; TeX output 1997.01.23:0051soQDtGGcmr17An7tExtensionoftheLdKGXQ cmr12AT[-E;gXtheoremenqvironment!", cmsy10޲FVrankMittelbacrhGElectronicDataSystems0(Deutscrhland)GmbHxEisenstrae569cD-65424RSvusselsheimFVederalRepublicofGermanry]fjί Janruary23,1997.!Kt : cmbx9Abstractэoo cmr9ThemacrosdescribAedinthispaperyieldanextensionoftheL5Aacmr6A TuAEXthe- borememec9hanism.AItisdesignedistosatisfythedi erentrequirementsofbv|rariousjournals.Th9us,*thelayoutofthe\theorems"canbAemanipulatedbybdeterminingJFa\st9yle".FThisarticledescribAesnotonlytheuse,Wbutalsothebde nition,Tofthenecessarymacros.!čI Nff cmbx12Prefacefftoversion2.2IK`y cmr10F*or3L5ffٓRcmr7A͉TU>'ExX2 b> cmmi10"-^this3packqagedidnotneedanyfundamentalchanges.aIonlymoGdi- I edthemessagesgeneratedsothattheoremlayoutstyleswillshowupwiththeI!'ExX.IPrefacefftoversion2.1IThisΛversionisidenticalto2.0gdescribGedin"p0J cmsl10TUGboatP10#3exceptforsomeIinternalUUdefaultswhicharenowsetdepGendingontheusedfontselectionscheme.XThis?wasdonetoavoidunpleasantsurprisesifthenewfontselectionschemeIisUUinforce.qF*orfurtherdetailsseesection3and[1].I1aLIntros3ductionIF*or:ourpurpGoseshere,s\theorems"arelabelledenunciations,softenseto fromtheImainntextbyextraspaceandafontchange.Theorems,corollaries,conjectures,Ide nitions,andremarksareallinstancesof\theorems".I~The\header"oftheseIstructurespiscompGosedofalabel(suchas#- cmcsc10TheoremorRemark)andanumbGerIwhichUUserializesaniteminthesequenceofitemswiththesamelabGel.IX-ffr @ -:q% cmsy6L|{Ycmr8ThisX lehasvÎersionnumb'ExXattheF*achbGereichMathematikin IMainz,K$thedesiretomanipulatethelayoutof\theorems"arose.InMainz,theIfollowingUUtwoconventionscameintogeneraluse:U81.bTheUUnumbGerofthetheoremisshowninthemargin.U82.bThereUUisalinebreakattheendofthetheoremheader.XAdditionally*,Qsomejournalsrequiredi erentformatswhichdepGendonthe I\sortoftheorem":cHe.g.oftenremarksandde nitionsaresetin\upshape,EwhileI\itshapeUUisemployedUUformaintheorems.XConfronted$withtheserequirements,-atheoremenvironmentwasdevelopGedinIMainz}whichallowsseparatedeterminationofthelayoutofthe\theoremssets",IcomparableUUto\pagestyle.!čI2aLTheffuserinterfaceI$N cmbx122.1gDe ningnewtheoremsetsuTIAswintheoriginalL5ffA͉TU>'ExXversion,9thecommand\newtheoremde nesanew\the- %ߤN cmtt9\newtheoremIoremKset"or\theorem-likestructure".UMTworequiredargumentsnamethenewIenvironment[andgivethetexttobGetypGesetwitheachinstanceofthenew\set",IwhileUUanoptionalargumentdetermineshowthe\set"isenumerated:I\newtheorem'Ɍ cmbsy10ffoogfbarg?ŲThetheoremsetfoo(whosenameisbar)usesitsownbcounter.I\newtheoremffoo2g[foo]fbar2gThe;Qtheoremsetfoo2(printednamebar2)busesUUthesamecounterasthetheoremsetfoo.I\newtheoremffoo3gfbar3g[section]The8theoremsetfoo3(printednamebar3)bisenumeratedwithinthecountersection,0i.e.witheverynew\sectionthebenumerationbGeginsagainwith1,mandtheenumerationiscompGosedfromthebsection-numbGerUUandthetheoremcounteritself.XAdditionally*,_thecommand\theoremstylecande nethelayoutofvqarious,orb\theoremstyleIall,theoremsets.1ItshouldbGenotedthatanytheoremsetde nedby\newtheoremIistypGesetinthe\theoremstylethatiscurrentatthetimeofthede nition.,Thus,ItheUUfollowing[X\theoremstyle{break}%̰\newtheorem{Cor}{Corollary} [X\theoremstyle{plain}%̰\newtheorem{Exa}{Example}[section]IleadsztotheresultthatthesetCorisformattedinthestylebreak,GwhilethesetIExaKandallthefollowingonesareformattedinthestyleplain,KunlessanotherI\theoremstyle follows.8 Sincethede nitionsinstalledby\newtheoremareglobal,IoneUUalsocanlimit\theoremstyleloGcallybygroupingbraces.XTheschoiceofthefontforthetheorembGodysiscompletelyindepGendentofthef\theorembodyfontIchosenUU\theoremstyle;thishasproventobGeveryadvqantageous.qF*orexample,W,{\theorembodyfont{\upshape}/?\newtheorem{Rem}{Remark}}2 soIde nes@atheoremsetRem,{whichwillbGesetin\upshapeinthecurrentlayout I(whichinourexampleisplain).3?Aswith\theoremstyle,@the\theorembodyfontIchosenĖisthatcurrentatthetimeof\newtheorem.If\theorembodyfontisnotIspGeci edoronede nes\theorembodyfont{},(NthenthefontusedwillbethatIde nedUUbythe\theoremstyle.XIt+isalsopGossibletocustomizethefontusedforthetheoremheaders.IThist\theoremheaderfontIis,however,aE&globaldeclaration,andthereforethereshouldbGeatmostoneI\theoremheaderfontUUdeclarationinthepreamble.^1XTwo2yadditionalparametersa ecttheverticalspacearoundthetheoremen-Ʋ\theorempreskipamount \theorempostskipamountIvironments:\theorempreskipamountand\theorempostskipamountde ne,)Ure-IspGectively*,theRspacingbeforeandaftersuchanenvironment.ֿTheseparametersIapplyHforalltheoremsetsandcanbGemanipulatedwiththeordinarylengthmacros.ITheyorarerubbGerlengths,l(`)m#R cmss10skips'),andorthereforecancontainplusandminusparts.XSince/thede nitionoftheoremsetsshould|mostsensibly|bGeplacedintheIpreamble,oweonlyallowinstallationthere.ItisthereforepGossibletoreleasetheImemoryusedhereafter\begin{document},SinordertomakeroGomforotherIapplications.I2.2gExistingtheoremstylesuTITheUUfollowingtheoremstylesexisttodate:Iplain߲ThisNtheoremstyleemulatestheoriginalL5ffA͉TU>'ExXde nition,exceptthatJadditionallytheparameters\theorem...skipamountareused.VIbreak߲InUUthisstyle,thetheoremheaderisfollowedbyalinebreak.Imarginbreak߲The9theoremnumbGer9issetinthemargin,?andthereisalinebreak asUUinbreak.Ichangebreak߲LikeUUbreak,butwithheadernumbGerandtextinterchanged.Ichange߲HeaderUUnumbGerandtextareinterchanged,withoutalinebreak.Imargin߲TheUUnumbGerissetintheleftmargin,withoutalinebreak.IAllUUstyles(exceptplain)select\slshapeasthedefault\theorembodyfont.I2.3gExamplesuTIGiventheabGovetheoremsetsCor,NExaandRem,suppGosethatthepreamblealso IcontainsUUthedeclarations:[X\theoremstyle{marginbreak},\newtheorem{Lem}[Cor]{Lemma} [X\theoremstyle{change}[X\theorembodyfont{\itshape}%̰\newtheorem{Def}[Cor]{Definition}[X\theoremheaderfont{\scshape}IThenHthefollowingaresometypicalexamplesofthetypGesetoutputresultingfrom ItheirUUuse.I9ffr J= "5-:1LIfkitisactuallynecessarytohaÎvekdi erentheaderfonts,Wonehastode nenewtheoremstyles (substitutingdQthedesiredfonÎt)orspx2ILemma(BenUser) IThisUUisasentencetypGesetinthetheoremenvironmentLem.I3Definition(VerUTyimpressiveDefinition)![This%isasentenc}'etypesetinthe 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ISinceitisthesameforalltheoremsets,fitisremovedfromthemacros\th@hstyle[i.IItUUsimplyendsthetrivlistenvironment,UUwhichwasbGegunin\@thm.E196S\global\let\@endtheorem=\endtrivlist 6\@preamblecmdsIAllcmacrosde nedabGovecaretobeusedonlyinthepreamble.9wTherefore,-wecinsertIthemin\@preamblecmdswhichwilldisablethematbGegindocument.4ThisisdoneIbyUUtheinternalL5ffA͉TU>'ExX2"+Tcommand\@onlypreamble.E197S\@onlypreamble\@xnthm E198S\@onlypreamble\@ynthmE199S\@onlypreamble\@othmE200S\@onlypreamble\newtheoremE201S\@onlypreamble\theoremstyleE202S\@onlypreamble\theorembodyfontE203S\@onlypreamble\theoremheaderfontXFinallyUUwedeclaretheplaintheoremstyletobGethedefault.E204S\theoremstyle{plain}E205Sh=pack9age#g i!čIReferencesI[1]X;M.WGoossens,7F.Mittelbach andA.WSamarin.TheL5ffA͉TU>'ExXCompanion. X;Addison-W*esley,UUReading,Massachusetts,UU1994.I[2]X;LamporUTt,Leslie.nlatex.tex,UUversion2.09,dateF*eb.1990.IChangeffHistory]Iv1.0 ,lXGeneral:TFirstdraft.n}.΍}.}.}.}.}.}.}.}.}. yz1Iv1.0aXGeneral:T`thistheoremst9yle'added.i%1Iv1.1aXGeneral:"Newconcept:rede nethe gin9ternalcL5A TuAEXcommands`@xn-gthm'Tetc.+}.΍}.}.}.}.}.}.}.}.}.}.}.}.}.}.}. 91 ,lIv1.1bXGeneral: j`theoremfon9t'usedto gspAecifyTfon9t.^}.΍}.}.}.}.}.}.}.}.}.}.}.}.}. 91Iv1.2aXGeneral:4`@endtheorem'no9wglob-gallyTde ned.j͍}.΍}.}.}.}.}.}.}.}.}.}.}.}.}. 91Iv1.2bXGeneral:~/`newtheorem'onlyallo9wedginTthepream9ble.}.΍}.}.}.}.}.}.}.}.}.}. 91Iv1.3aXGeneral:<<`theoremfon9t'nowatoksgregister.`}.΍}.}.}.}.}.}.}.}.}.}.}.}.}.}.}.}. 91v2.0a ZʍGeneral:LNewimplemen9tationand newTdoAcumen9tation.荑}.΍}.}.}.}.}.}.}. 91NoHgla9youtchangesbutinter-nalQ1moAdi cationsoldsubst9ylesw9on'tTwork.荑}.΍}.}.}.}.}.}.}.}.}.}.}.}.}. 91v2.0bGeneral:L`global'usedforallde ni-tions.}.΍}.}.}.}.}.}.}.}.}.}.}.}.}.}.}.}.}.}. 91v2.0cGeneral:DoAcumen9tationtranslatedtoEnglish.ThankstoLLLandNina{}.΍}.}.}.}.}.}.}.}.}.}.}.}.}.}.}.}.}.}. 91v2.0d\@thm:TF:orgottenpAercen9tadded.}.΍}. yz9v2.0eGeneral: Spacesremo9ved from`t9ypAeout'.,}.΍}.}.}.}.}.}.}.}.}.}.}.}.}.}.}. 95v2.0f\theorem@bodyfont: gUnnecessary`global'Tremo9ved.΍}.΍}.}.}.}.}.}.}.}.}.}. 9614soX\theorem@style:)Unnecessary g`global'Tremo9ved.΍}.΍}.}.}.}.}.}.}.}.}.}. 96X\theorempostskipamount:uUnnec-gessaryT`global'remo9ved.}.΍}.}.}.}. &P13Iv2.0gX\@preamblecmds:1`theoremhead-gerfon9tand`theorembAodyfontgadded.}.΍}.}.}.}.}.}.}.}.}.}.}.}.}.}.}.}. &P14X\theorem@bodyfont:0`theoremfon9tgtoT`theorem9bAodyfont.w}.΍}.}.}.}.}.}.}. 96X\theorem@headerfont:*Macrogadded.}.΍}.}.}.}.}.}.}.}.}.}.}.}.}.}.}.}.}. 96X\theoremheaderfont:lMacrogadded.}.΍}.}.}.}.}.}.}.}.}.}.}.}.}.}.}.}.}. 96Iv2.1aX\@begintheorem:@Relaxedatgtoplev9el.@}.΍}.}.}.}.}.}.}.}.}.}.}.}.}.}.}.}. 96X\@opargbegintheorem:IRelaxedatgtoplev9el.@}.΍}.}.}.}.}.}.}.}.}.}.}.}.}.}.}.}. 96XGeneral:@SuppAortfornewfon9tselec-gtion.@}.΍}.}.}.}.}.}.}.}.}.}.}.}.}.}.}.}.}.}.}. 91X\theorem@headerfont:7SuppAortforgnewTfon9tselection.)E}.΍}.}.}.}.}.}.}.}. 96X\theoremstyle:IGroupaddedgaroundT`th@.. +}.΍}.}.}.}.}.}.}.}.}.}.}.}. 95bResetinggNof`..@bAegin9theoremre-gmo9ved.ƨ}.΍}.}.}.}.}.}.}.}.}.}.}.}.}.}.}.}.}. 95v2.1b @General:a5Fixedmissing`itemb9y declaringTdefaultst9yle.Ӎ}.΍}.}.}.}. &P14v2.1c\th@marginbreak:@`endgroupout-sideTmacroAcodeen9v.}.΍}.}.}.}.}.}. &P13\theorem@bodyfont:ѿ`reset@fon9taddedTandlogicc9hanged.o鍑}.΍}.}.}.}. 96v2.1d\theorem@bodyfont:Resettoempt9yTifargisempty*捑}.΍}.}.}.}.}.}. 96v2.2a\@preamblecmds:5UseL5A TuAEXc.2"+-in-terfaceK}.΍}.}.}.}.}.}.}.}.}.}.}.}.}.}.}.}. &P14General:TClean9upforLaT:eX2e}.΍}.}. yz1\th@margin:Use`@input@toloadtheoremTla9yout lesŹ}.΍}.}.}.}.}.}.}.}. 97v2.2b\@othm:Buildinc9heckforcoun9terde ned}.΍}.}.}.}.}.}.}.}.}.}.}.}.}.}.}.}.}. 99\@xnthm:TUse\@newctr=}.΍}.}.}.}.}.}.}. yz7General:Announcemo9vedtotopof leō}.΍}.}.}.}.}.}.}.}.}.}.}.}.}.}.}.}.}.}.}.}. 95v2.2c\@xnthm:TUse\@newctrpropAerly:.?d}. yz715q; 0߆T cmtt12- cmmi10K`y cmr10ٓRcmr7