; TeX output 1995.02.02:0019NQ"V cmbx10User'sTGuidetoAMSF on9tsVersion2.2jK`y cmr10JanuaryUU1995Standard;distributionsofTU>VExXordinarilycomewithallthefontsspGeci edin VExX.Additionalfontsdesignedforuseinmathematicsandde nedin1 !", cmsy10AU>'M S-TU>VExXőarenotalways1includedamongsuchfontcollections. [F*orthisreason,ethe/dAmericanMathematicalSoGcietyhascompiledacollection,knownasAMSF*onts,Twhich!containsfontsofsymbGolsandseveralalphabGetscorrespondingtoH&symbGolsandalphabetsusedinAMSH"publications,JincludingtheMathScionlinedatabase.U>Con9tentsofthisdoQcument1.ContentsUUoftheAMSF*ontscollection 卑r. r.r.r.r.r.r.r.r.r.r.r.12.HistoryUUofthesefonts r. r.r.r.r.r.r.r.r.r.r.r.r.r.r.r.r.r.r.33.HowUUtouseAMSF*ontswithL1Ag!TU>VExX 2r. r.r.r.r.r.r.r.r.r.r.r.r.54.HowUUtouseAMSF*ontswithAU>'M S-TU>VExX%r. r.r.r.r.r.r.r.r.r.r.r.85.HowUUtouseAMSF*ontswithplainTU>VExXorothermacropackqages106.UsingUUcyrillicr. r.r.r.r.r.r.r.r.r.r.r.r.r.r.r.r.r.r.r.r.r.127.UsingUUtheextrasymbGolsN9r. r.r.r.r.r.r.r.r.r.r.r.r.r.r.r.r.16References̍r. r.r.r.r.r.r.r.r.r.r.r.r.r.r.r.r.r.r.r.r.r.r.r.r.21AppGendixUUA.PCInstallationGuider. r.r.r.r.r.r.r.r.r.r.r.r.r.22AppGendixUUB.$': cmti10T;extur}'es'v/MacintoshInstallationGuide卑r. r.r.r.r.r.26AppGendixUUC.UnixInstallationGuideߍr. r.r.r.r.r.r.r.r.r.r.r.r.31AppGendixUUD.F*orfurtherinformationr. r.r.r.r.r.r.r.r.r.r.r.r.34AppGendixUUE.F*ontchartsTr. r.r.r.r.r.r.r.r.r.r.r.r.r.r.r.r.r.r.36H +- cmcsc101.ContentsU>oftheAMSFUontscollectionTheUUAMSF*ontscollectioncontainsthefollowingfonts,inthesizesindicated: 9#qqǎTheU>Eulerfamily*,allbuteuexpin5,6,7,8,9,and10pGoint:{(F*rakturU>(German),medium-weightU>andbGold(eufmU2andeufb){(\Roman"U>cursive,medium-weightandbGold(eurmU2andeurb){(Script,U>medium-weightandbGold(eusmU2andeusb){(Euler-compatibleU>extensionfont(euex),in7,8,9,and10pGoint 9#qqǎAdditionalU>sizesofsomeComputerMoGdernmathfonts(the10-pointfontsareU>includedinstandardTU>VExXdistributions):{(bGoldU>mathitalic(cmmib?),in5,6,7,8,and9point{(bGoldU>mathsymbols(cmbsy?),in5,6,7,8,and9point{(mathU>extensionfont(cmex),in7,8,and9pGoint(the10-pGointfontis(includedU>instandardTU>VExXdistributions)*N2Zh1.ContentsUUoftheAMSF*ontscollection4 9#qqǎExtraU>mathsymbGols,in5,6,7,8,9,and10point: {( rstU>series,medium-weightU>(msam){(secondU>series,includingBlackbGoardBold,medium-weight(msbm) 9#qqǎCyrillic,U>developGedattheUniversityofW*ashington{(lightfaceU>(wncyr?),in5,6,7,8,9,and10pGoint{(bGoldU>(wncyb?),in5,6,7,8,9,and10point{(italicU>(wncyi?),in5,6,7,8,9,and10pGoint{(capsU>andsmallcaps(wncysc),in10pGoint{(sansU>serif(wncyss),in8,9,and10pGoint{(virtualU>fontpropGertylist(.vpl) lestoenabletheuseofthesefonts(withU>alternateencoGdingsandtransliterationschemes 9#qqǎComputerU>MoGderncapsandsmallcaps(cmcsc?),in8and9point(the10-pGointU>fontisincludedinstandardTU>VExXdistributions) 9#qqǎTheU>\dummyfont,"usedinAU>'M S-TU>VExXforsyntaxchecking,isprovidedonlyasU>metrics(dummy.tfm/?) 9#qqǎPackqagesU>forusingthesefontswithL1Ag!TU>VExX:|(amsfontsQ,U>aL1Ag!TU>VExXpackqageforusingthefontsmsamU2,msbm,andeufmpin(L1Ag!TU>VExX|(amssymbL,U>aL1Ag!TU>VExXpackqageforde ningenmasse(insteadofselectively)(commandU>namesforallthemathsymbGolsinthefontsmsampandmsbm|(eucalB?,U>aL1Ag!TU>VExXpackqageforusingtheEulerscriptfonteusm|(cmmib57L,U>aL1Ag!TU>VExXpackqageforadaptingthefontde nitionsforcmmib(andU>cmbsy mtoU>scalefromsizes5,7,10insteadofsizes5,6,7,8,9,10|(*.fd<,U>fontde nition les 9#qqǎMacroU> lesforusingthesefontswithplainTU>VExX:{(amssym.tex\,U>a lede ningthesymbGolsinfontsmsampandmsbm{(amssym.def\,U>a lethatloadsthefontsmsamU2,msbmpandeufmandde nes(someU>controlsequencesrequiredbyamssym.tex{(cyracc.def\,U>a lecontainingde nitionsneededforpropGeraccessto(charactersU>inthecyrillicfonts 9#qqǎDoGcumentationU> les:{(amsfndoc.texfܫ,U>thesource leforthisUser'sGuide{(amsfndoc.cyrfܫ,U>thesource leforthetableshowingcyrillicinput(conventions,U>inputbyamsfndoc.tex{(amsfndoc.fntfܫ,U>thesource leforthetablesoftheprincipal10-pGoint(fontsU>intheAMSF*ontscollection,inputbyamsfndoc.texBU;this lemay(alsoU>bGeTU>VExXedbyitself{(amsfndoc.deffܫ,U>themacrosusedtoformatthisUser'sGuide{(amsfndoc.insfܫ,U>thesource lefortheappGendixestothisUser'sGuide,(inputU>byamsfndoc.texBU;this lemayalsobGeTU>VExXedbyitselfEach+EfontataparticularsizeisprovidedinsevenstandardTU>VExX+magni cations,magsteps$0through5,.includingmagstephalf(excepttheT;extur}'es/Macintoshpack-age,UUwhichonlyincludesmagni cations0and1;seetheinstallationinstructions).TheRphilosophyunderwhichtheEulerfontswereimplementedwasdi erentfromߍthatusedforComputerMoGdern,andtheresultisalowerߍdegreeof\meta-ness".ZF*orMrthatreason,ytheappGearanceofthesefontsisnotverygoGodMratsmallSN|È2.HistoryUUofthesefontswÇ34sizeswhenoutputonlow-resolutiondevices,inparticularonscreens.2Evenso, theUfontsareincludedinAMSF*ontsinallthesizesandmagni cationso ered,ontheassumptionthattheprintedoutputwillbGepreparedonadeviceofhigherresolutionUU(atleast300dpi)wherethise ectwillnotbGenoticeable.F*ontUUchartsaregiveninAppGendixD.1.1.F on9tU>namingconventionsDevelopGersԼoffontsforusewithTU>VExX,atleastthoseusingm#R cmss10MET*AFONT,generallytrytomakethenamesdistinctive,Җsothatauserwillknowtheoriginofthefontbythefontname.(F*ormostofthefontsintheAMSF*ontscollection,(the rsttwolettersUUidentifythefontsource,asfollows: 9#qqǎ\CM":U>ThesefontsarebaseddirectlyonthespGeci cationsforKnuth'sComputerU>MoGdernfonts,asdescribedinV*olumeEof!p0J cmsl10Computers&TypGesettingU>[DEK86E]. 9#qqǎ\EU":U>ThesearemembGersoftheEulerfamily*,describedbelow. 9#qqǎ\MS":U>ThesefontsofmathsymbGolsweredevelopGedbyorunderthedirectionofU>theAMSsta . 9#qqǎ\WN":U>ThesecyrillicfontsweredevelopGedatorunderthedirectionoftheUniversityU>ofW*ashingtonHumanitiesandArtsComputingCenter,andaredistributedU>withtheirpGermission.Thetfontcalleddummy"@٫isaspGecialcase;VitwasdevelopGedaspartoftheStanfordUniversityUUTU>VExXPro8ject,andfollowsnoparticularnamingconvention.F*orȬinformationonComputerMoGdernfontsotherthanthosespeci callynameddhere,andonotherfontsingeneral,theTU>VExXcUsersGroup(TUG)isthebGestUUsource.qF*orTUG'saddress,seethesectionF orTfurtherinformation.r2.HistorUTyU>ofthesefontsWhen:theAMS:*bGeganusingTU>VExXtoproGduceitspublications,NtheavqailablecomplementeofsymbGolswasfoundtobGeinadequate. OSeveralalphabGetsusedextensivelyassymbGolswerenotavqailableeither. \hWhiledevelopmentofthesymbGolsscouldbeundertakenbyin-housepGersonnel,usingtheexistingTU>VExXVsymbGolfontasamoGdel,#thecreationofnewF*rakturandscriptalphabetsrequiredtheassistanceUUofsomeonewithexpGerienceinfontdesign.2.1.EulerWith`DonaldKnuth'sassistanceandencouragement,HermannZapf,oneofthepremier+fontdesignersofthiscentury*,wascommissionedtocreatedesignsforF*rakturandscript,|andforasomewhatexpGerimental,uprightcursivealphabGetthatwouldVrepresentamathematician'shandwritingonablackbGoardandthatcouldbGeusedinplaceofitalic.A-ThedesignsthatresultedwerenamedEuler,jinhonorof؃LeonhardEuler,Naprominentmathematicianoftheeighteenthcentury*.PZapf'sdesignss=wererenderedinMET*AFONTrcoGdebygraduatestudentsatStanford,working!RunderKnuth'sdirection;2theproGcessbywhichtheMET*AFONT!Efontswere#N4|È2.HistoryUUofthesefonts4implemented>isdescribGedinareportbyDavidSiegel[DRS85]..TheEulerfonts wereMathematics,writtenbyhimandtwoco-authors[GKP88]. DuringthecourseofpreparingthatbGook,n4anumbGeroferrors,n4particularlyinspacingparametersa ectingtheplacementofsub-andsupGerscripts,Ýwerediscovered.zsAlltheseݞerrorshaveݞbGeencorrectedinthenewmedium-weightݞversionsoftheEulerfontsa(almostnobGoldfacesymbGolswereusedinConcrete:Mathematicsi}).kKnuthalso{?noticedthatthestyleofsomesymbGolsintheComputerModernextensionfont,KinSparticulartheintegralsign,KwastoGoslantedtobGeattractivewithEuler,and>consequentlyhepreparedanew(partial)extensionfontforusewithEuler.KnuthComputerMoQdernfon9tsforuseinmathOnlyHthe10-pGointsizeoftheComputerModernboldmathitalic(whichincludesGreek),;'symbGol,and 0mathextensionfontsareincludedinstandarddistributionsofNTU>VExX.SincethesesymbGolsareoftenneededinmathematics,othersizeshavebGeenconstructed,usingtheprinciplesdemonstratedinKnuth'sComputerModernTypGefacesҫ[DEK86E],UUandincludedintheAMSF*ontscollection.2.3.Sym9bQolsTwoyfontsof\extra"symbGolsareincludedintheAMSF*ontscollection.vThesearenamedmsamΫandmsbm,SandhavebGeennewlyimplementedin\new"MET*AFONT(MF84);they~Jreplaceearlierfonts(namedmsxmandmsym~>)thatwerede nedinold] MET*AFONT\ǫ(MF79).ThesefontscontainsymbGolsneededinthepublishingprogram3/oftheAMS,includingtheMathScionlinedatabase,andincludetheuppGercaseUUlettersofanalphabetknownasBlackbGoardBold(5 msbm10A b> cmmi10;:::;Z).2.4.CyrillicTitlesofbGooksreviewedinMathematical߂Reviews raretraditionallyrenderedintheirmoriginallanguage.F*orbGooksmpublishedinRussianorotherSlaviclanguages,thisfrequentlyrequiresuseofthecyrillicalphabGet.DAcyrillicfontwasdevelopGedatAMSusing3MET*AFONT79withtheam`fontsasamoGdel.AThisfontwasorganizedinaFmannersuitableforusewiththetransliterationschemeadoptedbyMRFin1980,and4containedonlythoseletterswhichappGearincurrentmathematicalliterature.Inoparticular,thismeantthatthelettersdroppGedfromtheRussianalphabetafter#etheRevolutionof1917,Vandsomelettersusedinnon-SlaviclanguagesnowrenderedYincyrillic(suchasAzerbaijani,ZfromwhichnomathematicalliteratureiscurrentlyUUreviewedinMR)wereabsent.1Nap3.HowUUtouseAMSF*ontswithL1Ag!TU>VExX\p54Ink1988,1theHumanitiesandArtsComputingCenteroftheUniversityof W*ashington2undertoGokafontdevelopmentpro8jectforsuppGortofscholarsinSlaviclanguages.UKThe,fontsdevelopGedthroughthispro8jectincludeseveraldi erentfontlayouts.;OnelayoutisbasedonthatoftheoriginalAMScyrillicaugmentedwith`xcapsThe>fontcmcsc10)gisreferencedinplain.tex4haandshouldbGeincludedinallstandardTU>VExXdistributions. However,Knuthdidnotgeneratethisfontinanyothersizes.The^AMSF*ontscollectionincludes8and9-pGointsizes,ageneratedaccordingtothesameUUprinciplesasotherCMfontsofthesesizes.2.6.Dumm9yU>fontTheWdummyfontcontainsnoligatureorkerninginformation,andalldimensionsandparametervqaluesaresettozero.W>Thisisapseudo-font,whichhasonlygeneralfontȥmetricsandnocharacters.˷No.pkQAor.gf lesareneededforthisfont;MitisprovidedUUonlyin.tfmand.mfjform.ThedummyfontisusedinAU>'M S-TU>VExXBtoimplement\syntaxchecking."(Syntaxcheckingisactivqatedbythe\printoptionscommandasdescribGedinTheJoyofTU>VExXȫ[MDS86].)¹InthismoGde,Lethedummyfontreplacesalltheusual\printing"fonts,!wsothatTU>VExXnneveraccumulatesanytexttobGeset,!wandnevertriestowriteoutapage,butintheproGcessofreadingtheinput le,checksallcontrolsequencesforsyntacticcorrectness.nInthismoGde,)haninput lewillbeprocessedpGerhaps930percentfasterthanifitwereactuallybGeingset.sHowever,someerrorsandconditionsarenotdetectedduringasyntaxcheck;inparticular,^overfullbGoxescannotUUbGedetecteduntilsettingactuallyoccurs.V3.HowU>touseAMSFUontswithL1AT(4VE1X3.1.General.TheseČinstructionsareforcurrentL1Ag!TU>VExXp(version2e,Zdated1994orlater).mIfyouhaveversion2.09ofL1Ag!TU>VExX,dated1993orearlier,jRyoumusteitherupgradetocurrentL1Ag!TU>VExX(recommended),(orinstallversion1.1ofAMS-L1Ag!TU>VExXandrefertoitsuser'sUUguideforinstructionsonusingtheAMSF*ontscollection.T*o"usetheAMSFontscollectionwithL1Ag!TU>VExX"dyouchoGosefromanassortmentof,IL1Ag!TU>VExX,`packqages'thatprovidevqariouskindsofaccesstothefonts,bcallingthe@N6`S3.HowUUtouseAMSF*ontswithL1Ag!TU>VExX4packqages thatyouneedinagivendoGcumentthroughstandardL1Ag!TU>VExX\usepackage statements.qF*orUUexample,thestatement\usepackage{amsfonts}callskintheamsfontspackqage,4whichkprovidesblackbGoardboldlettersandselectiveaccessUUtothemathsymbGolfontsmsamandmsbmUI.TheUUcurrentlistofpackqagesis amsfon9ts; F*orU>blackbGoardboldletters,frakturletters,andmiscellaneoussymbGols. amssym9boftheamsfontspackqage,de nesthefullsetofsymbGolnamesU>forthemsampandmsbmfonts. eufrak.F*orU>frakturletters. eucal(0MakesU>\mathcaluseEulerscriptinsteadoftheusualComputerMoGdernscript. euscript72OldU>nameoftheeucalpackqage,nowobsoletebutincludedforconvenienceU>inprintingpre-existingdoGcuments.AlldoftheabGovedpackqageshavea`psamsfonts'optionthatshouldbGeusedifand3onlyifyourcopyoftheAMSF*ontscollectionistheY&Y/BlueSkyResearchPostScriptyversion.4Inthatversion,ׂthefont lesarenotprovidedinallthesizes10,9,8,7,6,5,@but;Lonlyinsizes10,7,5,withsizes6,8,9proGducedbyinterpGolation.iInpracticeit'seasytotellifyouneedtousethepsamsfontsoption:9you'llgetanerrorUUmessageabGoutamissing.tfm le:!?Font\U/AMSa/m/n/9=msam9notloadable:Metric(TFM)filenotfound.wherethementionedfontnameisoneoftheAMSMfontnames(msam,msbmv,eufm,ketc.),and3thefontsizeis6,k8,or39. ^IfthishappGenstoyou,kloGokatyour\usepackageUUstatementsandchange\usepackage{amssymb}to\usepackage[psamsfonts]{amssymb}or~\usepackage{eucal}to\usepackage[psamsfonts]{eucal}andUUsoforth.ThereasonthatuseofthePostScriptAMSfontsisexplicitlymarkedinindividualdoGcumentsisthattheinterpGolationprocessusedforsizes6,8,9doesnot[proGducecharactermetricsthatareidenticalwiththoseofthenoninterpGolatedfont{m lesforthosesizes.Ifthesediscrepanciesweresimplyignored,doGcumentsexchangedbGetweencolleaguesmighteasilysu erunexpGectedchangesinlinebreaks(andihencepGossiblyalsopagebreaks),ewithoutJaanywarnings.W#Asiitis,ifyou nditnecessaryJtoaddorremoveJthepsamsfonts;voptioninordertoprintacolleague'sdoGcument,jyou3arefreetogoaheadanddoso,butthefactthatyoumustmakethat.changeshouldbGeunderstoodasareminderthatasmallpossibilityofchangedlineUUbreaksorpagebreaksdoGesexist.Similarly*, apackqage\cmmib57isprovidedtoprovideanalogousfontde nitionsfor}thefontscmmib!: andcmbsy(yes,bGothinthesamepackqage,despitethename),for4"thoseuserswhohave4"theY&Y/BlueSkyResearchPostScriptversionsofthosefonts.qTypicalUUusageis:\documentclass{article}PN`S3.HowUUtouseAMSF*ontswithL1Ag!TU>VExX[S74\usepackage{cmmib57} 3.2.Blac9kbQoardU>boldletters(uppercaseonly).Theamsfontspackqagede nesa`mathalphabGet'command\mathbbforprintingletters$oftheblackbGoardboldalphabetthatresidesinthemsbmmathsym9bQols.Theamssymbpackqagede nesmathsymbGolcommandsforalltheextramathsymbGolsminthemsam`andmsbmfonts,saslistedinthetableinx7.Thusifyouwanttousethe\blacktriangle2 msam10Nand\nsubseteq*symbGols,NtheeasiestwayistoputUUthestatement\usepackage{amssymb}inUUthepreambleofyourdoGcument.IfyouwantmoreselectiveaccesstothemathsymbGolsinthosefontsyoucanuse1theamsfontspackqageinsteadandde nemathsymbGolcommandsindividuallyusingUUL1Ag!TU>VExX's\DeclareMathSymbol(cf.[LFG]or[GMS94]):\usepackage{amsfonts}\DeclareMathSymbol{\blacktriangle}{\mathord}{AMSa}{"4E}\DeclareMathSymbol{\nsubseteq}{\mathrel}{AMSb}{"2A}ThisalternativemightbGeusefultoyouifaddingtheamssymbpackqagetoyourdoGcumentUUleadstoanerrormessageoftheform!?TeXcapacityexceeded,sorry(hashsize=3000)ThiscouldhappGenifyouhaveanolderversionofTU>VExXwitharelativelylowlimiton/thenumbGer/ofcommandsthatcanbede nedinasingledocument.(Butinthatqcase, notethattheremaybGecon gurationoptionsforincreasingthatlimit;checkUUthedoGcumentationforyourTU>VExXsystem.)3.4.EulerU>F rakturletters.Amath'alphabGetcommand\mathfrakforusingF*rakturletterssuchas8%n eufm10A mgHin!mathcanbGeobtainedbyusinganyofthepackqagesamssymb,scriptletters(uppQercaseonly).The mainpurpGoseoftheeucalpackqageistochangeL1Ag!TU>VExX's\mathcalcommandsoUUthatitproGducesEulerscriptinsteadofComputerModerncalligraphicletters:,ޤCMUUcalligraphic:e˷ABCDEFGHIJKLMNOPQRSTUVWXYZ?B6EulerUUscript:e;LR eusm10ABCDEFGHIJKLMNOPQRSTUVWXYZ_N8V4.HowUUtouseAMSF*ontswithAU>'M S-TU>VExX4ThereaisalsoanoptionmathscrfortheeucalpackqagethatcausesEulerscriptto bGe-associatedtoa\mathscrcommand,leavingthe\mathcalcommanduna ected.ThisUUimitatesthebGehaviorofthepredecessorpackqageeuscript.@3.6.Univ9ersityU>ofW ashingtonCyrillicfon9ts.There`isnoAMSpackqageforL1Ag!TU>VExXatthepresenttimetosuppGorttheuseofCyrillicRlanguagesinL1Ag!TU>VExX;doGcumentswiththewncy*!fonts.ProGducingaproperCyrillic)packqageinvolvesratherdicultquestionsofinputandoutputencoGdings,forywhichitwouldbGeusefultorelyongeneralmechanismsprovidedbyL1Ag!TU>VExX;andthatareaofL1Ag!TU>VExXhasbGeenanareaofactivedevelopment,atleastthroughthe}endof1994.zTheonlypGossibilitythatcanbesuggestedatthepresenttimeistoconsulttheL1Ag!TU>VExXdoGcumentation[LFG],[L94]andusedirectlythecommandsdescribGedthere,suchas\DeclareFontFamily,\DeclareFontShape,and\symbol.F*urther4newsonthissub8jectwillbGereportedintheAMSF*ontsREAD.ME,S leasitbGecomesUUavqailable.ߍM!4.HowU>touseAMSFUontswithA(4'MȻS-T(4VE1X@In-TheJoyofTU>VExX,MichaelSpivqakdescribGesvariousfontsthatareusedinmathematicsinadditiontothefontsprovidedwiththestandarddistributionsofTU>VExX.TworeferencesinparticularareofinterestwithrespGecttoAMSF*onts:thesection9F on9ts$inmathmoQdeinChapter19,$andAppGendixG,F urtherfon9ts.TheH< rstdescribGestheuseoflettersfromalphabets,includingF*raktur,andthesecond,UUmostlynonalphabGeticsymbols.InstructionsqforusingthefontsoftheAMSF*ontscollectionwithAU>'M S-TU>VExXarealsogivenintheUser'spGuidetoAU>'M S-TU>VExXpV*ersion2.1ҫ[AMS91]andinAppGendixUUFofeditionsofTheJoyofTU>VExX[MDS90]dated1990orlater.AdditionalafontstobGeusedwithAU>'M S-TU>VExXHshouldbespeci edatthetopoftheK[doGcumentinput le,MZinwhatisknownasthe\preamble."ntThearrangementofcommandsUUatthetopofaninput leisthefollowing:\input?amstexhpreambleUUcommandsi\documentstyle{...}AU>'M S-TU>VExXprovidesYasimplemethoGdforaccessingmostofthefontsintheAMSF*onts!collection.|ThetwoextrasymbGolfontsandEulerF*rakturareloadedautomatically,6bythepreprintstyle(amsppt.sty4).dIfyouareusingAU>'M S-TU>VExX,butnotthepreprintstyle,EthemethoGdusedtoloadthesefontsandde netheassoGciatedsymbGol6namesdependsonhowmanysymbGolswillbeneeded. jIfalotofthesymbGolswillbeneeded,oryouaren'tworriedabGoutmemoryspaceandjustwanttodowhatiseasiest,XallthreefontswillbGeloadedandthesymbGolnamesde nedif_JyoutypGethecommand\UseAMSsymbolsinthepreamble.Thiswillloadthe leamssym.tex4,inwhichallthesymbGolnames(morethan200ofthem)arede ned.IfZonlyafewsymbGolsfromthesefontsareneeded,dthecommands\loadmsam,\loadmsbm,nandi\loadeufmwillloadthemedium-weightiversionsofthetwoextrasymbGolm fontsandEulerF*rakturrespGectively*.Thecommand\newsymbolcanthen jנNV눫4.HowUUtouseAMSF*ontswithAU>'M S-TU>VExXQ94bGequsedtode nejustthosesymbolsthatareneeded;itsuseisdescribedinx㎫7 UsingTtheextrasym9bQols.*Two*Vsizesoffonts,suitableforbGody*VtextandforpassagesrequiringsmallerPtypGe(e.g.abstractsandfootnotes),areincorporatedinthepreprintstyleamsppt.sty4.ZTheseareaccessedthroughthecontrolsequences\tenpointand\eightpoint,9xwhich2areordinarilyreferredtoonlybyhigher-levelcommandsthatidentifythekindoftextbGeinginput(e.g.\title,\abstract,\footnote).qMostfonts2intheAMSF*ontscollectionhave\load...instructionsde nedinAU>'M S-TU>VExXand2RwillbGeaccessedproperlyforusewiththepreprintstylewhenthe\loadinstructionsareincludedinthepreambleofthedoGcumentinput.Ifyouarenotusingthepreprintstyle,youcanusethefontde nitionsinamsppt.sty:EasamoGdel.4.1.EulerTheEulerfontsarede nedonlyinmathmoGde,insizesappropriatefortextandtwo5ordersofsub-andsupGerscripts.gTheycanbeactivqatedbyinvokingthepropGer\load]instructionsbGeforethe\documentstylecommand,+_inthepreambleofapapGerinwhichthefontsaretobGeused.(Themedium-weightF*rakturfontisactivqated5automaticallybythepreprintstyle.)gTheEulerfontscanbGeactivqatedbyUUthefollowingcommands:\loadeufmEulerUUF*rakturmedium(automaticwiththepreprintstyle)\loadeufbEulerUUF*rakturbGold\loadeurmEulerUUcursivemedium\loadeurbEulerUUcursivebGold\loadeusmEulerUUscriptmedium\loadeusbEulerUUscriptbGoldAfterWtheeufm΢fonthasbGeenloaded, themedium-weightF*rakturletterscanbGe>producedbytyping\frakfollowedbythedesiredletter.F*orexample,y$\frakg܁\frakA$C׫yieldsgA.=NAU>'M S-TU>VExXC2.1alsode nes\eufm,x\eufb,\eurm,\eurb,\eusmUUand\eusb4.2.ComputerU>MoQdernboldmathitalicandsym9bolsTheComputerMoGdernboldmathitalic(cmmib?)andboldmathsymbol(cmbsy?)fontscanbGothbeloadedbythecommand\loadbold;aFtherearenoprede nedcommandsӰtoloadthemseparately*.\loadboldmustbGeinvokedinthepreambleofUUthedoGcumentinput le.Aw1ratherwelabGoratemechanismhasbeende nedinAU>'M S-TU>VExXw1tosimplifyaccessutobGoldlettersandsymbols,=inmathmodeonly*.(ThreecontrolsequencesareUUavqailable,eachofwhicha ectsaparticularclassofcharacters:ffff=ff=  *AdditionalfontsfromtheAMSF*ontscollectioncanbGeaccessedeasilyinAU>'M S-TU>VExX. However,usersshouldbGeawarethatTU>VExXlimitsthenumbGerofmathmoGdefontfamiliesto16,Xofwhich11areprede nedinAU>'M S-TU>VExX.OnlythoseadditionalfamiliesshouldbGeactivqatedthatwillactuallybeusedinadocument,toUUavoidexceedingthelimit. {~N10 n5.HowUUtouseAMSF*ontswithplainTU>VExXorothermacropackqages4\boldaforUUasingleletterornumeral \boldkeyaforUUothersymbGolsthatappearonthekeyboard\boldsymbolaforUUasymbGolspeci edbyasinglecontrolsequenceThese^+facilitiesaredescribGedinmoredetailintheUser's.YGuidetoAU>'M S-TU>VExXV*ersionUU2.1!1[AMS91]andeditionsofJoy0publishedin1990orlater[MDS90].4.3.ComputerU>MoQdernmathextensionfon9tSmallerssizesofthemathextensionfontareappropriateforuseintextsmallerthan>ten-pGointandinsub-andsuperscripts. Theyareprovidedautomaticallyfortheseenvironmentsinthepreprintstyle.NIfyouarenotusingthepreprintstyle,_you]canusethefontde nitionsineitheramsppt.sty;;orAppGendixE]ofTheTU>VExXbGook[DEK86A]UUasamoGdel.4.4.ExtraU>sym9bQolsThe:medium-weightversionsofthetwoextrasymbGolfontsareavqailableautomati-cally*,"includingallthesymbGolnames,ifyouareusingthepreprintstyleorifyouhaveospGeci ed\inputu5amssym.eIfyouwishtoloadthesefontsseparately*,usetheappropriate;controlsequence\loadmsamor\loadmsbminthepreambleofyourdoGcument.UIf:youloadthefontsseparately*,safewsymbGolswillbede nedwhenoneofMthefontsisloaded,butmostmustbGede nedusingthe\newsymbolcommandbGefore?theycanbeused.1Seex7UsingEtheextrasym9bQols?forinformationonbGothUUthesymbolnamesandonusing\newsymboltode nethem.4.5.CyrillicCyrillicisnotreferredtointheAU>'M S-TU>VExX lesasdistributed.,sThecyrillicfontsincludedinAMSF*ontsareintendedforusemainlyintext, [notassymbGolsinmath.DetailedainstructionsforloadingandusingcyrillicappGearbelowinx Ӆ6Usingcyrillic.4.6.Caps/smallU>capsCaps/smallcapsareloadedautomaticallybytheAU>'M S-TU>VExXpreprintstyleforuseinten-pGointandeight-pGointtext. Ifyouarenotusingthepreprintstyle,5youcanusethefontde nitionsineitheramsppt.sty;orAppGendixEofTheh0TU>VExXbook[DEK86A]UUasamoGdel.4.7.Dumm9yU>fontNospGecialactionisneededtousethedummyfontwithAU>'M S-TU>VExX.ItisalreadybuiltUUintothesyntaxcheckingproGcedure. h&5.HowU>touseAMSFUontswithplainT(4VE1XorothermacropUTackagesIfTyouarenotusingL1Ag!TU>VExXBorAU>'M S-TU>VEXBthentherearetoGomanyvqariablesforustoprovidemuchspGeci cguidance.{Itwillbenecessarytoassumethatyoueither #N!5.HowUUtouseAMSF*ontswithplainTU>VExXorothermacropackqages114haveFsomeexpGeriencewithTU>VExXFmacrosorhaveFaTU>VEXnicianavqailabletohelpyou. However,UUsomegeneralguidelinesmaybGehelpful.TwoUUmoGdelsforde ningfontsshouldbGeaccessibletomostusers: 9#qqǎAppGendixh-Eg!ofTheTU>VExXbookqcontainssize-speci cfontde nitionsfor\tenpointC?,i\ninepoint@Mand\eightpointthatpGermitsize-switching,iin-cludingUUsuppGortofmathematics. 9#qqǎamsppt.styH,Cthe leofmacrossuppGortingtheAU>'M S-TU>VExX-preprintstyle,containsUUsimilarfontde nitions,\tenpointand\eightpoint.Theffont-size-switchingfacilitiesofL1Ag!TU>VExXfarenotrecommendedasamoGdelbGecausetheyincludemanyfeatures(suchasloadingfontsondemand)thatmakethem+utoGocomplextobeeasilybecopiedforusesoutsideofL1Ag!TU>VExX*exceptbysomeoneUUwithsubstantialTU>VExXexpGertise.Before=9attemptingtoloadallavqailablefontsintoeveryTU>VExX=3job,B determine(ifyoupcan)howmanyfontscanbGeaccommodatedbytheimplementationofTU>VExXyouUUareusing.qItisgenerallyagoGodUUideatoloadseldom-usedfontsselectively*.5.1.EulerThe7followingcommandswillloadthemedium-weightEulerF*rakturfont,=andcanbGeUUusedasamodelforaccessingtheotherEulerfonts.\font\teneufm=eufm10\font\seveneufm=eufm7\font\fiveeufm=eufm5\newfam\eufmfam\textfont\eufmfam=\teneufm\scriptfont\eufmfam=\seveneufm\scriptscriptfont\eufmfam=\fiveeufm\def\eufm#1{{\fam\eufmfam\relax#1}}IndividuallettersintheEulerfontsareaccessiblebytheordinarylettersonyour8WkeybGoard,qoncethefonthasbGeenloadedandnamedbyacontrolsequenceequivqalentUUto\eufm.Themedium-weightF*rakturfont,N eufmN,N canalsobGeloadedby\inputamssym.def;UUthisloadsthetwoUUextrasymbGolfontsaswell.5.2.ComputerU>MoQdernboldmathitalicandsym9bolsThecmmibandcmbsyfontscanbGeloadedandmadeaccessibletomathinten-pointenvironmentsUUbythefollowingcoGde:\font\tencmmib=cmmib10 \skewchar\tencmmib='177\font\sevencmmib=cmmib7?\skewchar\sevencmmib='177\font\fivecmmib=cmmib5 \skewchar\fivecmmib='177\newfam\cmmibfam\textfont\cmmibfam=\tencmmib?\scriptfont\cmmibfam=\sevencmmib?\scriptscriptfont\cmmibfam=\fivecmmib >N12 N5. HowU>touseAMSF*ontswithplainTU>VExXorothermacropackqages4\font\tencmbsy=cmbsy10 \skewchar\tencmbsy='60 \font\sevencmbsy=cmbsy7?\skewchar\sevencmbsy='60\font\fivecmbsy=cmbsy5 \skewchar\fivecmbsy='60\newfam\cmbsyfam\textfont\cmbsyfam=\tencmbsy?\scriptfont\cmbsyfam=\sevencmbsy?\scriptscriptfont\cmbsyfam=\fivecmbsyThe(TU>VExX(primitive\mathcharmustbGeusedtoaccessindividualcharactersfromafontinmathmoGde.G\mathchar,ulikethe\charprimitive,urequiresthatyouknowthe ypGositioninthefontofthecharacteryouareaccessing.2However,;\mathcharalsorequiresthatyouspGecifythe\class"andthefamilyofthemathcharacterbGeing[accessed.$SeeChapter17ofThe°TU>VExXbookformoredetailsontheuseof\mathchar,=,asۚwellas\mathchardef,whichwillallowyoutode neyourownmacroUUnamesforindividualcharactersinthesefonts.$Note: OThe leamssym.defBC.containsaconvenientmacro,$\hexnumber@,rto9determinethefamilynumbGer9ofthefontbeing$accessed0Ithrough\mathchar.F*orexample,'the\mathchar$statement topropGerlyaccesstheboldalphaintheCMMIB }font$wouldUUbGe:8\mathchar"0\hexnumber@\cmmibfam0B5.3.ComputerU>MoQdernmathextensionfon9tTheB10-pGointcmex `xfontisloadedbyplain.tex4'. T*oinstallthe7-pGointsizeappropriateforsub-andsupGerscriptsinaten-pointmathenvironment,includetheUUfollowingcoGdeinyour le:\font\sevenex=cmex7\scriptfont3=\sevenex?\scriptscriptfont3=\sevenexT*osuseothersizesimpliestheuseofswitchable-sizefonts,ʺwhichmaybGeimplementedUUaccordingtothemoGdelscitedatthebeginningofthissection.5.4.ExtraU>sym9bQolsDetailedtinstructionsforaccessingthemsamandmsbmfontsaregiveninxܫ7UsingtheTextrasym9bQols.5.5.CyrillicSeeUUx6UUUsingTcyrillicforinstructions.5.6.Caps/smallU>capsThew10-pGointcmcsc#߫fontisloadedbyplain.tex4\. ,T*ousethesmallerversions impliesQtheuseofswitchable-sizefonts,AwhichmaybGeimplementedaccordingtotheUUmoGdelscitedatthebeginningofthissection. N6.UsingUUcyrillic1345.7.Dumm9yU>fontThe6dummyfontwasdesignedtobGeusedforsyntaxchecking. jThegeneral techniqueisdescribGedinAppendixDwofTheTU>VExXbook,,p.401.f3ThishasbeenimplementedUUinthe leamstex.tex77,whichcanbGeusedasamodel./6.UsingU>cyrillicThecyrillicfontsintheAMSF*ontscollectionhavebGeendesignedsothatinputusingRthetransliterationconventionsRofMathematicalReviewswillbGeconverteddirectly"8tocyrillictext.`Othertransliterationschemesexist,,qaswellasmethoGdsforkeying(directlyfromthekeybGoardtoaccesscyrilliccharacters.AW*ehaveincludedtwo6setsofvirtualfontsinthisdistribution,(owhichprovideaccesstothecharactersofthecyrillicfontsthroughtheKOI-8orAlternativnyjV*ariant(AV)encoGdings.At>thepresenttimemacrosuppGortisprovidedonlyfortheMathematicalReviewstransliterationrscheme;0touseoneoftheotherencoGdings, youmustseeksuppGortfrom`othersources.rAlso,c\theinstructionsinthissectionareunsuitableforL1Ag!TU>VExX;they$applyonlytoAU>'M S-TU>VExX,plainTU>VEX,andothermacropackqagesthatuseplainTU>VExXUUfontloadingmethoGds.TheUUfollowingcyrillicfontsareincluded:wncyr1F(upright),UUinsizes5,6,7,8,9,and10pGointwncyb1F(bGold),UUinthesamerangeofsizesaswncyrwncyi1F(italic),UUinthesamerangeofsizesaswncyrwncysc6C(capsUUandsmallcaps),insize10pGointwncyss6C(uprightUUsansserif),insizes8,9,and10pGointThe lecyracc.def: |,whichisincludedintheAMSF*ontscollection,mustbGe inputctoanydoGcumentusingthecyrillicfontsasde nedwiththeAMSblayout.Since?2thecyrillicalphabGetcontainsmorelettersthantheromanalphabet,ysomecyrillicXlettersareaccessedbycombinationsofromanletters,accentedletters,orcontrol$sequences.C cyracc.def;containsthede nitionsoftheseaccentsandcontrolsequences.qIfUUthis leisnotinput,somecyrillicletterswillbGeinaccessible.6.1.MakingU>cyrillica9v\railabletoadoQcumentIfyouareusingplainTU>VExX,includethefollowinginstructionsnearthetopofthedoGcumentWZinput letomakethe10-pGointcyrillicfontavqailableforuseintext(seebGelowUUforcyrillicinmath):\input?cyracc.def\font\tencyr=wncyr10\def\cyr{\tencyr\cyracc}Ifyourequirecyrillictextinmorethanonesize,Ryoumusttakeadi erentapproachinvde ning\cyr.*AnappropriatemoGdelappearsinAppendixEZofThecTU>VExXbook[DEK86A],4#pages414{15. 1Thede nitionof\cyrshouldbGeincorporatedintosize-spGeci cmacrossuchas\tenpointand\eightpointsimilarlytowhatisdonethereUUfor\bf.qDon'tforgettoincludethecommand\cyraccinthede nition.\N146.UsingUUcyrillic4IfRyouareusingAU>'M S-TU>VExX&andthepreprintstyle,.thefollowinginstructions shouldCEbGeincludedinthepreambleofyourdoGcumentinput letomakecyrillicavqailableUUin10-pGointand8-pGointtext:\input?cyracc.def\catcode`\@=11\font@\tencyr=wncyr10\font@\eightcyr=wncyr8\catcode`\@=13\addto\tenpoint{\def\cyr{\tencyr\cyracc}}\addto\eightpoint{\def\cyr{\eightcyr\cyracc}}(The&\font@commandnotonlyloadsthefonts,butalsomakesthembGehavepropGerlyduringsyntaxchecking.)Ifyouarenotusingthepreprintstyle,qyoucanuse1thefontde nitionsineitheramsppt.sty<īorTheATU>VExXbGook5Appendix1E1asamoGdel.The< macrode nitionsincyracc.defVExX6GdepGendingonwhethertheyarebsinacyrillicoranoncyrillicenvironment. !Thebs\cyrillic"interpretationisnotZturnedo simplybyinvoking\rm.eF*ailuretofollowthispracticewillyieldgibbGerish.6.2.CyrillicU>inputThe tableinFigure2followsthealphabGeticalorderofthetablepublishedinthe1983pdMRp]authorindex.Thethreepairedcolumnscontain:(1)Cyrillic;}(2)Input;(3)UUT*ransliteration.The+lettersintheCyrilliccolumnswillappGearinthetypesetoutputwhenthecorrespGondingcodesfromtheInputcolumnsareusedinthe{\cyr?...}contextdescribGedabove.TheromanlettersintheT*ransliterationcolumnswillappGearinthe?qoutputwhenthecorrespGondingcodesfromtheInputcolumnsareusedinanoncyrillicUUenvironment,i.e.,havenotbGeenprecededby\cyr.JN6.UsingUUcyrillic154LٚfNFigureU>2.InputconventionsU>forAMScyrillic\,o cmr9Cyrillic0InputT:ranslit.,= G wncyr9Aa3ܟ L͑ߤN cmtt9AOa~&ʟ L͑Aa ,Bb3ܟ L͑BOb~&ʟ L͑Bb,Vv3ܟ L͑VOv~&ʟ L͑Vv,Gg3ܟ L͑GOg~&ʟ L͑Gg,Dd3ܟ L͑DOd~&ʟ L͑Dd,3ܟ L͑DjOdj~&ʟ L͑Djdjj&,G>&](g3ܟ L͑\'GO\'g~&ʟ L͍G`g,Ee3ܟ L͑EOe~&ʟ L͑Ee1 ,EI Qe3ܟ L͑\"EO\"e~&ʟ L͍uEDSXe, 3ܟ L͑\=EO\=e~&ʟ L͍uEDSXe,3ܟ L͑ZhOzh~&ʟ L͑Zhzh,Zz3ܟ L͑ZOz~&ʟ L͑Zz,Ii3ܟ L͑IOi~&ʟ L͑Ii, 3ܟ L͑\=IO\=\i~&ʟ L͍^I~g=8 ,L t=3ܟ L͑\"IO\"\i~&ʟ L͍^I~g,Jj3ܟ L͑JOj~&ʟ L͑Jj6$,I$& i3ܟ L͑\u?IO\u\i~&ʟ L͍^I~g,Kk3ܟ L͑KOk~&ʟ L͑Kk,Ll3ܟ L͑LOl~&ʟ L͑Ll, 3ܟ L͑LjOlj~&ʟ L͑Ljlj,Mm3ܟ L͑MOm~&ʟ L͑Mm,Nn3ܟ L͑NOn~&ʟ L͑Nn,3ܟ L͑NjOnj~&ʟ L͑Njnj,Oo3ܟ L͑OOo~&ʟ L͑Oo,Pp3ܟ L͑POp~&ʟ L͑Pp DQ@ٖQ@*Cyrillic5SInputfT:ranslit.*R-r"ڟ L͑RSrȟ L͑R%r *S-s"ڟ L͑SSsȟ L͑S%s*T-t"ڟ L͑TStȟ L͑T%t*-"ڟ L͑\'CS\'cȟ L͍Ccb&*K&Ek"ڟ L͑\'KS\'kȟ L͍賟KF%k*U-u"ڟ L͑USuȟ L͑U%u$*U$0u"ڟ L͑\u?US\u?uȟ L͍ПUgn;u*F-f"ڟ L͑FSfȟ L͑F%f*H-h"ڟ L͑KhSkhȟ L͑Kh%kh*C-c"ڟ L͑TsStsȟ L͑Ts%ts*Q-q"ڟ L͑ChSchȟ L͑Ch%c9h*- "ڟ L͑\DzhS\dzhȟ L͑Dzh cmsy9%dzh*X-x"ڟ L͑ShSshȟ L͑Sh%sh*W-w"ڟ L͑ShchSshchȟ L͑Shc9h%shc9h*_-"ڟ L͑\CdprimeS\cdprimeȟ L͍-=O!cmsy700d\q8%-=00*Y-y"ڟ L͑YSyȟ L͑Y%y*^-~"ڟ L͑\CprimeS\cprimeȟ L͍-=0%-=0*- "ڟ L͑\`ES\`eȟ L͍uEQXe*-"ڟ L͑YuSyuȟ L͑Y:u%yu*-"ڟ L͑YaSyaȟ L͑Y:a%y9a*-"ڟ L͑\DzS\dzȟ L͑Dz%dz*}"ڟ L͑N0ȟ L͑N0*<"ڟ L͑<ȟ L͑<*>"ڟ L͑>ȟ L͑>"ڟ L͑\cydotȟ L͑hhSeveralUUpGointsshouldbGenotedhere. 9#qqǎInputcoGdesforuppercasecyrillicwhichconsistofmorethanoneletter,e.g. ZhZ7!,UcanUalsobGeinputinallcaps,e.g.rZHZ7!,UifthecontextisentirelyinUUcaps. 9#qqǎParticularcareisnecessarywhenthelettert7!tisfollowedbys7!s.Thecontrolnsequence\cydot(\cyrillicdot")isprovidedasaseparatortokeepthoselettersdistinct:%t\cydotis(ts)7!ts.?VExX'sligaturingmechanism.)YF*orexample,shch7!wImight,inespGeciallyunluckycircumstances,bGedecomposedass-hq,x-qior7-h."Inotherwords,nifthereisanychancethatcyrillictextmightfallinto8apGositionwherehyphenationcouldoGccur,ptheresultsshouldbecheckedveryUUcarefully*,anddiscretionaryhyphensusedasappropriate. 9#qqǎHyphenation patternsdonotexistfortheAMScyrillicfontwhentheinputconventionsshownhereareused.RF*urthermore, itisprobablyimpracticabletoattempttodevelopsuchrules,sincetherulestorecognizecontrolsequencesands-complicatedligatures,bGothusedextensivelybytheAMSrcyrillicinputconventions,areMGnoteasilyspGeci edtoTU>VExX'shyphenationmechanism.Anotherapproachttohyphenation,requiringsomechangestothecyrillic.tfmܫ les,hasbGeenUUdescribedbyDimitriV*ulisinaTUGboat article[DLV89].6.3.CyrillicU>inmathAlthoughthecyrillicfontsareintendedforuseastext, theneedoGccasionallyarisestouseoneortwolettersinmath;?forexample,XimaybGeusedtorepresenttheShafarevichgroup.VWhencyrillicmustalsobGemadeavqailabletomathmoGde,thefollowinginstructions(whichwillsuppGorttheuseofcyrillicinbothtextandmath)shouldSreplacethede nitionof\cyrshownpreviously(whichwillworkonlyfortext):\newfam\cyrfam\font\tencyr=wncyr10\font\sevencyr=wncyr7\font\fivecyr=wncyr5\def\cyr{\fam\cyrfam\tencyr\cyracc}\textfont\cyrfam=\tencyr?\scriptfont\cyrfam=\sevencyr\scriptscriptfont\cyrfam=\fivecyrIfMonlythe10-pGointcyrillicfonthasbGeenaccessed,thereferencesto\sevencyrandR\fivecyrcanbGechangedto\tencyrtosavememory*.XWhenusingAU>'M S-TU>VExXand thepreprintstyle,9use\font@insteadof\font,remembGeringtochangethe\catcode˫ofthe@appropriately*,andembGedthefontfamilyspGeci cationsin\addto\tenpoint,UUasshownabGove.IfotherbasetextsizesareusedbGesidestenpoint,(thesuggestionsgivenabGoveunderUUMakingTcyrillica9v\railableapplyhereaswell.ϠNv7.UsingUUtheextrasymbGolsl174nF7.UsingU>theextrasymbolsMostusersoftheextrasymbGolfontswillprobablywanttomakethemaccessible toU{theirTU>VExXU9jobswiththeleastpGossiblefuss.r:F*orAU>'M S-TU>VEXU9users,thesefontsareήavqailableautomaticallywiththepreprintstyle,andothermethoGdsofloadingthemUUforusewithAU>'M S-TU>VExXaredescribGedabove.IfnyouarenotusingAU>'M S-TU>VExX,theeasiestmethoGdofloadingthesefontsandde ningUUthecontrolsequencesforaccessingthesymbGolsistoplacethecommand\input?amssym.texat.thetopofyourinput le.dThiswillloadthefontsmsam.u,6Emsbm69,6Eandeufm\insizes10,7,and5pGoint,suitableforuseinordinaryten-pointmathenvironments,andde nethenamesofallthesymbGolsinthesefonts.VHowever,Ythisassignsmorethan200^controlsequencenames,a+soifyouarelimitedforspace,a+analternativemethoGdmayUUbGepreferred.If$[youtypGejust\inputamssym.def,XthefontswillbGeloaded,XbutonlythenamesUUofthefewspGecialsymbolslistedbelowwillbede ned.FirstUUtherearefoursymbGolsthatarenormallyusedoutsideofmathmode:qUVX\checkmarkGrɪ\circledRUVz\malteseUɪ\yenThese5symbGols,<like{ RC,<x,<y,<andz,canalsobGeusedinmathmode,<andwillchangesizesUUcorrectlyinsubscriptsandsupGerscripts.NextarefoursymbGolsthatare\delimiters"(althoughtherearenolargerversionsOobtainablewith\left }and\right"ϴ),PsotheymustbGeusedinmathmode:㍍:p\ulcornerqɪ\urcornerx\llcorneryɪ\lrcorner㍍Finally*,twoCdashedarrowsareconstructedfromsymbGolsinthisfamily(notethatUUoneofthemhastwoUUnames;itcanbGeaccessedbyeitherone):q99K\dashrightarrowdj,UU\dasharrowL99ɪ\dashleftarrowThe[BlackbGoardBoldlettersA;:::;Zcanbeaccessedbytyping(inmathmoGde)UU\Bbb?A,::: UO,\BbbZ.Widerversionsoftheplain.tex4\widehatand\widetildearenowavqailable.LettersyIintheeufmfontcanbGeaccessed(inmathmode)bytyping,Fforexample,\frak A \frakg\togetAg. F*ortheotherEulerfonts,seethevqarious\Euler"subsectionsunderthesectionsfordi erentmacropackqages(L1Ag!TU>VExX,AU>'M S-TU>VExX,UUplainTU>VEX).7.1.TheU>\newsymbolcommandAll.othersymbGolsofthemsam]handmsbmfontsmustbGenamedbycontrolsequencessothattheycanbGeused(inmathmodeonly)whenthefontsareloaded.Ifyouareveryshortonspaceforcontrolsequencenames,LandneedonlyafewofthesesymbGols,Xyou|canomittheloadingofamssym.tex>bګandinsteadassignonlythenamesyouwillneedbyusingthecommand\newsymbolforeachsymbGolyouneed,tocreateacontrolsequencethatwillpropGerlyproducethatsymbol.ThecontrolàN18v7.UsingUUtheextrasymbGols4sequencecanbGeeitherthe\standard"name,aslistedbelow,oroneofyourown choGosing.The listofsymbGolsbelowshowsforeachsymbGolthesymbGolitself,xafour-character\ID,"andthe\standard"nameofthesymbGol. (The rstcharacteroftheeIDWidenti esthefontfamilyinwhichasymbGolresides._wSymbGolsfromthemsamfamily;have1asthe rstcharacter;@symbGolsfromthemsbmjfamilyhave2asthe rstUUcharacter.)qF*orexample,thesymbGol appearsass )230A\nleqslantT*oUUproGduceacontrolsequencewiththisname,theinstruction\newsymbol\nleqslant?230A appGearsinthe leamssym.tex9$c._JThissameinstructioncanbetypedbyauserwho isnotusingtheAU>'M S-TU>VExXpreprintstyleandhaschosennottoloadallthesymbGols,dandathereafterthecontrolsequence\nleqslantwillproGducethesymbGol UU(inmathmoGde),andwillactproperlyasa\binaryrelation."A9few:?symbGolsinthesefontsreplacesymbGolsde nedinplain.tex;cbycombinationsofsymbGolsavqailableintheComputerMoGdernfonts.(Theseare\angle(\)and\hbar(~)fromthegroup\MiscellaneoussymbGols," and\rightleftharpoons( )fromthegroup\Arrows"bGelow. ThenewsymbGolswillochangesizescorrectlyinsubscriptsandsupGerscripts,providedthatyouareusingsappropriaterede nitions.ͬInordertouse\newsymboltoreplaceanexistingde nition,Cthe namemust rstbGe\unde ned."Herearethelinesyoumustputin@Tyour leifyouarenotusingtheAU>'M S-TU>VExX@preprintstyleor\input3amssym(whichUUpGerformtherede nitionautomatically):\undefine\angle\newsymbol\angle?105C\undefine\hbar\newsymbol\hbar?207E\undefine\rightleftharpoons\newsymbol\rightleftharpoons?130ATheseblsymbGolsare aggedinthetablesbelowwitha\|{Ycmr8(U),"asareminderthattheyUUmustbGeunde ned.Note%inthetablesthatsomesymbGolsareshownwithtwonames;insuchacase,UUeitheronecanbGeusedtoaccessthesymbol. Lo9wercaseTGreekletterssz207A\digamma{ɪ207B\varkappa HebrewTletters*i2069\bethGjɪ206A\gimel *k206B\dalethNv7.UsingUUtheextrasymbGolsl194 MiscellaneousTsym9bQolss~207E\hbar'E(U) 8ɪ1038\backprime s}207D\hslashs?ɪ203F\varnothingM134D\vartriangleNɪ104E\blacktriangleO104F\triangledownHɪ1048\blacktriangledowns1003\squaresɪ1004\blacksquare*1006\lozenge*ɪ1007\blacklozenge+s1073\circledSFɪ1046\bigstar\105C\angle,B(U)^ɪ105E\sphericalangle]105D\measuredangle@2040\nexists{ɪ107B\complementf2066\mhogɪ2067\eth`2060\Finv:ɪ201E\diagupN:a2061\Game:ɪ201F\diagdown|207C\Bbbk BinaryTopQeratorssu1275\dotplussnɪ226E\ltimessr2272\smallsetminussoɪ226F\rtimes*e1265\Cap,UU\doublecapshɪ1268\leftthreetimes*d1264\Cup,UU\doublecupsiɪ1269\rightthreetimesqZ125A\barwedgefɪ1266\curlywedgeqY1259\veebargɪ1267\curlyveeq[125B\doublebarwedges 120C\boxminussɪ127F\circleddashs1202\boxtimess~ɪ127E\circledasts1200\boxdots}ɪ127D\circledcircs1201\boxplussɪ1205\centerdots>223E\divideontimes|ɪ127C\intercal BinaryTrelationss51335\leqqs=ɪ133D\geqqs61336\leqslants>ɪ133E\geqslants01330\eqslantlesss1ɪ1331\eqslantgtrs.132E\lesssims&ɪ1326\gtrsims/132F\lessapproxs'ɪ1327\gtrapproxsu2375\approxeqsl236C\lessdotsmɪ236D\gtrdotVn136E\lll,UU\lllessVoɪ136F\ggg,UU\gggtrs71337\lessgtrs?ɪ133F\gtrlesssQ1351\lesseqgtrsRɪ1352\gtreqlesssS1353\lesseqqgtrsTɪ1354\gtreqqlesss+132B\doteqdot5ꏫ,UU\DoteqsPɪ1350\eqcircs:133A\risingdotseqs$ɪ1324\circeqs;133B\fallingdotseqs,ɪ132C\triangleq N20v7.UsingUUtheextrasymbGols4sv1376\backsimssɪ2373\thicksim sw1377\backsimeqstɪ2374\thickapproxsj136A\subseteqqskɪ136B\supseteqqsb1362\Subsetscɪ1363\Supsets@1340\sqsubsetsAɪ1341\sqsupsets41334\preccurlyeqs<ɪ133C\succcurlyeqs21332\curlyeqprecs3ɪ1333\curlyeqsuccs-132D\precsims%ɪ1325\succsimsw2377\precapproxsvɪ2376\succapproxsC1343\vartriangleleftsBɪ1342\vartrianglerightsE1345\trianglelefteqsDɪ1344\trianglerighteqq130F\vDash ɪ130D\Vdash:130E\Vvdashs`1360\smallsmilecpɪ2370\shortmidsa1361\smallfrown:qɪ2371\shortparallelsl136C\bumpeqGɪ1347\betweensm136D\Bumpeq*tɪ1374\pitchforks_135F\varproptoZɪ237F\backepsilonsJ134A\blacktriangleleftsIɪ1349\blacktriangleright*)1329\therefore**ɪ132A\because NegatedTrelationss2304\nlesssɪ2305\ngtrs2302\nleqsɪ2303\ngeqs 230A\nleqslants ɪ230B\ngeqslant 8s2314\nleqqsɪ2315\ngeqqs 230C\lneqs ɪ230D\gneqs2308\lneqqs ɪ2309\gneqqs2300\lvertneqqsɪ2301\gvertneqqs2312\lnsimsɪ2313\gnsims231A\lnapproxsɪ231B\gnapproxs2306\nprecsɪ2307\nsuccs230E\npreceqsɪ230F\nsucceqs2316\precneqqsɪ2317\succneqqs2310\precnsimsɪ2311\succnsims2318\precnapproxsɪ2319\succnapproxs231C\nsimsɪ231D\ncongc.232E\nshortmid:/ɪ232F\nshortparallels-232D\nmid,ɪ232C\nparallelq02330\nvdashq2ɪ2332\nvDash12331\nVdash3ɪ2333\nVDashs62336\ntrianglelefts7ɪ2337\ntrianglerights52335\ntrianglelefteqs4ɪ2334\ntrianglerighteqs*232A\nsubseteqs+ɪ232B\nsupseteqs"2322\nsubseteqqs#ɪ2323\nsupseteqqs(2328\subsetneqs)ɪ2329\supsetneqӠNReferences214s 2320\varsubsetneqs!ɪ2321\varsupsetneq s$2324\subsetneqqs%ɪ2325\supsetneqqs&2326\varsubsetneqqs'ɪ2327\varsupsetneqq Arro9ws1312\leftleftarrowsɪ1313\rightrightarrows131C\leftrightarrowsɪ131D\rightleftarrowsW1357\LleftarrowVɪ1356\Rrightarrow1311\twoheadleftarrowɪ1310\twoheadrightarrow131B\leftarrowtailɪ131A\rightarrowtail"1322\looparrowleft#ɪ1323\looparrowright 130B\leftrightharpoons ɪ130A\rightleftharpoonsk(U)x2378\curvearrowleftyɪ2379\curvearrowrights 1309\circlearrowleftsɪ1308\circlearrowright131E\Lshɪ131F\RshUV1314\upuparrowsUVɪ1315\downdownarrowsj1318\upharpoonleftjɪ1316\upharpoonrightUj},UU\restrictionj1319\downharpoonleftjɪ1317\downharpoonright(1328\multimap ɪ1320\rightsquigarrow9!1321\leftrightsquigarrow NegatedTarro9ws82338\nleftarrow9ɪ2339\nrightarrow:233A\nLeftarrow;ɪ233B\nRightarrow=233D\nleftrightarrow<ɪ233C\nLeftrightarrow8References[AMS91]0bUser'sU>GuidetoAU>'M S-TU>VExXV*ersion2.1,January1991,American0bMathematicalU>SoGciety*,Providence,RI,1991;distributedwith0bAU>'M S-TU>VExXU>V*ersion2.1.[DEK86A]0bDonaldU>E.Knuth,TheTU>VExXbGook,U>V*olumeAofComputers&0bTypGesetting,U>Addison-W*esleyPublishingCo.,Reading,1986.[DEK86E]0bffPG,U>ComputerMoGdernTypefaces,V*olumeEofComputers&0bTypGesetting,U>Addison-W*esleyPublishingCo.,Reading,1986.[DEK89]0bffPG,U>\TypGesettingConcreteMathematics,"TUGboat10(1989),0bno.U>1,31{36;erratum,TUGbGoat10(1989),no.3,342.[DLV89]0bDimitriU>V*ulis,\NotesonRussianTU>VExX,"TUGbGoat10(1989),no.3,0b332{36.[DRS86]0bDavidU>RSiegel,TheEulerPro8jectatStanford,ComputerScience0bDepartment,U>StanfordUniversity*,1985.[GKP88]0bRonaldU>L.Graham,DonaldE.Knuth,andOrenPatashnik,Concrete0bMathematics,U>Addison-W*esleyPublishingCo.,Reading,1988.((N22References4[GMS94]0bTheU>L1#8)cmsl8ATU>VExXcompanion,MichelGoGossens,F*rankMittelbach,and 0bAlexanderU>Samarin,Addison-W*esleyPublishingCompany,1994.[L94]0bL1ATU>VExX:U>AdoGcumentpreparationsystem,LeslieLamport,0bAddison-W*esleyU>PublishingCompany,1994.[LFG]0b\L1Ag!TU>VExX2eU>fontselection",fntguide.texEXintheL1ATU>VExXdistribution.[MDS86]0bM.U>D.Spivqak,TheJoyofTU>VExX,AmericanMathematicalSoGciety*,0bProvidence,U>1986.[MDS90]0bffPG,U>TheJoyofTU>VExX,2^nd (revised)edition,American0bMathematicalU>SoGciety*,Providence,1990.5!NeAppGendixUUA.PCInstallationGuide[234Ǎ/'AppQendixTA |_PCTInstallationGuide!};A.1.IntroductionAMSF*ontsjareasetoffontswhichweredevelopGedattheAmericanMathematical SoGciety(exceptthecyrillicfonts,QwhichweredevelopGedattheUniversityofW*ashington),emforb5usewiththeTU>VExXtypGesettingsystem.hThesefontswereintendedfor2usewiththeAU>'M S-TU>VExXorAU>'MS-L1Ag!TU>VExXmacropackqages,buttheycanbGeusedwithUUplainTU>VExX,indepGendentlyofthesepackqages.AMSF*ontsN7canbGeusedwithanyfullimplementationofTU>VExX.TheinstallationproGcedureautomaticallyinstallsthefontsonyourIBMPCorcompatiblemachine.InIthisguide,KitisassumedthatyouhaveTU>VExXinstalledonyourPC,andthatyouhaveUUatleastsomefamiliaritywithit.6A.2.IfU>youharveAMSFUonts2.2butnotA(4'MȻS-T(4VE1XIfa|youobtainedAMSF*ontswithouttheAU>'M S-TU>VExX2.0+macropackqage,*dthenyouwillR rstneedtoplacethediskettelabGeledAMSFonts?2.2TFMfilesRintodriveA;D(or;driveB,inwhichcaseyouwillsubstitute\b"for\a"inthefollowingcommand),chand`copytheTFM` lesintothedirectorywhereyourotherTFM` lesare+Gstored.cThenameofthatdirectorywillvqarydepGendingontheimplementationofOTU>VExXwhichyouareusing.UF*orexample,ifyouareusingPCTU>VExX,thenyouwouldenter*hreturni,copyUUa:ntfmc:npGctexntextfmstocopytheTU>VExXfontmetric(TFM) lestoyourharddisk.QIfyouareusingan implementationofTU>VExXotherthanPCTU>VEX,youwillsubstitutethenameofyourTFMdirectoryfornpctexntextfms,andifyouhaveTU>VExXinstalledonadriveotherthan"C,youwillsubstituteitsdrivenamefor\c:";aintheabGovecommand..AftercopyingUUtheTFM les,proGceedwithSectionA.4.d^A.3.IfU>youharveA(4'MȻS-T(4VE1X2.0+The#TFM lesareinstalledautomaticallyaspartoftheinstallationofAU>'M S-TU>VExX2.0+. IfyouhavenotyetinstalledAU>'M S-TU>VExX2.0+,youshouldeitherinstallitorpGerformUUstepA.2aboveUUbeforeyouproceedwithsectionA.4.O"A.4.HowU>muchdiskspUTacedoyouneed?The+amountofdiskspacerequiredforinstallationoftheAMSF*ontsdepGendsontheresolutionofyouroutputdeviceandonwhichfamiliesoffontsyouchoGosetoinstall.ThefontshavebGeendividedinto vefamiliesfortheinstallation,MandyouKnmaychoGoseanyorallofthesefamiliestoinstall.TAlso,youmaychoGoseto tff=ff=  *AU>'M S-TU>VExXUU2.0+referstoanyreleaseofAU>'MS-TU>VExXfromversion2.0forward.8N24iA.5.qWhereUUdoyouputthefonts?4installallofthemagni cationsoronlymagni cations100%,109.5%and120% (TU>VExXV?magsteps0, 1&fesfes2 and1).tF*oramorecompletedescriptionofthesefamiliesandmagni cations,?pleaseCseetheappropriatesectionsoftheAMSF;onts2.2User'sGuide[.a(Note:YIf$youdonothaveaprintedcopyoftheUser'sg[Guide[,.youmayusethe lesamsfndoc.*ontheTFMdisktoproGduceitwithTU>VExX.However,youwillnot(F:on9tsޤ&fff>Eff>E 118dpi,100%Tthru120%mԲ200KԲ150KԲ350KԲ150KԲ250K;1100K,allTmagsmԲ550KԲ350KԲ850KԲ450KԲ750K;2950Kff>Eff>E 180dpi,100%Tthru120%mԲ250KԲ150KԲ350KԲ200KԲ300K;1250K,allTmagsmԲ750KԲ450KԲ950KԲ650K;1000K;3800Kff>Eff>E 240dpi,100%Tthru120%mԲ300KԲ150KԲ350KԲ250KԲ400K;1450K,allTmagsmԲ900KԲ500K;1000KԲ800K;1200K;4400Kff>Eff>E 300dpi,100%Tthru120%mԲ350KԲ200KԲ450KԲ350KԲ500K;1850K,allTmagsj;1100KԲ700K;1300KJ1000K;1500K;5600Kff>Eff>E 400dpi,100%Tthru120%mԲ450KԲ250KԲ500KԲ400KԲ550K;2150K,allTmagsj;1450KԲ825K;1625K;1250K;1850K;7000Kff>Eff>E\ A.5.WhereU>doyouputthefonts?Now#youwillneedtocopythe.pk leswhicharetheactualrasterimagesforthefonts.^Thesearespreadoverseveraldisks(theactualnumbGerdependsonthe׽resolutionoftheoutputdevice),Winsevendirectories.Thesesevendirectoriesrepresentfthefontsatsevendi erentmagni cationsavqailableinTU>VExX:nmagstep0, 33133&fesfes2b٫,1,2,3,4,and(5.?ThedirectoriesarelabGelednamsfontsndpiXXX,whereXXX istheresolutionoftheoutputdevicemultipliedbythemagni cation.F(ThenumbGerisuroundedtothenearestinteger.)\|F*orexample,";thesubGdirectorycontainingrasterimages}for300dotpGerinchoutputatnmagstep1(120%)willbecalledndpi360,sinceUU300multipliedby1.2equals360.T*oninstallthefonts,t ndwherethe.pk lesforyourotherfontsarestoredonyour-harddisk.Thisisdeterminedbytheneedsofthedevicedriverwhichwillreadthefonts. Ifyouareinstallingthesefontsforscreenpreviewingtheyshouldgob6whereyourpreviewerwill ndthem.jIfyouareinstallingthefontsforprintingtheyUUshouldgowhereyourprinterdrivercan ndthem.F٠N\ثA.6.qRunningUUtheinstallationproGcedureR254IfyouareusingadevicedriverfromPersonalTU>VExX,Inc.,thenmostlikelyyour other~TU>VExXfontsarestoredinsubGdirectoriesofnpctexnpixel.CIfyouareusingadevicebdriverfromArbGorT*ext,fthenmostlikelyyourotherTU>VExXfontsarestoredinsubGdirectories ofntexpixelncmpixel.IfyourdevicedriverismadebysomeoneotherthanthesetwocompaniesyouwillneedtoconsultthedoGcumentationofthatdevicedriverinorderto ndthedirectorywhereitloGoksfor.pk lesofthefontsUUwhichituses.:.KdA.6.RUunningU>theinstUTallationU>proceduretWhenyouhavedeterminedwhereyouaregoingtoputthefonts, insertthe rstofthediskslabGeledAMSFonts?2.2XXXdpiܫ(whereXXXistheresolutionofyouroutputPdevice)intodriveA/ordriveB,andtypGethefollowingcommands(ifyouputUUthediskindriveB,youwillsubstitute`b'for`a'inthe rstcommand):threturni,a:hhreturni,installY*ouwillbGeaskedanumbGerofquestions.^First,youwillhavetogivethe nameAoftheharddriveonwhichyouwillinstallthefonts.Then,;youwillbGeaskedforthenameofthedirectorywhereyouwantthefontstobGeplaced.fNext,you{?willbGeaskedwhetheryouwishtoinstallallofthemagni cationsoronlythemagni cations100%,109.5%,and120%.RFinally*,youwillbGeaskedwhetheryouwishtoinstallallofthefamiliesoffontsoronlycertainfamilies.(IfyouskippGedSectionUUA.4abGove,pleasegobackandreadit.)Once՗youhaveansweredallofthequestions,youwillbGepromptedtoinsertthe[remainingdisksofthedistribution.3The.pk leswillbGeplacedinsubdirectoriesofthespGeci edfontdirectory*,BnamedndpiXXX,whereXXXagainrepresentstheresolutionUUmultipliedbythemagni cation.:.XdefinitionfilesforL1AT(4VE1XtIf`DyouintendtousetheAMSF*ontscollectionwithL1Ag!TU>VExX`thenyouwillneedtocopy;alltheprovided.fd75 lestoyourL1Ag!TU>VExX;dinput lesarea.$The.fd75 lesarefontWBde nition lesthatsetupthecorrespGondencebetweenWBexternalfontnamesandUUthenamingschemethatisusedinternallybyL1Ag!TU>VExX.Note3thattherearetwo3setsoffontde nition lesprovided. The lesthatcontain[W576in[WtheirnamesaretailoredtoaPostScriptversionoftheAMSF*ontscollectionproGducedjointlybyY&YandBlueSkyResearch.VInthatversion,fontsizes6,8,9areproGducedbyinterpGolationfromneighbGoringsizesinsteadofhavingseparateFfontmetric les.{SelectionofthePostScriptornon-PostScript.fdƃ lesforIindividualdoGcumentsishandledthroughtheL1Ag!TU>VExX/packqageoptionmechanism,asUUdescribGedinx3Ho9wTtouseAMSF ontswithL̟"#2@cmbx8A3T<iE3sX.:.=A.8.AdditionalU>notesforusersofAMSFUontstTheGdevicedriverwithwhichyouareusingthesefontsmayhaveafonttablewhichneedstobGeupdatedinorderforthedrivertorecognizethefonts.|kF*orinstance,V۠N26QA.8.qAdditionalUUnotesforusersofAMSF*onts4theITU>VExXPreviewsoftwareIprovidedbyArbGorT*exthasa lecalledpreview.fnt whichcontainsthenamesofallfontswhichthePreviewprogramisexpGectedto nd,andthee ectiveresolutions(resolutionmultipliedbymagni cation)atwhichto1 ndthem.InordertouseAMSF*ontswiththis,goranyothersoftwarewhichusesk4suchatable,pyoumustenterthenamesofeachofthefontsintheAMSF*ontspackqage,.andthee ectiveresolutionsatwhichyouhavetheminstalled.QThe leamsfonts.lst^zonthe rstdistributiondiskcontainsalistofallofthefontnamesand%alloftheresolutionscontainedinyourdistribution.Y*oumayhavetoalterthe$~formatofthis letomakeitconformtoyourdriver'sneedsortore ectinstallationXPofonlysomeofthefonts,Ybutitprovidesyouwiththenecessarydata.See=%thedoGcumentationforyourdevicedrivertoseewhatformatisrequired.)7IfyourUUdevicedriverdoGesnotdependonsuchatable,thisstepisnotnecessary*.fZN> AppGendixUUB.T;extur}'es'v/MacintoshInstallationGuide4 274ǍpAppQendixTB P)T;extur}'esu/TMacin9toshInstallationGuide!WB.1.IntroductionAMSF*ontsjareasetoffontswhichweredevelopGedattheAmericanMathematical SoGciety(exceptthecyrillicfonts,QwhichweredevelopGedattheUniversityofW*ashington),enforb6usewiththeTU>VExXb2typGesettingsystem.iThesefontswereintendedfor5usewiththeAU>'M S-TU>VExXorAU>'MS-L1Ag!TU>VExXmacropackqages,buttheycanbGeusedwithUUplainTU>VExX,indepGendentlyofthesepackqages.This2SdistributionisdesignedforusewiththeT;extur}'estsoftware2SontheMacintosh1computer.ThesefontsrequireT;extur}'esիversion1.2orhigher.IfyouhavenpanearlierreleaseofT;extur}'es!,tyoumustupgradebGeforeusingthesefonts.T*oupgrade.T;extur}'es!,eOcontactthemanufacturer:$BlueSkyResearch,eO534SW.ThirdAve.,TPortland,OR97204;;(800)622-8398.>Inthisguide,itisassumedthatyouhavearecentversionofT;extur}'esinstalledonyourMacintosh,andthatyouhaveatUUleastsomefamiliaritywithitandwithTheTKßVE-Xb}'ook.BeforeyoubGegintheinstallationyoushould rstbackuptodisketteall lesfrom"previousreleasesofAMSF*ontsthatareonyourharddisk.`OnceyouaresurethatnHyouhavebackedupall lescontainingpreviousreleasesofAMSF*onts,tdeletethem(Wfromyourharddisk.bY*oumayhaveseriousfontID(Kcon ictsifyoudonotdothis.q(SeeUUSectionB.4.2foranexplanation.)jB.2.InstUTallationU>ProcedureB.2.1.WhatU>isonthedisk9ettes?Thedistributioncontainsthreediskettes.HThe rstdiskcontainsafolderwithsome$T;extur}'es`E les,Xthe leAMSFonts?2.2metrics,and$thecyrillictextfonts.TheTextures?filesfoldercontainseight les.Mostofthese lesareexplainedin+theAMSF;ontsڽ2.2User'sGuide.FIThe+TU>VExXsourcefortheuser'sguideisinthe les!amsfndoc.*intheTextures?filesfolder.]`The leamsfndoc.insistheTU>VExXsourceUUfortheinstallationguideyouarenowreading.The RseconddiskcontainstheextraCM fontsandtheAMS SymbGolfonts(MSAM:4and:MSBM).ThethirddiskcontainstheEulerfonts:<EulerF*raktur(EUFBprandpyEUFM),EulerRoman(EURBandEURM),EulerScript(EUSBandEUSM),UUandEulerExtension(EUEX).B.2.2.Ho9wU>muchspacedoyouneed?F*ontstakeuplotsofdiskspace.AMSF*ontsincludes89fonts,aeachateitherfourorPesixresolutions(seeSectionB.4.1foranexplanation).bThedistributiontakesup#nearlyfourmegabyteswheninstalled.jThetablebGelowshowsthediskspacerequireddforeachfontsuitcase leinthisdistribution.ConsultittomakesurethatUUyouhaveenoughspaceonyourharddisktoinstallthefontsyouneed.JdVExXsourceOforthatdoGcumentinthe lesamsfndoc.*intheTextures?filesfolderontheUU rstdistributiondisk.B.2.3.InstallingU>thefon9ts.81.Copy@the leAMSFonts?2.2metrics@fromthe rstdistributiondisktotheTeX?FontsUUfolderinsidetheTexturesfolderonyourharddisk.82.Decidewhichfamiliesoffontsyouwanttoinstallonyoursystem.F*orafulldescription_ofthesefamilies,bJseetheappropriatesectionoftheAMSF;ontsE2.2User'sGuide.83.Make`CsureyouhaveenoughspaceonyourharddiskforthefamilieswhichyouUUwishtoinstall.qSeethetableabGovefortheamountofspacerequired.84.Extractthefont lesfromthecompressed lesforeachofthefamilieswhichareUUtobGeinstalled.qThisisdoneinthefollowingway*.84.1(Double-clickUUontheiconforthecompressed le.84.2(InthedialogbGoxwhichappGears,clickthe\Drive"buttonsothatthe(nameUUofyourharddiskappGearsatthetop.84.3(Double-clickUUonthenameofyourTexturesfolderinthescrollbGox.84.4(Double-clickUUonthenameoftheTeX?FontsfolderinthescrollbGox.84.5(Clickӽ\Install".WhentheAutoUnStu Itinstaller nishes,WtherewillbGe(aUUnewfontsuitcase leinyourTex?Fontsfolder.Y*ou*arenowabletouseAMSFontsinT;extur}'es!.GHowever,Πpleasereadthesections\CustomizingY*ourInstallation"and\QuestionsandFurtherInformation"bGeforeUUattemptingtouseAMSF*ontsinT;extur}'es!.Ko:B.3.CustomizingU>YourOUwnInstUTallationB.3.1.De ningU>macrosforthesym9bQolfonts.Theq lesamssym.defandamssym.texareincludedintheTextures?filesfolderonUthe rstdiskofyourdistribution.sThese lesareforusewiththeAMSsymbGolfonts(MSAMtandMSBM).IfyouwillbGeusingthesefontsyoushouldplacebGothofUUthese lesintheTeX?inputsfolderwithinyourTexturesfolder.TheUUuseofthese lesisdescribGedintheAMSF;onts2.2User'sGuide[.yNh B.4.F*ontU>de nition lesforL1Ag!TU>VExX^ 294B.3.2.AddingU>fon9tsfordisplayandprinting.AsʀisexplainedintheT;extur}'esmanual,theShowF*ontscommanddisplaysthose fonts+qwhosefontmetricsarecurrentlyavqailabletoT;extur}'es!.Additionally*,`whenaVEfontisselectedthetwoscrollbGoxesintheShowF*ontsdialogbGoxdisplaythepGointLsizesavqailablefordisplayorprinting.WhenT;extur}'esVmhasopGenedAMSFonts2.2?metrics,dthis.spGermitsTU>VExXtorunwithouterrorson leswithreferencestoAMSF*onts.>]However,itdoGesnotenabletheirdisplayorprinting.>]T*oenabledisplayand6VprintingyoumayuseAddF*ontstobringinrasterinformationfromanyoftheUUfontsuitcaseswhichyoucreatedbyunstungthe lesinthedistribution.It>isnotnecessarytokeepusingthemenuitemAddF*ontstoimpGortAMSF*onts. [You2willprobablydeterminethroughyourownusewhichfontsyoufrequentlyuse. 7oByopGeningafontsuitcase leintheFinderanddraggingitscontentsintoanotherfontsuitcase le,;>youcancombinefontsfromdi erentsuitcasesintoasinglesuitcase le.i(Ifyouareunsurehowtodothis,bconsultthedoGcumentationw=foryourMacintoshsystem.)~Placethecombined leintheTeXfonts`folderinsideyourTexturesfolder,bmakingsurethatthe leAMSFonts?2.2metricsUUisalsointhisfolder.B.3.4.ConsolidatingU>AMSF on9tssuitcase les.AMSF*ontsxweredistributedinseveraldi erentsuitcase lessotheywould tonindividual+5disksfordistributionandinstallation. fT;extur}'esVandtheMacintoshsystem̊willhave̊amuch̊easiertimeifyouopGenfewer les.gY*oushoulduseyourMacintoshsystemconventionsformovingfontsbGetweenfontsuitcase lestocreateanew lewhichincludesthecontentsofseveralofthefontsuitcaseswhichwereprovidedUUinthedistribution.Y*oumayconsolidateallthreeofthedistributionsuitcase lesintoone.AnotheralternativewouldbGetosimplynotinstallsomeofthesuitcases.The leondisk2(whichincludesextraCMfontsandAMSsymbGolfonts),alongwithEulerF*rakturfromdisk3,areallthatthema8jorityofusersofAMSFontswillneed.UsersPwhohavePnotupgradedtoSystem7,pleasereadSectionB.4.3forimpGortantUUinformationaboutF;ont/DAMover.Xs~B.4.FUontU>definitionfilesforL1AT(4VE1XIf`DyouintendtousetheAMSF*ontscollectionwithL1Ag!TU>VExX`thenyouwillneedtocopyhalltheprovided.fdvǫ lestoyourL1Ag!TU>VExXFinput lesfolder.The.fdvǫ lesarefontWBde nition lesthatsetupthecorrespGondencebetweenWBexternalfontnamesandUUthenamingschemethatisusedinternallybyL1Ag!TU>VExX.Therearetwosetsoffontde nition lesprovided.JThe lesthatcontain57inԺtheirnamesaretailoredtoaPostScriptversionoftheAMSF*ontscollectionproGducedujointlybyY&YuwandBlueSkyResearch.FInthatversion,}fontsizes6,8,9arenproGducedbyinterpGolationfromneighbGoringsizesinsteadofhavingseparatefontDmetric les. SelectionofthePostScriptornon-PostScript.fd lesforbN30\B.5.qQuestionsUUandF*urtherInformation4individualVExXandFurUTtherInformationB.5.1.Wh9yU>aresomefontsincludedatfewersizes?Y*oumayhavenoticedthatalloftheAMSF*onts(excepttheextraCMfonts),areincludedNattwoNfewermagni cationsthantheT;extur}'es\odistributionfonts.ThisisbGecause:severalAMSF*ontsdonotgivegoGod:resultswhenrunthroughMET*AFONTatUUverylowresolutions,suchasthe72dpiMacintoshscreenresolution.BecauseIofthewayIinwhichtheMacintoshsystemscalesfontswhenitdoGesn'tNhaveafontintheexactsizeitwants,Ethemagni cationsincludedinthe distributiongivethebGestcombinationofscreenpreviewingandImageW*riteroutputfortheAMSF*onts.nLaserWriteroutputisnota ectedinanywaybythis.LaserW*riteryoutputisalwaysydeterminedfromthefontsat417%andhigher,whichareUUhandledinthesamemannerforallAMSF*onts.B.5.2.Help!TheU>fon9tdoQesn'tdisplaycorrectly!Then{Macintoshsystemhasaveryingeniouswayofhandlingfonts.9Unfortunately*,thisEingeniousandcomplexsystemsometimesleadstoproblems. Thereisaresource\IDnumbGerforeverypGointsizeofeveryfont. (F*orNFNTresources(the3kindusedforAMSF*onts2.2),jtheseID2numbGersareassignedarbitrarilybyMacintoshsoftwarewhenaresourceismovedintoafontsuitcase le.2WithinasingleUU le,theMacintoshsoftwarepreventsanyduplicationoftheseIDnumbGers.Con icts+WofID*numbGers+Wcan(andoccasionallywill)occurwhenyouhavemanydi erentsuitcase lesopGenatthesametime.%ThisisoneofthereasonsfortheinstructionsinSectionB.4.4|thefewersuitcasesyouhave,thelesslikelihoGodofUUcon icts.WhenafontIDcon ictdoGesoccur,afontwhichyoudidn'twantwillbGe4substitutedforthefontyouwanted,UatonlyasinglepGointsizeatasinglemagni cation.@Iffallothersizesandmagni cationsofthatfontarethecorrectfont,M~andKifthefontdisplayscorrectlywhenyouViewthedoGcumentonthescreenatadi erentmagni cation,&[itisafontIDbcon ict.goT*oremedythisproblem,&[dotheUUfollowing:A.IfUUyouha9veUUupgradedtoSystem7:81.(CreateUUatempGoraryfolderonyourharddisk.82.(Double-click@ontheiconforthefontsuitcase lecontainingthefont(whichUUyouwerenotabletodisplay*.83.(In!thenewwindowshowingthecontentsofthat le,,selectallsizesofthe(problemffontanddragthemintothetempGoraryfolderwhichyoucreated.84.(OpGenawindowshowingthecontentsofthetempGoraryfolder, }selectallof(thedcontents,handdragthembackintothefontsuitcase le.(Whenasked(ifUUyouwanttoreplaceexistingones,answerOK./N\B.5.qQuestionsUUandF*urtherInformationR31485.(DeleteUUthetempGoraryfolder.#B.IfUUyouha9veTnotUUupgradedtoSystem7:81.(Double-click@ontheiconforthefontsuitcase lecontainingthefont (whichUUyouwerenotabletodisplay*.82.(WhendF;ont/DA4Moverx$starts,opGenanewtemporary leontheright-hand(sideUUofthewindow.83.(Copyǥallsizesoftheproblemfontfromtheoriginal leintothetempGorary( le,UUandremoveUUthemfromtheoriginal le.84.(CopyUUthefontsbackintotheoriginal le.85.(QuitUUF;ont/DAMover,anddeletethetempGorary lewhichyoucreated.Thesef!stepswillcausetheMacintoshsystemsoftwaretoassignnewarbitrarynumbGersUUtotheNFNTresourcesinquestionandshouldclearupthecon ict.B.5.3.ImpQortan9tU>informationaboutF;ont/DAMover.IfUUyouarenotusingSystem7,pleasetakenoteofthefollowing:81.Y*ouHmusthaveF;ont/DA Mover\ZV*ersion3.8orlater.L/PreviousreleaseswillnotUUrecognizefontresourcesofthetypGeusedforAMSF*onts2.2.82.EvenAV*ersion3.8ofF;ont/DA MoverUhasabugofwhichyoushouldbGeaware.If;youcopyafontofthetypGeusedforAMSF*onts2.2intoa lemorethanonce,`youwillverylikelyendupwithtwocopiesofthefontinthat le.[LIfyounoticeUUthatthishasoGccurred,simplydeleteoneoccurrence. N32bfAppGendixUUC.UnixInstallationGuide4Ǎ`AppQendixTC x5?UnixTInstallationGuide!C.1.IntroductionAMSF*ontsjareasetoffontswhichweredevelopGedattheAmericanMathematical SoGciety(exceptthecyrillicfonts,QwhichweredevelopGedattheUniversityofW*ashington),emforb5usewiththeTU>VExXtypGesettingsystem.hThesefontswereintendedfor2usewiththeAU>'M S-TU>VExXorAU>'MS-L1Ag!TU>VExXmacropackqages,buttheycanbGeusedwithUUplainTU>VExX,indepGendentlyofthesepackqages.AMSF*ontsjBcanbGeusedwithanyfullimplementationofTU>VExX.Inthisguide,o}itisڑassumedthatyouhaveTU>VExXinstalledonyourUnixsystem,andthatyouhaveatUUleastsomefamiliaritywithit.6C.2.IfU>youharveAMSFUonts2.2butnotA(4'MȻS-T(4VE1XIf\youobtainedAMSF*ontsbuthavenotobtained(orhavenotyetinstalled)theAU>'M S-TU>VExX$2.0+macropackqage,*-thenyoumustplacethe.tfmH lesforAMSF*onts2.29intothedirectorywhereyourotherTFM lesarestored.tThenameofthatdirectory0!willvqarydepGendingonthelocalinstallationofTU>VExXwhichyouareusing.IfyouareusingthestandardUnixTU>VExXdistribution,ˍthenitwouldprobablybGeaXdirectoryinthepathindicatedbytheenvironmentvqariableTEXFONTS.oroneofthesubGdirectories@inthepathindicatedbytheenvironmentvqariableTEXFONTSEff&fff&fǫSUBDIRO.F*or example,6ifTEXFONTS1indicatesonlythedirectory/usr/lib/tex/fonts/tfmwMǫ,andCifTEXFONTSEff&fff&fǫSUBDIRS΋hasnode nition,Gthenyouwouldcopythe.tfm lesinto/usr/lib/tex/fonts/tfms.zIfX?yourenvironmentissetupdi erently*,Xthenyouwillhave`todeterminethecorrectdirectoryinwhichtoplacethem.AftercopyingtheTFMUU les,proGceedwithSectionC.4.dC.3.IfU>youharveA(4'MȻS-T(4VE1X2.0+TheupTFMuh leswereinstalledaspartoftheinstallationofAU>'M S-TU>VExX2.0+.Ifyouhave]notyetinstalledAU>'M S-TU>VExX2.0+,_youshouldeitherinstallitorpGerformstepC.2abGoveUUbeforeyouproceedwithsectionC.4.OC.4.HowU>muchdiskspUTacedoyouneed?The+amountofdiskspacerequiredforinstallationoftheAMSF*ontsdepGendsontheresolutionofyouroutputdeviceandonwhichfamiliesoffontsyouchoGosetoinstall.ThefontshavebGeendividedinto vefamiliesfortheinstallation,MandyouKnmaychoGoseanyorallofthesefamiliestoinstall.TAlso,youmaychoGosetoinstallallofthemagni cationsoronlymagni cations100%,109.5%and120%(TU>VExXV?magsteps0, 1&fesfes2 and1).tF*oramorecompletedescriptionofthesefamiliesandmagni cations,?pleaseCseetheappropriatesectionsoftheAMSF;onts2.2User's tff=ff=  *AU>'M S-TU>VExXUU2.0+referstoanyreleaseofAU>'MS-TU>VExXfromversion2.0forward.!NiʢC.5.qWhereUUdoyouputthefonts?_ʠ334Guide[.a(Note:YIf$youdonothaveaprintedcopyoftheUser'sg[Guide[,.youmayuse the lesamsfndoc.*ontheTFMdisktoproGduceitwithTU>VExX.However,youwillnotdoyouputthefonts?Nowyouwillneedtoinstallthe.pk leswhicharetheactualrasterimagesforthefonts.4Y*oushouldplacetheminthedirectorywhereyourdevicedrivers(printerdriversaandscreenpreviewers)loGokfor.pk les.TThenameoftheenvironmentvqariablewhichpGointstothatdirectoryordirectoriesvqariesfromonedrivertoanother. PleasecheckthedoGcumentationforyourdriversto ndwheretheyloGokfor.pkCs les.(F*orexample,xdviloGoksatanenvironmentvqariableXDVIFONTS4,whileUUsomedriversloGokatTEXPKS&*oryetanothervqariablename.)These lesarenamedaccordingtoaconventionwhichindicatesthenameof#thefontinthe lenameandtheresolutionmultipliedbythemagni cationinthetextension.#F*orexample,VExX:nmagstepUU0, 1&fesfes2 .,1,2,3,4,and5.If-y9ouobtainedthe lesfromanInternetarchiveorotherUnix-likesource, HtheD@ leshaveD@thecorrectnamesforuseinUnix.lAllyouneeddoisplacethemUUinthedirectorywhereyourdriverswill ndthem(describGedabove).Ify9oupurchasedthe lesonDOSdiskettes,youwillneedtomanipulatethe.6 lenamestomakethemcompatiblewithUniximplementationsofTU>VExX-relateddevicedrivers.=OntheDOSdiskettes,theextensiononthe lenameislimitedtonomore thanthreecharacters,+2which meansthatsomethinglikeeufm10.300pkEA.isnotallowed.PTheconventionforaccomoGdatingthislimitationintheTU>VExXcommunityistoogiveallsuch lestheextension.pkxիanddividethemupintodi erentdirectories.OntheAMSF*ontsDOS_diskettedistribution,thedirectoriesarelabGelednamsfontsndpiXXX,BwhereXXXBistheresolutionoftheoutputdevicemultipliedbytheX)magni cation(thenumbGerX)intheUnix lenameextensiondescribedabove).Once?youhavetransferredtheentiredirectorytreeovertoyourUnixenvironment,you]willneedtorenamethe.pk lesineachdirectorytotheextension.XXXpk#K,where)-XXXQis)-thenumbGer)-inthedirectorydpiXXX%Hinwhichthe leislocated.cOnceyouhavethusrenamedallofthe les,youmayplacethemalltogetherinthedirectoryUUwhereyourdriverswill ndthem(describGedabove).X_C.6.FUontU>definitionfilesforL1AT(4VE1XIf`DyouintendtousetheAMSF*ontscollectionwithL1Ag!TU>VExX`thenyouwillneedtocopy;alltheprovided.fd75 lestoyourL1Ag!TU>VExX;dinput lesarea.$The.fd75 lesare"N34RC.7.qAdditionalUUnotesforusersofAMSF*onts4fontWBde nition lesthatsetupthecorrespGondencebetweenWBexternalfontnames andUUthenamingschemethatisusedinternallybyL1Ag!TU>VExX.Note3thattherearetwo3setsoffontde nition lesprovided. The lesthatcontain[W576in[WtheirnamesaretailoredtoaPostScriptversionoftheAMSF*ontscollectionproGducedjointlybyY&YandBlueSkyResearch.VInthatversion,fontsizes6,8,9areproGducedbyinterpGolationfromneighbGoringsizesinsteadofhavingseparateFfontmetric les.{SelectionofthePostScriptornon-PostScript.fdƃ lesforIindividualdoGcumentsishandledthroughtheL1Ag!TU>VExX/packqageoptionmechanism,asUUdescribGedinx3Ho9wTtouseAMSF ontswithL̟"#A3T<iE3sX.=1C.7.AdditionalU>notesforusersofAMSFUontsTheGdevicedriverwithwhichyouareusingthesefontsmayhaveafonttablewhichneedstobGeupdatedinorderforthedrivertorecognizethefonts.KF*orinstance,thepreviewHsoftwareprovidedbyArbGorT*exthasa lewhichcontainsthenamesofallfontsnwhichthepreviewprogramisexpGectedto nd,tandthee ectiveresolutions(resolutioni!multipliedbymagni cation)atwhichto ndthem.+InordertouseAMSF*ontswiththis,4oranyothersoftwarewhichusessuchatable,4youmustenter8thenamesofeachofthefontsintheAMSF*ontspackqageandthee ectiveresolutionsatwhichyouhavetheminstalled. The leamsfonts.lst, NwhichappGears 0onthe rstdistributiondiskoratthetop/amsfonts5XElevelinUnixarchivedistributinos,%icontainsȘalistofallofthefontnamesandalloftheresolutionscontainedJinyourdistribution.QY*oumayhavetoaltertheformatofthis letomakeGitconformtoyourdriver'sneedsortore ectinstallationofonlysomeofthefonts, butitprovidesyouwiththenecessarydata.[SeethedoGcumentationforyourdevice-drivertoseewhatformatisrequired.dIfyourdevicedriverdoGesnotdependonUUsuchatable,thisstepisnotnecessary*.#0Nb׫AppGendixUUD.F*orfurtherinformationX354Ǎ'AppQendixTD xF orTfurtherinformationTheOAMSF*ontscollectionwasimplementedandpackqagedbytheSoGciety's Department8ofElectronicProGductsandServices. {oQuestionsorsuggestionsforimprovementsUUshouldbGedirectedtothatgroupatthefollowingaddress::T*echnicalUUSuppGortElectronicUUProGductsandServicesAmericanUUMathematicalSoGcietyP*.O.UUBox6248Providence,UURI02940Phone:q800-321-4AMS or401-455-4080Internet:qtech-suppGort@math.ams.orgtThex*cyrillicfontsincludedintheAMSF*ontscollectionweredevelopGedatthe[HumanitiesandArtsComputingCenteroftheUniversityofW*ashington.QuestionsUUregardingthesecyrillicfontsshouldbGedirectedto:DirectorHumanitiesUUandArtsComputingCenterDR-10UniversityUUofW*ashingtonSeattle,UUWA98195Phone:q206-543-4218tQuestionsUUorcommentsconcerningT;extur}'es'vcanbGedirectedto:BlueUUSkyResearch534UUSouthwestThirdAvenuePortland,UUOR97204Phone:q800-622-8398 UVor503-222-9571tTheaTU>VExXaUsersGroupisagoGodasourceofgeneralinformationabGoutfontsforuseUUwithTU>VExX.InquiriescanbGedirectedto:TU>VExXUUUsersGroupP*.O.UUBox869SantaUUBarbara,CA93102-0869Phone:q805-963-1338Internet:qtug@tug.orgFD.1.ObtUTainingU>theMET*AFONTsourcefilestTheAMSF*ontscollectionhasbGeenpreparedforanumbGerofdi erentresolutionssuitablek/foruseonwhattheAMSjsta hasdeterminedtobGethemostpopulardevicesscurrentlybGeingusedtoprepareTU>VExXPoutput.!Moresuchdevicescontinueto%#appGear,Ymanyofthemwithcharacteristicsdi erentfromthedevicesthatarecurrentlyUUsuppGorted.Usersb@ofunsuppGorteddeviceswhohaveb@accesstoanoperatingversionofMET*AFONTandhavesomeexpGeriencewithgeneratingMET*AFONTfontsmay$qN36QD.1.ObtainingUUtheMET*AFONTsource les4alsof-wishtoobtaintheMET*AFONTesource lesfortheAMSFontscollection. 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