tn.@ItcanbMesettoanumbMerbet!ween7zerotoFfour.ByB`settingnktoavdDaluebMelo!w4youleaveLAAGT,[wEB XtheoptionofignoringFy!ourfcommandiftheresultwouldloMokverybad.CWLAAGT,[wEB Xalw!aystriestoproMducethebestlinebreakspossible.PIfitcannotF ndXaw!ayXtobreakthelinesinamannerwhic!hmeetsitshighstandards,h\itFlets9onelinestic!koutontherightoftheparagraph.%WLAAGT,[wEB XthencomplainsF(\o!verfull hbMox")whileproMcessingtheinput le.ThishappensmostoftenFwhenLAAGT,[wEB Xcannot ndasuitableplacetoh!yphenateaword.BygivingtheFV\sloppyvcommandy!oucaninstructLAAGT,[wEB Xtoloweritsstandardsalittle. ItFthenJdprev!entssuchover-longlinesbyincreasingtheinter-wordspacing|Fev!enFifthe naloutputisnotoptimal.Inthiscaseawarning(\underfullFh!bMox")isgiv!entotheuser.\Inmostcasestheresultdoesnotlooktoobad.FThe{commandV\fussyactsintheoppMositedirection.ϔJustincasey!ouwantFtofseeLAAGT,[wEB Xcomplainingallo!verftheplace."7F[2.1.2o@HyphenationFLAAGT,[wEB Xh!yphenateswordswhenevernecessarye.*IfthehyphenationalgorithmFdoMesnot ndthecorrecth!yphenationpoin!tsyoucanremedythesituationFb!yfusingthefollowingcommands,totellT,[wEB XabMouttheexception.WThefcommand#F1ff{ ͤ ff͟fdq\hyphenation{@wor}'dlistq} ffff{Fcauses$thew!ordslistedintheargumenttobMehyphenatedonlyatthepMointsFmark!ed1by\V-". ThiscommandshouldbMegiveninthepreambleoftheFinput. leandshouldonlycon!tainwordsbuiltfromnormalletters.6TheFcaseofthelettersisignored.iQTheexamplebMelo!wwillallow\hyphenation"FtoIbMeh!yphenatedaswellas\Hyphenation"anditprevents\FOReTRAN",F\Feortran"xand\fortran"frombMeingh!yphenatedatall.Nospecialc!haractersForfsym!bMolsareallowedintheargument.WExample:>a`V\hyphenation{FORTRANHy-phen-a-tion}=WThe+commandV\-insertsadiscretionaryh!yphenintoaword.@+ThisalsoFbMecomes:Xtheonlypoin!thyphenationisallowedinthisword.ThiscommandFis+despMeciallyusefulforw!ordscontainingspMecialcharacters(e.g.accentedFc!haracters),GbMecauselLAAGT,[wEB Xdoesnotautomaticallyh!yphenatewordscon-FtainingfspMecialc!haracters.v |퍍냍U2.22SpYecialCharactersandSymtbolsqhX15zffhg3"Ilthinkthisis:GsupGercalifragilisticex- pialidociousqI?thinkthisis:su\-per\-cal\-% i\-frag\-i\-lis\-tic\-ex\-pi\-%al\-i\-do\-cious5g 'Sev!eralfwordscanbMekepttogetherononelinewiththecommandN,1ffAݟ ͤ ff͟fdq\mbox{@textq} ffffAݎƍ'Itfcausesitsargumen!tbMekepttogetherunderallcircumstances.SMyphonenumbGerwillchangesoon. ItUUwillbGe01162912319A .N8The parameter@ lename-Lshouldcon-tainUUthenameofthe le.:qMy?phonenumberwillchangesoon. It?willbe\mbox{01162912319}.The?parameter\mbox{\emph{filename}}?shouldcontain?thenameofthefile.ovY2.2:cSps3ecialffCharactersandSymbolsV[2.2.1?@QuotationMarksdFeor#quotationmarksy!oushouldnot usetheV"asonatypMewriter.Inpub- lishingtherearespMecialopeningandclosingquotationmarks.QsInLAAGT,[wEB X,usemCt!woV`sonforopMeningquotationmarksandtwoV'sforclosingquotationmarks.\PleaseUUpressthe`x'key*.":q``Please?pressthe`x'key.''3z[2.2.2?@DashesandHyphensdLAAGT,[wEB XF_kno!wsfourkindsofdashes.Yeoucanaccessthreeofthesewithdi er-en!tnumbMersofconsecutivedashes.;Thefourthsignisactuallynodashatall:Itfisthemathematicalmin!ussign:daughter-in-law,UUX-rated pagesUU13{67yes|orUUno?0,UU1and1qdaughter-in-law,?X-rated\\ pages?13--67\\yes---or?no?\\$0$,?$1$and$-1$B'The3namesforthesedashesare:DV-h!yphen,5pV--en-dash,V---em-dashandV$-$fmin!ussign.v|퍍냍FU16OHTtypYesetting2T\extFzffhg3"F[2.2.3o@Ellipsis(.@..)эFOn_at!ypMewriteracommaoraperiodtak!esthesameamountofspaceas Fan!yotherletter.InbMookprintingthesecharactersoMccupyonlyalittlespaceFand4aresetv!eryclosetotheprecedingletter.ThereforeyoucannotenterF\ellipsis"n,b!yjusttypingthreedots,ykasthespacingwouldbMewrong.InsteadFtherefisaspMecialcommandforthesedots.Itiscalled&&F1ff+ ͤ ff͟fdq\ldots ffff+-MFNotUUlikethat...qbutlikethat: FNewUUY*ork,Tokyo,BudapGest,...qNot?likethat...butlikethat:\\ New?York,Tokyo,Budapest,\ldots?CF[2.2.4o@LigaturesFSome! lettercom!binationsaretypMesetnotjustbysettingthedi erentlettersFonefaftertheother,butactuallyb!yusingspMecialsymbMols.܍a`ZXQ cmr12Z  .T.. 艹insteadfof 5Zfffiflffi.T..ݍFTheseso-calledligaturescanbMeprohibitedb!yinsertingaV\mbox{}bet!weenFtheǍt!wolettersinquestion.ARThismightbMenecessarywithwordsbuiltfromFt!wofwords.!yFNotUUshel ul FbutUUshelffulqNot?shelfful\\ but?shelf\mbox{}ful=߂F[2.2.5o@AccentsandSp`ecialCharactersFLAAGT,[wEB XsuppMortstheuseofaccen!tsandspecialc!haractersfrommanylan-Fguages. TeablegN2.1sho!wsallsortsofaccentsbMeingappliedtothelettero.FNaturallyfotherlettersw!orktoMo.+WTeoAplaceanaccen!tontopofanioraj,7theirdotshavetobMeremoved.FThisfisaccomplishedb!ytypingV\iandV\j.!yFH^otel,UUnaqve,8Geleve, Fsmrrebrd,UUTV?`D[ffv,|퍍냍FU18OHTtypYesetting2T\extFzffhg3"FY2.4jcTheffSpacebs3etweenffWfordsjUFTeoKDgetastraigh!trightmarginintheoutput,]~LAAGT,[wEB XinsertsvdDaryingamounts Fof ospacebMet!ween othew!ords.5At otheendofasen!tenceitinsertsslightlymoreFspace, asthismak!esthetextmorereadable.dLAAGT,[wEB XassumesthatsentencesFend withpMeriods,.question marksorexclamationmarks.IfapMeriod follo!wsFan3)uppMercaseletterthisisnottak!enasasentenceendingsincepMeriods3)afterFuppMercaseflettersarenormallyforabbreviations.WAn!yhexceptionfromtheseassumptionshastobMespeci edb!ytheau-Fthor. A`mbac!kslash`infrontofaspacegeneratesaspacewhichwillnotbMeFenlarged.FAtilde`V~'c!haractergeneratesaspacewhichcannotbMeenlargedFand3dwhic!hadditionallyprohibitsalinebreak.ThecommandV\@infrontofaFpMeriodm(speci es,xthatthisperiodterminatesasen!tenceevenwhenitfollowsFafuppMercaseletter.FMr.UUSmithwashappytoseeher Fcf.UUFig.5FIUUlikeBASIC.qWhatabGoutyou?qMr.~Smith?washappytoseeher\\ cf.~Fig.~5\\I?likeBASIC\@.Whataboutyou?4WThefadditionalspaceafterpMeriodsfcanbMedisabledwiththecommand)F1ffU֟ ͤ ff͟fdq\frenchspacing ffffU֎ÍFwhic!htellsLAAGT,[wEB Xnot toinsertanymorespaceafterapMeriodthanafterFordinaryc!haracter.Thisisverycommoninnon-Englishlanguages,exceptFforRbibliographies. uIfy!ouuseV\frenchspacing,thecommandV\@isnotFnecessarye.%\FY2.5jcTitles,ffChapters,andSectionsFTeo2helpthereader ndhisorherw!ay2throughy!ourwork,IyoushoulddivideFit}Win!tochapters,sections,and}Wsubsections..LAAGT,[wEB XsuppMortsthiswithspecialFcommandsiowhic!htakethesectiontitleastheirargument.ɋItisuptoyoutoFuseftheminthecorrectorder.WFeorSbtheVarticleclassthefollo!wingsectioningcommandsareavdDailable:Ѝa`V\section{...}?exampleofsomeoftheabMo!vet>mentionedcommandscanbMefoundin FFiguref1.2onpage7.WApart fromthesectioningcommandsexplainedabMo!ve,LAAGT,[wEB Xv2zC"1.intro-Fducedf3additionalcommands,forusewiththeVbookclass.nF1ffc+ ͤ ff͟fdq\frontmatter,UUq\mainmatterandq\backmatter ffffc+NWTheyareusefulfordividingy!ourpublication.Thecommandsalterchap-Fter)zheadings,Bvandpagen!umbMering)ztow!orkasyouwouldexpMectitinabook.%? FY2.6jcCrossffReferences`}FInbMooks,{reportsandarticlesthereareoftencrossreferencesto gures,FtablesandspMecialsegmen!tsoftext.VLAAGT,[wEB XprovidesthefollowingcommandsFforfcrossreferencingF1ff ͤ ff͟fdq\label{@markerq},UUq\ref{@markerq}andq\pageref{@markerq}͡ ffffNFWhereLmarkerzcisaniden!ti erchosenbytheuser. УLAAGT,[wEB XreplacesV\refFb!ythenumbMerofthesection,"subsection, gure,table,ortheoremwhereFthecorrespMondingV\labelcommandw!asissued.SV\pagerefprintsthepageFn!umbMer2ofthecorrespondingV\labelcommand.Herealsothen!umbers2fromFthefpreviousrunareused.+FA*referencetothissubsectionloGoks Flike:q\seeUUsection2.6onpage20.":qA?referencetothissubsection \label{sec:this}?lookslike:``see?section~\ref{sec:this}onpage~\pageref{sec:this}.''TFY2.7jcFfos3otnotes`}FWithfthecommandF1ff| ͤ ff͟fdq\footnote{@fo}'otnotetextq} ffff|NFaffoMotnotewillbeprin!tedatthefootofthecurren!tpage.FF*oGotnotes^zt}\cmti7zaare;oftenusedbypeople FusingUUL5ffٓRcmr7A͉TU>'ExX.F ff@o L͍ -=yaacThisTisafoAotnoteqFootnotes\footnote{This is?afootnote}areoftenusedby?peopleusing\LaTeX.vR|퍍냍U2.82EmphasizedW\ordsqhX21zffhg3"Y2.8:cEmphasizedffWfords퍑In"man!uscriptsproMducedbytypMewriter,=+important"wordsgetunderlinedp 25.In prin!ted4!bMooksthesew!ordsareemphasisepd. Thecommandtoswitchtoanemphasisepdfon!tfiscalled"⍍1ffAݟ ͤ ff͟fdq\emph{@textq} ffffAݎ$n|Itsfargumen!tisthetexttobMeemphasised.$;㍍@If_youusenemphasising@inanalr}'eady emphasise}'dAtext,lthenL雍QzA@TKß'E-Xusesanupright@fontforemphasising.q\emph{If?youuse \emph{emphasising}?inanalready?emphasisedtext,then\LaTeX{}?usesan\emph{upright}?fontforemphasising.}Y2.9:cEnvironmentsTeot!ypMesetspecialpurposetext,mLAAGT,[wEB Xde nesman!ydi erentenvironmentsforfallsortsofformatting:"⍍1ff ͤ ff͟fdq\begin{@name[q} @text q\end{@nameq} ffff$n|WhereUnameisthenameoftheen!vironment.EnvironmentsUcanbMecalledsev!eralftimeswithineachotheraslongasthecallingorderismaintained.!:1`V\begin{aaa}...\begin{bbb}...\end{bbb}...\end{aaa}!;Infthefollo!wingsectionsallimpMortantenvironmentsareexplained.,W卍[2.9.1?@Itemise,Enumerate,andDescriptionaThebVitemizeen!vironmentbissuitableforsimplelists,GtheVenumerateen-vironmen!t"forenumeratedlists,AandtheVdescriptionenvironmentforde-scriptions.v\|퍍냍FU22OHTtypYesetting2T\extFzffhg3"UWTL1.a`Y*ouZcanmixthelistenviron- a`mentsUUtoyourtaste:nuywBut itmightstarttoloGokywsilly*.p!-ywWithUUadash.TL2.a`ThereforeUUremembGer:a`pStupidvthings<willnotbGecomeywsmart bGecausetheyareinywaUUlist.a`pSmartthingsE(though,canbGeywpresentedbGeautifullyinaywlist.q\begin{enumerate} \item?Youcanmixthelistenvironments?toyourtaste:\begin{itemize}\item?Butitmightstarttolook?silly.\item[-]?Withadash.\end{itemize}\item?Thereforeremember:\begin{description}\item[Stupid]?thingswillnotbecome?smartbecausetheyarein?alist.\item[Smart]?thingsthough,canbepresented?beautifullyinalist.\end{description}\end{enumerate}ލF[2.9.2o@Flushleft,Flushright,andCenter FThe>gen!vironmentsVflushleftandVflushrightgenerateparagraphswhich Fareeitherleftorrigh!taligned.*TheVcenterenvironmentgeneratescentredFtext.If\y!oudonotissueV\\tospMecifylinebreaks,LAAGT,[wEB XwillautomaticallyFdetermineflinebreaks.FThisUUtextis FleftUUaligned.qL5ffA͉TU>'ExXisnottryingtoFmakeUUeachlinethesamelength.q\begin{flushleft} This?textis\\leftaligned.\LaTeX{}?isnottryingtomakeeach?linethesamelength.\end{flushleft}OȞj[ThisUUtextisright Haligned.qL5ffA͉TU>'ExXUUisnottryingtomakevUeachUUlinethesamelength.q\begin{flushright} This?textisright\\aligned.\LaTeX{}?isnottryingtomakeeach?linethesamelength.\end{flushright}Q,/y0AtUUthecentre }JofUUtheearthq\begin{center} At?thecentre\\oftheearth\end{center}BލF[2.9.3o@Quote,Quotation,andVerseFTheVquoteen!vironmentisusefulforquotes,1impMortan!tphrasesandexam-Fples.vdf|퍍냍U2.92EntvironmentsqhX23zffhg3"A)typGographicalVruleofthumbforthe lineUUlengthis:N81`NoI\lineshouldcontain1`more6than66characters.1`ThisiswhyL5ffA͉TU>'ExXpages1`havesuchlargebGorders1`byUUdefault.That'sPwhymulticolumnprintisof-tenUUusedinnewspapGers.:qA?typographicalruleofthumb for?thelinelengthis:\begin{quote}No?lineshouldcontainmorethan66~characters.This?iswhy\LaTeXpageshavesuch?largebordersbydefault.\end{quote}That's?whymulticolumnprintisoften?usedinnewspapers.>.'There4aret!wo4similaren!vironments:}xthe4VquotationandtheVverseen- vironmen!ts.+The5Vquotationenvironmentisusefulforlongerquotesgoingo!verseveralparagraphs,bMecauseitdoesinden!tparagraphs.TheVverseen-vironmen!tisusefulforpMoemswherethelinebreaksareimpMortant.u.Thelines areseparatedb!yissuingaV\\attheendofalineandaemptylineaftereac!hfverse.qIڨknowNonlyoneEnglishpGoemNby heart.qItUUisabGoutHumptyDumpty*.N81`HumptyUUDumptysaton@`aUUwall:1`HumptyUUDumptyhada@`greatUUfall.1`AllUUtheKing'shorses@`andUUalltheKing's@`men1`Couldn'tUUputHumpty@`togetherUUagain.:qI?knowonlyoneEnglishpoemby heart.?ItisaboutHumptyDumpty.\begin{flushleft}\begin{verse}Humpty?Dumptysatonawall:\\Humpty?Dumptyhadagreatfall.\\All?theKing'shorsesandallthe?King'smen\\Couldn't?putHumptytogetheragain.\end{verse}\end{flushleft}X[2.9.4?@PrintingVerbatim Teextwhic!hisenclosedbMetweenV\begin{verbatim}andV\end{verbatim}willwbMedirectlyprin!ted,tasifitwastypMedonatypMewriter,twithalllinebreaksandfspaces,withoutan!yLAAGT,[wEB XcommandbMeingexecuted.ύ'Withinfaparagraph,similarfunctionalit!ycanbMeaccessedwithf^1ffAݟ ͤ ff͟fdq\verb+@textq+ ffffAݎTheV+isjustanexampledelimiterc!haracter.WYeoucanuseanycharacterexceptNletters,`gV*orblank.Man!yLAAGT,[wEB XexamplesinthisbMookletNaretypMesetwithfthiscommand.vn|퍍냍FU24OHTtypYesetting2T\extFzffhg3"FTheUUq\ldotscommand...N8Fq10?PRINT"HELLOWORLD"; F20?GOTO10The?\verb|\ldots|command\ldots \begin{verbatim}10?PRINT"HELLOWORLD";20?GOTO10\end{verbatim}_P`Fthe starred version of Fthe verbatimFenvironment emphasisesFthe spaces in the text\begin{verbatim*} the?starredversionoftheverbatimenvironment?emphasisesthe?spacesinthetext\end{verbatim*}WӆWThefV\verbcommandcanbMeusedinasimilarfashionwithastar:Fqlike this :-) \verb*|likethis?:-)|YWThe?Vverbatimen!vironment?andtheV\verbcommandma!ynotbMeused Fwithinfparametersofothercommands.!5F[2.9.5o@TabularLFTheVtabularen!vironmentcanbMeusedtot!ypesetbeautifultableswithFoptionalhorizon!talandverticallines.LAAGT,[wEB XdeterminesthewidthoftheFcolumnsfautomaticallye.BWTheftablesppecD۹argumen!tofthe ZF1ffg ͤ ff͟fdq\begin{tabular}{@tablesp}'ecq} ffffgFcommandnde nestheformatofthetable.gUseanVlforacolumnofleftFaligned text,7Vrforrigh!talignedtextandVcforcentredtext,7Vp{width V}foraFcolumnfcon!tainingjusti edtextwithlinebreaks,andV|foraverticalline.WWithin}aVtabularen!vironment}V&jumpstothenextcolumn, V\\startsaFnewflineandV\hlineinsertsanhorizon!talline.aFL͉fffdͤ ff+fd7C0͡ ffI hexadecimal͟ ff ͤ ff(ԟfd3700͡ ffI oGctal& ffͤ ff͟fd11111000000 ffI binaryS ffffffͤ ff(ԟfd1984͡ ffI decimal ffffq\begin{tabular}{|r|l|} \hline7C0?&hexadecimal\\3700?&octal\\11111000000?&binary\\\hline?\hline1984?&decimal\\\hline\end{tabular}vz]|퍍냍U2.92EntvironmentsqhX25zffhg3".ffUfd͟$fffdͲW*elcome2Kwe$Ecan\c!heat"anddoitbyusingtwocolumns:aright-alignedinte-ger~andaleft-alignedfraction.kTheV@{}commandintheV\begin{tabular}linereplacesthenormalin!tercolumnspacingwithjusta\.", givingtheap-pMearance@ofasingle,Tdecimal-poin!t-justi edcolumn.Don'tforgettoreplacethedecimalpMoin!tinyournumbMerswithacolumnseparator(V&)!JAcolumnlabMelۯcanbeplacedabo!veۯourn!umeric\column"byusingtheV\multicolumncommand.d1PiUUexpressionmqV*alueffIfd b> cmmi10_'3.gE1416 %K[ٟ^ 0ercmmi7Z&36.gE46([ٟ^H)^K#80662.gE7q\begin{tabular}{c?r@{.}l} Pi?expression$&\multicolumn{2}{c}{Value}?\\\hline$\pi$N&?3&1416 \\$\pi^{\pi}$/?&?36&46\\$(\pi^{\pi})^{\pi}$?&80662&7\\\end{tabular}pKMffp L͍ {-=B2acIfTthe`toAols'bundleisinstalledony9oursystem,havealoAokatthe{ow cmss9{dcolumncpack|ragev|퍍냍FU26OHTtypYesetting2T\extFzffhg3"FY2.10rFloatingffBos3diesqFTeoMda!yUymostpublicationscontainalotof guresandtables.Theseelements Fneed~9spMecialtreatmen!tbecausetheycannotbebrok!enacrosspages.eVOneFmethoMdMw!ouldbetostartanewpageev!erytimea gureoratableistooFlargesto tonthepresen!tpage.\ThisapproachwouldleavepagespartiallyFempt!yfwhichloMoksverybad.WThesolutiontothisproblemisto` oat'an!y gureortable,whichdoMesFnot tonthecurren!tpage,Vtoalaterpagewhile llingthecurrentpagewithFbModytext.LAAGT,[wEB Xo erst!woenvironmentsfor oatingbModies.OnefortablesFand onefor gures.Teotak!efulladvdDantageofthesetwoenvironmentsitisFimpMortan!t;tounderstandapproximatelyhowLAAGT,[wEB Xhandles oatsinternallye.FOtherwise:D oatsma!ybMecomeamajorsourceoffrustrationbecauseLAAGT,[wEB XFnev!erfputsthemwhereyouwantthemtobMe.GWLet'sf rstha!vefaloMokatthecommandsLAAGT,[wEB Xsuppliesfor oats:WAn!y(4materialenclosedinaVfigureorVtableenvironmentwillbMetreatedFasJL oatingmatter.*Both oaten!vironmentsJLsuppMortanoptionalparameterb~F1ffcȏ ͤ ff͟fdq\begin{figure}[@plac}'ementspeci erq]UUorq\begin{table}[@plac}'ementspeci erq]͡ ffffcȏFcalledAtheplacpementyspeci er.zThisAparameterisusedtotellLAAGT,[wEB XabMoutFthe)loMcationsthe oatisallo!wed)tobemo!ved)to.gA)placpementcspeci erWcisFconstructedyEb!ybuildingastringof opateplacingpermissions.SeeyETeable2.2.WAftablecouldbMestartedwiththefollo!winglinee.g.Qra`V\begin{table}[!hbp]QsFThe=placemen!tspMeci erV[!hbp]allowsLAAGT,[wEB XtoplacethetablerighthereF(Vh)QoratthebMottom(Vb)ofsomepageoronaspecial oatspage(Vp)andFall thatev!enifitdoMesnotlookthatgood(V!). Ifnoplacemen!tspeci erisFgiv!en,fthestandardclassesassumeV[tbp].-!m %Teablef2.2:FloatPlacingP!ermissionsM]lZVSpMec|֜P!ermissionftoplacethe oat.3..ZVzff>T `:NVh"4FherpeBatothev!eryplaceinthetextwhereitoMccurred.˲Thisis"4Fusefulfmainlyforsmall oats.H:NVt"4FatfthetopWXofapage:NVb"4Fatfthebpottom}qofapage:NVp"4FonfaspMecialppageycon!tainingonly oats.:NV!"4Fwithoutrconsideringmostofthein!ternalparametersoaVUwhich "4Fcouldfstopthis oatfrombMeingplaced.F?~ffp L͍ -=yaacSuc9hTasthemaximumnumbAerof oatsallowedononepagev|퍍냍U2.102FloatingBoYdiesqhX27zffhg3"'LAAGT,[wEB Xqwillplaceev!ery oatitencounters,4accordingtotheplacement spMeci erίsuppliedb!ytheauthor.VIfa oatcannotbeplacedonthecurren!tpage&_itisdeferredeithertothe gurpes worthetablesqueueA3.]WhenanewpagePisstarted,aLAAGT,[wEB X rstc!hecksPifitispMossibleto llaspecial` oat'pagewith\L oatsfromthequeues.IfthisisnotpMossible,the rst oatoneac!hqueue2istreatedasiftheyhadjustoMccurredinthetext:]uLAAGT,[wEB XtriesagaintoplacethemaccordingtotheirrespMectiv!eplacementspMeci ers(except`h'whic!hisnolongerpMossible).nAnynew oatsoMccurringinthetextgetplacedin!to theappropriatequeues.LAAGT,[wEB XstrictlymaintainstheoriginalorderofappMearanceforeac!htypMeof oat.dThat'swhya gurewhichcannotbMeplaced,3zpushesallthefurther gurestotheendofthedoMcumen!t.Therefore:C1`If$LAAGT,[wEB Xisnotplacingthe oatsasy!ouexpMected,>itisoftenonly1`onef oatjammingoneofthet!wof oatqueues.$]Ha!vingg'ExX2";S"...O\ThenotsoShortIn-troGductionUUtoL5ffA͉TU>'ExX2"("q\newcommand{\tnss} {The?notsoShortIntroductionto?\LaTeXe}%?inthedocumentbody:``\tnss''?\ldots{}``\tnss''Ip'Theٻnextexampleillustratesho!wtousethenumƹargument.wTheV#1sequence>getsreplaceb!ytheargumentyouspMecifye.eIfyouwantedtousemorefthanoneargumen!t,useV#2andsoon.UW&i1`TheK@not:soIShortIntroGduction 1`toUUL5ffA͉TU>'ExX2"&i1`The@veryShortIntroGductionto1`L5ffA͉TU>'ExX2"q\newcommand{\txsit}[1] {The?\emph{#1}ShortIntroduction?to\LaTeXe}%?inthedocumentbody:\begin{itemize}\item?\txsit{notso}\item?\txsit{very}\end{itemize}mp'LAAGT,[wEB XEwillnotallo!wyoutocreateanewcommandwhichalreadyexists.If8ty!ouexplicitlywanttooverrideanexistingcommandyouhavetousetheGeV\renewcommand.Apartfromitsname,oitusesthesamesyn!taxastheV\newcommandcommand.IIncertaincasesy!oumightalsowanttousetheV\providecommandcommand.PItw!orkslikeV\newcommand,Ubutifthenewcommandfisalreadyde ned,LAAGT,[wEB Xv2zC"0Kjustignoresit.3#[2.11.2FNewEnvironments]AnalogouslytotheV\newcommandcommandthereisacommandtocreatey!ourownenvironments. 82WhenwritingthisintroMduction,vIxhavecreatedspMecialpen!vironmentsforthestructuresIp\usedrepMeatedlythroughoutthein!troMduction:/\examples",ً\bitsPofcode"and\commandde nitionbo!xes".ThefV\newenvironmentcommandusesthefollo!wingsyntax:N|1ffB ͤ ff͟fdq\newenvironment{@name[q}[@numcq]{@b}'eforeq}{@afterq}͡ ffffB㎎'Lik!emtheV\newcommandcommand,youcanuseV\newenvironmentwithan"Doptionalargumen!tandwithout. QxThematerialspMeci edinthebpeforeargumen!tisproMcessedbeforethetextintheen!vironmentgetsprocessed.v|퍍냍FU30OHTtypYesetting2T\extFzffhg3"FTheI*materialintheaftervargumen!tgetsproMcessedwhentheV\end{nameҡV} Fcommandfisencoun!tered.WThe]examplebMelo!willustratestheusageoftheV\newenvironmentcom-Fmand.ꨍUWa`MyUUhumblesub8jects...q\newenvironment{king} {\begin{quote}}{\end{quote}}%?usethisinthebodypart\begin{king}My?humblesubjects\ldots\end{king}VaōWThe/dnumoargumen!tisusedthesamewayasintheV\newcommandcom-Fmand. LAAGT,[wEB XCmak!essurethatyoudonotde neanenvironmentwhichFalreadyYjexists.Ify!oueverwanttochangeanexistingcommand,*youcanFusestheV\renewenvironmentcommand. E@Itusesthesamesyn!taxastheFV\newenvironmentfcommand.vė|퍍냎gChapter 32^cT8yp esetting T{MathematicalForm8ulae5WNo!wM#youareready!InthischapterwewillattackthemainstrengthofT,nEXpX: mathematical͏t!ypMesetting.SWButbew!arned,Ythis͏chapteronlyscratchesthesur-face. sVWhile-thethingsexplainedherea!resucientformanypMeople,Xdon'tdespair ify!oucan't ndasolutiontoyourmathematicaltypMesettingneeds.Itisthighlylik!elythatyourproblemisaddressedinAMS-L󏍑XAWT,nEXpXA1 Worsomeotherpack!age..WZY3.1:cGeneral(썑LAAGT,[wEB X\hasaspMecialmodefort!ypesettingmathematics.Mathematicaltextwithins'ExXUUispronouncedas!.100UUm^3ȲofwaterThisUUcomesfrommy~q\TeX{}?ispronouncedas $\tau\epsilon\chi$.\\[6pt]100~m$^{3}$?ofwater\\[6pt]This?comesfrommy$\heartsuit$?&'IttAispreferabletodispla!ylargermathematicalequationsorformulae,|thatistot!ypMesetthemonseparatelines.ThereforeyouenclosethembMetweenV\[andeWV\]orbMet!weeneWV\begin{displaymath}andV\end{displaymath}.This N߉ffp L͍ {-=B1asCTAN:/tex-archive/macros/latex/packages/amslatexv Ġ|퍍냍FU32ATtypYesetting2MathematicalF\ormulaeFzffhg3"FproMduces form!ulaewhicharenotnumbMered. IfyouwantLAAGT,[wEB XtonumbMer Fthem,fy!oucanusetheVequationenvironment.FAddSasquaredandbsquaredtogetc Fsquared.Y#Or gusingamoremathemat-FicalUUapproach:|?c2C=a2S+8b2FAndUUjustonemoreline.qAdd?$a$squaredand$b$squared to?get$c$squared.Orusinga?moremathematicalapproach:\begin{displaymath}c^{2}=a^{2}+b^{2}\end{displaymath}And?justonemoreline.bÍWWithfV\labelandV\refy!oucanreferenceanequationwithinthetext.ȟ ͦ>0q{(3.1)FF*romUU(3.1)wegather...q\begin{equation}?\label{eq:eps} \epsilon?>0\end{equation}From?(\ref{eq:eps})wegather\ldotsI12WNote-thatexpressionswillbMet!ypesetifadi eren!tstyleifdisplayed:Fcon!trast-FlimS㑟n O!cmsy7!1ju cmex10Pލun%uk+B=1 I1i*&feRk+BZcmr52%= K@Lr2K&feԏl6\slimpF n!1n X k+B=1<$O1=kwfe ɟ (֍kPr29=<$K[ٟ^2Kwfe (֍Ȳ6q$\lim_{n?\to\infty} \sum_{k=1}^n?\frac{1}{k^2}=?\frac{\pi^2}{6}$\begin{displaymath}\lim_{n?\to\infty}\sum_{k=1}^n?\frac{1}{k^2}=?\frac{\pi^2}{6}\end{displaymath}nÍWTherearedi erencesbMet!weenmath2[mopdeƯandtextmopde.Feorexample,Finfmathmopdeҡ:ҍSb%1.a`MostXspacesandlinebreaksdonotha!veXanysigni cance,asallspacesa`areAeitherderiv!edlogicallyfromthemathematicalexpressionsorhavea`tofbMespeci edusingspecialcommandssuc!hasV\,,V\quadorV\qquad.ȟ uqɸ8x2pR:x2C0(3.2)q\begin{equation} \forall?x\in\mathbf{R}:\qquad?x^{2}\geq0\end{equation}G#Sb%2.a`Empt!yflinesarenotallowed.OnlyoneparagraphpMerformula.Sb%3.a`Eac!h!letterisconsideredtobMethenameofavdDariableandwillbea`t!ypMesetassuch.lIfyouwanttotypMesetnormaltextwithinaformulav!|퍍냍U3.22GroupinginMathMoYdeqhX33zffhg3"1`(normalouprigh!tfontandnormalspacing)thenyouhavetoenterthe 1`textfusingtheV\textrm{...}commands.j ȟ=ʧx2C0forUUall11͵x2pR(3.3)װq\begin{equation} װx^{2}?\geq0\qquadװ\textrm{for?all}x\in\mathbf{R}װ\end{equation}Md'Mathematicians4canbMev!eryfussyaboutwhic!hsymbMolsareused:itw!ould^+bMeconventionalheretouse`blackbMoardbold'whic!hisobtainedbyV\mathbbU(fromthepac!kdDageWamsfontsorWamssymb.ThelastexamplebMecomesȟ3x2C0forUUall11͵x2; msbm10Rq\begin{displaymath} x^{2}?\geq0\qquad\textrm{for?all}x\in\mathbb{R}\end{displaymath}TjY3.2:cGroupingffinMathMos3deMostymathmoMdecommandsactonlyonthenextc!haracter. Soifyouwantsev!eralcharactersa ectedbyacommandyouhavetogroupthemtogetherusingfcurlybraces:V{...}.ȟ H +axAIJ+8y"6=ax+yq{(3.4)q\begin{equation} a^x+y?\neqa^{x+y}\end{equation}HjY3.3:cBuildingffBlos3cksofaMathematicalFformulaIn6%thissectionthemostimpMortan!tcommandsusedinmathematicaltypMe-setting$AwillbMedescribed.WnFeoralistofallsym!bolsa!vdDailabletakealoMokatsectionf3.10onpage42. 򦍑'ULotwercaseU;GreeklettersĎareen!teredasV\alpha,V\beta,V\gamma,.3..,uppMercaseflettersA2fjareen!teredasV\Gamma,V\Delta,.3..;u;[;;; q$\lambda,\xi,\pi,\mu,\Phi,\Omega$'UExpYonentts)isdonewiththeV\veccommand.Teodenotethev!ectorfromCAFto4CBOthet!wo4commandsV\overrightarrowandV\overleftarrowareuseful.ȟܵ~'a*Xo!TXABq\begin{displaymath} \vec?a\quad\overrightarrow{AB}\end{displaymath}3ڍWNamesoflog-lik!efunctionsareoftentypMesetinanuprightfontandnotFitalicBPasvdDariables. ThereforeLAAGT,[wEB Xsuppliesthefollo!wingcommandstoFt!ypMesetfthemostimportan!tfunctionnames:v#悠|퍍냍U3.32BuildingBloYctksofaMathematicalF\ormulaqhX35zffhg3"V\arccos>\cos\csc\exp\kerR\limsup T\min\sinh \arcsin>\cosh\deg\gcd\lg"}\ln\Pr\sup\arctan>\cot\det\hom\limR\log\sec>\tan\arg"}\coth>\dim\inf\liminf T\maxR\sin\tanhꍍȟqKulim-IҴn!0<$]Isink;Ix]Iwfe (֍xt찲=1q\[\lim_{n?\rightarrow0} \frac{\sin?x}{x}=1\]3r'FeorythemoMdulofunctiontherearet!woycommands:ǂV\bmodforthebinaryopMeratorf\Ca modCb"andV\pmodforexpressionssuc!has\Cx FCa &(moMd1Cb)."F'Abuilt-upEUfractionist!ypMesetwiththeV\frac{...}{...}command.OftenJtheslashedform1C=2ispreferable,sbMecauseitlooksbetterforsmallamoun!tsfof`fractionmaterial.'$1 33133&fes2 .hoursZ<$:=x^23wfe5 (֍kw+81_ xR233xW iӟPO \cmmi5k+1#P;x1=2q$1\frac{1}{2}$~hours \begin{displaymath}\frac{?x^{2}}{k+1}\qquadx^{?\frac{2}{k+1}}\qquadx^{?1/2}\end{displaymath}YK'Teot!ypMesetbinomialcoecien!tsorsimilarstructuresyoucanuseeitherthecommandV{...\choose...}orV{...\atop...}.QThesecondcom-mandfproMducesthesameoutputasthe rstone,butwithoutbraces.ȟF1^<$Mpn 卑MkS ^<$xx 卑py+82q\begin{displaymath} {n?\choosek}\qquad{x\atopy+2}\end{displaymath}>z'TheDUinttegralNopYeratorisgeneratedwithV\int,theUsumopYeratorwith!WV\sum.NTheuppMerandlo!wer!Wlimitsarespeci edwithV^andV_aswithsubscriptsfandsupMerscripts.ȟGn BSX tCFi=1focZiP q0q0xW UʟPwU2@k60q\begin{displaymath} \sum_{i=1}^{n}?\qquad\int_{0}^{\frac{\pi}{2}}?\qquad\end{displaymath}AK'Feorc b8+x0KinUUthemorningl0KallUUdaylongq\begin{displaymath} y?=\left\{\begin{array}{ll}?a?&\textrm{if$d>c$}\\?b+x?&\textrm{inthemorning}\\?l?&\textrm{alldaylong}\end{array}?\right.\end{displaymath}e'Feorform!ulaerunningoverseverallinesorforequationsystemsyoucanusetheen!vironmentsVeqnarrayandVeqnarray*insteadofVequation.JInVeqnarray eac!hlinegetsanequationnumbMer. bIntheVeqnarray*nolinen!umbMersfareproduced.X:'TheVeqnarrayandtheVeqnarray*en!vironmentsworklikea3-columntable>\oftheformV{rcl},S+wherethemiddlecolumncanbMeusedfortheequalsignaōNoticefthatthecommaisbMoldtoo,whic!hmaynotbMewhatisrequired.'Thezpac!kdDageWamsbsyh(includedbyWamsmath)makesthismucheasier.ItincludesfaV\boldsymbolcommand,ɚand\pMoorfman'sbMold"V\pmbwhic!hworksb!yfover-strikingforsystemswithoutthefontsrequiredforbMoldsymbMols.ȟ1;M+A;M!"ž":(A*;8MqĞMMq\begin{displaymath} \mu,?M\qquad\boldsymbol{\mu},?\boldsymbol{M}\qquad?\pmb{\mu},\pmb{M}\end{displaymath}v*8\|퍍냍FU42ATtypYesetting2MathematicalF\ormulaeFzffhg3"FY3.10rListffofMathematicalSymbs3olsqFInkthefollo!wingtablesyou ndallthesymbMolsnormallyaccessiblefrom Fmathmopde.WTeobusethesym!bMolslistedinTables3.12{3.16A5,O`thepac!kdDageWamssymbFm!ustܬbMeloadedinthepreambleofthedoMcumentandtheAMSܞmathfontsFm!ustxbMeinstalledonthesystem.IftheAMS&packdDageandfontsarenotFinstalled,fony!oursystem,havealoMokatFVCTAN:/tex-archive/macros/latex/packages/amslatex]|r޹Teablef3.1:MathMoMdeAccen!ts#v1;In^IFCa[V\hat{a}CaNMV\check{a} ~Ca V\tilde{a}[J?["-Can"?V\acute{a}ƍInIFCa[V\grave{a}_CaNMV\dot{a} Ca V\ddot{a}[J?["-Can"?V\breve{a}*InIFCa[V\bar{a} C~aNMV\vec{a};jXIu 3 cmex10IbĖ5CA V\widehat{A};j\IeĖYCAn"?V\widetilde{A}w􍍒%"Teablef3.2:Lo!wercaseGreekLettersI񍍑V`C ilV\alphalCV\thetauCo% VojۯC}ƁV\upsilonƍVC ilV\betao^C#V\vartheta+C% V\pijC}ƁV\phiV@C ilV\gamma@CV\iotalC$% V\varpijnYC'}ƁV\varphiWBCilV\deltaCV\kappaGC% V\rhojBC}ƁV\chiWCilV\epsilonzCV\lambdaGC%% V\varrhoj?C }ƁV\psiWY-C"ilV\varepsilon_CV\mu:C% V\sigmajhC!}ƁV\omegaW'CilV\zetaCV\nuC&% V\varsigmaVCilV\etaCV\xi C% V\taui 鍟ܹTeablef3.3:UppMercaseGreekLetters%bK`rYUV\GammaعaV\LambdaԹ9;V\SigmaYy nqV\Psiƍq5UV\DeltaǹaV\Xi9;V\UpsilonZ;X nqV\OmegaqUV\ThetaaV\PiԹ9;V\PhiFQ&:ffp L͍ {-=B5acThesetablesw9erederivedfromssymbols.texcbyDavidCarlisleandsubsequently c9hangedTextensivelyassuggestedbyJosefTk|radlecv+A|퍍냍U3.102ListofMathematicalSymtbYolsqhX43zffhgy􍍒_Teablef3.4:BinaryRelationsYeoucanproMducecorrespondingnegationsb!yaddingaV\notcommandas pre xftothefollo!wingsymbMols.x#EC<[mV<4C>SV>=(V=ƍEF[mV\leqorfV\le4FSV\geqorfV\geF(V\equivDzKF[mV\ll`FSV\ggC:5=(V\doteqEF[mV\prec4FSV\succF(V\simEF[mV\preceq4FSV\succeqF'(V\simeqEF[mV\subset4FSV\supsetF(V\approxEF[mV\subseteq4FSV\supseteqFl=(V\congERTq 3 lasy10R<[mV\sqsubsetD2cmmi8Da4R=SV\sqsupsetDa0R1(V\JoinDaEFv[mV\sqsubseteq4FwSV\sqsupseteq C.,/(V\bowtieFMF2[mV\in3F3SV\ni,fV\ownsF/(V\proptoF]F`[mV\vdashFaSV\dashvG-Fj,Ϲ=(V\modelsHnFj[mV\midFkSV\parallelF?(V\perpDzKC^[mV\smile`C_SV\frownF(V\asympHn:[mV:khC=3F2SV\notinF6=(V\neqorfV\nesch-=E;cmmi6EamDZcUseTthe{latexsymcpac9k|ragetoaccessthissymbAol=獠*ȹTeablef3.5:BinaryOpMeratorsp@~" +7+V+FQZV-ƍ" F7+V\pmFQZV\mpaOC/09OV\triangleleft$ȷF7+V\cdotFQZV\divaOC.09OV\triangleright" F7+V\timesFnQZV\setminusaOC?09OV\star"F[7+V\cup1YF\QZV\capaOF09OV\ast"Ft7+V\sqcup1YFuQZV\sqcapaOF09OV\circ"F_7+V\vee,fV\lor1YF^QZV\wedge,fV\landaOF09OV\bullet" F7+V\oplusF QZV\ominusaOF09OV\diamond" F 7+V\odotF QZV\oslashwF]09OV\uplus" F 7+V\otimes^%F QZV\bigcircFq09OV\amalg!p.F47+V\bigtriangleupF5QZV\bigtriangledown-Fy09OV\dagger" R7+V\lhdDaRQZV\rhdDa-Fz09OV\ddagger" R7+V\unlhdDaRQZV\unrhdDaFo09OV\wrv,L|퍍냍FU44ATtypYesetting2MathematicalF\ormulaeFzffhgaHGTeablef3.6:BIGOpMerators-7E}ViɖIPmV\sum얟ɖIS V\bigcupɖIWV\bigveeZhɖILr?V\bigoplusƍW͟ɖIQmV\prod얟ɖIT V\bigcapɖIVV\bigwedgeZhɖINr?V\bigotimesW͟ɖI`mV\coprod얟ɖIF V\bigsqcupZhɖIJr?V\bigodotX#-IRmV\int0-IH V\oint[ɖIUr?V\biguplusAڋJTeablef3.7:Arro!ws_ritH9|9F Q +V\leftarroworfV\gets~,F ,dV\longleftarrowpF"HUV\uparrowƍ9|9F!Q +V\rightarroworfV\to~,F/A!dV\longrightarrowpF#HUV\downarrow9|9F$Q +V\leftrightarrowFF ,!dV\longleftrightarrowpFlHUV\updownarrow9|9F(Q +V\Leftarrow~,F(,Ϲ=dV\Longleftarrowov2F*HUV\Uparrow9|9F)Q +V\Rightarrow~,=,F)dV\Longrightarrowov2F+HUV\Downarrow9|9F,Q +V\LeftrightarrowFF(,)dV\Longleftrightarrowov2FmHUV\Updownarrow9|9F7!Q +V\mapsto~,F7!dV\longmapstomU F%HUV\nearrow8|F ,C-Q +V\hookleftarrow:C,,F!dV\hookrightarrowmU F&HUV\searrow9|9C(Q +V\leftharpoonupֶC*dV\rightharpoonupmU F.HUV\swarrow9|9C)Q +V\leftharpoondownֶC+dV\rightharpoondownmU F-HUV\nwarrow9|9L 3 msam10L Q +V\rightleftharpoonsFF(,)dV\iff(biggerfspaces)mU R;HUV\leadstoDa\ -=EaDZcUseTthe{latexsymcpac9k|ragetoaccessthissymbAol&πbTeablef3.8:Delimiters: ڷ>Y(O7V(2)V)lF"~V\uparrowlF*jV\Uparrowƍ>[O7V[orfV\lbrackL]V]orfV\rbracklF#~V\downarrowlF+jV\Downarrow=FfO7V\{orfV\lbracevFgV\}orfV\rbracelFl~V\updownarrowlFmjV\Updownarrow>YFhO7V\langle2FiV\rangle\Fj~V|orfV\vertmUsFkjV\|orfV\Vert> FbO7V\lfloorcTFcV\rfloorFd~V\lceilmQFejV\rceil=C=O7V/vFnV\backslash~.(dual.empt!y)a0HTeablef3.9:LargeDelimiters hMM=pI8 獑M=p:b-V\lgrouphMuI9 獒u;1V\rgrouphM2I8 獒2;iV\lmoustachehMd=I9 獒d=:zaV\rmoustachePFjb-V\arrowvertFk1V\ArrowvertF2I>H2>2>2>iV\bracevertv-W|퍍냍U3.102ListofMathematicalSymtbYolsqhX45zffhg{nXvTeablef3.10:MiscellaneousSym!bMolsT<+C:1::+V\dots4tF1V\cdots7.7.7.V\vdots=R.Bs.FF.UV\ddotsƍ)O 3 msbm10O~+V\hbarӲC{V\imathVKC|V\jmathAAC`UV\ell*F<+V\ReaF=V\ImF@V\aleph@ C}UV\wpF8+V\forallF9V\exists|HR0V\mhoDa@SC@UV\partial@GK cmsy8G0+V'6F0V\prime峿F;V\emptyset>.F1UV\infty\Fr+V\nablaF4V\triangleY=R2V\BoxDa?4-R3UV\DiamondDa:F?+V\botUF>V\top|HL\V\angle>ȟ9FpUV\surd:F}+V\diamondsuitUF~V\heartsuit.iF|V\clubsuit?GFUV\spadesuitwF:+V\negorfV\lnotvC[V\flatO{C\V\naturalAhC]UV\sharpPT͍h-=EamDZcUseTthe{latexsymcpac9k|ragetoaccessthissymbAol퍍jTeablef3.11:Non-MathematicalSym!bMolsThesefsym!bMolscanalsobeusedintextmode.ACr=@FyV\dagyFxApV\S^cwF jV\copyrightƍr=@FzV\ddag^F{ApV\P# P 3 cmu10$jV\poundstw:sNTeablef3.12:AMSDelimiters#vA&-Lp? rV\ulcornerZLqV\urcornermLxvV\llcorner/[^Ly@V\lrcornerhw:sr{˹Teablef3.13:AMSGreekandHebrewvA&-Oz/V\digammanf3O{#V\varkappaƗOiV\bethYOkV\dalethSAOjdyV\gimelv.d|퍍냍FU46ATtypYesetting2MathematicalF\ormulaeFzffhg F<ɍ곹Teablef3.14:AMSBinaryRelationseލb䍍8wcOlPTV\lessdotOmQ~V\gtrdotJ^rL+_~sV\doteqdotorfV\Doteqƍ8wcL6PTV\leqslantL>Q~V\geqslantJ^rL:_~sV\risingdotseq8wcL0PTV\eqslantlessL1Q~V\eqslantgtrJ^rL;_~sV\fallingdotseq8wcL5PTV\leqqL=Q~V\geqqJ^rLP_~sV\eqcirc5lLnPTV\lllorfV\lllessLoQ~V\gggorfV\gggtrJ^rL$_~sV\circeq8wcL.PTV\lesssimL&Q~V\gtrsimJ^rL,_~sV\triangleq8wcL/PTV\lessapproxL'Q~V\gtrapproxJ^rLl_~sV\bumpeq8wcL7PTV\lessgtrL?Q~V\gtrlessJ^rLm_~sV\Bumpeq8wcLQPTV\lesseqgtrLRQ~V\gtreqlessJ^rOs_~sV\thicksim?D8wcLSPTV\lesseqqgtrLTQ~V\gtreqqlessJ^rOt_~sV\thickapprox8wcL4PTV\preccurlyeqL<Q~V\succcurlyeqJ^rOu_~sV\approxeq8wcL2PTV\curlyeqprecL3Q~V\curlyeqsuccJ^rLv_~sV\backsim8wcL-PTV\precsimL%Q~V\succsimJ^rLw_~sV\backsimeq8wcOwPTV\precapproxOvQ~V\succapproxKH L_~sV\vDash8wcLjPTV\subseteqqLkQ~V\supseteqqJPL _~sV\Vdash8wcLbPTV\SubsetLcQ~V\SupsetI¶L_~sV\Vvdash8wcR3WyV\divideontimes.Ld-V\CuporfV\doublecupNLe7 V\CaporfV\doublecap3Or3WyV\smallsetminus{LY-V\veebaraLZ7 V\barwedgeL[3WyV\doublebarwedge[L-V\boxplusL 7 V\boxminus3L3WyV\circleddash[L-V\boxtimesL7 V\boxdot3L}3WyV\circledcirc[Lh-V\leftthreetimesLi7 V\rightthreetimes3L~3WyV\circledastLg-V\curlyveeLf7 V\curlywedgev0zj|퍍냍FU48ATtypYesetting2MathematicalF\ormulaeFzffhgh.zTeablef3.18:AMSMiscellaneousP|jM$UO~`uV\hbarRO}%V\hslashLwO|`V\BbbkƍKtL`uV\squareL%V\blacksquareJLs`V\circledSL%RLM`uV\vartriangleSLN%V\blacktriangleLœL{`V\complementL%RLO`uV\triangledownSLH%V\blacktriangledownLOa`V\GameLs0L`uV\lozenge}L%V\blacklozengeJVLF`V\bigstarL%RL\`uV\angleSL]%V\measuredangleKL^`V\sphericalangleK;O`uV\diagupjO%V\diagdownNL8`V\backprimeMO@`uV\nexists=9O`%V\FinvK@=O?`V\varnothingMOg`uV\ethSR0%V\mho/pe`,#Teablef3.19:MathAlphabMetsST-ókExampleCCommand0Requiredfpac!kdDagekWff. `ABCdef7V\mathrm{ABCdef}ƍABCdef7V\mathit{ABCdef}CABCȁdef7V\mathnormal{ABCdef}FABU@C7V\mathcal{ABC}LR 3 eusm10ABC7V\mathcal{ABC}=TWeucalfwithoption:Wmathcal 5or7V\mathscr{ABC}=TWeucalfwithoption:Wmathscr%n 3 eufm10ABCdef7V\mathfrak{ABCdef}=TWeufrakOABC7V\mathbb{ABC}=TWamsfontsforWamssymbv1h|퍍냎g3"Chapter 42Sp ecialities5WDon't&readthischapter!C|Or,Жatleast,ify!oufeelcon dentenough,y!oucan no!w"kstartwritingyourdoMcumentsinL󏍑XAWT,nEXpX.QThepurposeofthischapteristoaddsome`spice'toy!ourL󏍑XAWT,nEXpXknowledge.`AmuchmorecompletedescriptionofKspMecialitiesandenhancementspossiblewithL󏍑XAWT,nEXpXcanbefoundintheLnoAT"R[wE)XManual[1y]fWandTheLnoAT"R[wE)XComppanion}q[3]W.$ލY4.1:cFfontsffandSizesqLAAGT,[wEB Xc!hoMosestheappropriatefontandfontsizebasedonthelogicalstruc-turesofthedoMcumen!t(sections,$footnotes,.3..).Inssomecasesonemigh!tliketo0lc!hangefontsandsizesbyhand.{TeodothisyoucanusethecommandslistedGsinTeables4.1and4.2.Theactualsizeofeac!hfontisadesignissueandfdepMendsonthedocumen!tclassanditsoptions.ꨍTheDsmallandpbQoldRomansruled 2XQ ff cmr12all/ofgreatbigItaly.q{\small?Thesmalland \textbf{bold}?Romansruled}{\Large?allofgreatbig\textit{Italy}.}>aō'OneyimpMortan!tfeatureofLAAGT,[wEB Xv2zC"0qis,thatthefontattributesareinde-pMenden!t.&Thismeans,thatyoucanchangeissuesizeorevenfontchangingcommandsandstillk!eepthebMoldorslantattributesetearlier.uWhilethisma!yTJbMeevidenttosomeonelearningLAAGT,[wEB Xfromscratch,itisnotallthatclearfthesomeoneusedtoLAAGT,[wEB X2.09.'Inmath mopdezy!oucanusethefontchangingcpommandstotempMorarilyexitmathmopde_anden!tersomenormaltext.Ifyouwanttoswitchtoanotherfon!ttformathtypMesettingthereexistsanotherspecialsetofcommands.x RefertofTeable4.3.'Inconnectionwiththefon!tsizecommands,curlybracesplayasigni cantrole.Theyˎareusedtotobuildgrpoups.GroupslimitthescopMeofmostLAAGT,[wEB Xcommands.v2Π|퍍냍FU50pSpYecialitiesFzffhgZOuPйTeablef4.1:Fon!tsHOHffUnݟ:V\textrm{...}Proman]V\textsf{...}YWsansfserif V\texttt{...}Ptypewriter\textmd{...}Pmedium]V\textbf{...}YUbYold2faceV\textup{...}Puprigh!t]V\textit{...}YitalicV\textsl{...}Pp0J 3 cmsl10slan!ted]V\textsc{...}Ynsmall"caps TV\emph{...}Pemphasisepd_V\textnormal{...}YdoMcumen!tffont6wffUnݎ5'ȖTeablef4.2:Fon!tsizesAOH˽cffUnݟ3V\tinyVBtin9yfont V\scriptsizeVAvÎeryXsmallfontV\footnotesizeVcquiteTsmallfon9tV\smallVsmallUUfontV\normalsizeVnormalffon!tV\largeVZlargefonrta덍'V\Largelarger/font}'V\LARGE&DtGGcmr17vqery7tlargefont{'V\huge%DtqGcmr17huNuge['V\HugeDtHGcmr17largest/ffUnݎmfZŧ#Teablef4.3:Mathfon!tsP.Lp08Gff[B#0a썍CommandgExample+OutputV\mathcal{...}g$\mathcal{B}=c$+FB_= Cc V\mathrm{...}g$\mathrm{K}_2$+KzA2V\mathbf{...}g$\sumx=\mathbf{v}$+ɖIP9RCx =UvV\mathsf{...}g$\mathsf{G\timesR}$+WGnFWRV\mathtt{...}g$\mathtt{L}(b,c)$+L(Cb;1c)V\mathnormal{...}g$\mathnormal{R_{19}}\neqR_{19}$+CRzD19@JF6= CRzA19V\mathit{...}g$\mathit{ffi}\neqffi$+9êF6= Cf-fi>Yff[v3[|퍍냍U4.22SpacingqhX51zffhg3"ȍHeElikeslargeAandsmalllet-ters.qHe?likes{\LARGElargeand {\small?small}letters}.-߾'Thefon!tsizecommandsalsochangethelinespacing,butonlyifthe paragraph4endswithinthescopMeofthefon!tsizecommand.GTheclosingcurlybraceV}shouldthereforenotcometoMoearlye.nNotethepositionoftheV\parfcommandinthenextt!wofexamples.YǍDon'tY4ou/canbdCelieveme!q{\Large?Don'treadthis!Itisnot true.?Youcanbelieveme!\par}5{#ǍThis@Risnottrue. Butre- membdCer/Iamaliar.q{\Large?Thisisnottrue. But?rememberIamaliar.}\par(ʍ'Teoconcludethisjourneyin!tothelandoffontsandfontsizes,hhereisalittlefw!ordofadviceA1:q1`URememtbYer!1`p DsyźTheįWMkAHG cmssbx10OVRU 3 cmssi10EAfon!tsyYou$uBuseZt : cmbx9inU=caqdocumentm󙛻@ cmti12the䍑1`morefnreadableandbMeautifulitbec}h! cmsl12o}h!ff cmsl12m}h!G cmsl12e}h!q cmsl12s.$鍍Y4.2:cSpacing[4.2.1?@LineSpacinglIfy!ouwanttouselargerinterlinespacinginadoMcument,>youcanchangeitsfvdDalueb!yputtingthe?1ffjݟ ͤ ff͟fdq\linespread{@factorq} ffffjݎٍcommandCin!tothepreambleofyourdoMcument.UseV\linespread{1.3}for\oneAandahalf"linespacing,andV\linespread{1.6}for\double"linespacing.jNormally< thelinesarenotspread,QRthereforethedefaultlinespreadfactorfis1.-[4.2.2?@ParagraphFormatingInMLAAGT,[wEB X,therearet!woMparametersin uencingparagraphla!yout.ByMplacingafde nitionlik!e&1`V\setlength{\parindent}{0pt}1`\setlength{\parskip}{1explus0.5exminus0.2ex} bffp L͍ {-=B1acA9ttention:pThisTisabitofsatire.IhopAey9ourealisethat!v4|퍍냍FU52pSpYecialitiesFzffhg3"Finnthepream!bleA2 .޹oftheinput letheappMearanceofparagraphscanbe Fc!hanged.WThesetwolinesincreasethespacebMetweentwoparagraphswhileFsetting&.theparagraphinden!ttozero. IncontinentalEuropMe,?paragraphsareFoftenseparatedb!ysomespaceandnotindented.ButbMeware,thishasalsoFitse ectonthetableofcon!tents.ItslinesgetspacedmoreloMoselyno!wasFw!ell.'WIffy!ouwanttoindentaparagraphwhichisnotindented,youcanusenF1ff0 ͤ ff͟fdq\indent ffff0뎎FatthebMeginningoftheparagraphA3.BOb!viouslythiscanonlywork,whenFV\parindentfisnotsettozero.WTeofcreateanon-inden!tedparagraphyoucanusenF1ff;? ͤ ff͟fdq\noindent ffff;?厎JFasXthe rstcommandoftheparagraph.DThismigh!tcomeinhandye,{whenFy!oufstartadoMcumentwithbModyftextandnotwithasectioningcommand. ~]F[4.2.3o@HorizontalSpaceFLAAGT,[wEB XydeterminesthespacesbMet!weenywordsandsentencesautomaticallye.FTeofaddhorizon!talspace,use:F1ffU ͤ ff͟fdq\hspace{@lengthcq} ffffUᎎJWIfLsuc!haspaceshouldbMekept,^evenifitfallsattheendorthestartofaFline,ruseV\hspace*insteadofV\hspace.ҢThelength[inthesimplestcasejustFis}an!umbMer}plusaunit.ڏThemostimportan!tunitsarelistedinTeable4.4.NSFThis*isUUaspaceof1.5cm.qThis\hspace{1.5cm}is?aspace of?1.5cm.&WThefcommandF1ffF㍟ ͤ ff͟fdq\stretch{@ncq} ffffF㍎JFgenerates6aspMecialrubberspace.LItstretc!hes,juntil6alltheremainingspaceFonalineis lledup.Ift!woV\hspace{\stretch{n V}}commandsareissuedFonfthesameline,theygro!waccordingtothestretchfactor.F ffp L͍ {-=B2acBet9weenTtheensdocumentclasscandtheensbeginefsdocumentegRccommands  {-=B3acT:oinden9tthe rstparagraphaftereachsectionhead,7usethe{indent rstcpack|ragein theT`toAols'bundlev5a|퍍냍U4.32PtageLayoutqhX53zffhg8طTeablef4.4:T,[wEB XUnitsABsffM1VmmTmillimetrefF 1C=25inc!h!L͎hLc˄!L͎ VcmTcen!timetref=10mm!L͎hLs玍+ZO!L͎VinTinc!hfF25.4mm!L͎hLHEW+!L͎VptTpMoin!tfF 1C=72inchFK=A1=ڟp @Kd3 Wwmm!L͎hLh!L͎VemTappro!xfwidthofanVminthecurrentfont!L͎hL 5ٝ!L͎VexTappro!xfheightofanVxinthecurrentfont!L͎hLV!L͎-wffM捍x' xkxqx\hspace{\stretch{1}} x\hspace{\stretch{3}}x5偍[4.2.4?@VerticalSpaceThespacebMet!weenparagraphs,sections,subsections,.3..~isdeterminedau- tomaticallyb!yLAAGT,[wEB X.rIfnecessarye,$additionalverticalspacebpetween&twopparagraphs~canfbMeaddedwiththecommand:I1ffU ͤ ff͟fdq\vspace{@lengthcq} ffffUᎎ,'This;,commandshouldnormallybMeusedbet!ween;,twoemptylines.Ifthespace:fshouldbMepreserv!edatthetop,_foratthebottomofapage,_fusethestarredfv!ersionofthecommandV\vspace*insteadofV\vspace.'Thej>V\stretchcommandinconnectionwithV\pagebreakcanbMeusedtot!ypMesetHtextonthelastlineofapage,Zortocentretextverticallyonapage.1`VSometext\ldots1`\vspace{\stretch{1}}1`Thisgoesontothelastlineofthepage.\pagebreak'AdditionalEspacebMet!weenEtwolinesofthe}same_paragraphorwithinatablefisspMeci edwiththeI1ff; ͤ ff͟fdq\\[@lengthcq] ffff;,command.!΍Y4.3:cPageffLayoutqLAAGT,[wEB Xv2zC"BSallo!wsyoutospMecifythepapersizeintheV\documentclasscom-mand.`Itthenautomaticallypic!kstherighttextmargins.`Butsometimes,v6e|퍍냍FU54pSpYecialitiesFzffhgrmqHc4Y,̍,*̎̉,d}fn}fx}f}f}f}f}f}f}f}f}f}f}f}f}f}f}f}f}f"}f,}f6}f@}fJ}fT}f^}fh}fr}f|}f}fd}fn}fx}f}f}f}f}f}f}f}f}f}f}f}f}f}f}f}f}f"}f,}f6}f@}fJ}fT}f^}fh}fr}f|}f}fdY}̎ٚ}̎dY̎ٚ̎}ffYf@ff@YfY̎Y̎Y\̎Y\̎hY̎ Y̎Y̎Y̎Y̎Y̎Y̎Y̎Y̎Y̎Y̎Y̎Y̎Y̎Y̎Y̎Y̎Y̎Y̎Y̎Y̎Y̎Y̎Y̎Y̎Y̎Y̎Y̎Y̎Y̎Y̎Y̎Y̎Y̎Y̎Y̎Y̎Y̎Y̎Y̎Y̎hY̎ Y̎Y̎Y̎Y̎Y̎Y̎Y̎Y̎Y̎Y̎Y̎Y̎Y̎Y̎Y̎Y̎Y̎Y̎Y̎Y̎Y̎Y̎Y̎Y̎Y̎Y̎Y̎Y̎Y̎Y̎Y̎Y̎Y̎Y̎Y̎Y̎Y̎Y̎Y̎Y̎,4̍KcHeader̎̉4))̍m͍MMBoMdy)̎̉4ɀ̍2LcF:oAoter̎̉Js46))̍se Margin e Notes5)̎̉6< lcircle10iB832fdUO line1032fdU-#-i/n!B7#Οfe#?#Π(fe#6vπintB1dϳ2fd ά{ϳ2fd -x32fd ~x32fd -yxiywB3eiijbYB10K@i32fdάji32fd-K@Z32fd =Z32fd -Z@Zi[XjB9 Οـ fe@ـ6 Ο fe@?@ހinYB11v@kimntjB2v Π} fev@}?v Πf fev@c6@kimnjB4 Π fe@6 Π} fe@}?kimnB5Π fe6Πfe?@kimnjB6 Π fe@6 Πfe@?5@s1tSs1 oneinch+\hoffset2oneinch+\voffset tS3 \oddsidemargin=22pt4\topmargin=22pttS5 \headheight=13pt6\headsep=19pttS7 \textheight=595pt8\textwidth=360pttS9 \marginparsep=7ptFj10\marginparwidth=106pto11 \footskip=27pt\marginparpush=5pt(notshown) \hoffset=0pt\voffset=0pt \paperwidth=597pt\paperheight=845ptVЧFiguref4.1:P!ageLayoutParametersv7|퍍냍U4.42BibliographtyqhX55zffhg3"y!oumaynotbMehappywiththeprede nedvdDalues.NNaturallye,youcanchange them. tFigureu4.1sho!wsalltheparameterswhichcanbMechanged.ͺThe g-urefw!asproMducedwiththeWlayoutpackdDagefromthetoMolsbundleA4.퍑'LAAGT,[wEB X8pro!videstwocommandstochangetheseparameters. TTheyareusuallyfusedinthedoMcumen!tpreamble.'Thef rstcommandassignsa xedvdDaluetoan!yoftheparameters:"#51ff ͤ ff͟fdq\setlength{@p}'arameterq}{@lengthcq} ffff#ύ'Thefsecondcommand,addsalengthtoan!yoftheparameters.1ff ͤ ff͟fdq\addtolength{@p}'arameterq}{@lengthcq} ffff 'ThissecondcommandisactuallymoreusefulthantheV\setlengthcom- mand,%-bMecause y!oucannowworkrelativetotheexistingsettings.!Teoaddone"cen!timetretotheoveralltextwidth,Iwouldputthefollowingcommandsin!tofthedoMcumentpreamble: N捑1`V\addtolength{\hoffset}{-0.5cm}1`\addtolength{\textwidth}{1cm}0^ڍY4.4:cBibliography(WithzT|퍍냎gz=FIndexÍ"z=@WV\!,f36 |FV",f15FV$,f31FV',f34@WV\(,f31@WV\),f31@WV\,,f32,36F-,f15FF,f15@WV\-,f14F{,f15F|,f15F.,fspaceafter,18F.3..,f16@WV\@,f18@WV\[,f31@WV\\,f13,22{24,53@WV\\*,f13@WV\],f31FV^,f33FV_,f33FV|,f24FV~,f18bՍFA4fpapMer,8FA5fpapMer,8Faccen!t,f16Facute,f17@WV\addtolength,f55FadvdDan!tagesfofLAAGT,[wEB X,3F,f17FWamsbsy,f41FWamsfonts,f33FWamsmath,f36,38,41FWamssymb,f33,42@WV\and,f19"z=ױV\appendix,f18,19 D Varray,f37 arro!wfsymbMols,34 articlefclass,8ױV\atop,f35ױV\author,f19ױV\authors,f19L B5fpapMer,8 WbabMel,f17ױV\backmatter,f20 bac!kslash,f5 baseffon!tsize,8ױV\begin,f21ױV\bibitem,f55 bibliograph!ye,f55ױV\Big,f36ױV\big,f36ױV\Bigg,f36ױV\bigg,f36 blac!kbMoardfbold,33ױV\bmod,f35 bMoldfface,50 bMoldfsym!bols,33,41ױV\boldmath,f41ױV\boldsymbol,f41 bMookfclass,8 braces,f35ױV\caption,f27ױV\cdots,f36 Vcenter,f22ױV\chapter,f18ױV\choose,f35ױV\cite,f55ױV\cleardoublepage,f28v? |퍍냍UINDEXqhX63zffhg3"WV\clearpage,f28 colouredftext,9comma,f16commands,f5*V\!,f36*V\(,f31*V\),f31*V\,,f32,36*V\-,f14*V\@,f18*V\[,f31*V\\,f13,22{24,53*V\\*,f13*V\],f31*V\addtolength,f55*V\and,f19*V\appendix,f18,19*V\atop,f35*V\author,f19*V\authors,f19*V\backmatter,f20*V\begin,f21*V\bibitem,f55*V\Big,f36*V\big,f36*V\Bigg,f36*V\bigg,f36*V\bmod,f35*V\boldmath,f41*V\boldsymbol,f41*V\caption,f27*V\cdots,f36*V\chapter,f18*V\choose,f35*V\cite,f55*V\cleardoublepage,f28*V\clearpage,f28*V\date,f19*V\ddots,f36*V\displaystyle,f39*V\documentclass,f7*V\emph,f21,50*V\end,f21*V\footnote,f203"V\footnotesize,f50 V\frac,f35V\frenchspacing,f18V\frontmatter,f20V\fussy,f14V\hline,f24V\hspace,f52V\Huge,f50V\huge,f50V\hyphenation,f14V\include,f11,12V\includegraphics,f58V\includeonly,f12V\indent,f52V\index,f56V\input,f12V\int,f35V\item,f21V\label,f20,32V\LARGE,f50V\Large,f50V\large,f50V\ldots,f16,36V\left,f36V\linebreak,f14V\linespread,f51V\listoffigures,f27V\listoftables,f27V\mainmatter,f20V\makeindex,f56V\maketitle,f19V\mathbb,f33V\mathbf,f50V\mathcal,f50V\mathit,f50V\mathnormal,f50V\mathrm,f38,50V\mathsf,f50V\mathtt,f50V\mbox,f15,16V\multicolumn,f25V\newcommand,f28,29V\newenvironment,f29,30V\newline,f13v@7|퍍냍FU647INDEXFzffhg3"ZV\newpage,f13 ZV\newtheorem,f40ZV\noindent,f52ZV\nolinebreak,f14ZV\nonumber,f38ZV\nopagebreak,f14ZV\normalsize,f50ZV\overbrace,f34ZV\overleftarrow,f34ZV\overline,f34ZV\overrightarrow,f34ZV\pagebreak,f14ZV\pageref,f20ZV\pagestyle,f11ZV\paragraph,f18ZV\parindent,f51ZV\parskip,f51ZV\part,f18,19ZV\pmb,f41ZV\pmod,f35ZV\printindex,f57ZV\providecommand,f29ZV\qquad,f32,36ZV\quad,f32,36ZV\ref,f20,32ZV\renewcommand,f29ZV\renewenvironment,f30ZV\right,f36,37ZV\right.,f36ZV\scriptscriptstyle,f39ZV\scriptsize,f50ZV\scriptstyle,f39ZV\section,f18ZV\setlength,f51,55ZV\sloppy,f14ZV\small,f50ZV\sqrt,f34ZV\stretch,f52ZV\subparagraph,f18ZV\subsection,f18ZV\subsubsection,f18ZV\sum,f35ZV\tableofcontents,f19ZV\textbf,f503"V\textit,f50 PV\textmd,f50V\textnormal,f50V\textrm,f38,50V\textsc,f50V\textsf,f50V\textsl,f50V\textstyle,f39V\texttt,f50V\textup,f50V\thispagestyle,f11V\tiny,f50V\title,f19V\underbrace,f34V\underline,f34V\usepackage,f9,17V\vdots,f36V\vec,f34V\verb,f23,24V\vspace,f53V\widehat,f34V\widetilde,f34 commen!ts,f5 crossfreferences,20 curlyfbraces,5,49! dash,f15ױV\date,f19 Wdcolumn,f25ױV\ddots,f36 decimalfalignmen!t,25 delimiters,f35 describingfvdDariables,40 Vdescription,f21 diagonalfdots,36 dimensions,f52 Vdisplaymath,f31ױV\displaystyle,f39 doMcumen!tffontsize,8 doMcumen!tftitle,8ױV\documentclass,f7 dotlessfand,17 doubleflinespacing,51 doublefsided,8vA|퍍냍UINDEXqhX65zffhg3"ellipsis,f16 Pem-dash,f15WV\emph,f21,50emphasise,f21Vempty,f11en-dash,f15EncapsulatedfP!ostScript,57WV\end,f21Venumerate,f21en!vironment,f21en!vironments*Varray,f37*Vcenter,f22*Vdescription,f21*Vdisplaymath,f31*Venumerate,f21*Veqnarray,f37*Vequation,f32*Vfigure,f26,27*Vflushleft,f22*Vflushright,f22*Vitemize,f21*Vmath,f31*Vquotation,f23*Vquote,f22*Vtable,f26,27*Vtabular,f24*Vthebibliography,f55*Vverbatim,f23*Vverse,f23Veqnarray,f37Vequation,f32equationfsystem,37executiv!efpapMer,8expMonen!t,f33Wexscale,f36!Vfigure,f26,27 oatingfbModies,26Vflushleft,f22Vflushright,f22fon!t,f49fon!tfencoMding,10fon!tfsize,49,503"ۀfoMoter,f11 ױV\footnote,f20ױV\footnotesize,f50ۀform!ulae,f31ױV\frac,f35ۀfraction,f35ױV\frenchspacing,f18ױV\frontmatter,f20ױV\fussy,f14ۀGerman,f17ۀGhostScript,f58ۀgraphics,f9,57ۀWgraphicx,f58ۀgra!ve,f17ۀGreekfletters,33ۀgrouping,f49ۀheader,f11ۀtextttheadings,f11ױV\hline,f24ۀhorizon!talbrace,f34dots,f36line,f34space,f52ױV\hspace,f52ױV\Huge,f50ױV\huge,f50ۀh!yphen,f15ױV\hyphenation,f14ۀh!yphenationfrules,17ױV\include,f11,12ױV\includegraphics,f58ױV\includeonly,f12ױV\indent,f52ۀWindent rst,f52ۀindex,f56ױV\index,f56ױV\input,f12ۀinputf le,6ۀWinputenc,f17ױV\int,f35ۀin!tegralfopMerator,35vB$|퍍냍FU667INDEXFzffhg3"Fin!ternational,f17 Fitalic,f50@WV\item,f21FVitemize,f21FKn!uth,fDonaldE.,1@WV\label,f20,32 FLampMort,fLeslie,1Flanguage,f17@WV\LARGE,f50@WV\Large,f50@WV\large,f50FLAAGT,[wEB Xf2.09,1FLAAGT,[wEB Xv2zC"n,f1FLAAGT,[wEB X3,f1,4FWla!yout,f55@WV\ldots,f16,36@WV\left,f36Fleftfaligned,22FlegalfpapMer,8FletterfpapMer,8Fligature,f16Flinefspacing,51Flinebreak,f13@WV\linebreak,f14@WV\linespread,f51@WV\listoffigures,f27@WV\listoftables,f27Flongfequations,38@WV\mainmatter,f20FWmak!eidx,f56Fmak!eidxfpackdDage,56@WV\makeindex,f56Fmak!eindexfprogram,56@WV\maketitle,f19Fmargins,f53FVmath,f31Fmathffon!tsize,38Fmathfspacing,36@WV\mathbb,f33@WV\mathbf,f50@WV\mathcal,f50Fmathematical3"accen!ts,f34 delimiter,f36functions,f34min!us,f15 mathematics,f31ױV\mathit,f50ױV\mathnormal,f50ױV\mathrm,f38,50ױV\mathsf,f50ױV\mathtt,f50ױV\mbox,f15,16 min!usfsign,15 Mittelbac!h,fFerank,1 moMduloffunction,35ױV\multicolumn,f25ױV\newcommand,f28,29ױV\newenvironment,f29,30ױV\newline,f13ױV\newpage,f13ױV\newtheorem,f40ױV\noindent,f52ױV\nolinebreak,f14ױV\nonumber,f38ױV\nopagebreak,f14ױV\normalsize,f50 ,f17 option,f7 optionalfparameters,5ױV\overbrace,f34 o!verfullfhbMox,14ױV\overleftarrow,f34ױV\overline,f34ױV\overrightarrow,f34 pac!kdDage,f6,7 pac!kdDagesWamsbsy,f41Wamsfonts,f33Wamsmath,f36,38,41Wamssymb,f33,42WbabMel,f17Wdcolumn,f25Wexscale,f36vC-|퍍냍UINDEXqhX67zffhg3"*Wgraphicx,f58 f*Windent rst,f52*Winputenc,f17*Wla!yout,f55*Wmak!eidx,f56*Wsho!widx,f57pagefla!yout,53pagefst!yle,11*Vempty,f11*Vheadings,f11*Vplain,f11WV\pagebreak,f14WV\pageref,f20WV\pagestyle,f11papMerfsize,8,53WV\paragraph,f18parameter,f5WV\parindent,f51WV\parskip,f51WV\part,f18,19pMeriod,f16placemen!tfspMeci er,26Vplain,f11WV\pmb,f41WV\pmod,f35P!ostScript,f58pream!ble,f6prime,f34WV\printindex,f57WV\providecommand,f29OWV\qquad,f32,36WV\quad,f32,36Vquotation,f23quotationfmarks,15Vquote,f22WV\ref,f20,32WV\renewcommand,f29WV\renewenvironment,f30repMortfclass,8reserv!edfcharacters,4WV\right,f36,37righ!tfaligned,223"ױV\right.,f36 fۀroman,f50Oۀsansfserif,50ۀScandina!vianfletters,17ױV\scriptscriptstyle,f39ױV\scriptsize,f50ױV\scriptstyle,f39ױV\section,f18ױV\setlength,f51,55ۀWsho!widx,f57ۀsinglefsided,8ۀslan!ted,f50ۀslidefclass,8ױV\sloppy,f14ױV\small,f50ۀsmallfcaps,50ۀspace,f4ۀspMecialfc!haracter,16ױV\sqrt,f34ۀsquarefbrac!kets,5ۀsquarefroMot,34ױV\stretch,f52ۀstructure,f6ױV\subparagraph,f18ۀsubscript,f33ױV\subsection,f18ױV\subsubsection,f18ױV\sum,f35ۀsumfopMerator,35ۀtable,f24ۀVtable,f26,27ۀtablefofcon!tents,f19ױV\tableofcontents,f19ۀVtabular,f24ױV\textbf,f50ױV\textit,f50ױV\textmd,f50ױV\textnormal,f50ױV\textrm,f38,50ױV\textsc,f50ױV\textsf,f50ױV\textsl,f50vD7|퍍냍FU687INDEXFzffhg3"@WV\textstyle,f39 @WV\texttt,f50@WV\textup,f50FVthebibliography,f55@WV\thispagestyle,f11Fthreefdots,36Ftilde,f34Ftildef(V~),18@WV\tiny,f50Ftitle,f8,19@WV\title,f19Ft!wofcolumn,8Fumlaut,f17@WV\underbrace,f34Funderfullfh!bMox,14@WV\underline,f34Funits,f52,53Fuprigh!t,f50@WV\usepackage,f9,17@WV\vdots,f36@WV\vec,f34Fv!ectors,f34@WV\verb,f23,24FVverbatim,f23FVverse,f23Fv!erticalfdots,36Fv!erticalfspace,53@WV\vspace,f53Fwhitespace,f4Zafterfcommands,5Zatfthestartofaline,4@WV\widehat,f34@WV\widetilde,f34FWYSIWYG,f2,3vEA|퍍냍UINDEXqhX69zffhg3"vE;*Q- cmcsc10}h!q cmsl12}h!G cmsl12}h!ff cmsl12}h! cmsl12󙛻@ cmti12U 3 cmssi10kAHG cmssbx10p0J 3 cmsl10%n 3 eufm10LR 3 eusm10 P 3 cmu10DF cmmib10t : cmbx9{ow cmss9zt}\cmti7yt}\cmti7vj cmti9sߤN cmtt9rp0J cmsl10q 3 cmmi10BAacmr6A|{Ycmr8@': cmti10; msbm102XQ ff cmr121@ff cmti120': 3 cmti10&DtGGcmr17%DtqGcmr17DFH cmmib10Nq cmbx12NH cmbx12DtHGcmr17K`y 3 cmr10 !", cmsy10 O!cmsy7 b> cmmi10 0ercmmi7O \cmmi5K`y cmr10ٓRcmr7Zcmr5< lcircle10O line10u cmex10E