; TeX output 1996.03.06:1220"*Ek⍑:fNff cmbx12PrintingffZandObfject-ZL++"V cmbx10AnTL32EdXdos3cumentsÌr': cmti10PaulKingN8K`y cmr10DepartmentUUofComputerScience UniversityUUofQueenslandfAustralia,UU40727king@batserver.cs.uq.oz.auTRMayUU29,1990!č1LIntros3ductionThisnotedescribGesapackqageofL5ffٓRcmr7A͉TU>'ExXmacrosforprintingZandOb8ject-ZspGeci cations.ThemacrosandthisnotearebasedoriginallyonMikeSpivey's#'ExXsetslettersinmathematicalformulassothatmulti-characteridenti ers loGokUUbetter.ItYprovidesvqariousbrandsof`bGoxedmathematics'whichappGearinZYandOb8ject-ZspGeci- cations.The3packqageiskeptina leoz.styinthedirectory/usr/local/lib/tex/localinputs.ThispdirectoryshouldbGementionedinyourTEXINPUTSGshellvqariable.LT*ousethemacrosyoujustUUbGeginyourL5ffA͉TU>'ExXdocumentwithsomethinglike:\documentstyle[11pt,oz]{article}"p2LSchemaffBoxesTheHexamplebGelowshowsaschemaontheleftandwhatyouneedtosaytogetitontheright.fdfffdff  fdBirthdayBo}'ok5ffk ffff ff fdknown{: msbm10P 2NAME ff fdbirthday:NAMEv7!DA;TEffffffPfffd ff fdknown{=domURbirthdayffff%@"&ߤN cmtt9\begin{schema}{BirthdayBook} known:\psetNAME\\birthday:NAME\pfunDATE"\STknown=\dombirthday"\end{schema}`L̍Thezcommand\STm(read`SuchThat')isthesameasthepreviouslyusedcommand\wherewhichllhasbGeenkeptasanaliasforupwardcompatibility*. Ifyouwantaschemawithnoname,justF_ahorizontalruleatthetop,usetheschema*environmentinstead.DY*oucansetvqariousparametersUU(seeSection7)tochangethebGoxstyle,forexample: BirthdayBo}'oku cmex10bڥ=h'XQ cmr12[W b> cmmi10:::]@"$BirthdayBook\sdef\lsch...\rsch$"1*"*Ek⍑AUUgenericschemaisproGducedasfollows.fdfffdff  fdPo}'olAi[RESOURCE3]ffS)ffff  ff fdownerڥ:RESOURCEv7!USER ff fdfr}'ees:P 2RESOURCEffffffPfffd ff fd(dom:owner)8[ lfr}'ees=RESOURCE ff fd(dom:owner)8\ lfr}'ees=?ffffff%@"\begin{genschema}{Pool}{RESOURCE} "owner:RESOURCE\pfunUSER\\"free:\psetRESOURCE"\ST"(\domowner)\unifree=RESOURCE\\"(\domowner)\intfree=\emptyset"\end{genschema}sޏ3LAxiomaticffde nitionsAUU`libGeral'axiomaticde nitionisproducedasfollows.fd ff fdlimit:NffffffPfffd ff fdlimit65536@"\begin{axdef} "limit:\nat"\ST"limit\leq65536"\end{axdef}NƍAUU`generic'axiomaticde nitionisproGducedasfollows.fdfffdff  fd[X;Y6]fffffffffdff )fdffffffff ff fd rst:X8YN!XffffffPfffd ff fd88fdx\:X;qy:YN ~g rstز(x4D;y})=xffff%@"\begin{gendef}{X,Y} "first:X\prodY\tfunX"\ST"\allx:X;y:Y\dotfirst(x,y)=x"\end{gendef}SAUU`unique'axiomaticde nitionisproGducedasfollows.fdfffdff  fdffUfffffffdff  fdffUffffff ff fd":RffffffPfffd ff fd"=3:14159265:::ffff%@"\begin{uniqdef} "\pi:\real"\ST"\pi=3.14159265\ldots"\end{uniqdef}[ޏ4LObfject-ZffClassBoxesOb8ject-Z;allows;classtypGestobede nedusingaboxverysimilartotheschemabGoxpreviously describGed.aIt%uallowsthepreviouslydescribedboxedenvironments(aswellasnestedsub-classes)tobGeplacedwithinaclassbox.[Inaddition,specialnamescanbeusedforsomeoftheboxed-environmentswhentheyappGearwithinaclassbox.Thefollowingexampleillustratesaclass"2 "*Ek⍲de nition.fdfffdff  fdShap}'ekff4fffffffd ff fdc}'olourڥ:Colour%%fffb  fffdp}'erim{:R ffff ff@ fffd  fffdp}'erim{>0ccfft $m#R cmss10Thisclasshas2constantsc}'olourWand p}'erimc.3:3:fffd ffffffUffff  ffx4D;y:R ffff ffU""fffb fffdff fdI1#fcmti8NIToLff]ffff  fffdx\=y=0 ffff ffUMMff fffdff fdT;r}'anslatekfflXQffff  fffd(x4D;y})  fffddx4D?;dy}?:R ffff ff@ fffd  fffdx4D^ O!cmsy70ɕ=xm$+8dx4D?  fffdy}^0wβ=y]+8dy}? ffff ffUffffff%@"\begin{class}{Shape} "\also"colour:Colour\\"\begin{axdef}"perim:\real"\ST"perim>0"\end{axdef}\\"\begin{classcom}"Thisclasshas2constants"$colour$and$perim$."\end{classcom}\\"\begin{state}"x,y:\real"\end{state}\\"\begin{init}"x=y=0"\end{init}\\"\begin{op}{Translate}"\Delta(x,y)\\"dx?,dy?:\real"\ST"x'=x+dx?\\"y'=y+dy?"\end{op}"\end{class}5ƍTheY4classcomenvironmentY4hasn'tbGeenseenbefore.}eItcreatesaparagraphoftextwiththe same'ExXwarningmessagesifyoutrytouseastateenvironmentoutsideofaclassbGoxorifyoutrytoplaceanenvironmentsuchassyntaxinsideaclass.b>Y*oucanaskfor,SadditionalhelpinthesecasesusingthenormalL5ffA͉TU>'ExXhorH,Ihelpcommands.dIfyouproGceedwithFL5ffA͉TU>'ExXing,IthemacroswillattempttodothebGesttheycantodowhatyouprobablyintend,evenUUthoughyouareviolatingtherecommendednestingguidelines.!č5LControllingfftheSpacingwithinEquationsandBoxesMostofthespGecialZsymbolsarede nedinawaythatallowsTU>'ExXtospacethemoutcorrectly*.Sometimes,3however,you'llneedtogiveTU>'ExXahelpinghandifyouwantittogetthespacingright.{F*orexample,togetmapL@fzyouneedtotypGemap\,f.{The\,givesyouathinspace:vifthisUUisomitted,theinputmap?fgivesmapf,bGecauseTU>'ExXignoresspacesinmathmode.Sometimesitisusefultoindenttheleftmargintoemphasisthelogicalstructureofthepredicate.`Thecommand\t1doGesthisbymakingthecorrespondinglineintheoutputhaveonefhelpingofindentation.Asthingsgetmorenested,jyoucansay\t2,j\t3,andfsoon.Butif+youshouldevergetbGeyondt9,`you'llneedtousebracesaroundtheargument:r\t{10},`andyou'dbGetterlookforsomewaytosimplifyyourspeci cation!_4Theselittletabmarksmightlookdi erent tonormaltabsbutareneverthelessconvenient.sThey'reshort,<andtheydon'tgetlongerXasthetabbinggetsdeepGer,0withinreason,sotheycanbGetuckedXinneatlyontheleft,wellCawayfromthemaths.Thesizeof`helping'yougetwith\tisdeterminedbythe\zedtabparameterUU(seeSection7)."3M"*Ek⍑Ifa youwantamorepGowerfulaligningmechanismthantabbingthenyoucanusethemargin stackzasshownintheexamplebGelow.=~Thecommand\MRsetsthefutureleftmargintothecurrenthorizontalpGositionandpushestheoldvqalueontoamarginstack.E}Thecommand\OղresetstheleftUUmargintoitspreviousvqalue(whichispGoppedUUo thestack).fdfffdff  fdT;estff9ffff ff fdx4D;y:NffffffPfffd ff fdxm$+81=x\=0)y]+1=y=0 ffMfdy=xffffff%@"\begin{schema}{Test} "x,y:\nat"\ST"x+1/x=0\imp\My+1/y=0\\"y=x\O\\"\end{schema}_IfiaschemaorotherbGoxcontainsmorethanonepredicatebGelowtheline,itoftenloGoksbGetterUUtoaddatinyverticalspacebGetweenthem,asinthisexample:fdfffdff  fdA}'ddBirthday%ffp#ffff ff fdBirthdayBo}'ok ff fdnc?:NAME ff fdd?:DA;TEffffffPfffd ff fdnc?62knownff ff fdbirthday}^0wβ=birthday][ fnc?7!d?gffffff%@"\begin{schema}{AddBirthday} ╹\DeltaBirthdayBook\\╹n?:NAME\\╹d?:DATE"\ST╹n?\nemknown"\also╹birthday'=birthday\uni\{n?\mapd?\}"\end{schema}zƍThis`isdonewiththecommand\also,cwhichbGehavessyntacticallylike\ST.Thecommand\alsoisprovidedinste}'adjoftheoptionalargumentto\\whichL5ffA͉TU>'ExXprovidesinotherenvi-ronments.If_largerverticalspacingisrequired,thecommands\Alsoand\ALSO?maybGeused(givingUU2and4timesasmuchUUspaceas\alsorespGectively).Normally*,the;contentsofaschemabGoxarekeptonasinglepage./F*orlargeschemasitmaybGenecessaryIFtosplitthebGoxacrosspages.mY*oumustspGecifywhichplacesaresuitableforsplittingusingmoneof\zbreak,\Zbreakor\ZBREAK.IfnosplitispGerformedatthispoint,averticalspacehwillbGeaddedasiftheuserhadtyped\also,m\Also,orh\ALSOhrespectively*.YouhcanalsouseV the\znewpagecommandtoforceapagebreakwithinabGox.s(ThesebreakingfacilitieswillhopGefullyUUneverbeneededforschemas,butmaybGecomenecessaryforclassspeci cations.)!č6LOtherffDisplayEnvironmentsThezedenvironmentcanbGeusedtosetmulti-lineformulaswithoutanenclosingbGox:zitisusefulforgiven-setdeclarations,&theorems,andthemiscellaneousbitsofmathematicsthatdon'tcomeinUUabGox:ȍfd8 8n{:N-nC+8n{2evenc:@"\begin{zed} \alln:\nat\dot\\"\t1*Fn+n\memeven."\end{zed}CƍTheformula\begin{zed}?...\end{zed}ҲmaybGeabbreviatedto\[?...\];thezeden-vironment4isageneralizationofthedisplaymathenvironmentofL5ffA͉TU>'ExX,,sothisrede nitionofcommands݂isfairlybGenign. MNoticethatthemathsisset ushleftonthesameindentationasschemasUUandtheirfriends.qHeretoGoyoucanuse\alsoforalittleextraspacebGetweenlines.F*oralgebraic-styleproGofs,*thereistheargueenvironment._Thisislikethezedenvironment,butNvtheseparationbGetweenNvlinesisincreasedalittle,OandpagebreaksmayoccurbetweenNvlines."4,Ϡ"*Ek⍲When.Ktheleft-handsideislongthisstylewasteslessspacethantheL5ffA͉TU>'ExXeqnarraystyle.dThe intendedUUuseisforargumentslikethis:r}'ev(append(cons!(x4D;s);tز))-=r}'ev(cons!(x4D;append(s;tز)))-=app}'end(rev(append(s!;tز));c}'ons(x4D;nil))-=app}'end(append(rev(tز);rev(s!));cons(x4D;nil)) byUUhypGothesis-=app}'end(rev(tز);append(rev(s!);cons(x4D;nil)))-=app}'end(rev(tز);rev(cons!(x4D;s))):HereUUistheinput:\begin{argue} -rev(append(cons(x,s),t))?\\\t1?=?rev(cons(x,append(s,t)))\\\t1?=?append(rev(append(s,t)),cons(x,nil))\\\t1?=?append(append(rev(t),rev(s)),cons(x,nil))l\quad?\hbox{byhypothesis}\\\t1?=?append(rev(t),append(rev(s),cons(x,nil)))\\\t1?=?append(rev(t),rev(cons(x,s))).\end{argue}TheOexamplebGelowshowsaninferencerule(theoptionalargumentto\derivegivesaside-conditionUUoftherule):ȍfd#` PffEXhXp[x\62fr}'eevars!()] fd#` 8ㄾx\ uP@:\begin{infrule} ҿ\Gamma\showsP:\derive[x\nemfreevars(\Gamma)]ҿ\Gamma\shows\allx\dotP:\end{infrule}NƍTheUUsyntaxenvironmentUUisusedformakingdisplayslikethis:EXPR;<::=N IDENTP{UUidenti er @<-!", cmsy10jN EXPR*EXPRP{UUapplication@l"*Ek⍑ThisUUcanbGecomparedwiththelayoutUUadoptedbytheUQZeditor(version1).fdTYPE::=givenTThUXhNAME3ii NjjTؾp}'owerTThUXhTYPE3iiNjjTؾtupleTThUXhseqUSTYPE3iiNjjTؾschemaTThUXhIDENT׸77!ϾTYPE3iiNjjTؾclassTThUXhIDENT׸77!ϾClassAttrii@"\begin{zed} "TYPE\ddef\MgivenT s,\langNAME\rang\\"\bbarpowerT\langTYPE\rang\\"\bbartupleT\lang\seqTYPE\rang\\"\bbarschemaT\langIDENT\ffunTYPE\rang\\"\bbarclassT\langIDENT\ffunClassAttr\rang\O"\end{zed}dƍThefsidebysideenvironmentfallowsadisplayasshowninthe rsttwocolumnsbGelowtobGe proGducedUUfromthetextofthethirdcolumn.qNotetheuseofthe\commentcommand.X3034fffdfffdSchemao ff#qffff fffd[declarations]ffffff(fffd fffda{<b ffG [pred-1] fffdaaaaa{<bbbbb ffG [pred-2]ffffffN*ގП=IThis. isapara-IgraphwhichhasIthe6samemarginsIasthestandardIschemasUUdo.@"\begin{sidebyside} "\begin{schema}{Schema}"\comment*{declarations}"\ST"a߲The~(horizontal)spacebGetweentheverticallineontheleftofschemas,Hetc.,and theUUmathsinside.qThedefaultis1em.\zedtab)TheUUunitofindentationusedby\t.qThedefaultis2em.\zedbar)TheUUlengthofthehorizontalbarinthemiddleofaschema.qThedefaultis8em.\leftschemasCܲA`(declaration`fwhichmakesschemanamesbGeset ushleft. #Useitinthedocumentpreamble.\zedlinethickness^?ͲThejthicknessofthelinesthatmakeupschemaandclassbGoxes.eY*oucanchangethethicknesswithacommandsuchas\zedlinethickness=0.1pt.ThismaybGeusefulUUifyouarecreatingoverheadslides.0.1pt:㇄qϟ0.4pt:㇄ffqϟ%(TheUUdefault)!1pt:㇄qϟ\baselinestretchXвThe spacingforthetextpartofyourdoGcument.MItdoGesn'tchangethespac-ing8withinZ8environments.It's8defaultvqalueis1.A8commandsuchas\def\baselinestretch{2}willUUmakeyourtextdoublespaced,butnotyourZenvironments.\zedbaselinestretchhDzThespacingfortheZenvironmentpartofyourdoGcument.*It'sdefaultvqalueUUis1.\zedsize.The,dsizeofthematerialwithintheZ,YpartofyourdoGcument.d!ItdoGesn'ta ectthere-mainderofyourdoGcument.JVF*orexample,\zedsize{\large}willgiveyoulargeZsymbGolsandUUequationsbutwillnota ectthesizeofthesurroundingtext.\zedcornerheightXвThe/heightof`corners'thatcanbGeplacedontherighthandsideofthetopandUUbGottomlinesofschemaandclassboxes.qThedefaultis0em(i.e.nocorners).!č8LSymbs3olsMulti-letteridenti ershavebGeenchangedtoloGokbetterthantheydowithvqanillaL5ffA͉TU>'ExX:insteadof=specificationsBֲ,uyou=getsp}'eci cations!.KThe=lettershaven'tbGeenspreadapart,uandtheligature ]޲hasUUbGeenused.Almost allofthemathematicalsymbGolsofL5ffA͉TU>'ExXcanbeused;esomehave beenrede ned|usuallyto xthespacingsothatitissuitableforZspGeci cations.^AThecommandsforobtainingadditionalsymbGolsarelistedbelow.NSometimesmorethanonecommandmayproGduceasymbGolyoumrequire.kY*oushouldusetheonethatseemstobGedesignedforthecontextyouhaveinmind.HuThis]isbGecausethespacingaround(andsizeof)symbolshasbeenchosenfortheirtypicalcontext.ThroughoutpthelifetimeofthesemacrosanumbGerpofalternatecontrolsequencesforanysymbGolYmayhaveexisted.AXlistofaliaseshasbGeensetupsothatoldcommandsmaystillbGeused.ItHisrecommendedhoweverHthatyousticktotherecommendedcommandnamesforsymbGolsasthesehnamesmaybGesupportedbyothertools.PxWithinthetablebelownon-recommendedaliasesareUUsurroundedbybrackets,e.g.,(\power).uL?쥍ㅸ>>?\geq\geqslantڢ=㈲+8*?/+-䍒բLogicGwڢ:\lnot"7\"*Ek⍍^+\land?(\wedge) _+\lor?(\vee)8+\all?(\forall)9+\exi?(\exists)9 51+\exione@+\nexi?(\nexists)+@?\dot(\spot))+\imp?(\implies),+\ifftrue+\truefalse+\falseB+\bool靍Sets:/f qjg0?\{?\cbar\}?0?\emptysetfg0?\varemptyset20?\mem?(\in)620?\nem?(\nmem\notin)P0?\pset?(\power)F0?\fset?(\finset)P 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"}\torderڢpartialfforder "}\porderA"բW ordTSt9ylesڢwor}'d\word{word} 32ڢword\keyword{word}ڢw9ord\boldword{word}ڢwor}'dڢfe\underword{word}ڢwordڢfej\underkeyword{word}ڢw9ordڢfej\underboldword{word}ڢ`word'\String{word}ڢ\word"\STRING{word}ڢa{r}'el{fe 􎎎7ba?\infix{rel}bA"բ8.3bSp`ecialLetterFonts/բGreekڢ \alpha ڢ \betaڢ ㍲\gamma?\Gammaڢ8\delta?\DeltaڢUU"\epsilon?\varepsilonڢ\zetaڢ\etaڢr#UU\theta?\vartheta\Thetaڢ\iotaڢUU{\kappa?\varkappaڢw޲\lambda?\Lambdaڢ\muڢ\nuڢ\xi?\Xiڢ.$r\pi?\varpi\PiڢUU%\rho?\varrhoڢ.&!Ų\sigma?\varsigma\Sigmaڢ\tauڢ.\upsilon?\UpsilonڢUU'\phi?\varphi\Phiڢ\chiڢ . \psi?\Psiڢ!. \omega?\Omega"9 }"*EkCaligraphicwA+\mathcal{A} B+\mathcal{B}C+\mathcal{C}D+\mathcal{D}E+\mathcal{E}F+\mathcal{F}G+\mathcal{G}H+\mathcal{H}I+\mathcal{I}J+\mathcal{J}K+\mathcal{K}L+\mathcal{L}M+\mathcal{M}N+\mathcal{N}O+\mathcal{O}P+\mathcal{P}Q+\mathcal{Q}R+\mathcal{R}S+\mathcal{S}T+\mathcal{T}U+\mathcal{U}V+\mathcal{V}W+\mathcal{W}X+\mathcal{X}Y+\mathcal{Y}Z+\mathcal{Z}Blac9kBoardTBoldA+\mathbb?AB+\mathbb?BC+\mathbb?CD+\mathbb?DE+\mathbb?EF+\mathbb?FG+\mathbb?GH+\mathbb?HI+\mathbb?IJ+\mathbb?JK+\mathbb?KL+\mathbb?LM+\mathbb?MN+\mathbb?NO+\mathbb?OP+\mathbb?PQ+\mathbb?QR+\mathbb?RS+\mathbb?ST+\mathbb?TU+\mathbb?UV+\mathbb?VW+\mathbb?WX+\mathbb?XY+\mathbb?YZ+\mathbb?Zk⍒բMiscellaneous?Cڢ}\hslash ڢ~\hbarڢ\backepsilonڢg\ethڢi\bethڢj\gimelڢk\dalethڢ{\complementڢ|\intercalڢ@\alephڢr\nablaڢ~\hbarڢ{\imathڢ|\jmathڢ`\ellڢ}\wpڢ<\Reڢ=\Imڢf\mhoڢz\digamma#{բ8.4bShap`esf_ڢ2\Boxڢ\squareڢ\blacksquareڢ\diamondڢ3\Diamondڢ\lozengeڢ\blacklozengeڢB\vartrianglerightڢC\vartriangleleftڢH\blacktriangledownڢI\blacktrianglerightڢJ\blacktriangleleftڢM\vartriangleڢN\blacktriangleڢO\triangledownڢ4\triangleڢ/\triangleleftڢ.\trianglerightڢ4\bigtriangleupڢ5\bigtriangledownڢ|\clubsuitڢ}\diamondsuitڢ~\heartsuitڢ\spadesuitڢ\astڢ?\starڢz\malteseڢF\bigstarڢ \bigcircڢ\circˢ10 "*Ek⍍+\bullet +\centerdot+\cdot+\cdots:::+\ldotsԍ...+\vdots3. q. UM.+\ddotsCircledTOpQerations6s+\circledS }+\circledcirc~+\circledast+\circleddashr+\circledRײc +\copyright+\fovr +\ominus +\otimes +\oslash +\odotBo9xedTopQerators6+\boxdot +\boxplus+\boxtimes +\boxminus8.5ArrowSymb`olsX{LeftTArro9ws +\leftarrow\gets(+\Leftarrow UX-+\hookleftarrow(+\leftharpoonup)+\leftharpoondown UX+\longleftarrow(UX=+\Longleftarrow+\twoheadleftarrow+\leftleftarrows+\leftarrowtailW+\Lleftarrow8+\nleftarrow:+\nLeftarrowRigh9tTArrows!+\rightarrow?\to)+\Rightarrow7!+\map7v!+\longmapstok⍍ڢ,UX!\hookrightarrowڢ*\rightharpoonupڢ+\rightharpoondownڢ;\leadstoڢ!\longrightarrowڢ=UX)\Longrightarrowڢ\twoheadrightarrowڢ\rightrightarrowsڢ\rightarrowtailڢ \rightsquigarrowڢV\Rrightarrowڢ9\nrightarrowڢ;\nRightarrow+<բLeftTRigh9tArrows)wڢ$\leftrightarrow ΍ڢ,\Leftrightarrowڢ \rightleftharpoonsڢ UX!\longleftrightarrowڢ(UX)\Longleftrightarrowڢ \rightleftharpoonsڢ \leftrightharpoonsڢ\leftrightarrowsڢ\rightleftarrowsڢ!\leftrightsquigarrowڢ<\nLeftrightarrowڢ=\nleftrightarrowբUpTDo9wnArrows)wڢ"\uparrowڢ*\Uparrowڢ#\downarrowڢ+\Downarrowڢl\updownarrowڢm\Updownarrowڢ\upuparrowsڢ\downdownarrowsڢ\upharpoonrightڢ\downharpoonrightڢ\upharpoonleftڢ\downharpoonleftˢ11 ʠ"*EkMiscellaneousCƍ%+\nearrow2&+\searrow.+\swarrow-+\nwarrow+\circlearrowright +\circlearrowleft+\Lsh+\Rsh"+\looparrowleft#+\looparrowrightx+\curvearrowlefty+\curvearrowright2ˢ12 "*Ek⍍8.6Relations"+\llfg+\ggn+\lll?\lllesso+\ggg?\gggtr@+\sqsubsetA+\sqsupsetv+\sqsubseteqw+\sqsupseteq3+\owns`+\vdash +\Vdash+\vDasha+\dashv+\VvdashjUX=+\models0+\nvdash1+\nVdash2+\nvDash3+\nVDash?+\perp+\sim'+\simeqh+\eqsimv+\backsimw+\backsimeqs+\thicksim+\nsim+\approx6+\napproxt+\thickapproxu+\approxeq+\asympT͍+3=+\cong+\ncongT΍:2=+\doteq++\Doteq?\doteqdot:+\risingdotseq;+\fallingdotseql+\lessdotm+\gtrdotP+\eqcirc$+\circeql+\bumpeqm+\Bumpeq*,+\triangleqk⍍ڢ(\multimapfgڢ/\proptoڢ_\varproptoڢ.\lesssimڢ&\gtrsimڢ/\lessapproxڢ'\gtrapproxڢ\xprecڢ\xsuccڢ\preceqڢ\succeqڢ-\precsimڢ%\succsimڢw\precapproxڢv\succapproxڢ0\eqslantlessڢ1\eqslantgtrڢ2\curlyeqprecڢ3\curlyeqsuccڢ4\preccurlyeqڢ<\succcurlyeqڢ5\leqqڢ=\geqqڢ6\leqslantڢ>\geqslantڢ7\lessgtrڢ?\gtrlessaڢQ\lesseqgtr#ڢR\gtreqless"ڢS\lesseqqgtr !ڢT\gtreqqless(ڢ\lvertneqqڢ\gvertneqqڢ\nleqڢ\ngeqڢ\nlessڢ\ngtrڢ\nprecڢ\nsuccڢ\lneqqڢ \gneqqڢ \nleqslantڢ \ngeqslantڢ \lneqˢ13"*Ek⍍ +\gneqfg+\npreceq+\nsucceq+\precnsim+\succnsim+\lnsim+\gnsim1+\nleqqM+\ngeqq+\precneqq+\succneqq+\precnapprox+\succnapprox+\lnapprox+\gnapproxb+\Subsetc+\Supsetj+\subseteqqk+\supseteqq"+\nsubseteqqfg#+\nsupseteqq$+\subsetneqq%+\supsetneqqfg(+\subsetneq)+\supsetneq*+\nsubseteq++\nsupseteqD+\trianglerighteqE+\trianglelefteq4+\ntrianglerighteq5+\ntrianglelefteq6+\ntriangleleft7+\ntrianglerightG+\betweenj+|?\vert\midk+\|?\Vert\parallelkqj+\interleavep+\shortmidq+\shortparallelpq+\shortinterleave,+\nparallel-+\nmid.+\nshortmid/+\nshortparallelk⍍բ8.7bBinaryOp`erations)ڢf\curlywedge32ڢg\curlyveeڢY\veebarڢZ\barwedgeڢ[\doublebarwedgeڢ\pmڢ\mpڢ\timesڢn\ltimesڢo\rtimesڢh\leftthreetimesڢi\rightthreetimesڢ>\divideontimesڢ\dividesڢ]\uplusڢu\sqcapڢt\sqcupڢd\Cup?\doublecupڢe\Cap?\doublecapڢn\backslashڢn\setminusڢr\smallsetminusڢo\wrڢ\lhdڢ\rhdڢ\unlhdڢ\unrhdڢ\restrictionڢq\amalgڢ>\topڢ?\botڢ`\smallsmileڢa\smallfrownڢ^\smileڢ_\frownڢt\pitchforkڢu\dotplusڢ1\Joinڢ.UX/\bowtieˢ14"*Eۺ⍍8.8MiscellaneousSymb`ols/ۍy+\dagger z+\ddaggerx+\sectionsymbol{+\P\+\angle]+\measuredangle^+\sphericalangle0+\prime8+\backprimefp+\surds+\smallint[+\flat\+\natural]+\sharp@+\partial1+\inftyU+\yen)+\therefore*+\becauseX+\checkmarkA卍8.9Variable-sizedSymb`olsuTThesegsymbGolscomeintwosizeswhichdonotvqarywiththepGointsizeofyourfont.{-ThebigsizecanbGeobtainedbyprecedingthesymbGolcommandUUwiththecommand\displaystyle.soP8ޟX+\sumoQlY+\product`la+\coprod䍍īR UNcZ+\integralZīH UNcI+\oint卍T\+\bigcapS[+\bigcupFG+\bigsqcupW_+\bigveeV^+\bigwedgeJK+\bigodotNO+\bigotimesLM+\bigoplusU]+\biguplusբ8.10"DelimitersxբThesersymbGolscanbemadelargetosurround բlargeUUformula.qE.g.,(<\$3;?n .X Ñ/0Iif=1>x4Di攟\%3wբwasUUgeneratedusing;Lբ\left\lfloor...\right\rfloor썍ڢ( )(?)fgڢf g\{?\}ڢb c\lfloor?\rfloorڢd e\lceil?\rceilڢh i\langle?\rangleڢp q\ulcorner?\urcornerڢx y\llcorner?\lrcornerڢ"\uparrowڢ#\downarrowڢl\updownarrowڢ*\Uparrowڢ+\Downarrowڢm\UpdownarrowLǍբ8.11"MathAccents^ڢa\hat{a} ׫bڢa\widehat{a}!+cڢaa\widehat{aa}vdڢaaa\widehat{aaa}~ڢa\tilde{a}׫eڢa\widetilde{a}!+fڢaa\widetilde{aa}vgڢaaa\widetilde{aaa}ڢa\check{a}ڢa\breve{a}ڢa\acute{a}ڢa\grave{a}ڢa\bar{a}N~ڢa\vec{a}/e_ڢa\dotaccent{a}ڢa\ddot{a}բ8.12"SizeCommandsڢ =5" cmmi9 +2cmmi8\mu?\zsmall\mu\zSmall\mubڢ gff cmmi12ڭDgG cmmi12D\zbig\mu?\zBig\mu\zBIG\muˢ15;"EDgG cmmi12Aӱ msam9@/2i lasy9=5" cmmi9 cmmi10K`y cmr10ٓRcmr7Zcmr5u cmex10