; TeX output 1997.04.15:122763׍׍ӗYf8"Vff cmbx10AGen=tleIntrouductiontoT=L33E X}9"V cmbx10AManualforSelf-studya[K`y cmr10MichaelUUDoGob DepartmentUUofMathematicsTheUUUniversityofManitobaWinnipGeg,UUManitoba,CanadaR3T2N2MDOOB@UOFMCC.BITNETMDOOB@CCU.UMANITOBA.CA*63׍׍).ܟ63׍׍)In=trouduction ffff|(/eFirstthebadnews:-)TU>'ExXisalargeandcomplicatedprogramthatgoGestoextraordinary lengthspxtoproGduceattractivetypGesetmaterial.%~ThisverycomplicationcancauseunexpGectedthingstohappGenattimes.TNowthegoodnews:FsstraightforwardtextisveryeasytotypGesetusing 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lar6theproGofreadingandsuggestionsofthefollowingpeoplehave6beeninvqaluable:W*aleedA.^Al-Salam(University^ofAlbGerta),DebbieL.Alspaugh(University^ofCalifornia),Nel-sonʟH.F.BeebGe(UniversityʟofUtah),BarbaraBeeton(AmericanMathematicalSociety),AnneBrGuggemann-Klein(UniversityofF*reiburg),BartChilds(TexasA.&M.University),Maryc Coventry(UniversityofW*ashington),DimitriosDiamantaras(T*empleUniversity),RobGertoFDominimanni(NavqalUnderwaterSystemsCenter),LincolnDurst(Providence,RI),VictorEijkhout(UniversityofNijmegen),MosheF*eder(St.LawrenceUniversity),JosepɧM.F*ont(UniversidadBarcelona),JonasdeMirandaGomes(InstitutodeMatematicaPura<"eAplicada-Brazil),RobGross(BostonCollege),KlausHahn(University<"ofMar-burg),AnitaHoGover(UniversityofDelaware),JGurgenKoslowski(MacalesterCollege),KeesvqanNderLaan(RijksuniversiteitGroningen),JohnLee(NorthropCorpGoration),SilvioLevy(PrincetoneUniversity),RobGertMesser(AlbionCollege),EmilyH.Moore(GrinnellCollege),Y*oungnPark(UniversityofMaryland),CraigPlatt(UniversityofManitoba),KaukoSaari-nenD((UniversityofJyvaskyla),JimW*right(IowaStateUniversity),andDominikW*ujastyk(W*ellcomeUUInstitutefortheHistoryofMedicine).InadditionseveralpGeoplehavesentmepartsoralloftheirloGcalmanuals.IhavereceivedAafewothersontherebGound. 4InparticularElizabethBarnhart(TV@Guide),Stephanv.Bechtolsheim(PurdueUniversity),NelsonH.F.BeebGe(UniversityofUtah)andLeslieLampGort(DigitalEquipmentCorporation),MarieMcPartland-ConnandLau-rieJMann(StratusComputer),RobGertMesser(AlbionCollege),NoelPeterson(LibraryofCongress),_CraigPlatt(University_ofManitoba),AlanSpragens(StanfordLinearAcceler-atorPqCenter,nowofAppleComputers),ChristinaThiele(CarletonUniversity),andDanielM.Zirin(CaliforniaInstituteofT*echnology)havewrittenvqarioustypGesoflecturenotesthathaveUUbGeenmosthelpful.ii63׍׍)Con=tents ffff|(#eIntroGduction T b> cmmi10:qōT:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T: ȫi 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w699.3UUHorizontalandverticallinesT:qōT:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T: S709.4UUBoxeswithinbGoxesT:qōT:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T: ,{7210.UUControlwordlist;T:qōT:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:h7711.UUIgetbywithalittlehelpT:qōT:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T: %80¶ivb63׍׍)Section1GettingStarted32ff|(B<1.1WhatTE XisandwhatTEXisn'tFirst|Eofall,let'sseewhatstepsarenecessarytoproGduceadocumentusingTU>'ExX.The rstYstepistotypGethe lethatTU>'ExXYreads.~pThisisusuallycalledtheTU>'EXY leortheinput le,.and6itcanbGecreatedusingasimpletexteditor(infact,ifyou'reusingafancywordproGcessor,youvNhavetobGesurethatyour leissavedinASCIGIvornondocumentmodewithoutanysjspGecialcontrolcharacters).TheTU>'ExXsbprogramthenreadsyourinput leandproGduceswhat'~iscalledaDVI's le(DVI'sstandsforDeViceIndepGendent).bThis leisnotreadable,0atleast#snotbyhumans.a'TheDVI#g leisthenreadbyanotherprogram(calledadevicedriver)thatproGducestheoutputthatisreadablebyhumans.Whytheextra le?ThesameDVIǍ~9mTȟE Xb7ook::23 9 le4DcanbGereadbydi erentdevicedriverstoproGduceoutputonadotmatrixprinter,kalaser.printer,ascreenviewer,oraphototypGesetter.JOnceyouhaveproGducedaDVI lethatgives#therightoutputon,-say*,a#screenviewer,-youcanbGeassuredthatyouwillgetexactlytheUUsameoutputonalaserprinterwithoutrunningtheTU>'ExXprogramagain.TheUUproGcessmaybethoughtofasproceedinginthefollowingway:'8?<$JeditUUtext 卍 ' !Ac*ffոff37 $[2 ګTU>'ExX input leDff37 37 *ff<$5TU>'ExXUUprogram 卍|%!c*ffոff37 [2jDVIj le Dff37 37 *ff<$IdeviceUUdriver 卍-~ I!I`c*ffոff37 preadableoutput ff37 37 *ff/*This meansthatwedon'tseeouroutputinits nalformwhenitisbGeingtypGedatthe6terminal.iButinthiscasealittlepatienceisamplyrewarded,E.foralargenumbGerofsymbGols$mnotavqailableinmostwordproGcessingprogramsbecomeavqailable.azInaddition,.5thetypGesetting isdonewithmoreprecision,andtheinput lesareeasilysentbGetweendi erentcomputersUUbyelectronicmailoronamagneticmedium.OurMfoGcuswillbeonthe rststep,thatis,creatingtheTU>'ExX.input leandthenrunningtheRTU>'ExX=programtoproGduceappropriateresults.gTherearetwoRwaysofrunningtheTU>'ExXprogram;itMcanbGeruninbatchmodeorinteractively*.[%InMbatchmoGdeyousubmityourTU>'ExXinput letoyourcomputer;pitthenrunstheTU>'EXprogramwithoutfurtherinterventionand_agivesyoutheresultwhenitis nished.IninteractivemoGdetheprogramcanstopandgetffurtherinputfromtheuser,ethatis,theusercaninteractwiththeprogram.Using>1˟63׍L̍󙚉ff|( ff AUUTU>'ExXintro(CanadianspGelling)uSection1:qGettingStarted fffff|(׍)TU>'ExX interactivelyHallowssomeerrorstobGecorrectedbytheuser,EwhiletheTU>'ExX program makesthecorrectionsinbatchmoGdeasbestitcan.&Interactiveisthepreferredmode, uofcourse. KAll,pGersonalcomputerandmanymainframeimplementationsareinteractive. KOnsomeUUmainframes,however,UUtheonlypracticalmethoGdofrunningTU>'ExXisinbatchmode.*1.2FٚromTE X letoreadableoutput,thebigsetup[NotefromMD:!p0J cmsl10ThisistheonlysystemdepGendentsectioninthemanualandmaybGereplaced{byaloGcalguide.rNoreferenceismadetoitoutsideofthesectionitself.ThefollowingUUloGcalinformationshouldbeincluded: WhatGhinitialsteps,J1ifany*,shouldbGetakenbythereadertopGermittherunningofTU>'ExXandUUyourloGcaldevicedriver(s). HowUUtorunTU>'ExX. HowUUtoreadthelog le. HowUUtopreviewand/orprintthedvi le.TheϲfollowingsampleisapplicablehereattheUniversityofManitoba.E'ExXattheUniversityofManitoba.ItisassumedthatUUthereaderisfamiliarwithMANTESandcancreatetext lesusingit.First,rthereareseveralthingsthatmustbGedoneone8timeonly.u?T*ostartyoumustdoUUthefollowing(youtypGeinthematerialthatlooksliketypGewritertypGe):8(1)alloGcateUUthe lesthatTU>'ExXwillusebytypingthefollowinglines(whileinMANTES):(C:UU.SOURCE.TEX,DISP=SHR//DVI?DDDSN=.DVI,DISP=OLD>2s63׍L̍󙚉ff|( ff AUUTU>'ExXintro(CanadianspGelling)uSection1:qGettingStarted fffff|(׍)The^nameisreplacedbyyourownuserid,`Eofcourse.TheuseofuppGercase andUUthespacesmustbGefollowedexactly*.8(3)Createa lecalledPRINTTEXvinyourMANTESaggregatecontainingthefollowingJCL://?JOB,'PRINTTEX'//?EXECTEXP//DVIFILE?DDDSN=.DVI,DISP=SHROncecyouhavecompletedthesethreesteps,gyouarereadytorunaTU>'ExXcjob.The lesyouUUhavecreatedwillallowyoutoproGduceabouttenpagesofordinarytext.HereUUarethestepsyouuseeac9hTtimeyourunajob.8(1)createUUaMANTES lecontainingyourTU>'ExXinput.8(2)saveUUandsubmityour leusingthecommands(C:UUsave?f/ltoda=source.texnoseq(C:UUsubmit?runtex8(3)whenUUyougetamessagesayingthatyourjobis nished,enterthecommand(C:UUout?;listttyoutInwthiscommand,isreplacedbyyouruseridwithadollarsignappGended.This lelistingwilltellyouofanyerrorsthatmighthaveoGccurred..Itisanabbreviatedversion\lofwhatiscalledthe\log le";_wewillusetheterm\log le"torefertothettyout leUUproGducedbyTU>'ExX.If]Lyouwant,_Iyoucancheckonthestatusofyourjobwhileitisexecutingbyusingthecommand(C:UUq?Whenyouare nishedloGokingatthelog le,"thecommandend?scratchwillthrowaway\thelog lewhilethecommandend?releasewillsendthelog letotheprinter,^VanditUUcanthenbGepickedUUupwithyourTU>'ExXoutput.>363׍L̍󙚉ff|( ff AUUTU>'ExXintro(CanadianspGelling)uSection1:qGettingStarted fffff|(׍)8(4)whenmyouroutputfromRUNTEXm}programiserrorfree,sTU>'ExXwillhavemcreatedalegal DVIUU le.qT*oprintit,usethecommand(C:UUsubmit?printtexnoholdAsUUin(3),youcancheckonthestatusofyourjobwhileitisexecuting.8(5)Pick[upyouroutputattheI/O3window,sixth oGorEngineeringbuilding.BItusuallytakesUUabGouttwentyminutesfortheoutputtobGeready*.qAskforitby\".The lescreatedarelargeenoughforrunningTU>'ExXjobsofabGout10pages.2\AjobofthatqsizewilltakeabGoutonesecondofCPUZtimetorunthroughTU>'ExX.S{ItwilltakeabGout15secondsUUofCPUtimetoprint10pagesontheXerox8600usingthecurrentdevicedriver.Y*ouqcanprintyourowncopyofthismanualusingthecommand%docu?tex. Y*oucanalsoUU ndlotsofotherusefulonlineinformationabGoutTU>'ExXbyusing%texinfo.*1.3Let'sdoit!So,from:ourviewpGoint,thenameofthegameistocreatetheTU>'ExX' lethatproGducesthe rightreadableoutput.XWhatdoGesaTU>'ExX lelooklike?XItconsistsofcharactersfromanordinaryterminal,thatis,uppGerandlowercaseletters,numbGers,andtheusualpunctuationandaccentcharacters(thesearetheusualASCIGIcharacters). T*ext,[forthemostpart,isjusttypGednormally*.Specialinstructionsusuallystartwithoneofafewspecialsymbolssuchas#or&(thesewillbGedescribedinmoredetaillater).WHereisanexampleofaTU>'ExXinputUU le:Here?ismyfirst\TeX\sentence.\byeFirstxnotethatthecharactersinthisexampleloGokliketypGewritertypGe.۲W*eusethesecharacters]withallexamplesthataremeanttobGetypGedfromthecomputerterminal.Sec-ond,lnoteqthatthebackslashappGearsthreetimesinthetext.Z{W*e'llsoonseethatthisisoneofthespGecialsymbolsmentionedpreviously*,IanditisusedveryfrequentlywhenmakingTU>'ExX*doGcuments.UkMake@a lecontainingthisexample.UsetheTU>'ExX*programtomakeaDVI leM6andadevicedrivertoseewhatyouhaveproGduced.oIfallgoeswell,Nyou'llM6haveasinglepageUUwiththefollowingsinglesentence:HereUUismy rstTU>'ExXsentence.>463׍L̍󙚉ff|( ff AUUTU>'ExXintro(CanadianspGelling)uSection1:qGettingStarted  fffff|(׍)ThereaywillalsobGeapagenumberayatthebottomofthepage.2Ifyou'veaygottenthisfar, congratulations!MOnceyoucanproGduceoneTU>'ExXdocument,wit'sjustamatteroftimebeforeyouRJcandomorecomplicatedones.pNowlet'scomparewhatwetypGedinwithwhatwegotout.gThe6straightforwardwordswerejusttypGedinnormally*,'ExX6settheminordinarytypGe.UgBut5theword\TU>'ExX",whichcan'tbGetypGedinonaterminalbecausethelettersaren'tonthesameline,isenteredbyusingawordstartingwithabackslash,andTU>'ExXmadethepropGerinterpretation.RMostsymbGolsthatarenotordinaryletters, numbGers,orpunctuationaretypGesetbyenteringawordstartingwithabackslash.IKIfweloGokalittlecloser,*we'llnotethattheword\ rst"isalsochanged. The rsttwolettershavebGeenjoinedtogetherandǍ~9mTȟE Xb7ook::4 9thereYisn'taseparatedotoverYtheletter\i".~ThisisstandardtypGesettingpractice:zcertainletter^combinationsarejoineduptoformwhatarecalledligatures.\ThereisactuallyagoGodA!stheticreasonforthis.k Comparethe rsttwoA!lettersof\ rst"and\first"toseethedi erence. W*ecnotethat\byeappGearsintheinput lewithnocorrespondingwordinthe nalcopy*. ThisatypGesettinginstructionthattellsTU>'ExXythattheinputis nished.wW*e'lllearnUUabGoutlotsofdi erenttypGesettinginstructionsaswegoalong.Let'sloGokatthelog lethatwascreatedwhenweranTU>'ExX.VItmayvqaryslightlyatyourUUsite,butshouldloGoksomethinglikethis:1.2. This?isTeX,MVSVersion2.9(noformatpreloaded)3. **?FilePLAIN.FMT<--DD=FMTLIBMEM=PLAIN4.5. **?FileSRC.TEX<--DD=SRC6. (src.tex?[1]7. Output?writtenonDVI(1page,256bytes).8. Transcript?writtenonTEXLOG.Thisisthe lethatwillcontainanyerrormessages.Online6,k(src.tex indicatedthatTU>'ExXvhasstartedreadingthat le.TheappGearanceof[1]indicatesthatpage1hasbGeenUUprocessed.qIftherewereerrorsonpage1,theywouldbGelistedatthatpoint.29.UUExercise1.1 AddasecondsentencetoyouroriginalTU>'ExX letoget:Here?ismyfirst\TeX\sentence.I?wastheonewhotypesetit!\byeUseUUTU>'ExXandloGokatyouroutput.qIsthesecondsentenceonanewline?>5o63׍L̍󙚉ff|( ff AUUTU>'ExXintro(CanadianspGelling)uSection1:qGettingStarted fffff|(׍).UUExercise1.2 NowaddthislinetothebGeginningofyour le:\nopagenumbersGuessnwhatwillhappGenwhenyourunthenew lethroughTU>'ExX.Nowtryitandseewhat happGens.$.,Exercise1.3 Addthreeorfourmoresentencestoyour le.>Useletters,numbGers,periods,commas,UUquestionmarks,andexclamationpGoints,butdon'tuseanyothersymbGols..&?Exercise1.4 Leave&?ablanklineandaddsomemoresentences.Y*oucannowgetnewparagraphs.W*ehavenowseenama8jorprincipleconcerningthepreparationofTU>'ExXinput les.HTheplacementCofthetextonyourcomputerterminaldoGesnotnecessarilycorrespondtotheplacementZbofthetextonyouroutput.Y*oucannot,[forexample,addspacebGetweenZbwordsinєyouroutputbyaddingspacesinyourinput le.ESeveralconsecutivespacesandonespacewilla lethatwillbGeheavilyedited,-xitisconvenienttostarteachsentenceonaseparateline.qSpacesUUatthebGeginningofaline,however,UUarealwaysUUignored..UUExercise1.5 Addthefollowingsentenceasanewparagraph,andthentypGesetit:Congratulations! You?receivedagradeof100%onyourlatestexamination.Thev%signisusedforcommentsinyourinput le.EverythingonalinefollowingthissymbGol visignored.`(Noticethateventhespacethatnormallyseparatesthelastwordononelinepfromthe rstwordonthenextlineislost.èNowputabackslashinfrontofthe%signtoUUcorrectthesentence.$.UUExercise1.6 Addthefollowingsentenceasanewparagraph:You?oweme$10.00andit'sabouttimeyousentittome!>663׍L̍󙚉ff|( ff AUUTU>'ExXintro(CanadianspGelling)uSection1:qGettingStarted fffff|(׍)This͟willproGduceanerrorinyourlog le(ifyourimplementationofTU>'ExX|isinteractive,that is,*sendsJyoumessagesandwaitsforanswers,*justhitthecarriagereturnorenterkeywhenyou.Vgettheerrormessage).Y*ouwillgetoutput,dbutnotwhatyoumightexpGect.Lookatethelog leandseewheretheerrormessagesarelisted.'ExXJusesforitsownpurpGoses.AUUtableofthesecharacterswillbGeprovidedshortly).*1.4TE XhaseverythingundercontrolW*e]haveseenthatthebackslashhasaspGecialrole.OAnywordstartingwithabackslashwillbGegivenaspecialinterpretationwhenTU>'ExXreadsitfromyourinput le.Suchawordiscalledacontrolsequence.8Thereare,infact,twotypGesofcontrolsequences:acontrolwordis6abackslashfollowedbylettersonly(forexample,n\TeX)&andacontrolsymbGolisabackslashҫfollowedbyasinglenonletter(forexample,\$).Sinceaspaceisanonletter,abackslashCfollowedbyaspaceisalegitimatecontrolsymbGol.WhenwewanttoemphasizeǍ~9mTȟE Xb7ook::7{8 9thattaspaceispresent,wetwilluseaspGecialsymbol toindicatethespace,asinthecontrolsymbGolUU\ .qThisconventionisusedinTheTT<8E3sXbQookUUaswellasinthismanual.WhenLTU>'ExX&I?like\TeX!the"controlword\TeX"۫isterminatedbytheexclamationpGoint.`ButthispresentsaproblemifUUyouwanttohaveaspaceafteracontrolword.qIfyouhave,forexample,thesentenceh>JI?like\TeXanduseitallthetime.in yourinput le,7thecontrolword\TeX ]isterminatedbythespace(whichis,7ofcourse,aVnonletter). oButthenyouwon'thaveaspacebGetweenthewords\TU>'ExX"and\and";insertingOmorespaceswon'thelp, sinceTU>'ExXdoGesn'tdistinguishbetweenOonespaceandseveraleconsecutivespaces.ButifyouputthecontrolsymbGol\ afteracontrolword,youwill^bGothterminatethecontrolwordandinsertaspace.VIt'sreallyeasytoforgettoputin>763׍L̍󙚉ff|( ff AUUTU>'ExXintro(CanadianspGelling)uSection1:qGettingStarted fffff|(׍)somethingIlike\ afteracontrolword.\I9promiseyouthatyouwilldoitatleastoncewhile you'reUUlearningtouseTU>'ExX.$.UUExercise1.7 Makeaninput lethatwillproGducethefollowingparagraph:Ilike!TU>'ExX!Onceyougetthehangofit,TTU>'ExXisreallyeasytouse.T,Y*oujusthavetomasterUUtheTU>'ExXnicalaspGects.Most(controlwordsarenamedsoastogiveahintoftheiruses."AY*oucanuse\partomakeUUanewparagraph,forexample,insteadofputtinginablankline.*1.5WhatTE Xwon'tdoTU>'ExXEisvverygoGodvatsettingtypGe,D>buttherearethingsthatTU>'ExXEcan'tdowell.+Oneismaking gures.SpacecanbGelefttoinsert gures,buttherearenographicproceduresbuiltintothelanguage(atpresent).|USomeimplementationsallowgraphicinstructionstobGeinsertedusingthe\specialcontrolwordbuttheseareexceptionalandde nitelysitedepGendent.TU>'ExXsetstypGeinhorizontalstraightlinesandnotinstraightlinesatotherangles.HInparticular,Bit}isgenerallynotpGossibletomakeinsertionsin\landscapemode",Bthatis,withtheHtextrotatedsothatthebaselineisparallelwiththelongedgeofthepapGer,Kortoincludetext#thathasacurveforabaseline.aRPerspGectivetypGe(graduallyincreasingordecreasinginheight)UUisnothandledwellbyTU>'ExX.W*eDXhaveseenthatthereisan\edit,zTU>'ExX,driver"cyclethatisnecessaryforeachdi erentcopy-ofoutput.LOThisistrueevenwhentheoutputdeviceisaterminal.LOInparticular,cit'snot pGossibletotypetheinput leandseetheresultsonthescreenimmediatelywithoutgoingthroughthefullcycle.ޠSomeimplementationshavebGothtextandgraphicsdisplayswith,reasonablyquickturnaround(afewsecondsforasinglepage);ashardwarebGecomeslessUUexpGensiveandprocessorsbecomefaster,wemayseeimprovement.>8 E63׍׍)Section2Allc=haractersgreatandsmall32ff|(B<2.1Somecharactersaremorespb"ecialthanothersW*e42sawinthelastsectionthatmosttextisenteredattheterminalassentencesof ordinaryT wordsjustaswhentypingwithatypGewriter.qYButwealsosawthat,TMinparticular,thesbackslashcouldbGeusedforatleasttwodi erentpurpGoses.͎Itcanbeusedforsymbols(orocombinationsofsymbGols)thatdon'tappearonthekeyboardsuchastyping\TeX]togetTU>'ExX.!ItscanalsobGeusedtogiveTU>'EXYspGecialinstructionssuchastyping\byetoindicatetheendoftheinput le.[Ingeneral,awordstartingwithabackslashwillbGeinterpretedbyTU>'ExXVaseonerequiringspGecialattention.ThereareseveralhundredwordsthatTU>'ExXVknows,andyoucande nemoreyourself,%8andsothebackslashisveryimpGortant.dW*e'llspGendalot5oftimeasweproGceedlearningsomeofthesewords;@ fortunatelywe'llonlyneedtouseasmallUUnumbGerofthemmostofthetime.There~)aretencharacterswhich,2likethebackslash,2areusedbyTU>'ExX}forspGecialpurposes,andn3wenowwanttogivethecompletelist.bWhatifwewanttouseasentencewithoneofǍ~9mTȟE Xb7ook::37{38 9theseUUspGecialcharactersinit?qWiththisinmindwe'llaskthefollowingquestions:8(1)WhatUUarethedi erentspGecialcharacters?8(2)HowUUdoweuseaspGecialcharacterifwereallywanttotypGesetitinourtext?HereisatableofeachspGecialcharacter,5[itspurpGose,andthemethoGdoftypesettingtheUUspGecialcharacteritselfifyouneedit:>9 O63׍L̍󙚉ff|( ff AUUTU>'ExXintro(CanadianspGelling)6Section2:qAllcharactersgreatandsmall  fffff|(׍)􍍠m'ӍnCharactersTrequiringspQecialinput-CharacterXPurpQoseDcInputTforliteraloutputfff\h ٽn@ѫSpGecialUUsymbolsandinstructionsߺ$\backslash$ ٽf@ѫOpGenUUgroupߺ$\{$ٽg@ѫCloseUUgroupߺ$\}$/%@Commentsߺ\%v/&@T*absUUandtablealignmentsߺ\&ٽ~@UnbreakqableUUspaceߺ\~{}ٽ$@StartingUUorendingmathtextߺ\$ٽ^@MathUUsupGerscriptsߺ\^{}&ff@ѫMathUUsubscriptsߺ\Eff&fǫ{}/#@De ningUUreplacementsymbGolsߺ\#*2.2Typb"esettingwithanaccentNowwe'regoingtostartusingsomeofTU>'ExX'sgoGodies!Sofarwe'vejustbGeenusing TU>'ExX}Pto}ZmakeouroutputloGokattractive,[butnowwe'llstarttodothingsthataredicultor(impGossibleonthetypewriter.AInparticular,Gwe'regoingtolookataccentsnow.AHowdo|jyouproGduceanaccentwhenthesymbGoldoesn'tappearonthekeyboard?Justaswiththe symbGolTU>'ExX,itisnecessarytoenterawordstartingwithabackslash.=F*ortheword\premiGere",[as`a rstexample,youneedtotypGeinpremi\`ere(youmayhavetohuntaroundto ndthe\backprime"or\grave"symbGol`onyourkeybGoard, )butit'stheresomewhere^2|s).V*InL!general,toputanaccentonaletter,theappropriatecontrolsequenceprecedesUUtheletter. X-ff=  ^2IfFyouhaveaveryoldorobscurekeybGoardandthebackprimeis$': cmti10r}'eally)XnotFthere,Iyoucan(&use\lq{}instead.bSimilarly\rq{}canbGeusedforthesymbol'.bY*oucanthinkofthesymbGolsXasbeingabbreviationsfor\leftquote"and\rightquote."Inaddition,Y\lq\lq{}and\rq\rq{}givetheusualquotationmarks.PButthiswon'tworkasamethoGdtoproduceanUUaccentoverthefollowingletter,soyou'rereallybGettero withaproperkeyboard.10 {63׍L̍󙚉ff|( ff AUUTU>'ExXintro(CanadianspGelling)6Section2:qAllcharactersgreatandsmall  fffff|(׍)HereUUaresomeexamples:V-T<8E3sXTinput̽6T<8E3sXToutput~}\fffp \`a?lamodeN?ګaUUlamoGde ?r\'esum\'eN?ګrGesume?soup\c conN?ګsoup9con?No\"elN?ګNoGel na\"\i veN?ګnaqve$W*ecseeseveralprinciplesillustratedbytheseexamples.MostaccentsareproGducedby usingVacontrolsymbGolwithasimilarshape.uAfewofthemareproducedbycontrolwordscontaining0)asingleletter.ecSomecaremustbGeusedinthiscase,7foraspacemustbGeusedtoterminateVthecontrolword.vIfyouhavesoup\cconinyour le,Wforexample,TU>'ExXwillloGokforUUthecontrolword\ccon^3|s.S~9mTȟE Xb7ook::52{53*Notice,thatthereisacontrolword\ialso.KThisproGducestheletter\i"withoutthedotoverit;.[thisallowsanaccenttobGeputoverthelowerpartoftheletter.#ThereisananalogousUUcontrolword\jthatproGducesadotless\j"foraccentingpurpGoses.v􍍟'Ӎ=Accen9tsTthatmaybQeimmediatelyfollowedbyalettern-kqName/T<8E3sXTinputT<8E3sXToutputGxfff[ '#grave\`oה;o'#acute\'oה;ocircum ex\^oה;^oumlaut/dieresis/trGemat\"oה;o)xtilde\~oה;~o#macron\=oה;o+dot\.oذ_qo ffff=  ^3W*e'llNseethatthereisanothermethoGdwhenwelookatthegroupingconceptinSec-tionUU4.11 ̟63׍L̍󙚉ff|( ff AUUTU>'ExXintro(CanadianspGelling)6Section2:qAllcharactersgreatandsmall  fffff|(׍)v􍍟'Ӎb1Accen9tsTrequiringaninterveningspacen-kqNameT<8E3sXTinput VT<8E3sXToutputT.<fff cedillak\c?opGo underdotk\d?o)o!ƍF.vunderbark\b?o)o) haGcekk\v?o)o?brevek\u?o)o @tieh\t?oos/ooHungarianUUumlautk\H?o)}oTU>'ExXUUalsoallowssomelettersfromlanguagesotherthanEnglishtobGetypGeset.ZkmmNAv\railableTforeignlanguagesym9bQolsc4fAExampleJT<8E3sXTinputT<8E3sXToutputJq̟fff gean,UUstheticsty\AE,?\aeʞ,UU uvres,UUhorsd'uvrew\OE?\oeɌ,UU 6f;aAngstromty\AA,?\aa~;a~A,Ua Si?9?`>(*'ExXisabGout53.63;aA..UUExercise2.3 TheytoGoksomehoneyandplentyUUofmoneywrappedupina$5note.12 663׍L̍󙚉ff|( ff AUUTU>'ExXintro(CanadianspGelling)6Section2:qAllcharactersgreatandsmall  fffff|(׍).UUExercise2.4 x ElGeves,UUrefusezvosle9cons!qJetezvoscha^qnes!$.UUExercise2.5 ZaxstotakopGolakopijete8Gca8j?.UUExercise2.6 MeinT*eeisthei..UUExercise2.7 Peut-^GetreUUqu'ilprefereUUlecafeglace..UUExercise2.8 >PorquGenobGebesUUvinoblanco?q'ExX,thereisnoneedtobGesorestricted._Inthissectionwe'lllookatsomedi erencesUUbGetweentypingandusingTU>'ExX.ThereF+arefourtypGesofdashesthatareused.lThehyphenisusedforcombiningwordsintoƎoneunitaswithmother-in-law. Theen-dashisusedtoindicateasequenceofpageǍ~9mTȟE Xb7ook::3{5 9numbGers,yearsXorsuchthings.Theem-dashisagrammaticalsymbGol.TheminussignisusedUUfornegativenumbGers.qHeretheyarewiththeiruses:1363׍L̍󙚉ff|( ff AUUTU>'ExXintro(CanadianspGelling)6Section2:qAllcharactersgreatandsmall  fffff|(׍)\f'ӍrDi eren9tTtypQesofdashesJ-̙xNameDUYT<8E3sXTinputT<8E3sXToutputSFExample*fff&؟ jhyphenT--_TheUUspaceis3-dimensional. :en-dashRG--{ReadUUpages3{4.*em-dashO---0|ЊVIUUsawthem|therewere3menalive.minusUUsignO$-$MƦīTheUUtempGeraturedroppedto3degrees.-.CBExercise2.12 ICenteredtheroGomand|horrors|IsawbGothmyfather-in-lawandmy mother-in-law.$.UUExercise2.13 Thewinterof1484{1485wasoneofdiscontent."JAnother!di erencebGetween!typingandusingTU>'ExXistheuseofquotationmarks.K OpGen-ingvandclosingquotationmarksarethesameonatypGewriter.)TheyareproducedinTU>'ExXbyusingtheapGostropheorprimekey'andbackprimekey`.;AnopGenquoteisproducedby``andtheclosequoteby''.CSimilarlytheopGeningsinglequoteisproducedby`andǍ~9mTȟE Xb7ook::3 9theNclosingsinglequoteby'.QNoticethatthereisnoneedtousetheusualtypingquotationmarkUU(itnormallygivesaclosequote,butdon'tcountonit)..UUExercise2.14 His\thoughtfulness"wasimpressive..UUExercise2.15 F*rankwondered,\Isthisagirlthatcan'tsay`No!'r?""JSometimes ellipses(threedots)areusedtoindicateapassageoftimeormissingma-terial.Typingz?threepGeriodsz?willgivethreedotsveryclosetogether.ThedotswithpropGerspacingUUwillbGeproducedbyhaving\dotsinyourinput le.Ǎ~9mTȟE Xb7ook::173"9.a'Exercise2.16 Hethought,\::: UOandthisgoGesonforever,pGerhapstothelastrecordedsyllable."AnotherCproblemwithdotsisthatthepGeriodCafteranabbreviationnormallyhaslessspace afteritthandoGestheperiodattheendofasentence.Therearetwowaystosolve1463׍L̍󙚉ff|( ff AUUTU>'ExXintro(CanadianspGelling)6Section2:qAllcharactersgreatandsmall  fffff|(׍)this"problem:X%thedotcanbGefollowed"byeither\ or~tochangethespacing.`ThesecondǍ~9mTȟE Xb7ook::91{92 9alternativewillgiveanunbreakqablespace;whensuchaspaceisbGetweentwowords,`these wordsamusttypGesetonthesameline.V TheinputProf.~KnuthwouldcausethosetwowordstopvbGetypesetononeline.)ThisisdesirablefornameslikeV*ancouver,w>B.C.andMr.Jonessothat\Mr."eqand\Jones"donotenduponseparatelines.NoticethatnobackslashisusedUUwiththeunbreakqablespace.$.UUExercise2.17 HaveUUyouseenMs.Jones?.Exercise2.18 Prof.SmithandDr.Gold ewfromHalifaxN.S.toMontrGeal,P*.Q.via Moncton,UUN.B.*2.4Di erentfontsThe'ExX'ExXbutevensothereareseveraldi erenttypGefacesi1avqailableascanbGeseeninthefollowingtable.[AhcompletelistofthesixteenfontsisgiveninAppGendixFlofTheT<8E3sXbQook. (Mostofthemareusedautomatically;8㍟~9mTȟE Xb7ook::427{432 amathematicalsubscript,!forexample,isputinsmallertypGebyTU>'ExXwithnospGecialuserintervention.T*ochangefromtheusual(roman)typGefacetoitalic,ٚthecontrolword\itisused.T*o-HchangebacktotheusualromantypGeface,cEuse\rm.F*orexample,youcouldhavethefollowingsentence:HI?startedwithromantype,\itswitchedtoitalictype,\rmand?returnedtoromantype.Thisjwouldgivethefollowing:IjstartedwithromantypGe,switche}'dtoitalictype,^4ZandUUreturnedtoromantypGe.TypGefaces73otherthanitalicarealsoavqailable.aThosegivenbGelowaretheonesmostcommonly0used.XTheyareavqailableimmediatelywhenTU>'ExXstarts.Alittle0laterwe'llseehowUUtouseothertypGefacesthataren'tavqailablewhenTU>'ExXstarts. ff=  g^4Notic}'edrthatthecommaandthisfootnoteareinitalictype,mandthislooksalittlefunny.We'll)se}'ethatthereisanothermethodforchangingfontswhenwetalkaboutgroupinginSe}'ction4.15q63׍L̍󙚉ff|( ff AUUTU>'ExXintro(CanadianspGelling)6Section2:qAllcharactersgreatandsmall  fffff|(׍)v􍍟'Ӎ%F on9tTSamplesb-F on9tTnameaT<8E3sXTswitc9hsequenceKSampleToft9ypQefacefffg Romany1\rmThisUUisromantypGe. zBoldfacey1\bf2ThisTisbQoldfacet9ype.Italicy1\it'ExXwhendesired(assum-ing thattheyareavqailableonyourcomputersystem,ofcourse).YDi erentsizescanbGeusedwithetheaidofthecontrolword\magstep.T*ode neyournewfontyouwillhavetoknowitstnameonyourcomputersystem.ώF*orexample,|htheromantypGefaceiscalled\cmr10"onmost[Xsystems.Ifyouuse\font\bigrm?=cmr10scaled\magstep1,you[Xcanthenuse\bigrmUUinexactlythesamewayUUasyouuse\itor\rm.8䍟~9mTȟE Xb7ook::13{17Switching'via\bigrmwillgiveromantypGethatislargerthantheusualby20%.\font\bigbigrm?=cmr10scaled\magstep2awillde neafontthatisabGout44%largerthan46theusualromantypGeface.iThesizes\magstep?0to\magstep5areavqailable.iOnmostBrcomputers\magstephalfisalsoavqailable;thisrepresentsanenlargementofabGout9.5%.qHereUUaresomesamplesatvqarioussizes: X-ff= ^5ThisexampleischeatingsinceyouneedtoknowalittleabGoutmathematicsinputtouse*it,&butIwanted*toincludeitanyway*.^You'll*bGeabletousetheselettersafteryoustudytheUUuseofmathematicalsymbGols.1663׍L̍󙚉ff|( ff AUUTU>'ExXintro(CanadianspGelling)6Section2:qAllcharactersgreatandsmall  fffff|(׍)hzDi eren9tTF ontMagni cations@1Magni cationWi1Sample1fffwƟ \magstep?0VgSampleUUtextatmagstep0. \magstephalfVg3K`y 3 cmr10Sampleftextatmagstephalf.\magstep?1Vg2K`y cmr10Sampletextatmagstep1.\magstep?2Vg4K`yff cmr10Sampletextatmagstep2.\magstep?3Vg5K`yG cmr10Sampletextatmagstep3.\magstep?4Vg6K`yp cmr10Sampletextatmagstep4.O\magstep?5Vg7K`yG cmr10SampleKtextatmagstep5.It's܁alsopGossibletousecompletelynewtypefaces.IThesearedependentonsystemavqailabil- ity*,ofcourse.jManysystemshavea lecalledCMSS10whichisafontthatcontainssansserifletters.Using\font\sf?=cmss10īwillallowthecontrolword\sftobGeusedinthesameUUmanneras\bf.qHavingmadethisde nition,theinputH\\sf?HereisasampleofournewSansSeriffont.willUUproGducejHm#R cmss10HereUUisasampleofournewSansSeriffont.+.别Exercise2.19 Whatproblemmighthavearisenifwehadused\ssinsteadof\sftoturnontheSansSeriffont?UHint:liftheanswerdoGesn'toccurtoyouat rst,;thinkabouttheGermanUUalphabGetanditwill nallycometoyou.$.UUExercise2.20 TypGesetaparagraphofmagni edsansseriftext.Theextrafontsavqailablemayvqaryfromsitetosite.{TheonesinthefollowingtableareUUavqailableatmostplaces.17)(63׍L̍󙚉ff|( ff AUUTU>'ExXintro(CanadianspGelling)6Section2:qAllcharactersgreatandsmall  fffff|(׍)X-GϗExternalTF on9tsNamesff>lUfflQ CMBSY10>CMBXSL10|CMBXTI10CMBX10CMBX128oCMBX5 CMBX6>CMBX7|CMBX8CMBX9CMB108oCMCSC10CMDUNH10>CMEX10|CMFF10CMFIB8CMFI108oCMITT10CMMIB10>CMMI10|CMMI12CMMI5CMMI68oCMMI7CMMI8>CMMI9|CMR10CMR12CMR178oCMR5CMR6>CMR7|CMR8CMR9CMSLTT108oCMSL10CMSL12>CMSL8|CMSL9CMSSBX10CMSSDC108oCMSSI10CMSSI12>CMSSI17|CMSSI8CMSSI9CMSSQI88oCMSSQ8CMSS10>CMSS12|CMSS17CMSS8CMSS98oCMSY10CMSY5>CMSY6|CMSY7CMSY8CMSY98oCMTCSC10CMTEX10>CMTEX8|CMTEX9CMTI10CMTI128oCMTI7CMTI8>CMTI9|CMTT10CMTT12CMTT88oCMTT9CMU10>CMVTT10Here's alittlebackgroundabGoutthesenames.`BThe rsttwolettersCM standsforComputer MoGdern,lthegnamegiventothisfontfamilybythedesigner.ThenumbGerattheendisthepGointPsize:o10pointtypGeisthenormalsize,Q7pointisthenormalsizeforsubscripts,Qand5pGointisthenormalsizeforsubscriptsofsubscripts,Х12pointis20%largerthan10point,etc.lIfEthelettersCMEarefollowedEbyB,itisabGoldfacetypGe.lSimilarlyREindicatesroman,I Iisforitalics,CSCisforsmallcaps,SLisforslanted,SSisforsansserif,SYisforsymbGols,andUUTTisfortypGewritertypGe.$.Exercise2.21 Findthefontsavqailableonyoursystem,andprintoutallthelettersandnumbGersUUinseveralofthem..nvExercise2.22 ThefontCMR12is20%largerthanCMR10.+Also\magstep?1magni esthentypGeby20%.T*akesometextandprintitusingCMR12thenusingCMR10scaledby\magstep?1.qTheUUresultsarequitedi erent!18163׍׍)Section3Theshapueofthingstocome32ff|(/eIn_thissectionwewanttoseehowtomaketexthavedi erentshapGesorsizes.One may,useTU>'ExX,withthedefaultsizes,4ofcourse,justaswehavebGeendoingsofar.dCW*e'llnowbGecomemorecreativewithouroutput.&qIndiscussingthesizeofvqariouspartsofapageoftext,UUthereareseveralunitsofmeasurewecanuse.*3.1Units,units,unitsTU>'ExXЇcanЦmeasurelengthusingmanytypGesofunits.Themostcommonaretheinch,the?centimetre,thepGoint,thepica.Theabbreviationsfortheseunitsarein,cm,pt,andpcrespGectively*.VThepointisde nedbytheequation1inch=72.27pGoints,andthepicaby17pica=12pGoints.mThus7apointisrathersmallandisaboutthesizeofadecimalpoint.HereUUisasampletogiveanideaofthecomparativesizes:Ǎ~9mTȟE Xb7ook::579K1UUinch:iffffGxRff1UUcentimetre:9yffffff20UUpGoints:affff34ffh1UUpica:hffff 34ffThuspGointsareusedtomake nechanges;/apicaisabGoutthedistancebetweenthe baselinesoftwoconsecutivelinesof(unmagni ed)normaltext.TU>'ExXisquiteexactabGoutdimensions;internallyitssmallestunitislessthanonefour-millionthofaninch.BHenceitisUUtheresolutionoftheoutputdevicethatwilldeterminetheaccuracyoftheoutput.Therearetwootherunitsthataresometimesusefulthathavedi erentsizesindi erentfonts.JTheexisabGouttheheightofasmall\x"andtheemisalittlesmallerthanthewidthofUUacapital\M".Ǎ~9mTȟE Xb7ook::609The2shapGeoftheoutputisgenerallydeterminedbycontrolwords. TherearemanysuchY#words;[ theseallowvery necontroloftheresultingtext.}2ButmostofthetimeonlyasmallUUnumbGerofthemarenecessary*.19:63׍L̍󙚉ff|( ff AUUTU>'ExXintro(CanadianspGelling)> Section3:qTheshapeofthingstocome  fffff|(׍)3.2Pageshapb"eTheIztextonapageconsistsofthreebasicparts.mThereistheheadlineabGoveIzthemain text;thisoftencontainsachaptertitle,/sectiontitle,orapagenumbGer,andmaydi eronoGdd"andevenpages.`Belowthisisthemaintext,,whichincludesanyfoGotnotes.`And nallythereUUisthefoGotlinethatmightcontainapagenumbGer.In&theexampleswehaveseensofar,[TtheheadlinehasbGeenblank.ThefootlinehascontainedheitheracentrednumbGeror,if\nopagenumbershadbeenused,hasalsobeenblank.W*e'llhavemoretosayabGoutheadlinesandfootlineslaterinthissection.F*orthemomentUUlet'sconcentrateonthemaintext.T*o nishonepageandstartanewone,F\vfill?\ejectcanbGeused.T,Thecontrolword\ejectѫforcesthecompletionofthecurrentpage, Rwhile\vfillcausesanyleftoververticalspace~tobGegatheredatthebottomofthepage(youmighttryleavingoutthe\vfillasan \expGerimenttoseehowtheverticalanalogueofjusti edhorizontallinesoftextworks).TheY currenthorizontalwidthofthetextonthepageisde-scribGedbythecontrolword\hsize.!ItcanbGechanged,_sayto4inches,4+by\hsize?=4in GatanydesiredtimeusingmethoGdstoabGedescribedinthenextfewsections.Thevqalueof\hsizeine ectawhentheparagraphiscompleteddeterminesthewidthoftheparagraph.=AscanbGeseeninthisparagraph,thetextwidthcan]bGechanged(inthiscaseto4inches)forasingleparagraph.Becauseitrepresentsthecurrentvqalueofthehorizontalwidth,expressionsxsuchas\hsize?=0.75\hsizexcanmakeanewvqaluethatUUisrelativetotheoldone.Theverticalanalogueof\hsizeis\vsize,3whichisthecurrentheightofthemaintext.ItcanbGereset,$ justlike\hsize.]FThus,$ \vsize?=8inWϫcanbGeusedtochangetheverticalheightDofthemaintext.Notethat\vsizeisthesizeofthetextexclusiveofanyheadlineorUUfoGotlinematerial.T*extuOcanalsobGeshiftedacrossthepage.ѶTheupperleftcornerofthetextisoneinchdownpandoneinchinfromtheuppGerleftcornerofthepage.Thecontrolwords\hoffsetand[\voffsetareusedtoshiftthetexthorizontallyandvertically*.Thus\hoffset?=.75inand\voffset?=-.5inwouldshiftthetextanadditional.75inchestotherightand.5inchesup.SMostofthetimeyou'llneedtoset\hoffset,z\voffset,and\vsizeatthebGeginningUUofyourdocumentonly*.Ǎ~9mTȟE Xb7ook::25120DS63׍L̍󙚉ff|( ff AUUTU>'ExXintro(CanadianspGelling)> Section3:qTheshapeofthingstocome  fffff|(׍)^􍍟'Ӎ}mCon9trolTwordsforpagesizesJ-̙HNamewiT<8E3sXTCon9trolW ordL.T<8E3sXTdefaultv\ralue(inc9hes)fffSQ horizontalUUwidthydk\hsize e6.5 uverticalUUwidthydk\vsize e8.9horizontalUUo set^6t$n\hoffset 0 cverticalUUo set^6t$n\voffset 0$.[Exercise3.1 Enteraparagraphoftextthatisafewlineslong.T*akeseveralcopiesof your¶graphandput\hsize?=5in f̫bGefore&oneand\hsize?=10cmin&frontofasecondUUone.qT*ryafewothervqaluesfor\hsize..٭Exercise3.2 Put\hoffset?=.5inand٭\voffset=1inbGefore٭the rstparagraphofUUyourpreviousexercise..'Exercise3.3 T*akeyourpreviousexerciseandput\vsize?=2ingbGefore'the rstpara-graph.IntheprevioussectionwesawthatitispGossibletousefontsoflargersizebyusingthe\magstepcontrolword.It'salsopGossibletomagnifytheentiredoGcumentatonce.If\magnification?=\magstep1appGearsatthetopofyourdocument,Tthenallofyouroutputismagni edby20%.\Theothervqaluesof\magstepcanbGeused,#7too.\ItJshouldbQeemphasizednPthat\magnificationcanonlybQeusedbeforeev9enasinglecharacterisbt9ypQeset.(ThisWwmagni cationcreatesaprobleminunits;ifthedoGcumentistobemagni edbyT20%and\hsize?=5inTappGearsintheTU>'ExXinput le,T\shouldthe naloutputhavean\hsize;of5inchesorshoulditbGemagni edby20%to6inches?i-Unlesstoldotherwise,@alltheEdimensionswillbGemagni edsothat,inthiscase,\hsizewouldbGe6inchesinthe naloutput.:Thisq{meansthatallthedimensionswillincreaseuniformlywhen\magnificationisused.gButforsomespGecialsituationsitmightnotbedesirableforthistohappen;lforexample,youPRmightwanttoleaveaspaceofexactly3inchestoinserta gure.bInthiscasemanyunitcanbGemodi edbytruesothat\hsize?=5trueinmwillalwayssetthelinewidthUUto5inches,regardlessofmagni cation.Ǎ~9mTȟE Xb7ook::59{60 ffff= ^6TheUUtextisinitially1inchdownand1inchinfromuppGerleftcornerofthepage.21QH63׍L̍󙚉ff|( ff AUUTU>'ExXintro(CanadianspGelling)> Section3:qTheshapeofthingstocome  fffff|(׍).JExercise3.4 Put\magnification?=\magstep1Jasthe rstlineinoneofyourinput lesUUandseehowtheoutputchanges.*3.3Paragraphshapb"eWhenjTU>'ExXAisreadingthetexttobGetypesetfromyourinput le,itreadsinaparagraphatatimeandthentypGesetsit.dThismeansthatthereisalotofcontroloverparagraphshapGes,but3alsothatsomecaremustbetaken.GgW*e've3alreadyseenthat\hsizecanbeusedto controlthewidthofasingleparagraph.HButsuppGosethefollowingappGearedaspartofyourUUinput le:\hsize?=5inFour?scoreandsevenyears:::x䍍...:::from?thisearth.\hsize?=6.5inWhat|isthewidthoftheparagraph?NThe\hsizewaschangedatthestartoftheparagraph?andagainattheend.dSincetheparagraphwasnotcompleted(byputtinginablanklineor\par)untilafterthesecondchange,theparagraphwouldbGetypGesetwithawidthof6.5inches.However,˼ifablanklinewereinsertedbGefore\hsize?=6.5in,thenthe*paragraphwouldbGetypGesetwithawidthof5inches.cSo,36ingeneral,whenaparagraphisset,thevqaluesoftheparametersthatareine ectwhentheparagraphiscompletedaretheUUonesthatareused.HereUUisatablewithsomeparagraphparameters:[s'ӍmMSomeTparagraphshapQeparametersJ-̙xFF unction:T<8E3sXTCon9trolW ord&T<8E3sXTdefault' fff>\ e widthҧ\hsize֫6.5UUinchesrindentationUUon rstlineR\parindent20UUpGointsdistanceUUbGetweenlinesr\baselineskip12UUpGointsdistanceUUbGetweenparagraphs\parskip ի0UUpGointsPThecontrolword\noindentmaybGeusedatthebeginningofaparagraphtoavoidtheautomatic!dindentationonthe rstline.Thiscontrolwordwillonlya ecttheparagraph22\ß63׍L̍󙚉ff|( ff AUUTU>'ExXintro(CanadianspGelling)> Section3:qTheshapeofthingstocome  fffff|(׍)bGeingEsetwhenitisinvokedE(ofcourse\parindent?=0ptEwillcausenoindentationforall paragraphs).(Amore exiblewaytocontrolthewidthofaparagraphistouse\rightskipandy\leftskip.4Setting\leftskip?=20ptycausestheleftmarginofthepara-graphotobGemovedoinanextratwentyopoints.Negativeovqaluesmaybeassignedto6\leftskiptomove6theleftmarginout.Thecontrolword\rightskipdoGesthesametotherightsideoftheparagraph._1Thesinglecontrolword\narroweristheequivqalentofsettingbGoth\leftskipand\rightskipequalto\parindent.This5isquiteusefulforlongquotations,1-andthisparagraphisanexampleofitsuse.ZAs1with\hsize,thevqalueof\leftskipand\rightskipine ectwhentheparagraphUUiscompletedistheonewhichwillapplytothewholeparagraph.Ǎ~9mTȟE Xb7ook::100"9.Exercise3.5 MaketwoparagraphswiththefollowingspGeci cations:O>theleftmarginofbGothparagraphsisindentedby1.5inches,therightmarginofthe rstparagraphisindentedbyUU0.75inches,andtherightmarginofthesecondparagraphisindentedby1.75inches.$LinesecanbGemadewithdi erentlengthswithinoneparagraphbyusing\hangindentand\hangafter.Theamountoftheindentationisdeterminedbyvqalueof\hangindent.If\hangindentispGositive,theindentationismadefromtheleft,andifitisnegativeitismade fromtheright.,YThelinesonwhichtheindentationoGccursiscontrolledby\hangafter.If\hangafterispGositivethenitdeterminesthenumbGeroflinesatfullwidthbeforetheindentation}starts.?Thusif\hangindent?=1.75inand\hangafter=6,>thenthe rst~xsixlineswillbGeatfullwidthandtherestwillbeindentedby~x1.75inchesfromtheleft.GOntheotherhandif\hangindent?=~x-1.75ineand\hangafter?=-6,thenethe rstsixlineswillbGe~xindentedAby1.75inchesfromtherightandtherestwillbGeat~xfullOwidth.oTU>'ExXOresetstothedefaultvqalues\hangindent?=0~xpt(and\hangafter?=1(aftereachparagraph.@Thesecontrol~xwordsc areusefulforparagraphswith\hangingindents"and~xfor owingaparagrapharoundspacereservedfora gure.~xTheڠcontrolword\hangatthebGeginningoftheparagraphwill8䍟~9mTȟE Xb7ook::355 ~xcauseuthe rstlinetobGeoffullwidth(\hangafter=1)andthe~xrest_oftheparagraphtobGeindentedbythecurrentvqalueof~x\parindent.Butܹyoudohavetouse\noindentifyouwant~xtheUU rstlinetoextendallthewayUUtotheleftmargin.~9mTȟE Xb7ook::1029Here*isthepreviousparagraphrepGeatedwith\hangafter?=-6*and\hangindent?=-1.75?in.23f63׍L̍󙚉ff|( ff AUUTU>'ExXintro(CanadianspGelling)> Section3:qTheshapeofthingstocome  fffff|(׍)LinescanbGemadewithdi erentlengthswithinonepara- graphMbyusing\hangindentand\hangafter.[2Theamountof.theindentationisdeterminedbyvqalueof\hangindent.SIf\hangindentSispGositive,theindentationismadefromtheleft,and8%ifitisnegativeitismadefromtheright.8ThelinesonwhichotheindentationoGccursiscontrolledby\hangafter.If\hangafterispGositivethenitdeterminesthenumbGeroflinesatfullwidthbeforethein-dentationnstarts.Thusif\hangindent?=1.75inand\hangafter=6,t-thenthe rstsixlines -willbGeatfullwidthandtherestwillbeindentedby1.75inchesfromtheleft.OOnthesotherhandif\hangindent?=-1.75$insand\hangafter?=-6,{thensthe rstsixlineswillbGeindentedby1.75inchesfromtherightandtherestwillbGeatfullwidth.XTU>'ExXչre-setstothedefaultvqalues\hangindent?=0ptand\hangafter?=1aftereachparagraph.Thesescontrolwordsareusefulforparagraphswith\hangingindents"andfor owingaparagraphkaroundspacereservedfora gure. Thecontrolword\hangatthebGeginningof8䍟~9mTȟE Xb7ook::355 theparagraphwillcausethe rstlinetobGeoffullwidth(\hangafter=1)andtherestofthedparagraphtobGeindentedbythecurrentvqalueof\parindent.ZButyoudohavetouse\noindentUUifyouwantthe rstlinetoextendallthewaytotheleftmargin.Ǎ~9mTȟE Xb7ook::1029The*controlword\parshapecanbGeusedtomakeparagraphswithagreatervqarietyofshapGes.~9mTȟE Xb7ook::1019Another3usefulcontrolwordforsettingparagraphsis\item.`ItcanbGeusedtomakevqarioustypGesofitemizedlists,B>andisinvokedusingthepattern\item{::: }.^ThiscausestheCnextparagraphtobGeformedwitheverylineindentedby\parindentand,Ginaddition,the rstlinelabGeledontheleftbywhateverisbGetweenthebraces.Itisusuallyusedwith\parskip?=0pt, jsinceothatcontrolworddeterminestheverticalspacebGetweenthedi er-entitems.ZThecontrolword\itemitemisthesameas\itemexceptthattheindentationistwiceUUasfar,thatis,twicethevqalueof\parindent.qHereisanexample:8䍟~9mTȟE Xb7ook::102\parskip?=0pt\parindent=30pt\noindentAnswer?allthefollowingquestions:\item{(1)}?Whatisquestion1?\item{(2)}?Whatisquestion2?\item{(3)}?Whatisquestion3?\itemitem{(3a)}?Whatisquestion3a?\itemitem{(3b)}?Whatisquestion3b?willUUproGduce24tǟ63׍L̍󙚉ff|( ff AUUTU>'ExXintro(CanadianspGelling)> Section3:qTheshapeofthingstocome  fffff|(׍)AnswerUUallthefollowingquestions: 8(1)WhatUUisquestion1? 8(2)WhatUUisquestion2? 8(3)WhatUUisquestion3?%8(3a)<WhatUUisquestion3a?$(3b)<WhatUUisquestion3b?$.Exercise3.6 Makeaparagraphseverallineslonganduseitwiththe\itemcontrolwordtoJseethe\hangingindent."n6NowJtakethesameparagraphanduseitwithdi erentvqaluesofUU\parindentand\hsize.Nowqlet'sseehowtoputspacebGetweenparagraphs.9&Thecontrolword\parskipisusedto3determinehowmuchspaceisnormallyleftbGetweenparagraphs.fSoifyouput\parskip=?12ptatthebGeginningofyourTU>'ExXZsource le,Ptherewillbe12pointsbetweenparagraphsunlessotherinstructionsaregiven.2aThecontrolword\vskipcanbGeusedtoinsertextraverticalV6spacebGetweenparagraphs.tjIf\vskip?1inV6or\vskip?20ptV6appGearsbetweenV6twoparagraphs,UUthentheextraspaceisinserted.ThereareacoupleofpGeculiaritiesof\vskipthatseemquitestrangeat rst.8Ifyouhave\vskip?3inandtheskipstartstwoinchesfromthebGottomofthepage,therestofthepage1isskippGed,8buttheextraoneinchisnot$skippedatthetopofthenextpage.eInotherwords,3\vskip willnotinsertspaceacrosspagebQoundaries.(Infact,3\vskip?1inwillܕhavenoe ectatallifithappGenstoappearatthetopofapage!F*ormanytypGesofvertical`spacingthisisquiteappropriate.ThespacebGeforeasectionheading,cforexample,shouldUUnotcontinueUUacrosspagebGoundaries.AJBsimilarJEphenomenonoGccursatthebeginningofyourdocument.nIf,L{forexample,youwant/'atitlepagewiththetitleabGouthalfway/'downthepage,6youcannotinsertthespaceatUUthetopofthepageusing\vskip.Butwhatifyoureallywantsomeblankspaceatthetopofapage?KY*oucouldstartthepagewith\ butthisine ecttypGesetsaonelineparagraphcontainingablank.3{SowhilenothingyistypGeset,theextraspaceduetothevqaluesof\baselineskipand\parskipwilladdNextraspace.AneasiermethoGdistouse\vglueinsteadof\vskiptogetthedesiredresult.qThusUU\vglue?1inwillleaveoneinchofblankspaceatthetopofthepage.8䍟~9mTȟE Xb7ook::352W*ecannoteinpassingthatthereisanothermoregeneralmethoGdtoputmaterialattheFtopofapageusingthecontrolwords\topinsertand\endinsert.lIf\topinsert?:::\endinserto)isusedwithinapage,uthematerialbGetweeno)\topinsertand\endinsertwillappGearUUatthetopofthepage,ifpossible.qF*orexample:25͟63׍L̍󙚉ff|( ff AUUTU>'ExXintro(CanadianspGelling)> Section3:qTheshapeofthingstocome  fffff|(׍= \topinsert \vskip?1in\centerline{Figure?1}\endinsertisUUusefulforinserting guresofaprescribGedsize.Ǎ~9mTȟE Xb7ook::1159TherearealsosomespGecialcontrolwordsformakingsmallverticalskips.Theyare \smallskip,UU\medskip,and\bigskip.qHereisthesizeofeachone:2u\smallskip:qǟff$"ffff$"5\medskip:qǟff$"ffff$"\bigskip:qǟ󙚉ff$" ffff$"*3.4Lineshapb"eF*or6mostmaterialTU>'ExX6ZdoGesagoodjobofbreakingupaparagraphintolines.Butsometimes9it'snecessarytoaddfurtherinstructions.It'spGossibletoforceanewlinebyinserting*\hfill?\breakinyourinput le.It'salsopGossibletoputsometextonalinebyitselfusingthecontrolword\line{::: };(thenthematerialbGetweenthebraceswillbGerestricted1tooneline(althoughtheresultwillbGespreadoutover1thewholelineandmaybGe[horrible).Thecontrolwords\leftline{::: },]c\rightline{:::},and[\centerline{:::}will,respGectively*,setthematerialbetweenthebracesonasinglelineontheleftmargin,ontheUUrightmargin,orcentred.qThus\leftline{I'm?overontheleft.}\centerline{I'm?inthecentre.}\rightline{I'm?ontheright.}\line{I?justseemtobespreadoutallovertheplace.}proGducesUUthefourlines:I'mUUoverontheleft.JI'mUUinthecentre.DI'mUUontheright.I5just2seemtobGespreadoutallover2theplace.OthertypGesofspacingcanbeobtainedbyusingthecontrolword\hfil.`ThiscausesalltheextraspaceinthelinetobGeaccumulatedatthepositionwhere\hfilappears.KThusifwealterourlastexampleto\line{I?justseemtobespreadout\hfilalloverthe?place.}UUwewillget2663׍L̍󙚉ff|( ff AUUTU>'ExXintro(CanadianspGelling)> Section3:qTheshapeofthingstocome  fffff|(׍)IUUjustseemtobGespreadoutĴalloverUUtheplace.If=wehavemorethanone\hfil, theywilldivideanyextraspaceamongthemselves equally*.qHenceUU\line{left?text\hfilcentretext\hfilrighttext.}willproGduceleftUUtextacentretextrighttext.$.UUExercise3.7 TypGesetthefollowingline:leftUUend|lefttackleleftguardcentrerightUUguardrightUUtacklerightUUend.iЫExercise3.8 TypGesetthefollowinglinewithtwiceasmuchspacebGetween\left"and\right-centre"UUasbGetweenUU\right-centre"and\right":leftCright-centreiLrightIt'sUUpGossibletomoveUUhorizontallyusing\hskipinamanneranalogouswith\vskip..UUExercise3.9 WhathappGenswiththefollowinginput:\line{\hskip?1inONE\hfilTWO\hfilTHREE}#KTheUUrightjusti cationcanbGecanceledbyusingthecontrolword\raggedright.*3.5Fٚob"otnotesTheUUgeneralpatterntomakefoGotnotesusingTU>'ExXis\footnote{::: }{:::}.ThefoGotnotemarkgoesinbetweenthe rstsetofbraces."\Someavqailablemarksare \dag?(yq),؄\ddag(z),؄\S(xq),and\P({r).ThetextofthefoGotnotegoesbetweenthesecond_setofbraces.TheuseofnumbGers_asmarksisalittlelessstraightforward.ThefoGotnote^21 Ϋat7thebottomofthepagewasproducedbyusing\footnote{${}^{21}$}{Thisis?thefootnoteatthebottomofthepage.}=aftertheword\foGotnote"inthetext.ThisBconstructionissomewhatcomplicated;we'llseewhyit'sthiswaywhenweknowalittleO moreabGouttypesettingmathematics.oButforthemomentwecanloGokatitasawayofĨgettingthejobdone.Y*oumaywanttouse\rmwithinthefoGotnotetoensurethattheright7fontappGears.FhUsuallyyouwillnotwantaspacebGetweenthetextandthecontrolwordfootnote.~9mTȟE Xb7ook::117Xff= ^21ThisUUisthefoGotnoteatthebottomofthepage.2763׍k-PageUU28׍).UUExercise3.10 MakeupapagewitharelativelylongfoGotnotespanningseverallines.$.UUExercise3.11 Makeupapagewithtwodi erentfoGotnotesonit.*3.6HeadlinesandFٚob"otlinesTheKMlinesfortitleandpagenumbGersKMthatgoaboveKMandbelowthemaintextareproduced byUUusing\headline={::: }and\footline={:::}.Ǎ~9mTȟE Xb7ook::252{2539Theȿprincipleisthesameasusingthecontrolword\line{::: }withintheusualtextontheSpage.AShelpfulcontrolwordis\pagenowhichrepresentsthecurrentpagenumbGer.Thus\headline={\hfil?\tenrmPage\the\pageno}-wouldcausethepagenumbGertoappearin*theuppGerrightcornerprecededbytheword\Page"(nowloGokattheupperrightcornerof@thispage).=Itissafertoexplicitlynamethefontthatyouwanttouse(inthiscase\tenrmto|xusethe10pGointromanfont),AsinceyouareneverguaranteedthataparticularfontwillbGe#Vinusewhentheheadlineorfootlineisset.Thecontrolword\thetakestheinternalvqalueofthenextwordifitisanappropriatecontrolwordandprintsitastext.`Y*oucanalsousethecontrolword\folioinsteadof\the?\pageno.uPThedi erenceisthat\foliowillUUgiveromannumeralswhen\pagenoisnegative.Y*oucanalsoassignvqaluesto\pagenoifyouwantyourdoGcumenttouseadi erentsequenceZofpagenumbGersZfromtheusual.RomannumeralscanbeproducedbyusingnegativePnumbGers;R"\pageno=-1atthebeginningofadocumentwillcausepagenumbGerstobGeUUinromannumerals.~9mTȟE Xb7ook::252Di erentUUheadlinescanbGeproducedforevenandoddpagesinthefollowingmanner:\headline={\ifodd?\pageno{::: }\else{:::}\fi}wheresthematerialbGetweensthe rstsetofbracesisfortheright-handpagesandthematerialbGetweenUUthesecondsetofbracesisfortheleft-handpages.$.ӫExercise3.12 ChangethefoGotlinesothatthepagenumberiscentredwithanen-dashonUUeitherside.2863׍L̍󙚉ff|( ff AUUTU>'ExXintro(CanadianspGelling)> Section3:qTheshapeofthingstocome  fffff|(׍)3.7Overfullandunderfullbb"oxesOneofthemostfrustratingexpGeriencesforthenewTU>'ExXuseristheoccurrenceof overfull)andunderfullbGoxes.cTTheyaredulynotedinthelog leandarealsowrittentothescreen]whenTU>'ExX3isbGeingruninteractively*.:uOverfull]boxes]arealsomarkedontheoutputbyan2slug(alarge lled-inblackrectanglethatloGokslikethis: )intherightmargin._V*ariousobscene=termsareappliedtothisslug.iItappGearseventhoughthereisnothingwrongwiththeUUTU>'ExXinput.qSowhyistheslugthereandwhatcanbGedoneaboutit?AgoGodwaytovisualizethewayTU>'ExXorganizesapageistothinkoftheprintedmaterialasbGeingputintoboxes.BTherearetwotypGesofboxes:+hboxes1andvboxes.BMostofthetimethese correspGondtotheorganizationofhorizontaltextintolinesandverticalparagraphsinto:pages.hInparticular,?itisthespacingofthewordsinahbGoxcorrespGondingtoalineoftextUUthatcausestheslugtoappGear.Recall0thatTU>'ExX readsinthecompleteparagraphbGeforedecidinghowtobreakitupintoblines.5ThisisbGetterthanworkingalineatatime,`sinceaslightimprovementinonelinemight_causecatastrophicchangesfartherdownintheparagraph.S Whenwordsaregatheredtogether@dtoformaline,DspaceisaddedbGetween@dthewordstojustifytherightmargin.jV*erylargespacesbGetweenwordsisobviouslyundesirable;DthebadnessofthelineisameasureofW{howbadlythewordsarespaced.x8AnunderfullhbGoxmeansthatthereistoGomuchspacebGetweenwords.JMorespGeci cally*,thebadnessofanylineisanumbGerbetween0(pGerfect)andu10000(horrible).n'Thereisaparametercalled\hbadnesswhosedefaultvqalueis1000.Any{Plinewhosebadnessisgreaterthan\hbadnessisrepGortedasanunderfullhbGox.Ifthevqalueof\hbadnessisincreased,thenfewerunderfullhbGoxeswillbGereported.bInfact\hbadness?=10000ޯwillsuppresstherepGortingofunderfullhboxesޯaltogether. Similarly*,ifothewordsmustbGesqueezedintoalinesothatthespacesareverysmallorevensothewordsUUextendalittleintotherightmargin,thenanoverfullhbGoxresults.Inasimilarway*,ssometimesTU>'ExXallowsalinetobGeslightlylongerthan\hsizeinordertoachieveamorebalancedappGearance.1 Thecontrolword\tolerancedetermineswhenthishappGens.X{If othebadnessofalineisgreaterthan\tolerance,TU>'ExX \willmakethelinelongerbyq+addinganewwordattheendoftheline, eventhoughitmightexceedthevqalueof\hsize.JPAlinewhichisonlyslightlylongerissetwithoutbGeingreported.JPThecontrolword\hfuzzVdetermineshowmuchexcessisallowed;ګthedefaultis\hfuzz?=0.1pt.4rA'lineVthatis%morethanslightlylongerthan\hsizeisobviouslyaseriousproblem;5TU>'ExX%putsaslugintheimargintomakeitspGointforcefully*.ZIt'spGossibletoavoidoverfullhbGoxesaltogetherbyincreasing"thevqalueof\tolerance.OWith\tolerance?=10000"therewillneverbGeoverfullbGoxesUUorslugs.qThedefaultis\tolerance?=200.Ǎ~9mTȟE Xb7ook::292963׍L̍󙚉ff|( ff AUUTU>'ExXintro(CanadianspGelling)> Section3:qTheshapeofthingstocome  fffff|(׍)The#Hwidthoftheslugisdeterminedbythecontrolword\overfullrule.۠Including \overfullrule?=0ptΫinyour lewilldeleteanyfurtherprintingoftheslugs..TheoverfullbGoxesUUwillstillbethere,ofcourse,andtheywillprobablybehardertospot.SoEweseewhyoverfullbGoxesandunderfullbGoxesarerepGorted;J|wecanalsochangetherepGortingYlbychangingthevqaluesof\badness,q\hfuzz,andYl\tolerance.~ Inaddition,qasmallvqalueof\hsizeobviouslymakesitmorediculttosetlinesandcausesmoreoverfulland underfullhbGoxes tobereported.YThesearewarningsthatyouignoreatyourownpGeril!AddingTnewpGossibilitiesofhyphenationwillsometimeseliminateanoverfullbGox.\TU>'ExXhasautomatichyphenationandusually ndsgoGodplacestohyphenateaword;|however,݄it'spGossible(toaddhyphenationstoletlinesbreakatnewplaces.AF*orexample,]theautomatichyphenationwillneverputahyphenintheword\database".V.IfyoutypGeindata\-base,itwillallowahyphentobGeinsertedafterthesecondletter\a"intheword.Q_Moregenerally*,ifyouPput\hyphenation{data-base}inthebGeginningofyourinput le,thenalloGccurrencesof}Otheword\database"willallowhyphenationaftertheletter\a". jThelog lewillshowǍ~9mTȟE Xb7ook::28 9thepGossiblehyphenationsonthelinecontainingtheoverfullorunderfullbGox.&SometimestheebGestsolutiontoanoverfulleorunderfullhboxeisalittlejudiciouseditingoftheoriginaldoGcument.Our|discussionhasinvolved|thesettingoftypGeintolines,thatis,thehorizontalpagestructure.cThere+areseveralverticalanalogues.cOverfullandunderfullhbGoxesindicatehowwellewordsaregatheredintolines.Similarly*,overfullandunderfullvbGoxesarerepGortedwhenCparagraphsaregatheredtoformpages.;&ABlargetablethatcan'tbGebrokeninthemiddle,Aforexample,canproGduceanunderfullvboxthatisreportedinthelog lewhenthe pagebGeingtypesetiscompleted.Thecontrolword\vbadnessworksfortheverticalplacementUUoftextinthesamewayas\hbadnessworksforhorizontaltext.$.Exercise3.13 T*akeafewparagraphsandprintthemusingvqarious(small)valuesof\hsize.toseewhatkindofoverfull.bGoxesresult.dRepGeatwithvqariousvaluesof\hbadness,\hfuzz,UUand\tolerance.3063׍׍)Section4`nGroups,b ZsGroups,fandMoreGroupsgb W`olff|(/eTheNconceptofgatheringtextintogroupsallowsTU>'ExXinput lestobGegreatlysimpli ed. Anewgroupisstartedbythecharacter{andterminatedbythecharacter}.5AChangesmadewithin-agroupwilllosetheire ectwhenthegroupterminates.]So,cforexampleif{\bfthree?boldfacewords}+appGearsinyourtext,48theopeningbracestartsthegroup,48the\bfcontrolOwordchangestoabGoldfacefont,PFandtheclosingbrace nishesupthegroup.oUpGoncompletionofthegroupthefontbGeingusedistheoneine ectbeforethegroupstarted.Thisjisthe(easier)wayjofhavingafewwordsinadi erentfont.>It'salsopGossibletohavegroupsUUnestedwithingroups.As>anotherexample,sizechangescanbGemadeinthetextthatareonlytemporary*.FForexample{\hsize?=4in\parindent?=0pt\leftskip?=1inwill?produceaparagraphthatisfourx䍍...(this?isaneasymistaketomake).\par}HEwill=proGduceaparagraphthatisfourincheswideHEwithithetexto setintotheparagraphbyoneinchHEregardless;ofthesettingsine ectbGeforethestartHEofthegroup.'ExX_)willgobacktotheHEold,parametersbGeforetheparagraphisactuallyHEtypGesetUU(thisisaneasymistaketomake).31 ۟63׍L׍홏ff|(  ff AݦTU>'ExXintro(CanadianspGelling)Section4:5`n ફGroups,bGroups,fandMoreGroupsgb W`o fflff|(׍)When>~line-spacingcontrolwords(like\centerline)actontextfollowingitinbraces, that(textisimplicitlyinagroup.@Thus\centerline{\bf?Aboldtitle}(willproGduceacentredJGbGoldfaceline,L}andthetextfollowingthatlinewillbGeinwhateverfontwasine ectbGeforeUUthe\centerlinewasinvoked.Theemptygroup{}isuseful.Y=OneuseallowsaccentstobGetypGesetwithnoaccom-panying letter.'F*orexample,;\~{}willprintatildewithnoletterunderit.'ItcanalsobGeusedtostopTU>'ExXfromeatingupconsecutivespaces.'ExX"intheoutput._Thisisanalternativetousing\ aswedidinSectionUU1.~9mTȟE Xb7ook::19{21GroupingpScanalsobGeusedtoavoidpSspacesinthemiddleofawordwhenincludingaccents.qEitherUUsoup\c conorsoup\c{c}onwillproGducethewordsoup9con.$.ᾫExercise4.1 Changethedimensionsofoneparagraphonapageusingthegroupingidea..Exercise4.2 Mathematicianssometimeusetheword\iff"asanabbreviationfor\ifand onlyif".mOInthiscaseitloGoksbetterifthe rstandsecondletter\f"arenot67joinedasaligature.qHowUUdoyoudothis(thereareseveralsolutions)?It'sDreallyeasytoforgettomatchbracespropGerly*.-lThee ectcanbedramatic;̟ifyougetoutput thatsuddenlychangestoanitalicfontfortherestofthedoGcument,vamismatchedbracelisprobablythecause.VIfyouhaveanextra{TU>'ExXlwillgiveamessageinthelog le:(\end?occurredinsideagroupatlevel1).yJAn+extra}willresultinthemessage! Too?many}'s.Here'salittlehinttohelpyoukeeptrackofthebracesinmorecomplicatedgroups:put9theopGeningbraceonalinebyitselfanddothesamefortheclosingbrace.hIftherearebraceslnestedwithintheoriginalones,putthemonseparatelinesalso,butindentthemafewspaces. ThetextwithinthenestedbracescanalsobGeindentedsinceTU>'ExXignoresallspacesatthebGeginningofaline.$ThematchingbraceswillthenstandoutwhenyouloGokatyourTU>'ExXsource le.]Infact,$ifyoureditorissmartenough,$youcancreatethetwolineswiththebraces rstandtheninserttheappropriatematerialwithinthemwithautomaticindenting.$.$lExercise4.3 Insection2wechangedfontsthefollowingmethoGd:I?startedwithroman?type,\itswitchedtoitalictype,\rmandreturnedtoromantype.ǦGettheUUsameresultusingtheideaofgrouping.32!63׍׍)Section5Nomathanxiet=yhere!32ff|(/eTU>'ExX_is~atitsbGestwhentypesettingmathematics.CTheconventions~fordoingthisare many*andcomplex,"andtheabilityofTU>'ExXtotakethemintoaccountmakestheproGductionof4highquality*,ۡattractive4mathematicaloutputpGossible.?Ifyouplantoproducepaperswithmathematical[symbGolsinthem,ZthissectionwillgiveyouallthebasicsnecessaryforcreatingbGeautifuloutputinalmostallcircumstances;iTU>'ExXmaybeusedwithoutanymathematics,of tcourse,+andifthisisyourgoal,thenthefollowingtwosubsectionsareprobablysucientforUUyourneeds.*5.1Lotsofnewsymbb"olsMathematicalktextisinsertedintonormaltextintwopGossibleways:itcanbGein-lineg,that\is,^}aspartoftheusuallinesoftext.ItcanalsobGedisplayed,that\is,centred\inagapbGetween8theusualtext.qTheresultsinthespacingandplacementofsymbGolscanbequite ,di erentineachcase.XDThein-lineequationPލ O!cmsy71%  0ercmmi7k+B=1 !1u&feRk+BZcmr52+p= K@Lr2K&feԏl6 ٫iseasilyseentobGedi erentfromtheUUsameequationwhendisplayed:$11 X 箴k+B=1<$1Qwfe ɟ (֍kPr2M0=<$K[ٟ^2Kwfe (֍ȫ6:,ISincegUthespacingandthefontsusedformathematicsarequitedi erentfromthoseofordinary.text,MTU>'ExXneedstobGetoldwhenmathematicsratherthannormaltextisbeingtypGeset.lThisaisdoneusingthe$symbGol.lMorespeci cally*,mathematicsistypesetin-line[bysurroundingthesymbGolstobeenteredbysingledollarsigns:$::: $,andistypGesetdisplayed5bysurroundingthesymbGolstobeenteredbydoubledollarsigns:a$$::: $$.g@Hence$x?=y+1$UUwillgivex=y+81UUin-linewhile$$x?=y+1.$$UUwilldisplaycex=y+81:#cThewspacingforbGothin-lineanddisplayedwmathematicsiscompletelycontrolledbyTU>'ExX.uAddingspacestoyourinputhasnoe ectatall.Whatifyouneedaspaceorsometextinthemiddleofsomemathematics?iY*oucaninserttextbyinsertingitintoanhbGox(don'tQworryabGoutthede nitionofanhbGoxfornow):j-\hbox{::: }.f`Thisisparticularly33" 63׍L̍󙚉ff|( ff AUUTU>'ExXintro(CanadianspGelling)X=Section5:qNomathanxietyhere!  fffff|(׍)usefulfordisplayedmathematics. Hence\x_=y<+c1UUwhenever/@y8=x1"canbGetypeset usingx$x=y+1?\hbox{whenever}y=x-1$.(BNotethespacesoneithersideofthewordwithinthewbraces.Usuallyitisn'tnecessarytoinsertspacesintomathematicaltext,=butherearetheUUcontrolsequencesthatdothejob.Ǎ~9mTȟE Xb7ook::1679v􍍟'ӍlAddingTspacetomathematicaltextn-NameControlUUSequence MĄff qff Size!ffff qF@fff 1ɫDoubleUUquadzs\qquad\ff ffffff >Quad}Ur\quad\ff ff ffff <㕫Space5m\ \ffbׄffUUffffb׎"*ThickUUspace5m\;\ffffffffUXMediumUUspace5m\>\ffff8ffff&>ThinUUspace5m\,\ff8.ffffff8.NegativeUUthinspace5m\!\ffքffUXffff֎ IfyouloGokcloselyatthenegativethinspace,ɞyou'llnoticethat,ɞunliketheotherentries,thetwoarmsoverlap.ThisisbGecausethenegativespaceisoneintheoppGositedirection,thatuis, whiletheothercontrolsequencesincreasetheamountofspacebGetweentwosymbGolsbGeingtypeset,Ethenegativethinspacedecreasesthespacebetweenthem,EevenifitcausesthemUUtooverlap.$.Exercise5.1 TypGesetthefollowing:B2C(n;rG)t=n!=(r!(n~Yr)!).hNotethespacinginthedenominator.# Y*ouVshouldn'thaveVanyblanklinesbGetweenthedollarsignsdelimitingthemathematicaltext.lQTU>'ExXDassumesDthatallthemathematicaltextbGeingtypesetisinoneparagraph,H;andablanklinestartsanewparagraph;consequently*,vthiswillgenerateanerrormessage.-JThisturnsKouttobGeuseful,foroneoftheeasiesterrorstomakeistoforgettoputinthetrailingdollarrsign(s)afterthemathematicalinput(I_promisethatyou'lldoitatleastoncewhilelearning$TU>'ExX);ifTU>'EX$allowed$morethanoneparagraphtobGebetween$thedollarssigns,thenAoneomittedtrailingdollarsignmightcausetherestofthedoGcumenttobGetypGesetasmathematics.Mostamathematicaltextisenteredinexactlythesamewayforin-linetypGesettingasfordisplayedtypGesetting(exceptforthesurroundingdollarsigns,@ofcourse).cTheexceptions,such asaligningmultilinedisplaysandplacingequationnumbGersattheleftorrightmarginwillUUbGediscussedinthelastpartofthissection.34#63׍L̍󙚉ff|( ff AUUTU>'ExXintro(CanadianspGelling)X=Section5:qNomathanxietyhere!  fffff|(׍)ManynewsymbGolscanappearwhentypesettingmathematics.AMostoftheonesthat actually@SappGearonthekeyboardcanbeuseddirectly*.jThesymbols+?-/*='|<>(andUU)areallentereddirectly*.qHeretheyareasmathematics:+8==^0 j<8>().$.۫Exercise5.2 TypGesettheequationa+bá=cdá=xyz=wD=z]rasin-lineanddisplayedmathematicalUUtext..hiExercise5.3 TypGesettheequation(fg[٫)^0Q=f^0ȱg+_ fg^0{ashiin-lineanddisplayedhimathematicaltext.ManyKothersymbGols,asyouwouldexpGect,areprede nedcontrolwords.UAllGreeklettersUUareavqailable.qHereisatableofthem:~9mTȟE Xb7ook::434-{GreekTlettersfeffj* X t\alpha_ s*\beta \gamma$ H61H\deltat\epsilona+f"s*\varepsilonϢ\zeta#61H\eta:t\theta_#s*\vartheta5\iota#61H\kappaDZt\lambda_Φs*\mu,\nu$*61H\xi:oto_s*\piϔ\rho#c%61H\varrhott\sigmaagر&s*\varsigma>\tau#61H\upsilonȱt\phi_J's*\varphi}߱\chi! 61H\psi1ʱ!t\omega_+s*\GammajM\Delta!ԫ61H\ThetaWt\Lambda_*s*\Xi?\Pi!61H\Sigmat\Upsilon^Hs*\Phi \Psi! 61H\Omega$.UUExercise5.4 TypGeset z N4= +88asUUin-lineanddisplayedmathematicaltext..UUExercise5.5 TypGeset(n)=(n81)!UUasin-lineanddisplayedmathematicaltext.Sometimes܁accentsareputabGoveorbGelowsymbGols.IThecontrolwordsusedforaccents inmathematicsaredi erentfromthoseusedfornormaltext.0ThenormaltextcontrolwordsmayUUnotbGeusedformathematicsandvice-versa.Ǎ~9mTȟE Xb7ook::135{13635$63׍L̍󙚉ff|( ff AUUTU>'ExXintro(CanadianspGelling)X=Section5:qNomathanxietyhere!  fffff|(׍)Qv $6MathematicalTaccen9ts?@qffd' z^o.:\hat?oe7d߱ov\check?o4[~㹯o\tilde?o zo.:\acute?oe7d߱ov\grave?oPͫ_㹯o\dot?ozo.:\ddot?oe7d߱ov\breve?o4[㹯o\bar?oɱ~o.:\vec?o\q]c[abcv\widehat?{abc}\qܞfڪޱabc\widetilde?{abc} bBinaryzopGeratorscombinetwomathematicalob8jectstogetanotherobject.7Ordinary addition1andmultiplication,8forexample,combinetwonumbGerstogetanothernumbGer,8andsotheyarebinaryopGerators.7Whenabinaryoperatorsuchas+oristypGeset,dalittleextraUUspaceisputaroundit.qHereisalistofsomeoftheavqailablebinaryopGerators:Ǎ~9mTȟE Xb7ook::4369PV'Ӎ BinaryTopQerators>-wЀffPq: t\cdotTNi8\times?• \ast ?X\start\circVki8\bulletx• \div X\diamondr\t\capU8[i8\cup _• \veeV^X\wedget\oplusTN i8\ominusx • \otimes X\odotEllipses1arecommonlyusedwithbinaryopGerators.eThecontrolword\cdotswillraisethedotssothattheyarelevelwiththebinaryopGerator.2qThus$a?+\cdots+z$willproGduce(a+6+zp.Thecontrolword\ldotswillputthedotsonthebaseline,]andso$1\ldots?n$UUproGduces1:::n.$.UUExercise5.6 TypGeset:qDZx8^(y_zp)=(x8^y[٫)_(x^z)..UUExercise5.7 TypGeset:q28+4+6+g+2n=n(n8+1).#*֍A+2relation+iindicatesapropGertyoftwomathematicalob8jects.W*ealreadyknowhow toshowtwoob8jectsequal,orhowtoshowonenumbGerlessthanorgreaterthananothernumbGer(sincethesearesymbolsonmostterminalkeyboards).T*onegatearelation,4?thecontrolUUword\notisputinfrontoftherelation.qHerearesomerelations:Ǎ~9mTȟE Xb7ook::43636%63׍L̍󙚉ff|( ff AUUTU>'ExXintro(CanadianspGelling)X=Section5:qNomathanxietyhere!  fffff|(׍)Y9eRelationsHfĀff1 t\leqY\K6nx\not?\leqǸ\geq+Ϸ6@C\not?\geq t\equivY\K6nx\not?\equivǸ\sim+Ϸ6@C\not?\sim't\simeqY\K6'nx\not?\simeqǸ\approx+Ϸ6@C\not?\approxt\subsetY\Knx\subseteqǸ\supset+Ϸ@C\supseteqr2t\inZx3nx\nik\parallel+Ϸ?@C\perpaɤ$.UUExercise5.8 TypGeset:O~qx a÷#~8y B=0ifandonlyif3~x Ӊ?~y ..UUExercise5.9 TypGeset:O~qx a÷#~8y B6=0ifandonlyif3~x Ӊ6?~y .HereUUaresomeotheravqailablemathematicalsymbGols:Ǎ~9mTȟE Xb7ook::435{4389O+'ӍJMiscellaneousTsym9bQols>-+Ѐffl[ӟ 8@\alephdֱ`v\ell< \Re#M=7\Im x@\partial_*1v\infty̸k \|L$'6{%J\W 䎎7\angler\nablad*nv\backslash*P8 \forall$a97\exists:\negeF[v\flat] \sharp& \7\natural.UUExercise5.10 TypGeset:q(8x2<)(9y"2<)UUy>x.*5.2FٚractionsTherearetwomethoGdsoftypesettingafraction:+itcanbetypeseteitherintheform 1=2orintheform 414&fes2 #ګ.The rstcaseisjustenteredwithnospGecialcontrolsequences,thatDwis,@$1/2$.?.Thesecondcaseusesthecontrolword\overandthefollowingpattern:{?\over}.qHenceUU$${a+b\overc+d}.$$givesǍ~9mTȟE Xb7ook::139{140l<$t*a8+bt*wfe̸ (֍c8+dt:37& ԟ63׍L̍󙚉ff|( ff AUUTU>'ExXintro(CanadianspGelling)X=Section5:qNomathanxietyhere!  fffff|(׍).UUExercise5.11 TypGesetthefollowing: a+b&fe D5c ${a &fe :b+c C19&fea+b+cUY6= 'J1K&feVpa Ϋ+ l1l&fes<b ԙ+ l1l&fes4ɴc.&.UUExercise5.12 TypGeset:qWhatarethepointswhere @&fe <[@n9xf(x;y[٫)= !@K&fe @n9y/|f(x;y[٫)=0?,$5.3Subscriptsandsupb"erscriptsSubscriptsN andsupGerscriptsareparticularlyeasytoenterusingTU>'ExX.oXThecharactersNff&f andy:^areusedtoindicatethatthenextcharacterisasubscriptorasupGerscript.(iThus$x^2$gives_x^2Tҫand$xEff&fǫ2$givesx2|s.T*ogetseveralcharactersasasubscriptorsupGerscript,!theyaregroupGedtogetherwithinbraces.H`Hencewecanuse$x^{21}$togetx^21 Rand$xEff&fǫ{21}$togetpx21x.NoticethatthesupGerscriptsandsubscriptsareautomaticallytypesetinasmallertypGeȣsize.˱ThesituationisonlyslightlymorecomplicatedforasecondlayerofsubscriptsorsupGerscripts.^Y*oucannotT9use$xEff&fǫ2Eff&f3$sincethiscouldhavetwopGossibleinterpretations,namely*,\$xEff&fǫ{2Eff&f3}$or${xEff&fǫ2}Eff&f3$;)thisgivestwodi erentresults:x23 Fandx23,\the rstofwhich istheusualmathematicalsubscriptnotation._Thusyoumustputinthecompletebraces=todescribGemultiplelayersofsubscriptsandsupGerscripts.iTheymaybGedonetoanylevel.~9mTȟE Xb7ook::128{130T*ousebGothsubscriptsandsuperscriptsononesymbol,!youuseboththeff&f and^ineitherUUorder.qThuseither$xEff&fǫ2^1$or$x^1Eff&f2$willgivex^1l2|s.$.UUExercise5.13 TypGeseteachofthefollowing:qDZe^xe^xHe^i z+81=0 x0|tx^2l0x0^2',w2^xr O \cmmi5x ~;.&.危.UUExercise5.14 TypGeset:qǷr^2|sf(x;y[٫)=K@n9r2UYfK);fe I@n9x2+l@n9r2UYfl);fe I0M@n9y@L2.AsimilarmethoGdisusedforsummationsandintegrals.f/Theinputof$\sumEff&fǫ{k=1}^n k^2$UUwillgivePލ 㐴n% k+B=1˱kP^2 ,and$\intEff&fǫ0^x?f(t)dt$UUwillgiveĽRj x #90f(t)dt.<~9mTȟE Xb7ook::144{145qčAnotheruseofthistypGeofinputisforexpressionsinvolvinglimits. Y*oucanuse$\limEff&fǫ{n\to?\infty}({n+1\overn})^n=e$UUtogetlim8n!1&.( 33n+133&fenw)^n8=e.%.UUExercise5.15 TypGesetthefollowingexpression:qlimUXx!0#S(18+x) zO133#&feWx ի=e.$.UUExercise5.16 TypGeset:qThecardinalityof(1;1)is@1|s.38'D63׍L̍󙚉ff|( ff AUUTU>'ExXintro(CanadianspGelling)X=Section5:qNomathanxietyhere!  fffff|(׍).UUExercise5.17 TypGeset:qlimUX㐴x!0+*бx^x=1.$Here'sahinttomakeintegralsloGokalittlenicer:lookatthedi erencebetween ĽRjx #0 ^7f(t)dt|andĽRj '>x # 5w0ʱf(t)dt.Inthesecondcasethereisalittleextraspaceafterf(t),banditUUloGoksnicer;\,wasusedtoaddtheadditionalspace.% .UUExercise5.18 TypGesetthefollowingintegral:qǟĽRj r1 # *0C3x^2'dx=1.*5.4Rob"ots,squareandotherwiseT*otypGesetasquarerootitisonlynecessarytousetheconstruction\sqrt{::: }.MHence$\sqrt{x^2+y^2}$nwillgive8pn8fe +؟ xr2S+8y[ٟr2.«.NoticethatTU>'ExXntakescareoftheplacementofsymbGols=andtheheightandlengthoftheradical.iT*omakecubGeorotherroots,Athecontrolwordsi\rootand\ofareused.#Y*ouget0 un \$p ^$feay18+xrn+)4fromtheinput$\root?n\of{1+x^n}$.Ǎ~9mTȟE Xb7ook::130{1319ApGossibleBalternativeistousethecontrolword\surd;theinput$\surd?2$willproGduceUUfp 2.'W.UUExercise5.19 TypGesetthefollowing:qǟPp PfeE2 q%!fe}ҟ 䍍Alx+y33);felxyD Zt3APpJ:SPfe E10aeHpɟHW Ax .'<.UUExercise5.20 TypGeset:qǷkxk=Pp oPfeEx8xÄ.%c.UUExercise5.21 TypGeset:qDZ(t)= 1K&fe{]*pɟ*W 据2SџĽRj|t # 0".ze^xr2 =2dx.,5.5Lines,abb"oveandbelowUse{$theconstructions\overline{::: }and\underline{:::}toputlinesabGove{$orbelowmathematical>expressions.lHence$\overline{x+y}=\overline?x+\overliney$>gives|fe2x8+yI=~fegx ȫ+~feBgy .ͱButnoticethatthelinesoverthelettersareatdi erentheights,Pandsosomecareisnecessary*.jTheuseof\overline{\strut?x}willraisetheheightofthelineoverUUx.~9mTȟE Xb7ook::130{131T*oUUunderlinenon-mathematicaltext,use\underbar{::: }.39('63׍L̍󙚉ff|( ff AUUTU>'ExXintro(CanadianspGelling)X=Section5:qNomathanxietyhere!  fffff|(׍).UUExercise5.22 TypGesetthefollowing:qDZxqǟfe(~feBgy#kݟ|fe2x8+y#kݟ[fe2:ϫ.+G5.6DelimiterslargeandsmallTheImostcommonlyusedmathematicaldelimitersarebrackets,Lbraces,andIparenthe- ses.TAsKwehaveseen,@theymaybGeproducedbyusing[?]\{\}()Ktoget[]fg().SometimesUUlargerdelimitersincreasetheclarityofmathematicalexpressions,asinIba8(b+c)bWb *(ab)+cbW:T*owmakelargerleftdelimitersthecontrolwords\bigl,=\Bigl,\biggl,andw\Bigglareused infrontofthedelimiter;similarly*,2\bigr,\Bigr,\biggr,and\Biggrareusedfortheright8䍟~9mTȟE Xb7ook::145{147 delimiters.qHenceUU$\Bigl[$and$\Bigr]$willproGduce`h cand`i9.q͍HereUUisatabletocomparethesizeofsomeofthedelimiters.݀sf+DelimitersTofv\rarioussizesfZן̉ffp{ :fc\{g1gy\}M߫(݆(0M)A)8bc\bigl\{f\Eb y\bigr\}˜b݆\bigl(/bA\bigr) c`nc\Bigl\{e`oy\Bigr\}8`݆\Bigl(.8\`A\Bigr) :^c\biggl\{d^y\biggr\}^݆\biggl(,̟^A\biggr) \(c\Biggl\{d#a\)y\Biggr\}FŸ\ ݆\Biggl(,F\!A\Biggr)If4youwant,kyoucanletTU>'ExX choGosethesizeofdelimiterbyusingthecontrolwords \leftiand\rightbGeforeyourdelimiters.,Thus\left[::: \right]willcausethematerial8䍟~9mTȟE Xb7ook::148 toA`bGeenclosedbybracketsthatareappropriatelybig.5Notew9ell:Iܫeachuseofa\leftdelimiterkmusthaveamatching\rightdelimiter(althoughthedelimitersthemselvesmaybGeUUdi erent).qHence$$\left|{a+b?\overc+d}\right|.$$UUgives'N N N N <$ֱa8+b֟wfe̸ (֍c8+dО О О О ՞:40)3063׍L̍󙚉ff|( ff AUUTU>'ExXintro(CanadianspGelling)X=Section5:qNomathanxietyhere!  fffff|(׍)-MMathematicalTdelimiterslfff`T 8(q(*e)cJ)_[[ UU]q] fcJ\{{g\}bq\lfloor-ccJ\rfloor d\lceileq\rceil*ehcJ\langlei\rangleq=q/ ncJ\backslash_j|qkq\| "cJ\uparrowc *\Uparrowq#q\downarrow+cJ\Downarrow{l\updownarrowmq\Updownarrow$.UUExercise5.23 TypGesetb9bxcbbdxeb.*5.7Thosespb"ecialfunctionsThereareseveraltypGesoffunctionsthatappearfrequentlyinmathematicaltext.In anequationlike\sin G*2n9x+cos^2C8xK=1"thetrigonometricfunctions\sin"and\cos"areinromanratherthanitalictypGe.GThisistheusualmathematicalconventiontoindicatethatitisafunctionbGeingdescribedandnottheproductofthreevqariables.MThecontrolwords\sind!and\coswillusetherighttypGefaceautomatically*.*HereisatableoftheseandsomeotherUUspGecialfunctions:Ǎ~9mTȟE Xb7ook::1629R􍍟'Ӎv^SpQecialTmathematicalfunctions>-^cЀfffb \sin3\cosg\tan\cot\sec\csc\arcsinq63׍L̍󙚉ff|( ff AUUTU>'ExXintro(CanadianspGelling)X=Section5:qNomathanxietyhere!  fffff|(׍).UUExercise5.25 TypGeset:@9~cZE(cscQ2X% xdx=cotx8+Clim-aƴ !0<$*g۫sin8Y *g۟wfe` (֍ B =1K8lim !1<$-1sin; -1wfe` (֍ F_=0:4q΍.UUExercise5.26 TypGeset:jqtanp;(2G)=<$ 2tanKwfe*ʨ c18tanRH2ű/&:6A5.8Hearye,hearye!ThereisaparticularmacrothatisusedinalmosteverymathematicalpapGer,%Sandis di erentsenoughtorequireaspGecialexplanation.!Thisisthe\proclaimmacro.Itisusedwhenstatingtheorems,corollaries,propGositions,andthelike.crTheparagraphfollowing\proclaim?isbrokenintotwoparts:fthe rstpartgoGesuptoandincludingthe rstperiodthatmisfollowedmbyaspace,andthesecondpartistherestoftheparagraph.TheideaisǍ~9mTȟE Xb7ook::202{203 9thatNthe rstpartshouldbGesomethinglike\Theorem1."or\CorollaryB."ThesecondpartUUisthestatementofthetheoremorcorollary*.qHereisanexample:\proclaim?Theorem1(H.~G.~Wells). Inthecountryoftheblind,the?one-eyedmanisking.givesTheoremT1(H.G.W ells).InUUthecountryoftheblind,theone-eyedmanisking.TheUUstatementofthetheoremmaycontainmathematicalexpressions,ofcourse.42+GU63׍L̍󙚉ff|( ff AUUTU>'ExXintro(CanadianspGelling)X=Section5:qNomathanxietyhere!  fffff|(׍).UUExercise5.27 TypGeset:TheoremT(Euclid).ThereUUexistanin nitenumbGerUUofprimes.*.UUExercise5.28 TypGeset:PropQositionT1.1n`Rmٽp`Smىfe$-'Qލ qɴn% qi=1Xi8U[ tѮ1K&fe~n ɤPލWߴn%Wi=1%vֱXiwithUUequalityifandonlyifX1C=8׫=Xnq~.05.9MatricesMatricesaretypGesetusingcombinationsofthealignmentcharacter&andthecontrol word\crtoindicatetheendoftheline.sStartwith$$\pmatrix{::: }$$.IntothespacebGetweenz"thebracesgotherowsofthematrix,Ueachoneendedby\cr./TheentriesareseparatedUUbythe&.qF*orexampletheinputǍ~9mTȟE Xb7ook::176{1789$$\pmatrix{a?&b&c&d\crb?&a&c+d&c-d\cr0?&0&a+b&a-b\cr0?&0&ab&cd\cr}.$$givesUUasprintedoutputqǍX0Bfi@oHa7bcdbyaqc8+d*c8d00a8+bca8b00abcdXEý1ECfiEAl:The},matrixentriesinourexampleshaveallbGeencentredwithintheircolumnswithalittlespaceoneachside.lTheycanbGemade ushrightor ushleftbyinserting\hfillbGefore|joraftertheentry*.Noticethedi erencesbetween|jthefollowingexampleandthepreviousUUone.$$\pmatrix{a?&b&c\hfill&\hfilld\crb?&a&c+d&c-d\cr0?&0&a+b&a-b\cr43,N63׍L̍󙚉ff|( ff AUUTU>'ExXintro(CanadianspGelling)X=Section5:qNomathanxietyhere!  fffff|(׍)0?&0&ab\hfill&\hfillcd\cr }.$$givesUUasprintedoutputX0Bfi@oHa7bcfdbyaqc8+d*c8d00a8+bca8b00abcdXEý1ECfiEAl:sG9.UUExercise5.29 TypGesetqǍ7ܱI4C=X0Bfi@ 1110+10:10 1011+10:10 1010+11:10 1010+10:11X@p1@pCfi@pAIt'spGossibletohavematricesthatuseotherdelimiters.Using\matrixinsteadof\pmatrix\willleave\o theparentheses,^[sothedelimitersmustbGeexplicitlyincludedusing\leftUUand\right.qHereishowwecanchangethematrixofour rstexample.$$?\left|\matrix{a?&b&c&d\crb?&a&c+d&c-d\cr0?&0&a+b&a-b\cr0?&0&ab&cd\cr}\right?|$$givesUUasprintedoutputqǍ. . . . . . . +apbcSid'nb\a@Tc8+d c8dë00:a8+bFa8bë00Vab)|cd~ ~ ~ ~ ~ ~ ~ /qǍIt'sevenpGossibletouse\left.Tand\right.toindicatethattheopGeningorclosingdelimiterUUisdeleted(notetheuseofthepGeriod).44-V63׍L̍󙚉ff|( ff AUUTU>'ExXintro(CanadianspGelling)WSection5:qNomathanxietyhere!  fffff|(׍).UUExercise5.30 UseamatrixconstructiontotypGeset-jxj=^Px#ox0 x#ox0$qύThisMexerciseandmoregeneralconstructionsofthistypGemayalsobGetypGesetusingthe \casesUUmacro.S~9mTȟE Xb7ook::175*Sometimes}ellipsesareusedwithinmatrices.w@Thecontrolwords\cdots,G\vdots,and\ddotsUUcanbGeusedtoinserthorizontal,vertical,anddiagonaldots.ThusUUwecanuse$$?\left[\matrix{aa?&\cdots&az\cr\vdots?&\ddots&\vdots\crza?&\cdots&zz\cr}\right?]$$toUUgetasprintedoutputx㍍Z2 4䍍oiaaʷ֬raz8U .U .U ..s.W.y .y .y .rzpaʷ{zpzZh3 h5+x㍑Matrices'jmayalsobGetypGesetin-line,0buttheyareprettyuglyunlesstheyhaveasmallnumbGerUUofrows.*5.10DisplayedequationsAllofthemathematicscoveredsofarhasidenticalinputwhetheritistobGetypGesetin-linep1ordisplayed.[Atp1thispGointwe'llloGokatsomesituationsthatapplytodisplayedequationsUUonly*.Ther] rstisthatofaligningmultilinedisplays.& Thisisdonewiththealignmentcharacter&{3andthecontrolwords\crand\eqalign.)Startingwith$$\eqalign{::: }$$,theequationsto]bGealignedareenteredwitheachoneterminatedby\cr.;IneachequationthereshouldbGe45.^h63׍L̍󙚉ff|( ff AUUTU>'ExXintro(CanadianspGelling)X=Section5:qNomathanxietyhere!  fffff|(׍)onebjalignmentsymbGol&toindicatewherethealignmentshouldtakeplace.Thisisusually doneUUattheequalsigns,althoughitisnotnecessarytodoso.qF*orexampleǍ~9mTȟE Xb7ook::190{1929$$\eqalign{a+b?&=c+d\crx?&=w+y+z\crm?+n+o+p&=q\cr}$$yieldsqǍa8+bg=c8+dxg=w}ë+8y+zLm8+n+o+pg=q-qǍDisplayedf"equationscanbGenumberedf"ateithertherightorleftmargin.-WhenthecontrolQword\eqnoappGearsinadisplayedequation,GeverythingafterthecontrolwordisputUUattherightmargin.qHence$$?x+y=z. \eqno(1)$$UUyieldsױx8+y"=zp: (1)T*oUUnumbGeranequationattheleftmargin,use\leqnoinplaceof\eqno.It'swpGossibletonumberwalignedequationsbyusingthecontrolword\eqalignno. ThealignmentUUcharacter&isusedtoseparatetheequationfromtheequationnumbGer.$$\eqalignno{a+b?&=c+d&(1)\crx?&=w+y+z\crm?+n+o+p&=q&*\cr}$$yieldsa8+bg=c8+d (1)xg=w}ë+8y+zLm8+n+o+pg=q|($UseUU\leqalignnotoputtheequationnumbGersUUontheleft.8䍟~9mTȟE Xb7ook::192{19346/fz63׍L̍󙚉ff|( ff AUUTU>'ExXintro(CanadianspGelling)X=Section5:qNomathanxietyhere!  fffff|(׍)Finally*,OsuppGose Nsometextneedstoappearinthemiddleofadisplayed Nequation.XThis canbGedonebyputtingitinanhbGox.W*ewilldescribGehbGoxesinmoredetailinthenextsection.CF*ornowwewanttousethemtotempGorarilyresumeusingordinaryromantypGeandtoalsoallowtheinsertionofspacebGetweenwords(remembGerthatallspacesareignoredwhenHtypGesettingmathematics).mHence$$X=Y?\hbox{ifandonlyif}x=y.$$HwillgivetX=Y9ifUUandonlyifAG&x=y[:NoteUUcarefullythespacesinthehbGox.$.UUExercise5.31 Dosomeofthechallengeproblemsonpages180{181ofTheTU>'ExXbGook.470mȟ63׍׍)Section6Allinaro=w ffff|(/eIt'snotuncommontowanttoputatableinthemiddleofsometext.TRF*ortunatelyTU>'ExX makes%iteasytodothis.C InfacttherearetwoseparatemethoGdsofaligningtext.C The rstisbyZusingthetabbingenvironment. ThisissimilartosettingthetabstopsonatypGewriter.Eachblineishandledindividually*,faccordingtosettabcolumns,butwithgreater exibilitythanthatprovidedbyatypGewriter.ZThesecondisthehorizontalalignmentenvironmentwhichUUtypGesetsthewholetableatonceusingaprescribedpattern.*6.1PickingupthetabT*oalignmaterialusingthetabbingenvironment,Zyoumust rstsetthetabpGositionsusing+Athe\settabscontrolword.cHavingdonethis,3alinetousethesetabsstartswiththecontrolsymbGol\+Ոandendswith\cr(remembGerthattheactualspacingonlinesintheinputUU leinunimpGortant).Theeasiestwaytousethe\settabscontrolwordistoputthetextintoequalcolumns.UsingzW\settabs?4\columnswillsetthetabsthatwillproGducefourequalcolumns.TheǍ~9mTȟE Xb7ook::231 9tabbinghisthendonebyusingthealignmentcharacter&tomovetothenexttabstop.So,forUUexample,\settabs?4\columns\+?BritishColumbia&Alberta&Saskatchewan&Manitoba\cr\+?Ontario&Quebec&NewBrunswick&NovaScotia\cr\+?&PrinceEdwardIsland&Newfoundland\crwillUUproGducethetableBritishUUColumbiac_ AlbGertaƾSaskqatchewan*ManitobaOntarioc_ QuebGecƾNewUUBrunswick*NovqaUUScotiac_ PrinceUUEdwardIslandƾNewfoundlandNotice3dthatitispGossibletoskipover3dsometabpositions,janditisnotnecessarytouse$allofthetabsinagivenline.o4T*omakethesametableusing vecolumns,)itisonlynecessary"}touse\settabs?5\columns"}toresetthetabstops;thenthesamethreelinesfromUUthelastexamplewillproGduce:481qߟ63׍L̍󙚉ff|( ff AUUTU>'ExXintro(CanadianspGelling)YSection6:qAllinarow  fffff|(׍)BritishUUColumbiaO;AlbGertavSaskqatchewan}Manitoba OntarioO;QuebGecvNewUUBrunswick}NovqaUUScotiaO;PrinceUUEdwardIslandvNewfoundlandInthisexample,Lthecolumnsaresmaller,ofcourse. Infacttherearetwooverlappingentries#inthelastrow._aThisisbGecauseTU>'ExXwilltabtothenexttabpositionevenif(unlikeaUUtypGewriter)itmeansgoingbackwardonthepage.ThereisaninterestingrelationshipbGetweengroupingandtabbing.The\settabsvqaluesareonlyapplicabletothegroupinwhichitisde ned,?aswouldbGeexpected.ThusitispGossibletotemporarilychangethetabsettingsbygroupingwithinbraces.UInaddition,eachjtableentryisinagroupofitsown.nHencewemaymakeasingleentrybGoldface,oforexample,byusing\bfwithoutbraces.AInaddition,foranycolumnbutthelastoneitispGossibletocentretheentryortoaligniteitherontheleftorontheright,orto llacolumnwithalineordots.ƓEachentryhasanimplicit\hfilattheendsothatitwillbGeattheleftofthecolumnbydefault.HAdding\hfilatthebGeginningoftheentrywillthencauseit?vtobGecentred,Cjustaswiththe\linecontrolword.j}Adding\hfilltothebGeginningwillcausetheentriestobGepushedtotheright(\hfillactsjustlike\hfilinthatitabsorbsexcessUUspace;whenbGoth\hfiland\hfillappear,the\hfilltakesprecedence).\settabs?4\columns\+?\hfilBritishColumbia&\hfillAlberta\qquad&\bfSaskatchewan&?Manitoba\cr\+?\hfilOntario&\hfillQuebec\qquad&\bfNewBrunswick&?NovaScotia\cr\+?\hfil---&\hfill*\qquad&\bfNewfoundland&?PrinceEdwardIsland\cr\+?\dotfill&&\hrulefill&\crwillMproGduceatablewiththe rstcolumncentred,5Kthesecondcolumn ushrightwithazc\qquadofpadding,æandthethirdcolumnbGoldface.Thecontrolwords\dotfilland\hrulefillUUgivealternativecolumnentries. hcBritishUUColumbia FAlbGertaƾSask\ratc9hewan*Manitoba3OntarioQuebGecƾNewTBrunswic9k*NovqaUUScotia+|h*ƾNewfoundland*PrinceUUEdwardIslandT:qōT:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:ƾffc_ $.2Exercise6.1 T*akethetableofCanadianprovincesabGoveandcentreeachentrywithinitsUUcolumn.492{d63׍L̍󙚉ff|( ff AUUTU>'ExXintro(CanadianspGelling)YSection6:qAllinarow  fffff|(׍)The$tabpGositionscanbesetwithmuch$more exibilitythanjustinequalcolumns. Thengeneralpatternistouseasamplelineoftheform\settabs?\+:::*&:::&:::\cr.ThespacingbGetweenthealignmentcharacters&determinesthepGositionofthetabs.EF*orexample,M\settabs?\+\hskip1in&\hskip2in&\hskip1.5in&\crOwouldsetthe]; rsttaboneinchfromtheleftmargin,_4thenextanothertwoinchesfurtherin,_4andthethird#1.5inchesmore.aPIt'salsopGossibletousetexttodeterminethedistancebetween#tabs.So,forS>example,anotherpGossiblesamplelineis\settabs?\+\quadProvince\quad&\quad?Population\quad&\quadArea\quad&\cr.mTheTtabcolumnwouldthenbGejustwideenoughtoaccepttheheadingswithaquadofspaceoneachside.Here'samorecompleteUUexample:\settabs?\+\quadYear\quad&\quadPrice\quad&?\quadDividend&\cr\+?\hfillYear\quad&\quadPrice \quad&\quadDividend\cr\+?\hfill1971\quad&\quad41--54\quad&\qquad\$2.60\cr\+?\hfill2\quad&\quad41--54\quad&\qquad\$2.70\cr\+?\hfill3\quad&\quad46--55\quad&\qquad\$2.87\cr\+?\hfill4\quad&\quad40--53\quad&\qquad\$3.24\cr\+?\hfill5\quad&\quad45--52\quad&\qquad\$3.40\crgivesǍ~9mTȟE Xb7ook::2479 Y*ear5\vPricec]Dividend 19715\v41{54m^$2.6025\v41{54m^$2.7035\v46{55m^$2.8745\v40{53m^$3.2455\v45{52m^$3.40$.UUExercise6.2 T*akethetablegivenabGoveandmoveitclosertothecentreofthepage..RExercise6.3 OnewayRtocentreabloGckoftext,pGossiblyseverallineslong,istouse: $$\vbox{::: }$$.UsegthistocentrethetablegivenabGove.Doesgthe\settabslineneedtobGeUUincludedinthe\vbox?$.Exercise6.4 Improveyourlastresultbyputtingalineunderthecolumnheads.\ThecontrolIword\hrulewillinsertahorizontallineifintroGducedbetweentworowsofatable.NowBrepGeatwiththecontrolword\strutafterthe\+?ofthelinecontainingthecolumn50363׍L̍󙚉ff|( ff AUUTU>'ExXintro(CanadianspGelling)Section6:qAllinarow  fffff|(׍)heads.(A^\strut^e ectivelymakesthespacingbGetweenlinesalittlegreater.Thesizecan bGeUUalteredfromthedefault.)qNotetheextraspacethatresults.~9mTȟE Xb7ook::82!.DExercise6.5 Makethefollowingtablewithdecimalalignment,Gthatis,withthedecimalpGointsjabovejeachother(thinkofthedollar gureasbGeingrightalignedandthecents gureasUUbGeingleftalignedagainstthedecimalpoint):=Plums1$11.22=Co ee111.78=Granola111.98=MushroGoms1.63=KiwiUUfruit1.39=OrangeUUjuice111.09=T*una111.29=Zucchini1.64=GrapGes111.69=SmokedUUbGeef1.75=BroGccoli11ׇPfe 1.091fe =T*otal1$121.55$.2Exercise6.6 DeviseamethoGdtomakearoughtableofcontentsbyusing\settabsandhavingUUentriesloGokingsomethinglike:Getting?Started\dotfill&\hfill1All?CharactersGreatandSmall\dotfill&\hfill9.*6.2HorizontalalignmentwithmoresophisticatedpatternsThe\settabsenvironmentisnotdiculttouse,iandoncethepatternisset,itcanbGeused,repGeatedlyindi erentportionsofthetextthatfollows.d*Itdoeshave,somedrawbacks,however.F*orhone,FthecolumnsizemustbGesetbeforetheentriesareknown.Also,FeventhoughBinonecasewewantedthethirdcolumntobGeboldface,ithadtobespeci edineachline.qTheseUUproblemscanbGehandledmoreeasilybyusingthe\halignenvironment.8䍟~9mTȟE Xb7ook::235{238TheUUgeneralpatterninthe\halignisasfollows:\halign{?\cr\cr\cr514ڟ63׍L̍󙚉ff|( ff AUUTU>'ExXintro(CanadianspGelling)YSection6:qAllinarow  fffff|(׍\)... \cr}Both*athetemplatelineandthedisplaylinesaredividedintosectionsbythealignmentsymbGolL&.nInthetemplatelineeachsectionusescontrolwordsinthesamemannerasdoGes\line{}.+Thezvcontrolword\hfil,ÿforexample,canbGeusedtodisplay ushleft, ushright,orƔcentred.ŅF*ontscanbGechangedusing\bf,\it,etc.ŅT*extmayalsobGeenteredinthe)templateline.cIInadditionthespGecialsymbol#mustappearonceineachsection.cIEachdisplaylineisthensetbysubstitutingeachsectionofthedisplaylineintoitscorrespGondingsectionUUofthetemplatelineattheoGccurrenceofthe#.ConsiderUUthefollowingexample:\halign{\hskip?2in$#$&\hfil\quad#\hfil&\qquad$#$\&?\hfil\quad#\hfil\cr\alpha?&alpha&\beta&beta\cr\gamma?&gamma&\delta&delta\cr\epsilon?&epsilon&\zeta&zeta\cr}Thertemplatelineindicatesthatthe rstsectionofthetypGesettextwillalwaysbGesettwoinches&infromtheleftandalsobGesetasmathematics.9Thesecondsectionwillbecentredafteraddingaquadofspaceontheleft.>6Thethirdandfourthsectionsarehandledsimilarly*.HereUUistheresult:= alphaN *bGeta= [gammaN*delta=ǕepsilonNzetaIn:thiscasethe rstdisplaylineisformedbysubstituting\alphaforthe rst#inthetemplateline,?alphaforthesecond#,\betaforthethirdandbetaforthefourth.Thewhole[lineisthensaved[forsetting.Thiscontinues[untilallthelinesareaccumulated,]IandthentheyaresetwitheachcolumnbGeingaswideasnecessarytoacceptallofitsentries(animplication ofthisaccumulationproGcessisthatatablewithtoomanyentriescouldcauseTU>'ExX to runoutofmemory;d\it'sbGetternottosettablesthataremorethanapageorsolong).Hence(thetemplatelineestablishesthepatternforthetableentriesandthedisplaylinesUUinserttheindividualentries.525s63׍L̍󙚉ff|( ff AUUTU>'ExXintro(CanadianspGelling)Section6:qAllinarow  fffff|(׍)Sometimesjhorizontalandverticallinesareusedtodelimitentriesinatable.T*oput in horizontallines,xweuse\hrule,xjustaswedidinthe\settabsenvironment.6However,weI>don'twanttheruletobGealignedaccordingtothetemplate,Ksoweusethecontrolword\noalign.mmHenceHHhorizontallinesareinsertedbyputting\noalign{\hrule};LverticallinesareYinsertedbyputting\vruleineitherthetemplateorthedisplayline.[Butstillallisnotcompletelyi]straightforward.SuppGosewetakeourlastexampleandchangethetemplatetogetUUverticallinesandalsoinserthorizontallines.\halign{\hskip?2in\vrule\quad$#$\quad&\vrule\hfil\quad#\hfil=&?\quad\vrule\quad$#$\quad=&?\vrule\hfil\quad#\quad\hfil\vrule\cr\noalign{\hrule}\alpha?&alpha&\beta&beta\cr\noalign{\hrule}\gamma?&gamma&\delta&delta\cr\noalign{\hrule}\epsilon?&epsilon&\zeta&zeta\cr\noalign{\hrule}}doGesn'tUUgiveexactlywhatwewant.X-ff1/Ǎ=DŽff 9 _ŸDŽff 㐟9alphaDŽff 9  DŽff @9bGetaꫡffX-ff1/=DŽff 9 _ŸDŽff 9gammaDŽff 9 DŽff 9deltaffff1/=DŽff 9_ŸDŽff ;9epsilonDŽff 9 DŽff ɟ9zetasffff1/ǍThereareseveralde ciencies:themostobviousistheextendedhorizontallines,0but also@thetextloGokssomewhatsquashedintotheboxes.:Inaddition,ϫthetexthasalittleextraspaceontherightratherthanbGeingperfectlycentred.' Asinthe\settabsenvironment,linescanbGemadetallerbyincludingthecontrolword\strutinthetemplate.AfurtherǍ~9mTȟE Xb7ook::82 9problemcanoGccurwhenthepageissetsinceTU>'ExX`mayspreadlinesapartslightlytoimprovethe|appGearanceofthepage.KThiswouldleaveagapbGetweentheverticallines,tsoweusethecontrolVword\offinterlineskipwithinthe\haligntoavoidthis.vFinallywecangetridofthelinesstickingoutontheleftbydeletingthe\hskip?2infromthetemplateline.\T*omove[[thetabletothesamepGositionweuse\moveright.Finally*,\wecanseehowtocentrethe textbynotingthattheextraspaceoGccursinthetemplatelineafterthe#wherethetextUUisinserted.qHencewecanimproveourresultbyusing\moveright?2in\vbox{\offinterlineskip\halign{\strut?\vrule\quad$#$\quad&\vrule\hfil\quad#\quad\hfil&\vrule?\quad$#$\quad&\vrule\hfil\quad#\quad\hfil\vrule\cr\noalign{\hrule}536ȟ63׍L̍󙚉ff|( ff AUUTU>'ExXintro(CanadianspGelling)YSection6:qAllinarow  fffff|(׍)\alpha?&alpha&\beta&beta\cr \noalign{\hrule}\gamma?&gamma&\delta&delta\cr\noalign{\hrule}\epsilon?&epsilon&\zeta&zeta\cr\noalign{\hrule}}}toUUget4_=ΉffH ff  Յ ff 㐟alphaR; ff  lw ff @bGetaV fffffH ff  Յ ff gammaR; ff lw ff delta UV ffffH ff Յ ff ;epsilonR; ff lw ff ɟzetaG ffffHInpgeneral,IifwewanttoconstructatablewithbGoxedentriesthatiscentredonthepage, wecandosobyputtingthe\vboxwithina\centerline{}.{JButhereisatrickthatwillproGduce-anicerresult.dIfthe\vboxisputinbetween-doubledollarsigns,5itwillbetypesetasdisplayedmathematics.SOfcourse,dthereisnoactualmathematicsbGeingdisplayed,dbutTU>'ExXwillputinalittleextraspaceabGoveandbelowthetableasisappropriateforadisplay*.HenceaacentredtablewiththisnicespacingmaybGeformedusingthefollowingfoursteps:(1)o?puta\vboxbGetweeno?doubledollarsigns,D(2)putan\offinterlineskipandan\halignwithin>the\vbox,x(3)inthe\halignputatemplatelinewitha\strutinthebGeginning,andA~a\vrulesurroundingeachentry*,|(4)eachrowofthetableshouldbGeprecededandfollowedUUby\noalign{\hrule}.HereUUisthepatterntobGefollowed:$$\vbox{ \offinterlineskip\halign{\strut?\vrule#&\vrule#&:::L&\vrule#\vrule\cr\noalign{\hrule}&&:::L&\cr\noalign{\hrule}:::\noalign{\hrule}&&:::L&\cr\noalign{\hrule}}}$$54763׍׍)Section7Rollingy=ourown32ff|(/eInthissectionwe'llcreatenewcontrolwords.:Themakingofthesenewde nitions,also calledr`macros,yisoneofthemostpGowerfulr`techniquesavqailableinTU>'ExX.F*orthe rstappli-cationofthisfacility*,)we'llseehowanewde nitioncansavealotoftypingbysubstitutingshortUUstringsforlongones.*7.1ThelongandshortofitTheycontrolword\defisusedtode nenewcontrolwords.`Thesimplestformfordoing@thisis\def\newname{::: }.cThenwhenever\newnameappGearsinyourinput le,$itwillىbGereplacedbywhateverisbGetweenthebracesinthede nition.bOfcourse\newnamemustsatisfytheconventionfornamingcontrolsequences,4thatis,itmustbGeacontrolword&(allletters)oracontrolsymbGol(exactlyonenonletter).bGSo,0"forexample,suppGoseyouwrite4adoGcumentthatcontainsthephrase\UniversityofManitoba"manytimes. Then\def\um{University?ofManitoba}Xde nesanewcontrolsequence\umwhichcanthenbGeDusedatanytime.@ThesentenceI?takecoursesatthe\um.Dthenmakessense.@Ifthecontrolwordexists,yournewde nitionwillreplaceit(thisincludesthecontrolwordsde ned byTU>'ExX,soalittlecaremustbGetakeninthechoiceofname).zAnyde nitionis,however,UUloGcaltothegroupinwhichitisde ned.qF*orexample,\def\um{University?ofManitoba}I?tookmyfirstcourseatthe\um.{\def\um{Universit\'e?deMontr\'eal}Then?Itookmynextcourseatthe\um.}Finally?Itookmylastcourseatthe\um.givesI9toGok9my rstcourseattheUniversityofManitoba. 9ThenI9toGokmynextcourseattheUUUniversitGedeMontrGeal.FinallyItoGokmylastcourseattheUniversityofManitoba.558z63׍L̍󙚉ff|( ff AUUTU>'ExXintro(CanadianspGelling)okSection7:qRollingyourown  fffff|(׍)RemembGer1thatallspacesafteracontrolwordareabsorbGed;thisincludesthecontrol wordsnxthatyoude ne.0Inthepreviousexample,anyspaceafter\umwouldbGeignored.However,theWgspaceafterthe rstpGeriodWgandthespaceafterthe rstopGeningbracearedi erent;ifkyouloGokcloselyattheendofthe rstsentencetypGesetusingtheexample,fyou'llsee6Lsomeextraspace.ThiscanbGeeliminatedbyputtinga%aftertheopeningbracetomake|therestofthelineacomment.D*Thesameholdsforthelinewiththelastclosingbrace.Careful 1controlofspacesoftencallsforthe\commentingout"oftheendoflinesinthismanner.Once";anewcontrolsequencehasbGeende ned,,titmaybGeusedinnewde nitions.`ThisisUUonewayUUofmakingsimpleformletters.qFirstlet'sde neasimpleletter.\def\letter{\par?\noindentDear?\name,?Thisisalittlenotetoletyouknowthatyournameis\name.?\hskip2inSincerelyyours,\vskip?2\baselineskip\hskip?2inTheNameNoter\smallskip?\hrule}Nowthisletterusesthecontrolword\name,whichisunde nedatthispGoint.$When\letterUUisused,thecurrentvqalueof\namewillappGearinthebodyoftheletter.qHence\def\name{Michael?Bishop}\letter\def\name{Michelle?L\'ev\^eque}\letterwillEproGducetwoEcopiesoftheletter,eachwiththecorrectname,followedEbyahorizontalrule:DearUUMichaelBishop,ThisUUisalittlenotetoletyouknowthatyournameisMichaelBishop.=SincerelyUUyours,0=TheUUNameNoterffff|(569663׍L̍󙚉ff|( ff AUUTU>'ExXintro(CanadianspGelling)okSection7:qRollingyourown  fffff|(׍)DearUUMichelleLGev^eque,ThisUUisalittlenotetoletyouknowthatyournameisMichelleLGev^eque.=SincerelyUUyours,0=TheUUNameNoterffff|(ǍW*ecouldhaveputanythingbGetweenthebracesin\def\name{::: };-itcouldbGeseveral paragraphs2longanduseothercontrolsequences(althoughinthiscontextitwouldbGealittle |strange).=OfcourseitispGossibletouse\vfill?\ejectaspartofthede nitionof\letterUUtoejectthepagewhentheletteriscompleted.$.&Exercise7.1 Makeaformletterthatusesthecontrolwords\name,4\address,\city,\province,UUand\postalcode..Exercise7.2 AnunnumbGeredlistofitemsisoftenmadeusing\item{$\bullet$}./De nea;macro\bitemthatdoGesthis,anduseitforseveralparagraphs.yNowchangeeachbullettoadash(notethatasimplechangeinthemacropropagatesallthenecessarychangesinallUUoftheparagraphs)..?Exercise7.3 SuppGosethatyouaregoingtohavetoformatseveralparagraphsinapapGerusing,\hangindent?=30pt,b\hangafter=4,and,\filbreak(don'tworryabGoutwhattheseEcontrolsequencesactuallydo;JtheonlyimpGortantthingfornowisthatoncetheyareset,theyremainine ectforonlyoneparagraph).Q_De neasinglecontrolsequence\setparwhichUUcanthenbGeputinfrontofeachparagraphthatneedstobGesoformatted.*7.2FillinginwithparametersIt'sW6pGossibletousemacrosinmuchW6greatergeneralitybyallowingparameterstobGepassed.[TheMideaissomewhatsimilartothetemplatelineinthe\halignenvironment.First,Hlet'sDloGokatthecasewherethereisoneparameter.lBInthiscaseacontrolsequenceisde nedby\def\newword#1{::: }.#ThesymbGol#1mayappGearbetweenthebraces(severaltimes)/inthede nitionof\newword.e'ExXintro(CanadianspGelling)okSection7:qRollingyourown  fffff|(׍)materialmnbGetweenthebracesinsertedintothetemplateateveryoGccurrenceof#1inthe originalGde nition.=TheIspacingintheoriginalde nitioniscrucialhere;#therem9ustTbQenospacesbeforetheopeningbrace.AsUUanexample,wecouldusetheformletterofthelastsectioninthefollowingway:\def\letter#1{ \par?\noindentDear?#1,This?isalittlenotetoletyouknowthatyournameis#1.\hskip?2inSincerelyyours, \vskip?2\baselineskip\hskip?2inTheNameNoter\smallskip?\hrule}NowUUwecanuse\letter{Michael?Bishop} \letter{Michelle?L\'ev\^eque}toUUgetDearUUMichaelBishop,ThisUUisalittlenotetoletyouknowthatyournameisMichaelBishop.=SincerelyUUyours,0=TheUUNameNoterffff|(58;؞63׍L̍󙚉ff|( ff AUUTU>'ExXintro(CanadianspGelling)okSection7:qRollingyourown  fffff|(׍)DearUUMichelleLGev^eque,ThisUUisalittlenotetoletyouknowthatyournameisMichelleLGev^eque.=SincerelyUUyours,0=TheUUNameNoterffff|(CǍ0Now8let'sde ne\def\displaytext#1{$$\vbox{\hsize?=12cm#1}$$} as!anewmacrotodisplaytext.,Then\displaytext{::: }willcausethema-terialbGetweenthebracestobGeputinaparagraphwithwidth12centimetresandthencentredwithsomespaceaddedabGoveandbGelowasisappropriateforaUUdisplay*.qThisparagraphwassetusingthis\displaytextmacro.$The parameterofamacrocanbGenomorethanoneparagraphlong.:YIfanewparagraph isencounteredaspartofaparameter,anerrorwillbGegenerated.Thisisasafetyfeature,forEotherwisetheaccidentalomissionofaclosingbracewouldcauseTU>'ExXEtoeatuptherestofUUthe leastheparameter..qxExercise7.4 De neamacro\yourgradesothat\yourgrade{89}willcausethefollowingsentenceXUtobGetypGeset:wThegradeyoureceivedis89%.zItshouldbGeabletoworkwithanyotherUUpGercentage,ofcourse.It'sAnotreallyanyhardertousemorethanoneparameter.Theformusedtode neanewcontrolwordwithtwoparametersis\def\newword#1#2{::: }.Thede nitionbGetweenthebraces}mayhave#1and#2oGccurringinit,perhapsseveraltimes.)When\newword{::: }{:::}appGears inthetext,qthematerialbetween the rstsetofbracesreplaces#1inthede nitionandwthematerialbGetweenwthesecondsetofbracesreplaces#2inthede nition.jHereisanexampleUUfollowedbyitsresult:\def\talks#1#2{#1?talksto#2.}\talks{John}{Jane}\talks{Jane}{John}\talks{John}{me}\talks{She}{Jane}59<#63׍L̍󙚉ff|( ff AUUTU>'ExXintro(CanadianspGelling)okSection7:qRollingyourown  fffff|(׍)JohnUUtalkstoJane.qJanetalkstoJohn.Johntalkstome.ShetalkstoJane.$.Exercise7.5 Inamannersimilartothepreviousexercise,de neamacro\yourgrade sothat\yourgrade{89}{85}causesthefollowingsentencetobGetypGeset:NY*oureceivedagradeUUof89%onyour rstexamandagradeof85%onyoursecondexam..UUExercise7.6 W*riteamacro\fracsothat\frac{a}{b}willtypGesetthefraction a&feVpib +.It's`,impGortantnottoputanyspacesbGeforethe rstbraceinthede nition.KIfyoudo,TU>'ExX#will#Ninterpretthede nitiondi erentlyfromthewaydescribGedhere.۳F*ormorethantwo"parameters,JthemethoGdofde nitionissimilar..T*ode neacontrolwordwiththreeparameters,7Cstart/with\def\newword#1#2#3{::: }.e?Then#1,#2and#3mayoGccurbetweenthecbraces.gWhen\newword{::: }{:::}{:::}cappGearsinthetext,gthematerialbetweenceachsetofbracesreplacesitscorrespGondingsymbolinthede nitionofthecontrolword.\TheparametersUUmaygoupto#9.*7.3ByanyothernameSometimes it'sconvenient tobGeabletogiveacontrolwordanalternativename.2YF*orex-ample,ifYyoupreferadi erentspGelling,youmightwanttocallthecontrolword\centerlinebythenameof\centreline.VThiscanbGedonebyusingthe\letcontrolword.VTheuseof\let?\centreline=\centerlinecAnowmakesanew(aswellastheold)controlwordavqail-able.ThiscanalsobGeusedwithmathematicalnamesaswith\let?\tensor=\otimes.ItUUisthenpGossibletouseǍ~9mTȟE Xb7ook::206{2079$$?(A\tensorB)(C\tensorD)=AC\tensorBD.$$toUUget(A8 Bq)(C DG)=AC 8BqDG:+.EExercise7.7 De necontrolsequences\ll,{\cl,andE\rlthatareequivqalentto\leftline,\centerline,UUand\rightline.60=863׍L̍󙚉ff|( ff AUUTU>'ExXintro(CanadianspGelling)okSection7:qRollingyourown  fffff|(׍)TheU\letcontrolwordallowsuserstonametheirowncontrolsequences."Thisallows apGersonalizedsetofcontrolsequencesthatmaybGeusedinplaceoftheonesprovidedbyTU>'ExXUUwhendesired.61>;63׍׍)Section8Toerrish=uman ffff|(/eInʪsomewaysʪTU>'ExXʇisnotcompletelydivine.CTU>'EXʇwillrespGondtoinvqalidinputbygiving anierrormessagetothescreenifyouareusingitinteractivelyandalsotothelog le.Because+TU>'ExX+isverycomplicated,4theactualpGointwheretheerrorisdetectedmaybGedeepwithin$(theprogram,-soafullrepGortoftheerrormayberatherlongandinvolved.acNot$(onlythat,vTU>'ExXYwill~trytorecover~fromerrors,andwillrepGortwhatwasdoneinthatprocess.AF*orthis)reasonthereadingoferrormessagesmaybGealittledicultfortheuninitiated.DThekeyistoknowwhatisimpGortantfromyourpGerspectiveandwhatcanbGesafelyignored.Z Solet'sUUloGokatsometypicalerrorsandthemessagesthattheygenerate.*8.1TheforgottenbyeThe rstmistakethatwe'llloGokatisonethateveryonemakesatsometime,namely*,theUUomissionof\byeattheendofthe le.qIfyou'reusingTU>'ExXinteractively*,anasterisk*willp7bGeprintedonthescreenandnothingwillhappensince,vhavingnotbeentoldto nishup,TU>'ExXis waitingforinput(fromyourkeybGoard).ZWhateveryoutypGeinwillbeappendedtoe5whateverhasbGeeninputfromyour les.gTheusualrespGonseistotypGe\bye^7ᨫsincethatUUwill nishthingsup.8.2Themisspb"elledorunknowncontrolsequenceUsingamisspGelledorothercontrolsequenceunknowntoTU>'ExXisacommonerror.!IfTU>'ExXisbGeingrunasabatchjob,tanerrormessageisprintedandthejobgoGesonignoringthecontrolsequence.PWhenusingTU>'ExXfinteractively*,DitispGossibletorepairerrors(ofcoursethisdoGesnotchangetheoriginalinput le,sothatmustbGedonewhentheTU>'ExXvjobiscompleted).qSuppGoseUUwehaveaTU>'ExXinput leconsistingofthefollowingtwolines:\line{The?leftside\hflitherightside}\bye Jff=  ^7ëisthekeyusedtoendalineofinput.@ItmightbGecalledthecarriagereturn,Genter,orUUsimplythereturnkeyonyourterminal.qSometimesitisindicatedbyalargeleftarrow.62?*63׍L̍󙚉ff|( ff AUUTU>'ExXintro(CanadianspGelling)t}Section8:qT*oerrishuman  fffff|(׍)TheIcontrolwordshouldbGe\hfil,ofcourse.HereisthemessagethatwouldbGesent toUUyourterminal:! Undefinedcontrol?sequence.l.1?\line{Theleftside\hflithe?rightside}?The rstlinestartswith!^andgivestheerrormessage.NextcomesthelinenumbGeronwhichtheerroroGccurredandthepartofthelinethatwasreadsuccessfully*.VThenextlinegivesthecontinuationofthelineaftertheerror.EAtthispGointthequestionmarkmeansthatUUTU>'ExXiswaitingforarespGonse.qThereareseverallegalones:"׍෍piRespQonsesTtoT<8E3sXerrormessagesoIZ'DesiredTrespQonseoCInputTtoT<8E3sX CResultZ'fff|۟ Help|ch]0ReasonUUforstoppinglistedonterminal.q\Insert|ci]0NextUUlineinsertedintoTU>'ExXinput le.!Exit|cx]0ExitUUfromTU>'ExX.qCompletedpagestoDVI le."Scroll|cs]0ListUUmessageandcontinueUUafterminorerrors.!#Run|cr]0ListUUmessageandcontinueUUafteranyerrors.Quiet|cq]0AllUUterminallistingssuppressed.!CarryUUon|c]0TU>'ExXUUcontinuesasbGestitcan.InourlastexampleareasonablerespGonsemightbetoenterhtogetahelpmessage,thenitoinsertmoretext,(atwhichpGointTU>'ExXݭrespGondswithinsert> ͫand nally\hfilUUasthecorrectcontrolword.qHereistheresult:? h?The?controlsequenceattheendofthetoplineof?yourerrormessagewasnever\def'ed. Ifyouhavemisspelled?it(e.g.,`\hobx'),type`I'andthecorrectspelling?(e.g.,`I\hbox'). Otherwisejustcontinue,and?I'llforgetaboutwhateverwasundefined.? i?insert>\hfil[1]The*k nal[1]meansthatthe rst(andonly)pagehasbGeencompletedandsenttotheDVIUU le.qTheoriginalinput lestillneedstobGe xed,ofcourse.63@63׍L̍󙚉ff|( ff AUUTU>'ExXintro(CanadianspGelling)t}Section8:qT*oerrishuman  fffff|(׍)8.3ThemisnamedfontAh?misspGelledhfontnameisanerrorsimilartothemisspelledcontrolsequence.YThe error}messageisdi erentandalittleconfusingat rst.SuppGoseforexamplethefollowingappGearsUUinyourinput le:\font\sf?=cmss01It shouldbGecmss10,<&thatis,thenumbGers havebGeentransposed.HerearetheerrorandUUhelpmessages:! Font?\sf=cmss01notloadable:Metric(TFM)filenotfound.c\par\bye?->\par>\vfill?\supereject\endl.2?\bye? h?I?wasn'tabletoreadthesizedataforthisfont,so?Iwillignorethefontspecification.[Wizards?canfixTFMfilesusingTFtoPL/PLtoTF.]You?mighttryinsertingadifferentfontspec;e.g.,?type`I\font='.The׺TFMך(TU>'ExXfontmetric) leisanauxiliary lethatisusedbyTU>'ExX.GSothisstrangemessageisjusttellingyouthatthefontyoude neddoGesn'texistonyourcomputersystem.*8.4MismatchedmathematicsAnother2commonerroristouse$or$$tostartamathematicalexpressionandthentoforgetKthesecond$or$$when nished.EThetextthatfollowsisthentreatedasmathematics,andrtomakemattersworse,9ifmoremathematicsisstartedbyanew$or$$,9itwillthenbGe\"treatedasordinarytext.-Needlesstosay*,]errormessagesgaloremaybGegenerated.-TU>'ExXwillattempttocorrecttheproblembyinsertinganew$or$$;)!inanycase,theproblemiso#correctedbytheendoftheparagraphsinceanewparagraphwillautomaticallystartasordinaryUUtext.ConsiderUUthefollowingcorrectinputanditsoutput:Since?$f(x)>0$,$a0$.64AΟ63׍L̍󙚉ff|( ff AUUTU>'ExXintro(CanadianspGelling)sSection8:qT*oerrishuman  fffff|(׍SinceUUf(x)>0,a0.Ifwenowleaveouttheseconddollarsignin$f(x)$wethengetthefollowingerror andUUhelpmessages:! Missing?$inserted.N$^\intop\int?->\intopD?\nolimitsl.2?$\int5!'ff&f8Ga^b?f(x)\,dx>0$.? h?I've?insertedabegin-math/end-mathsymbolsinceIthinkyou?leftoneout. Proceed,withfingerscrossed.?The7linestartingwith!ZtellsuswhathasbGeendone.Thelinestartingwithl.2showsus{owherewewereintheinput lewhentheerroroGccurred.Asinourotherexamples,thepartofthelinesuccessfullyread,_>thatis,through\int,appGearsononeline,andthe?4continuationappGearsonthenextline./dTheremainingmaterialmayseemsomewhatobscure.ThesecJintermediatemessagesshowwhatwashappGeningfurtherinthegutsoftheTU>'ExXUUprogramwhentheerroroGccurred.qThenewerusermayignorethem.HereUUiswhatyougetasoutputafterTU>'ExXtriestorecoverfromtheerror.獑SinceUUf(x)>0,a0.ThereNisastretchoftextthatisitalicwithnospacing.o`ThisistypicalfornormaltextbGeingprocessedasmathematics;ifyouseethisinyouroutput,SyouhavealmostcertainlyleftUUouta$or$$.*8.5MismatchedbracesIt'seasytoforgetormismatchtheclosingbraceswhenmakinggroups.NMTheresultmaybGeJarelativelybenignerror,Koritmaybecatastrophic.R}Suppose,Kforexample,youhave{\bf?AboldtitleAinvDyourtextwiththeclosingrightbraceomitted.ԕTheresultwillbGe65Bʟ63׍L̍󙚉ff|( ff AUUTU>'ExXintro(CanadianspGelling)t}Section8:qT*oerrishuman  fffff|(׍)the@sameasifnoopGeningbracewerethere;Gthatis,Dtherestofthepaperwillbeboldfaceif noUUotherfontchangesaremade.qY*ouwillgetthefollowingmessageattheendofthe le:(\end?occurredinsideagroupatlevel1)Ifyouhadmadethesamemistaketwice,PthentherewouldbGetwomoreopGeningbracesthanUUclosingbraces,andyouwouldgetthemessage:(\end?occurredinsideagroupatlevel2)TU>'ExXfdoGesn'tknowthattheclosingbraceismissinguntilitreachestheendoftheinput'v le.*HencethemessagedoGesn'ttellyouwhereyouwentwrong.*IftheloGcationofthe'ExXRdagainwillcauseonlythe rsthalftobeprocessed,andiftheerror7messagepGersists,=youwillknowthattheerrorisinthe rsthalfofthedoGcument.gBymovingHthe\byetodi erentplaces,KNtheerrorcanbGelocalized.mAlso,KNlookingattheoutputoftenUUrevealswhathasgonewrong.Missing\opGeningbracesaremuch\easiertospot.Hereisatwo\lineinput leandtheresultingUUerrorandhelpmessages:\bf?Hereisthestart},butthereisthefinish.\bye! Too?many}'s.l.1?\bfHereisthestart},?butthereisthefinish.? h?You've?closedmoregroupsthanyouopened.Such?booboosaregenerallyharmless,sokeepgoing.It'sDquitepGossible,ofcourse,thatthelinethatissuppGosedtohaveDthemissingleftbraceUUwillnotbGeonthelinewhereTU>'ExXcatchestheerror.Amismatchedbraceinthede nitionofanewcontrolsequencecancauseama8jorerror.Sincesuchade nitionmayincludeseveralparagraphs,-@itmaynotbGecaughtbytheendofCaparagraph,7but,ratherCwilljustkeeppilingmoreandmoretextintotheun nishedde nition.xIt'swevenpGossibleforTU>'ExXwtorunoutofmemoryasitkeepseatingupmoretext!Thisiscalleda\runawayde nition". 2Hereisatwolineinput lewitharunawayǍ~9mTȟE Xb7ook::206 9de nition:66C63׍L̍󙚉ff|( ff AUUTU>'ExXintro(CanadianspGelling)t}Section8:qT*oerrishuman  fffff|(׍1 \def\newword{the?def \newword\byeHereUUaretheresultingerrorandhelpmessages:Runaway?definition? ->the?def! Forbidden?controlsequencefoundwhilescanningdefinitionof\newword.S}c\byel.3?\bye? h?I?suspectyouhaveforgottena`}',causingmeto?readpastwhereyouwantedmetostop.I'll?trytorecover;butiftheerrorisserious,you'd?bettertype`E'or`X'nowandfixyourfile.? No?pagesofoutput.Thisisobviouslyaseriouserror.2IfitoGccursatthebeginningofa le(asinthepreviousexample),UUtherewillbGenooutputatall!Ifaclosingbraceisleftoutwhileusingamacrowithparameters,therunawayde nitionwill?bGeterminatedattheendoftheparagraph.5kSoif\def\newword#1{::: }hasbeende nedandvyouuse\newword{:::rwithouttheclosingbrace,thenatmostoneparagraphwillbGeruined.~9mTȟE Xb7ook::205Inwshort,RwhenanerroroGccurs,makeanoteofthelinenumbGertoseehowmuchofthe_input lehasbGeenread,!andalsothelinestartingwithanexclamationpointtogetashortdescriptionoftheerror.Iftheerrorisstillnotclear,һaskTU>'ExXformoreinformationbyձtypingh.F*orsmallerrors,TU>'ExXՐcancarryonquiteawayifyoujustkeephittingtheUU.67D#63׍׍)Section9Diggingalittledeepuer32ff|(/eIn+thissectionweloGokatafewtopicsthatallowTU>'ExXtobGeusedwithgreater exibility or+eciency*.AsthedoGcumentsbeingproducedgetlonger,a5di erenttechniquescanhelpmakeUUtheircreationeasier.*9.1Big les,little lesTU>'ExXH#canHhreadandwrite lesasitruns.#ThismakesitpGossibletouse lesthataresmallerandmoreconvenienttohandlebycreatingamaster lethatreadsthesmaller lesinthepropGer/order.e Thisdocument,6forexample,consistsoftensectionsplusanintroGduction.e Inaddition,therearemacrosthatareusedforallsections.wThemacroscanbGeputina lecalled,say*,macros.tex,thezintroGductioncanbeputinintro.tex,andeachsectionputinitsown le.'ExXintro(CanadianspGelling)X0Section9:qDiggingalittledeeper  fffff|(׍)Thea\inputcontrolwordalsoallowstheuseofpredesignedmacros.aThemacrosfora memorandum,forexample,mightbGeputina lecalledmemo.tex.WThesemacrosmightsetuptheright\hsize,.\vsizeandotherparameters,andmightstampthetimeanddate.OnceIthishasbGeensetup,allmemorandamaybestartedwith\input?memotomakethemcomeUUoutwithacommonformat.Be&surethatyoudon'thavethecontrolword\byeinyourinput leortheTU>'ExXprogramwillUUstopatthatpGoint.$.TExercise9.1 MakeaTU>'ExX>input lethatreadsinasecond le.UT*ryreadinginthesecond leUUtwiceusingthe\inputcontrolwordtwice.*9.2Largermacropack;agesDesigningdWmacrosthatcanbGeusedwithmanytypGesofdocumentsisobviouslyuseful.MostBuniversities,&forexample,haveBspGeci candoftencomplicatedformatrequirementsfortheses.Acollectionofmacros,thatis,amacropackqagethatmeetsallthesespGeci cationscouldW{bGesomewhattimeconsumingtodesignandcouldbequitelong.x8Itispossibletousethe8Y\inputcommandtousesuchamacropackqage,>%justasitispGossibletouseitwithyourownUUmacros.qButTU>'ExXhasabGetterfacilityforlargerpackqages.Amacro*packqagecanbGeputinaspecialformthatcanbequicklyreadbyTU>'ExX.EThisis/ycalledaformat le,7 andtheexactformisoftechnicalinterestonly*.e)TheimpGortantthingis"itallowsTU>'ExX"tobGerunwithmanynewcontrolsequencesprede ned.`CertaincommandscalledUUprimitivesҫarepartofthede nitionofTU>'ExX.WhatDJwehavedescribGedinthismanualissometimescalledplainTU>'ExX,andconsistsoftheCTU>'ExXprimitivesplusasetofmacrosinaformat le(thatisusuallyincludedinTU>'EXautomatically)calledplain.fmt.F*orthecurious,?anycontrolwordcanbGeviewedusing\show.qTheUUcommand\show\centerlinewilldisplay>?\centerline=macro:#1->\line?{\hss#1\hss}.on ?thescreenandinthelog le.Y*oucanuse\showwithyourownmacros,;9toGo.Ifyouend upusingseveralmacropackqages,youcanusethe\showcommandtoseeifaparticularmacroUUisde ned.69F263׍L̍󙚉ff|( ff AUUTU>'ExXintro(CanadianspGelling)X0Section9:qDiggingalittledeeper  fffff|(׍)ManycomputercentreshavetheLffU+- cmcsc10aTU>ExXmacropackqage.DThispackqageallowstheuserto createanindex,߃atableofcontents,andabibliographyautomatically*.@Italsohastheabilityto~insertsomeelementarygraphic guressuchascircles,IHovqals,lines,and~arrows.CLffUaTU>ExXalsoyusesspGecialprede ned lescalledstyle lestosetupspeci cpageparameters.ޕManydi erent}style lesareavqailable;NsomejournalswillacceptpapGersonamagneticmediumforLdirectproGcessingiftheyarepreparedusingLffUaTU>ExX=andadesignatedstyle le."ItisnotdicultJtoshiftfromTU>'ExX"toLffUaTU>EX.HA"user'sguidebytheauthorofthemacropackqage,LeslieUULampGort,isavqailable:qLffUaTU>ExX:TAdoQcumen9tpreparationsystem^8|s.TheAmericanMathematicalSoGcietyusestheAU>'M S-TU>'ExXmacropackqageforitsjournals.ItoisreadilyavqailablefromthatSoGciety*,v9andpapGersmaybGesubmittedtotheirjournalsona]NmagneticmediumusingAU>'M S-TU>'ExX.A]LmanualbyMichaelSpivqak,_LTheJo9yofT<8E3sX^9|s,]NisavqailableUUfromtheAmericanMathematicalSoGciety*.Other!macropackqagesexist,andundoubtedlymorewillbGedevelopGed.6 Theyareusuallyof_moGdestcostandcanbeverye ectiveinsomecircumstances.nTheTU>'ExX_HUsersGroupannouncesUUtheexistenceofnewmacropackqagesinitspublications.*9.3HorizontalandverticallinesMakingzhorizontalandverticallinesiseasyusingTU>'ExX.5Whentypingintext,C\hrulewillcausethecurrentparagraphtoend,^willdrawahorizontallinewhosewidthisthecurrentvqalueof\hsize, andthenwillcontinueonwithanewparagraph.c}It'spGossibletospGecifythewidthofthehruleas,mforexample,with\hrule?width5cm; alsoyoucanuse\vskipUUor\bigskiptoputsomespaceabGoveUUorbelowthehrule.qHereisanexample:\parindent?=0pt\parskip=12ptHere?isthetextbeforethehrule.\bigskip\hrule?width3inAnd?hereissometextafterthehrule.thatUUproGducesCJ=ff=  ^8Addison-W*esley,UUReading,Massachusetts,UU1986,ISBN0-201-15790-X. ^9AmericanUUMathematicalSoGciety*,1986,ISBN0-8218-2999-870G>`63׍L̍󙚉ff|( ff AUUTU>'ExXintro(CanadianspGelling)X0Section9:qDiggingalittledeeper  fffff|(׍)HereUUisthetextbGeforethehrule. ffff\ǍAndUUhereissometextafterthehrule.Infactthishrulenotonlyhaswidthofthreeinches,9butalsobydefaulthasaheight (theLamountbywhichthehruleextendsabGovethebaselineonwhichthetypGeisbeingset)ofN0.4pGointsandadepth(theamountbywhichthehruleextendsbGelowthebaselineonwhichthetypGeisbeingset)of0points.Eachoftheseparameterscanbeindividuallyset.ThusUUifwechangethelastexampletosay\hrule?width3inheight2ptdepth3ptRweUUgetHereUUisthetextbGeforethehrule.\ǍAndUUhereissometextafterthehrule.TheUUthreeparameterswidth,height,anddepthmaybGegiveninanyorder.8䍟~9mTȟE Xb7ook::221{222AyvruleymaybGede nedanalogouslytoanhrulebyspGecifyingthewidth,height,anddepthifdesired.1But,(unlikethehrule,thevrulewillnotautomaticallystartanew~9mTȟE Xb7ook::221{222 paragraphwhenitappGears.L;Bydefaultthevrulewillbe0.4pointswide,7andwillbeashighasUUthelineonwhichitisbGeingset.qHenceHere?issometextbeforethevrule\vrule\and?thisfollowsthevrule.willUUgiveHereUUissometextbGeforethevruleffandthisfollowsthevrule.$.→Exercise9.2 Makethreehorizontallinesthatare15pGointsapart,3inchesinlength,andoneUUinchinfromtheleftmargin.Although [weusuallythinkofhrulesandvrulesashorizontalandverticallines,6\theyneedUUnotnecessarilybGeusedthatway*.qForUUexample:\noindentName: \vrule?height0ptdepth0.4ptwidth3in71HJ63׍L̍󙚉ff|( ff AUUTU>'ExXintro(CanadianspGelling)X0Section9:qDiggingalittledeeper  fffff|(׍)willUUgiveName:qǞffff\$.UUExercise9.3 Makethefollowinggrid(eachbGoxis1centimetresquare):`uM=qffU[s獍sffssff8΄sffU[sffffffU[sffssff8΄sffU[sffffU[sffssff8΄sffU[sffffU[*9.4Boxeswithinbb"oxesW*eNqhavealreadyseen(inourdiscussionoflineshapGes)thatvboxesandhbGoxesare ob8jects@thatmaybGeoverfullorunderfull.InthissectionwewillloGokattheseboxesinabit8bmoredetail.h!TheymaybGestackedorlineduptoallowavqarietyofpGositionsfortextontheUUpage.AnDhbGoxisformedbyusing\hbox{::: }.@OncethematerialbGetweenthebraceshasbGeenSputintoanhbGox,T1itissetandcannotbGefurthersplit(thismeansthatmaterialthatmust3goononelinecanbGeputintoanhbGox,jnanditwillthenremainasoneunit). It'spGossibletospecifythesizeofanhbox.sThus\hbox?to5cm{contentsofthebox}willǍ~9mTȟE Xb7ook::64{66 9proGduceaanhboxaexactly vecentimetreswidecontainingthetypGesettext\contentsofthebGox".ȑIt'seasytogetanunderfulloroverfullbGoxinthisway*.ȑAnunderfullbGoxcanbGeavoidedBbyusing\hfiltoabsorbtheextraspace.kWhennodimensionisgiven,FvanhbGoxisformedUUthatisjustwideenoughtoholdtheenclosedtext.Similarly*,hkvbGoxesdareformedusing\vbox{::: }.WhatmakesthesebGoxesinterestingisthat._whenavbGoxcontainshbGoxes,6*thesehbGoxesarestackedoneabGovetheotherandsetasaUunit.s3Similarly*,UanhbGoxUcancontainvboxes,UwhichUwillbesetinarow.s3SupposewetakethreeUUhbGoxesandputtheminavbGox:\vbox{\hbox{Contents?ofbox1}\hbox{Contents?ofbox2}\hbox{Contents?ofbox3}72ISf63׍L̍󙚉ff|( ff AUUTU>'ExXintro(CanadianspGelling)X0Section9:qDiggingalittledeeper  fffff|(׍)}gives-㎍ContentsUUofbGox1 ContentsUUofbGox2ContentsUUofbGox3NowUUsuppGosewetakeanothervbGox:\vbox{ \hbox{Contents?ofbox4}\hbox{Contents?ofbox5}}ThesetwovbGoxescanbGeputintoanhbGox;_thiswillcausethemtobGeplacedsidebyside.qInUUotherwords\hbox{?\vbox{9\hbox{Contents?ofbox1}9\hbox{Contents?ofbox2}9\hbox{Contents?ofbox3}9}?\vbox{9\hbox{Contents?ofbox4}9\hbox{Contents?ofbox5}9}?}gives-㎍UUContentsofbGox1UUContentsofbGox2UUContentsofbGox3T ContentsUUofbGox4T ContentsUUofbGox5Notice0thatthetwo0vbGoxesarealignedsothatthebGottomsarelevel;UalsothereisalittleFuspaceatthebGeginningofeachlineandalsobetweenFuthevboxes.lActually*,IothereasontheseIspacesappGearisrathersubtle.mUnlessalineendsinacontrolword,Kthereisalwaysaspace(bGetweenthelastentryinonelineandthe rstoneinthenextline.R?F*orthisreasonthe]spacebGetween]thevboxescomesfromtheendofthelinecontainingtheclosingbraceof;the rstvbGox.KySimilarly*,thespaceatthebeginningofthelineiscausedbythespace73J]f63׍L̍󙚉ff|( ff AUUTU>'ExXintro(CanadianspGelling)X0Section9:qDiggingalittledeeper  fffff|(׍)aftertheopGeningbraceofthehbox.WThesespacescanbeavoidedby\commentingout"the endQoftheline,Rthatis,byputtinga%immediatelyaftertheclosingbraceofthe rstvbGoxoryttheopGeningbraceofthehbox.$IfytyoutrytoputsomevbGoxestogetherandaccidentallygetuextraspacebyforgettingtocommentouttheendoftheline,~ you'reingoGoducompany*.SomeUUveryableandexpGeriencedTU>'ExXusershavedonethesamething!Extraspace,sayonecentimetre,canbGeaddedbyputtingan\hskip?1cm bGetweentheMvbGoxes.9Theycanbealignedsothatthetopsarelevelbyusing\vtopJinsteadof\vbox.MakingUUthesetwoUUchangesresultsin:UUContentsofbGox1UUContentsofbGox2UUContentsofbGox3pContentsUUofbGox4pContentsUUofbGox5+ǍW*ecancombinevbGoxes,hboxes,vrules,andhrulestogetbGoxedtext.VPHowmightweconstructQsuchabGox?ROnewayistotakethematerialtobGeboxedandputitinanhbGoxprecededV>andfollowedV>byavrule.tThenputthisinavbGoxwithhrulesabGoveandbGelowit.ThisUUgivesus:\vbox{\hrule\hbox{\vrule{}?Thetexttobeboxed\vrule}\hrule?}whichUUresultsinӉffdǍffUUThetexttobGeboxedffffffdThiszproGducesboxedmaterial,butthereisnomarginarounditandsoitlooksverycrampGed'(ofcourseTU>'ExXisjustgivinguswhatweaskedfor).>W*ecanimprovethespacingby puttinga\strutatthebGeginningofthehbGoxtomakeitalittletalleranddeepGer.Y\ThisgivesUUus:󙚉ffd ffUUThetexttobGeboxed fffffd$.>Exercise9.4 WhyisitthatwewereforcedtoaddextraspaceabGoveandbGelowthetextbutUUnotbGeforeandafterit?74Kdl63׍L̍󙚉ff|( ff AUUTU>'ExXintro(CanadianspGelling)X0Section9:qDiggingalittledeeper  fffff|(׍).Exercise9.5 UsethemethoGdofboxingmaterialtoputtextcentredinabGoxwhich extendsUUfromthelefttotherightmargin.$.UUExercise9.6 BystackingninelittlebGoxes,makethefollowingmagicsquare:5X+fh=󙚉ff ww ffUU6 fffff ww󙚉ff ww ffUU1 fffff wwy+󙚉ff ww ffUU8 fffff ww ̍=󙚉ff ww ffUU7 fffff ww󙚉ff ww ffUU5 fffff wwy+󙚉ff ww ffUU3 fffff ww=󙚉ff ww ffUU2 fffff ww󙚉ff ww ffUU9 fffff wwy+󙚉ff ww ffUU4 fffff ww.Exercise9.7 Noticethatthemagicsquareinthepreviousexercisehasinternallinesthatareutwiceasthickastheoutsideones.Also,}thereisatinyspaceattheintersectionoftheinternalUUlines.qFixupthemagicsquaresothisdoGesn'thappen..uExercise9.8 W*riteamacro\boxtext#1{::: }whichwilltakethetextbGetweenthebracesanddputabGoxaroundit.T*estyourmacrobymakingupasentencewitheveryotherwordbGoxed.I'm󙚉ff> ffnot fffff>vquite󙚉ff? ffsure fffff?Wwhy󙚉ff% ffsomeone fffff%-3would󙚉ff [ ffdo fffff [this󙚉ffx ffsince fffffxXthe󙚉ffS ffresult fffffS뎑!is󙚉ff~ ffpretty fffff~#,wstrange.NoteUUhowthebaselineandthebGottomofthesurroundingboxesalign.It'seasytomovebGoxesup,down,left,orrightonthepage.mAܿ\vboxcanbGemovedtotherightoneinchbyusing\moveright?1in\vbox{::: UO}.tT*omoveittotheleft,use\moveleft.qSimilarly*,UUan\hboxcanbGemovedUUupordownusing\raiseor\lower..իExercise9.9 Rewritethe\boxtextmacrofromthepreviousexercisesothatallofthetextisaligned(hint:bydefaultthedepthofastrutis3.5pGoints).Thiswouldgiveasen-tence9likethefollowing:I'mff> ffnot fffff>%$quiteff? ffsure fffff?whyff% ffsomeone fffff%,lBwouldff [ ffdo fffff [Athisffx ffsince fffffxtheffS ffresult fffffS뎎 :yis ̍ff~ ffpretty fffff~strange.It's\pGossibleto llaboxwitheitheranhruleorwithdots.Theideaistouse\hrulefillorUU\dotfillRinthehbGox.\hbox?to5in{GettingStarted\hrulefill1}\hbox?to5in{AllCharactersGreatandSmall\hrulefill9}\hbox?to5in{TheShapeofThingstocome\hrulefill17}\hbox?to5in{NoMathAnxietyHere!\hrulefill30}gives75Ln63׍L̍󙚉ff|( ff AUUTU>'ExXintro(CanadianspGelling)X0Section9:qDiggingalittledeeper  fffff|(׍)GettingUUStartedff]1 AllUUCharactersGreatandSmallff9TheUUShapGeofThingstocomeffو17NoUUMathAnxietyHere!ff30IfUU\hrulefillisreplacedby\dotfillwegetGettingUUStarteduT:qōT:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:篫1 AllUUCharactersGreatandSmallQT:qōT:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:D 9TheUUShapGeofThingstocome nT:qōT:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:{*17NoUUMathAnxietyHere!YT:qōT:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:T:30$.Exercise9.10 MakeabGoxedheadlineappGearatthetopofthepagethatisliketheoneusedUUinthismanual.76M}63׍׍)Section10Con=trolwordlist ffff|(/eHereT7isalistofthecontrolwordsgiveninthismanual.qhIfyouwantmoredetailabGout theseUUwordsthanisgivenhere,checktheindexofTheTT<8E3sXbQook.$ControlUUsymbGols\ ?4lg\!?34j\"?11A\'?11\,?34lg\.?11j\/?16A\;?34\=?11lg\>?34j\#?10A\$?6\%?6lg\&?10j\{?10A\}?10\fe? 10lg\`?11j\~?10A\^?10\|?40ڃControlUUwords\AA?12lg\aa?12j\acute?36A\AE?12\ae?12lg\aleph?37j\alpha?35A\angle?37\approx?37lg\arccos?41j\arcsin?41A\arctan?41\arg?41lg\ast?36j\b?12A\backslash?37\bar?36lg\baselineskip?22j\beta?35A\bf?16\biggl?40lg\Biggl?40j\biggr?40A\Biggr?40\bigl?40lg\Bigl?40j\bigr?40A\Bigr?40\bigskip?26lg\break?26j\breve?36A\bullet?36\bye?4lg\c?12j\cap?36A\cdot?36\centerline?26lg\centreline?60j\check?36A\chi?35\circ?35lg\columns?48j\cos?41A\cosh?41\cot?41lg\coth?41j\csc?41A\cup?36\d?12lg\ddag?27j\ddot?36A\def?55\deg?41lg\delta?35j\Delta?35A\det?41\diamond?36lg\dim?41j\div?36A\dot?36\dotfill?49lg\dots?14j\downarrow?41A\Downarrow?41\eject?20lg\ell?37j\endinsert?26A\epsilon?35\eqalign?45lg\eqalignno?46j\eqno?46A\equiv?37\eta?35lg\exists?37j\exp?41A\flat?37\folio?28lg\font?16j\footline?28A\footnote?2777Nn63׍L̍󙚉ff|( ff AUUTU>'ExXintro(CanadianspGelling)jSection10:qControlwordlist  fffff|(׍)\forall?37lg\gamma?35j\Gamma?35A\gcd?41 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