; TeX output 2003.02.18:1310y?DtGGcmr17A7tShortGuidetoNathXQ cmr12M.MarvXan*14FVebruary2003!>Ɍ cmbsy10x"V cmbx101.tAnnotation. K`y cmr10NathYisaL5ffٓRcmr7A͉TU>'ExXstyletoseparatepresentationandcontent >in_mathematicaltypGography*._Thestyledeliversaparticularcontext-depGendent>presentationsonthebasisofarathercoarsecontext-indepGendentnotation.Al->though@essentiallybackwardcompatiblewithL5ffA͉TU>'ExX,NathaimsatproGducing>traditionalmathtypGographyevenfromsourcesdevoidofaestheticambitions.>ItsUUnameisderivedfrom\': cmti10nacturalmathnotation"(see[4]).dۍ>x2.License. Nath=sisafreesoftware=sdistributedunderthetermsoftheGNU>GeneralUUPublicLicense,seex3.Usage. T*o<'ExXinputdirectory.>AUUL5ffA͉TU>'ExX2.09doGcumentmaystartlike7>\documentstyle[nath]{article}>UnderUUL5ffA͉TU>'ExX2 0ercmmi7"G4,thee ectisachievedUUwith>\documentclass{article} >\usepackage{nath}>NathwdoGesnotintroduceanynewfonts.See !", cmsy10x28forcombiningNathandother>L5ffA͉TU>'ExXUUstyles.dۍ>x4.LoQcaloptions. AlfewlNathoptionsmaybGesetinthebodyofadocument.>Thecommand\nathstyleacceptsalistofargumentsoftheform`name[=value'>orM`name';thelatterhavingthesamemeaningas`name[=on'.Currentlysup->pGorted;optionsaregeometry(seex10),tensors(seex18),leqno(seex22),and>silentUU(seex5).܍>x5.?Errorsandw9arnings. Natherrorsarevisualizedby N8 K(orwhateveris>\natherrormark)Oplacedwheretheerrormanifestsitself(whichmayloGokmis->placed).Unlikeerrors,NathwarningsappGearonlyinthelog leanddosoonly>ifUUtheloGcaloption(seex4)silentissettoon.MBeawarethatonceadmissibleconstructionsmayproGduceTU>'ExXerrorsnow.>E.g.,supGer uousbracesmaybeharmfulinmathformulasexceptaroundmacro>arguments.mTherefore,{and}shouldbGeusedjustwheresomething(asub-or>supGerscript,UUanumerator,adenominator,andsimilar)beginsorends.1*y?>x6.\AMathmoQdes. Nath"uses twodistinctmathmoGdes.Thesingledollarsign >$Finvokesthein-linelmoGde.Thedoubledollarsign$$aswellasothermath>environmentsUUinvokethedisplay7ҲmoGde.MObserveUUthedi erence:$(1?+\fracxy)^2$UUtypGesetsas(818+ b> cmmi10x=y[ٲ)?h^2۲,UUwhilei;>$$>(1?+\fracxy)^2>$$>typGesetsUUas꧍nu cmex10u\t18+<$lxljBL ׍:y Vb֟2/I; >evenUUthoughthenotationisoneandthesame.MCommands\inlineand\displayedforceeithermoGdeonasubexpression.>Sub-UUandsupGerscriptsarenormallytypesetinin-linemode;but>$$>(\sum_{i=1}^n?x_i^p)^{\displayed{\frac1p}}>$$>proGducesUUthedisplaymodeinthescriptH-size:n`x n sX tti=1Ux1ɍpˍiR`󩖍 ٱ1 iLRS卍p:ō>NeverUUleavedelimitersun\displayedinthesecases.MThe ~fourmathstyleswitchesofTU>'ExXnewlyreferonlytothesizeofmath>expressions:\scriptstyleand\scriptscriptstyletothescriptandsecond->level-script4sizeofthecurr}'ent size;\textstyleisvoid;whereas\displaystyle>hasaspGecialmeaninginthecontextoftheprincipleofsmallestfences(seex8).>x7.andUUmayoGccurinthreeshapes:΁nbuilt-up<$(AjBL9 ׍B'O;piece 7311731&fes2NathW>providesLasingleuniversalcommand\frac(bGesidesoftheobviousslash,>`/').UUTheresultingshapGeisdeterminedbyspecialalgorithms(see[4]).>x8.aDispla9yedfractions. Non-numericfractionscomeoutasbuiltup.Ac->cording1towhatwecalltheprinciple,ofsmallestfenc}'es,1numericfractionsare>typGesetUUbuiltupifandonlyifthisdoesnotextendanypaireddelimiters.E.g.,i;>$$>(\frac?12+x)(\frac12+\frac1x)>$$2 y?>resultsUUin*n( s±1sŸ&fes2zH+8x)㏟<$ s61 s6wfe (֍2J+<$ǡ1ljBL ׍x Vbֵ:fT>OneUUcancircumventUUtheruleintwoUUpGossibleways. Kq(i)ZN8In6ordertoforceabuilt-upfraction,place\displaystyleanywhere>withinUUthenearestpairofdelimiters.E.g.,񍍍n <$v1vwfe (֍2~+8x \t<$1wfe (֍2X/+<$ǡ1ljBL ׍x VbO>resultsUUfromݍ>$$>(\frac?12+x\displaystyle)(\frac12+\frac1x)>$$H(ii)ZN8Inlordertoforceacasefraction,insertanextrapairofinvisibledelimiters.>E.g.,@ncZyxdx= K1K&fes2 ԙx2t'>resultsUUfrom>$$>\int?x\,dx=\left.\frac12x^2\right.>$$>Comp}'oundfractionsUUhavetheirnumeratoranddenominatorindisplaymoGde:$1o3318+<$lxljBL ׍:yo33 uULVa \18<$lxljBL ׍:y:$c>OneUUcan,ofcourse,forcethein-linemoGde.Namely*,>$$>\frac{\inline{1?+\fracxy}}{\inline{1-\fracxy}}>$$>or,UUevenbGetter,>\newcommand\ifrac[2]{\frac{\inline{#1}}{\inline{#2}}}>$$>\ifrac{1?+\fracxy}{1-\fracxy}>$$>(cf.UUx26)typGesetsas<$o3318+x=yo33jBL!2 ׍18x=yZ:3y?>x9.pIn-linefractions. Aɹ\frac%withnumericargumentsresultsinacase >fraction,suchastheBernoullinumbGerB12 ?= 1m69133&fe̟2730X2.Otherwisewegetasolidus>fractionandparenthesesareaddedwheneverneededforpreservqationofthe>mathematicalUUmeaning.E.g.,>$\frac{\frac?ab}{\fraccd}$>proGducesUU(8a=b)㏵=(c=d). MExamplesi\bGelowpresentoneandthesameexpressionindisplayandin-line>moGde.Roughlyspeaking,Nathassumesthatbinaryoperationsotherthanslash>haveUUlessbindingpGowerUUthantheslash,j<$o33a8+bo33jBL̸ ׍c8+dϟ(.a8+b)㏵=(c8+d)뿵;)"؍<$pffa8bpffjBL̷ ׍Inparticular,thisruleappliestothebinaryopGerationsofcommutativealgebra:<$o~OAo33jBL9 ׍Bz <$CljBL ׍DϟA=BQ 8C=D ;"<$oA8 Bo33jBL> ׍C 8Dϟ(.A8 Bq)d=(㏵C DG),2;5|>eventhoughexistingtraditionmaybGedi erentinthisparticularcase.Onthe>otherUUside,juxtap}'ositionhasmorebindingpGowerUUthantheslash:ۍ<$o33ao33jBLI0 ׍Cb<$wScvɟjBL4r ׍dϟ(.a=b)(c=d) z;<$r@o33jBL q ׍@8x<$}. f}. jBL ׍lgϟ(.@8=@x)(f=g[ٲ)l;]͍nd<$33u33jBL~ ׍Bavϟd(㏵u=v[ٲ)k;<$uw@83 fo33jBLٟ @@8x@y[ٟ2ϟ@8^3 f=@8x@y[ٟ^2';e6<$pao33jBL ׍bcϟa=bcU:D>NathonlyavoidsinsertingparenthesesbGetweenafractionandanumericcoGef-> cient,UUe.g.,'jn<$33u33jBL~ ׍Bav XIJ+82<$33u33jBL~ ׍Bav<$l1lwfe (֍2<$ }"a }"jBLI0 ׍Cbϟu=v+82u=v l1l&fes2a=b9ۦ;4Ny?>unlessUUthereisadangerofconfusion,e.g.,򹍍n2<$33u33jBL ׍%vϟ2(㏸u=v[ٲ)L:ƍ>IncaseofloGosejuxtapositionbetweenoperatoranditsargument,thereisno >obviousUUwinner,thus<$o33sin}$xo33jBL ׍Tq2H(+8sin<$]ٵx]ٟjBL ׍[2ϟ(.sinx)㏵=28+sin(cx=2)5=ٵ:>Of course,noparentheseswillbGeinsertedwhentheyarealreadypresentinone>orUUanotherform:nA<$zQuzQjBL~ ׍Bav g 2ϟA[u=v[ٲ]"^2H;'I<$s(wϧx;y[ٞ)o33jBL ׍kxkk y[ٞkϟ(.x;y[ٲ)?h=kxkk y[ٸk:PH>(the*lastexampleuses\lVert?x\rVert\,\lVerty\rVert*inthedenomi->nator).MGroupingpreventsNathfromaddingparenthesesaroundthewholefraction:>$a{\frac?bc}$typGesetsasab=c ,otherwiseasa(㏵b=c).T*obeonthesafeside,>avoidUUsupGer uousbracesinmathformulas(cf.x5).MT*odisableparenthesesaroundthenumeratorordenominator,apairofinvis->ible/parenthesesisneeded:$\frac{\left.\sin?x\right.}{\cosx}$/typGesets>asUUsinGx=cos7x,UUotherwiseas(8sin*x)㏵=cosx.MAn=impGortantremarkisdue.ProfessionaltypGographersgenerallyfollowthe>rule&that`a=bcmeansadividedbybc.'Stillsomemathematicians(espGecially>thosewithaprogrammingbackground)arguethatifjuxtapGositiondenotesmul->tiplication,thena=bcmeansa=bc,whichis(ea=b)srcbythecommonlyaccepted>rulesofprecedence.However,abandabaredi erentnotationsanditisthe>notationjwhatmattersintypGography*.jYettheAIPj stylemanual[1]iscautious>enoughutosayjust:\donotwrite1=3xunlessyoumean1=(3x)."uAltogether,no->tationa=bcisconsideredambiguousbyanonignorablepartofthemathematical>community*.Then,atleast,thechoicesmadebyNathareknown,traditional,>andUUeasytoremembGer.MAnd,UUofcourse,itisneverunwisetodisplaydicultfractions.>x10._Delimiters. TU>'ExX's쬹\leftand\rightproGduceratherpoorresults,es->pGeciallywhenoverusedorunderused.Undernaturalnotation,everyfenceisa>left]orrightdelimiterbyitsverynature,anddelimitersdotheirbGesttomatch>theUUmaterialenclosed:񍍍<$/Mo33jBLË1\t18lx1S+g+xn^+pZlLRD ׍&rV[x^?0 ^?@fв1pٍ@8ZffL ׍@8x2]+g+; @8ZlL ׍@8xn33 LJ ׍"j:xLfh1 LfhAY):5*Ǡy?>F*ormatchingpurpGoses,everyNathmathematicalob8jectisassignedanauxiliary >heightFanddepth;sub-andsupGerscriptsaswellasaccentsdonotcontributeto>theseUUdimensions,hence\smallparts"mayexceedthefences: 󀍍n(x䍑sXeq㏵PqP|5x䍑;e8Q8Q [)`β18+򣊍 O!cmsy7b΍0Opp zOpW ~2 znoc \vY tVi=1µpiTL` M0ޱ2 ɣ:5ҍ>NeedlessUUtosay*,linebreaksareallowedbGetweendelimiters.E.g.,nsin{2nx=2ncosߵxGsin8x p+n EşX 8k+B=1s(4)㏟k<$ R( n2S812|s)`( Cn222|s) _(Cn2kP2 ) RjBLqß ׍0(4v82kw81)!Qsin*2k+B1h-x?o{>resultsUUfromthesimpleߍ>$$>\sin?2nx=2n\cosx[\sinx\\>\qquad?+\sum_{k=1}^n(-4)^kC?\frac{(n^2?-1^2)(n^2-2^2)\dots(n^2-k^2)}{(2k-1)!}C?\sin^{2k?-1}x]>$$.>ThemoGdi ers\leftand\rightstillmustbeusedwithsymmetricdelimiters>(e.g.,1verticallinesjandk)orwhenintendedtooverridethenaturaldispGo->sition(e.g.,\left]).ThenewlyintroGducedmodi ers\doubleand\triple>createdoubleandtripledelimiters.E.g.,$\double[u_1,\dots,u_n\double]$>proGducesUU[[ȵu1|s;:::;unq~]6] .MThemiddle 0delimiters!,suchas\midand\middle|forjײ,\Midand\double|>for\Sj!jƲ,\Sand\triple|forj!jj ,have\Sthesizeofthenearestouterpairofdelimiters.>F*orUUexample:n`nt(x;xiTL) 2Rǟ1 Sī  S S 1 p1X t.i=1!x2፴iC=1`o:5ҍMWithWnesteddelimiters,therearetwoWwaystoensurethatouterdelimiters>comex^outbiggerthaninnerones.IndisplaymoGdethisiscontrolledbyacount>\delimgrowth.]Settingthe\delimgrowthtonmakes(approx.)everynthde->limitergbigger.Oneshouldset\delimgrowth=1whenadisplaycontainsmany>verticalUUbars(andinsertextra\,bGetweenadjacentrightandleftbars).MInain-linemoGde,thec}'ommand\bighasthee ectthatthenextenteredlevel>ofdelimitersissetinbigsize(inthesenseofplainTU>'ExX).Itisnotnecessarythat>the`E\bigisimmediatelyfollowed`Ebyadelimiter;and\biggisanabbreviationfor>\big\big.u F*orinstance,$\Delta\big?\frac1{f(x)}$u proGducesbW1=f(x)㏟bx;>in`Cthisway`Conecanenlargeimplicitdelimiterssuchasthoseinducedbythe>commande\frac.Itisanerrortoplacea\bigwithindelimitersthatarenot69y?Fp]1(LeftUUdelimitersYRightUUdelimitersuFfftfd(fG(t ffzػ)۵) [,\lbrackfG[t ffzػ],\rbrack۵]\{,UU\lbracefGft ffzػ\},UU\rbrace۵g<,UU\langlefGht ffzػ>,UU\rangle۵i\lfloorfGbt ffzػ\rfloor۵c\lceilfGdt ffzػ\rceil۵e\lvert,UU\left|fGjt ffzػ\rvert,UU\right|۵j\lBrack,UU\double[fG[h[t ffzػ\rBrack,UU\double]۵]zW]\lAngle,UU\double۵isi\lFloorfGbi Gbt ffzػ\rFloor۵cc\lCeilfGdi Gdt ffzػ\rCeil۵ee\lVert,UU\ldouble|fGjhjt ffzػ\rvert,UU\rdouble|۵jzWj\triple[fG[h[jf[t ffzػ\triple]۵]zW]?]\triple۵isii\ltriple|fGjhjjfjt ffzػ\rtriple|۵jzWj?jw>o cmr9T:ableT1:P9aireddelimiters7>big?themselves.UnbalanceddelimitersmaybGepresentinanin-lineformula(as >isUUusualintensorcalculus|cf.x18),butthencannotbGeresized.MT*able?|1listspaireddelimiters.Toenableasanotationforangle>braces,Xonemustset\nathstyle{geometry}(thismisusageofnotationiscom->moningeometryandmathphysics).AssymbGolsofordering,canbe>alwaysUUaccessedthrough`\lt'and`\gt'.MWhilevJinmathmoGdes,bracketsvJ[,]neverdenoteoptionalarguments.This>helps}toavoid}commonL5ffA͉TU>'ExXmisinterpretations,aswith\\[.Ontheotherside,>gr}'oupinginterspGersedwithdelimiters|onceharmless|isaseriousdefectnow>(cf.UUx5).E.g.,({x)}derailsTU>'ExXifusedindisplaymoGde.>x11.TOpQerators. NathUUtypsets\lambda\mathop{\rm?id}-gUUasnid 8߸8g[;>whereasTU>'ExXwouldputunevenspacingaroundtheminussign:id g"g,erro- >neouslyUUconsideringtheminussignaunaryopGerator(by[3,rule5onp.442]).MInUUsubscriptsofbigopGerators,\\isallowedUUandstartsanewline,e.g.,7>$$>\sum_{i,j?\inK\\i\nej}a_{ij}>$$>printsUUasЍq9X,ni;jg2K8⍍rji6=j.aij :7Hy?MWithin4math,theexclamationmark!aloneensuressuitablespacingaround >factorials:4C^n_k?=\frac{n!}{(n-k)!k!}typGesetsasC^nvkﲲ=n!=(㏵n<kP)4&!kP!or)nCnkﲲ=<$n!KjBL,D$ ׍(㏵n8kP)4&!kP!1q:_>MayUUbGedoubled:(82n)!!=n!2^nq~.MFinally*,K]integralsignsstickonetoanotherunlesssomethingelseintervenes:>$$>\int\int\int_M?dV.>$$>proGduces,ncZscZyG cZ~Z yM`^dV9:>x12.u|Abbreviations. AccordingtotypGographictradition,namesofvqariables>thathwareabbreviationsshouldbGetypesetinroman,forwhichNatho ersahandy>notation:/abbreviationsareletterstringsstartingfromthebackquote``'.E.g.,>$`e^{\pi`i}$UUand$`ad_x?y$typGesetase^@Li?2=1andad 㐟xy[ٲ,respectively*.MStringsKcontainingmorethanoneletter,suchas`span,bGecomemathoper->ators.UntilnowtheymusthavebGeendeclaredinadvqancewithsomeadditional>careUUtoavoidUUcon icts(\spanisaTU>'ExXprimitive).Somemoreexamples:unH0eO=H0ፍsymm; +8H0ፍantisymm";W\qp'!nfnfwj=fjint U};Nna=constp1Ë; {nG=SOp(n)㏵:L0>x13.uRoQots. Nath's2\sqrtdi ersinseveralaspGects.Firstly*,itsverticalsize>neverUUdepGendsonthepresenceofsubscripts:nn6rpvÍrfeI0yovÍaH+rp mrfe ܟyo maj:>Secondly*,UUnested\sqrt'sarealignedatthetop: ncos<$9ܵ~AjjBL  ׍10;=<$K1Kwfe (֍4 F] opF^ ofe*G 󑎎qkF^108+2n6rpÍrfeyoÍ5A#:G>(CompareUUitwiththeTU>'ExX'sNncos<$9ܵ~AjjBL  ׍10;=<$K1Kwfe (֍4 'q(fe(9 108+2=VpUW=Vfeª5>fa:)z>Thirdly*,nooptionalargumentsareallowed.L5ffA͉TU>'ExX's\sqrt[3]{x}mustbGere->placedUUwith\root{3}{x}toproGduceލ|qP>Zcmr53兩p=雷fe[Y"=x.8 V0y?>x14.(SpQecialsym9bols. Nathj introGduces\vinand\nivasnamesoftheim- >pGortantUUsymbolsUU`n:B!N8B!t'and`pB!B!N8'notincludedinanystandardmathfont.MArrowsX\to,\ot,\otto,and\mapstoareexpandableanddescriptablevia>sub-UUandsupGerscripts.Thus,!g>$$>A?\to^f_{\text{isomorphism}}B,\qquada\mapsto^fa'>$$>gives lnA̍f4lUXq΍UXUXUXUXUXUXUXUX4isomorphism' !?D\Bq;a7̍f4UXÎ0!a09::yMTheAcommand\adotdenotesthecentereddottobGeusedaanargument>placeholder,UUasinf( h)org[ٲ(?f +;m) .K>x15.Horizon9talbraces. The7uppGerandlower7horizontalbracesarecreated>withh\underbrace{expr}'essionc}_{label}and\overbrace{expressionc}_{label},>respGectively*.UUForinstance,>$$>f^n(x)?=\underbrace{f(f(\dotsf(}_{n\text{times}}x)\dots))>$$>resultsUUinnfn ( hx)==f~` sf~b5f( K7=|31 {z31 }7nȱtimesﷵx)78ޟ~b5~`%>ObservejthattheconstructiondoGesnotinterferewiththedisplayedmoGdeof>delimiters.K>x16.VhAccen9ts. Hat,tilde,andbaraccentsareextensibleandgrowwiderwith>theUUsizeoftheaccentedmaterial:n$^nanav,+\q;b8ab8abC+\q,c8abc8abc>:>Whentheseaccentsoutreachtheirlimitofextensibility*,theytakethesupGer- >scriptUUpGosition:n(q㏵a8+b+c) k^:>A Zsequence lofaccentsgoGesfromtoptodownorfromrighttoleft.F*orinstance,>\hat\bar?a+UU\hat\bar{ab}+\hat\bar{abc}gives]On$naǍn$^^9nanav,+_>{0䍍8ab8;bȍ8ab8abC+ ,|0䍍8abc8,cȍ8abc8abc>;>whereasUU\hat\bar{a?+b+c}typGesetsas_rn(q㏵a8+b+c) k^D:9 by?>AllUUkindsofthingsmayhappGenifbracesinterveneasin\bar{\bar{ab}}. MLet7usnotethat\barisnotarbitrarilyextensible,unlike\overline.F*or>instance,n\hat{\overline{a?+b+c}}gives~l7#]a8+b+c*^^3Z(over-andunderlines>and@arrowsarenotaccents).Overasinglecharacter,thereisnolimitonthe>numbGerUUandtypeofaccentsinthesequence;e.g.,LЍx䍑njfnWpꫲUnWrnjcCnWnW{>results`from\hat\ddot\tilde?W.Overanexpression,anon-extensibleaccent,>like"\dot,makesothersnon-extensibleaswell.Thus,\hat{ab}?+\dot{ab}+>\dot\hat{ab}?+UU\hat\dot{ab}givesf\qpЫbnabnabzwc+8(oab)؟O.~~+8(oab)؟k^~:. +8(oab)؟O.Şk^-:6>x17.TArra9ys. EntriesUUaretypGesetindisplaymoGde:xn n n n n XrxEڲ1 5s[1<$E1LjBL ׍xC C C C C =0:>Moreover,UUarraysgrowsmallerwhenusedinsub-andsupGerscripts:ۍnerqǟR̫lxjab#,xsc3dR̫lq:{>Aҹmatrixenvironmentdi ersfromarrayinthatitdoGesnothaveanypreamble. >AsUUaspGecialcase,\binom{m}{n}createsthebinomialcoecienta1ꬴm#,;naG.6>x18.T ensors. With\nathstyle{tensors}, rst-levelsub-andsupGerscripts>toUUordinarysymbGolsoccupypredeterminedpositions.Thus,b%nAg[Cgk/Bgql `]J( k Col `)>resultsUUfromc>\nathstyle{tensors=on}>$$>A^{[k}?B^{l]}_{(k}C_{l)}>$$>(unbalancedUUdelimitersareallowedinin-linestyle).6>x19.UDispla9yedformulas. Displayedvformulasareindentedby\mathindent>ofdefaultvqalueof4pGc.With\mathindentsettoanegativelength,displayed>formulastarecentered.F*ormulasenclosedbGetweendoubledollars$$areunnum->bGered.+@AlternativelyonemayenclosethembGetween\[and\].Endsoflines>(anyt#formulamaybGemultiline)aremarkedwith\\.NathdoGesnotsupport>automaticUUlinebreaks(asdoGestheDownesstyle[2]).10 n\y?ME.g.,HZ$$<stu =<stu ?,?\\<stu =<stu .?$$HZtypGesetsasaleft-alignedmul- >tilineUUformula(thepunctuationisimpGortant,seex24):rnJl18ώ=Jl1C ;ύnJl1qϟ▷=Jl18ώ;:"F獑>T*o@achieve nerarrangements,onemaybGegineverycontinuationlinewitha>numbGer7vof\quad's;e.g.,two7vinfrontofabinaryrelation,threeinfrontofa>binaryUUopGeration:덑>$$=stu X?=<stu +?(stu ?\\>\qqquad?+<stu ?)\\>\qquad?=<stu \\>\qquad?=<stu .>$$>givesnJl1qϟ▷=Jl1s玑!s+8(oJl18ώ0p+8Jl1C|g)=Jl1+V𳍍=Jl1n).:G>x20.%W alls. W*alls!representasimpleandconvenienttoGoltoachievebGetter>visualZappGearanceofcomplexdisplayedZequations.Thesyntaxis\wall<stu \\=stu X?\\?G%\\<stu \return,?andcanbGearbitrarilynested.The\wallmakes>everyUUnextlinetostartatthe\wall"untilremovedby\return.F*orinstance,>$$=stu >\wall?=<stu +(\wall-<stu \\+<stu ?)\return]=<stu \\]=<stu ?.>\return>$$>givesnJl1s玎:=Jl1s玑!s+8(YJl1qϟc_Q+8Jl1C|g) !g:=Jl1n).:/ >The_,typicalplacementof\wallisinfrontofarelationsymbGolorimmediately>afterUUanopGeningdelimiteranywhereinthelefthalfofaformula.MAsimplealternativeis\padded{A},whichpre xeseachcontinuationline>withUUAuntilstoppGedby\return.Typically*,Aisakern:11 zy?>$$ >\padded\qquad?\padded\quad<stu =<stu +(stu ?\\ +<stu \\ +<stu ?)\return=<stu \\=<stu >\return>$$>givesnJl1qϟ▷=Jl1*ێ/+8(oJl18ώq+8Jl1nc_q+8Jl1C|g)/o=Jl1qϟvA_:?ፑ>With߸shortformulasitmaybGeeasiertopre xeachlinewithexplicit\quad's>asUUwedidinx19.MSeeUUx24ontheinterplayUUbGetweenwallsandpunctuation.6>x21.YAlignmen9ts. Unfortunately*,displaymoGdeofdelimitersinterferesbadly>with!,alignmentsunlesseverycellisbalanced(asis,e.g.,withmatrices).The>recommendedBsolutionisto llthecellswithbalancedwall/returnbloGcks.E.g.,>\begin{eqnarray*}=stu X?&=&?\wall<stu \\?+<stu \\?+<stu ?,m?\return>\\=stu X?&=&<stu >\end{eqnarray*}>proGduces@$ӰgnJl19󎎎 =AJl1+V𳍍 +8Jl1+V +8Jl1U[W;,OsȟJl1+ =AJl1Cȵ:>W*allsUUsave&'sandensureverticalcenteringoftheequationnumbGers(seex22).6>x22.Equationn9umbQering. AformulaenclosedbGetween\begin{equation}>and׹\end{equation}obtainsasinglenumbGer(thevqalueof\theequation)on>theright.Puttingthecommand\numberedinsideofanunnumbGeredformula>hasUUthesamee ect:12 y?>$$ =stu R.?\numbered>$$:>resultsUUin nJl1>Q>:8(1)>Alternatively*,UU\eqno{A}makesAtheequationnumbGer. MInUUemergency*,theequationnumbGerUUgoesonelinebelowtheformula:&$nJl18(2) >W*ealreadyknowthatanyformulamaybGemultiline.Ifso,theequationnumbGer>isUUcentered:ImnJl1>Q>;ύnJl1+V5+V:8(3)j>T*o^havecenterednumbGerswithintheeqnarrayenvironment,usewall/return>bloGcksZasdescribedinx21(butthentheequationnumbersZmaybGeoverwritten>withUUtheformulacontentwithoutwarning).MThereUUisalsotheeqnsenvironment,UUwhichputsanumbGeroneachline: nJl1>Q>;8(4)8nJl1+V5+V:8(5)>Italsouseslargerandbreakqableinterlinespace.MultilinebloGcksthenmaybGe>createdUUbyusingthewalls(x20).MEquationXnumbGeringisnormallydeterminedby\theequation.Theenvi->ronmentUUsubabcintroGducesasubordinatenumberingUUbyletters,nA=Bq;8(6a)>noUUmatterhowmanynumbGeredequationsareenclosed,nC~4=DG:(6b)>ThisUUoutputwasobtainedfrom:>\begin{subabc}>\begin{equation}>A?=B,\label{A}>\end{equation}>no?matterhowmanynumberedequationsareenclosed,>\begin{equation}>C?=D.\label{C}>\end{equation}>\end{subabc}13ày?>AfterUU\end{subabc},theoriginalnumbGeringUUmodeisrestored:-nEZ=FG:8(7)>EveryRnumbGeredequationshouldbereferredtosomewhere,henceitshouldhave >aUUlabGel|awarning(x5)isissuedifitdoesnot.MT*oputequationnumbGersontheleft,calleitherthedocumentstyleoption>leqnoUUortheloGcaloption\nathstyle{leqno}.)>x23.3Items. LaytypGographerstendtooveruselistenvironments.Ratherthan>listitems,numbGeredstatementssooftenencounteredintheoremsandde ni->tionsPmaybGealternativelyformattedasnumbGeredparagraphs.Nath'scommand>\paritem{itemTlab}'el}startsanumbGeredparagraphandmayoccurevenwithin>aUUdisplayedformula.Ournextexampledemonstratesthis:$ɍ>TheUUfollowingstatementsonarealfunctionfhareequivqalent:Kq(i)ZN8fhisUUcontinuous;-H(ii)nf( olimLpisC forUUeveryconvergingsequencexiTL.MIn}aleft-numbGered}formula,\paritemsupGersedesthenumbGeringandawarn->ingUUisissued.)>x24.Punctuation. NathprovidesasimpletoGoltoencouragelinebreaksafter>punctuation͐inin-linemoGde.Namely*,\ denotesabreakqablespacenomatter>wheremeitisused.Therefore,$a?=b,\c=d$mewillbreakafterthecomma,a=b;>c"c=d,ratherthanafterthe`='sign.Theinclinationtobreakismeasuredby>\punctpenaltyUU(ifapGositiveintegerlessthan10000).MThree5dotsaredenotedby\dots.Insomecontexts,theirpropGerplaceisat>thelevelofmathaxis,e.g.,a1Hw+ B+anq~.Nathusesaverysimplerule|thedots>arenotraisedifandonlyiftheyfollowacommaorasemicolon.Accordingly*,>weUUhavea1|s;:::;anӲanda1;:::;anq~.MPunctuation3afterdisplayed3formulasisimpGortantforrecognizingcontinuing>lines.UUWithoutpunctuation,whatseemstobGeasystemofequations-nUx=AUmqȸ8Uy=BqU9>mayUUwellbGeachainofthem:nUx=AUO8Uy=BqU:>T*odisambiguateyournotation,bGesuretoinsertcomma(orsemicolonorfull >stopUUor\text)attheendofeachlinethatisnotcontinued:nUx=AU;ύnUy=BqU: :>(Observe{thattheminussignstartingthesecondlineistypGesetclosertoU|>bGecomesUUaunaryoperator.)14y?>x25.YSpacing. Nath's"displayedformulasusefrozenspacing(TU>'ExX's\skips" >andޟ\glues"neitherstretchnorshrink).Whileitisseldomusefultostretcha>displayed#formula,onemaywishtoshrinkformulastoGowideto tbetweenthe>margins.Withinthetightenvironment,displayedformulasoGccupyslightlyless>horizontalUUspace.E.g.,StnsinzG*6n9x= 1۟&fe32 cos6x8+ jM3l&fe16BԲcosQ 4x l15l&fe32BԲcos2x+ jM5l&fe16>bGecomesnsinzG*6x= 1&fe32 cos6x+ 3ܟ&fe16 _Gcos(4x ܱ15ܟ&fe32 _Gcos2x+ 5ܟ&fe16>ifUUwrittenas]>\begin{tight} >$$>\sin^6?x=C?-\frac?1{32}\cos6x+\frac3{16}\cos4xC?-?\frac{15}{32}\cos2x+\frac5{16}>$$>\end{tight}MStrivingTforsafedefaults,Nathsetseveninterwordspacesintext.TU>'ExXpGerts>maywishtocall\nonfrenchspacing(see[3,p.74])toachieveacentury-old>loGok.R>x26.#Userde nitions. F*eelLfreetointroGduceyourowncommandsbyusing>\newcommandUUor\def.W*ealreadygaveUUausefulexampleof\ifracinx8.MHereisanotherexample:A rst-orderpartialderivqativesuitableforallmath>moGdesUUandsizescanbeintroducedvia>\newcommand\pd[2]{\frac{\partial#1}{\partial#2}}󳍑>W*eUUthenhaveUUbꬲ( ;@8f=@x)(@g[=@y)?hbԿ^2orUUe^( ^(^@n9f=@x) (@@g@L=@y)`M)Nr2NͲor΍n<$v@8fvjBL ; ׍ @8x<$S@8gHjBL M ׍@8yȟ|<2>fromUUoneandthesame(\pd?fx\pdgy)^2.MThepriceisthatfragilecommandsoGccurringinsidein-linemathmayhave>to wbGeprotected(anyin-linemodematerialmustbeconsidereda\movingargu->ment").7Nathcommandsarerobustbydesignandneedno\protecting.When>encounteringoamysteriouserror,suchas\unde nedcommand\wrapfrac@,">fragile;commandsaretobGeblamed.Besides\protect,Natho ers\makerobust,>acommandthattakesanalreadyassignedcontrolsequenceasargumentand>makesUUitrobust.R>x27.KEciency . Nath[ helpstoprevent[ wastinghumanworkonsomething>that|canbGedonebycomputer.Onaverage,L5ffA͉TU>'ExXrunsabGoutthreetimesslower>withUUNaththanwithoutit,depGendingonthecomplexityofmathformulas.15y?>x28.O]Otherpac9k\rages. NathsisnotguaranteedtobGecompatiblewithother >L5ffA͉TU>'ExX:=packqages.However,somecombinationsturnouttobGesafeanduseful.>F*orUUexample,whenstartingaL5ffA͉TU>'ExX2.09doGcumentwith>\documentstyle[amssymb,nath]{article}>orUUaL5ffA͉TU>'ExX2"doGcumentwith>\documentclass{article} >\usepackage{amssymb,nath}>oneKinvokesamssymb,acompGonentofthefamousAU>'M S-L5ffA͉TU>'ExXpackqagefromthe>American}MathematicalSoGciety*,therebyintroGducingawiderrangeofmathe->maticalfsymbGols.Userscanalsoenabletextmodeamsmathcommandsbystart->ingUUaL5ffA͉TU>'ExX2"doGcumentwith>\usepackage{amsmath,nath}>(mathUUmoGdecommandsmustbethoseofNath).6>x29.Commandsofenhancedfunctionalit9y . AGnumbGerH3ofmathcommands>have bGeenrede ned;\old{c}'ommand}oftenprovidesaccesstowhat\command>wasUUbGeforeNathrede nedit(seethesourcecodeofthisguideforexamples).MHereUUisthelistofallenhancedandnewlyintroGducedcommands:>\ ʲaUUbreakqablespaceinmath(x25)>\\SвseeUUx11andx19>\abbreviation?aUUlongformof?`inUUmath(x12)>\adotD?ٲargumentUUplaceholder(x14)>\arraycolsepmacro,UUformerlyadimensionregister(x17)>\bigIֲmakingUUinlinedelimitersbigger(x10)>\biggD?ٲsameUUas?\big\big(x10)>\biggg>ܲsameUUas?\big\big\big(x10)>\biggl>ܲsameUUas?\big\big\left>\biglD?ٲsameUUas?\big\left>\binom>ܲbinomialUUcoGecient(x17)>\delimgrowthseeUUx10>\displayed)forcingUUdisplayedmathmoGde(x6)>\double9߲doublingUUadelimiter(x10)>\eqnoD?ٲequationUUnumbGer(x22)>\natherrormarkaUUmarktovisualizenatherrors(x5)>\factorial)longUUformof?!inUUmath(x11)>\fboxD?ٲmakingUUframearoundasubformula>\fracD?ٲfractionUU(x7)>\gtNӲgreaterUUthansign(x10)>\hatIֲattachingUUhataccent(x16)>\inline9߲forcingUUin-linemathmoGde(x6)>\intIֲintegralUUsign(x11)16by?>\langle9߲leftUUanglebracketUU(x10) >\lAngle9߲leftUUdoubleanglebracketUU(x10)>\lbrace9߲leftUUbrace(x10)>\lbrack9߲leftUUbracket(x10)>\lBrack9߲leftUUdoublebracketUU(x10)>\lceil>ܲleftUUceilingbracketUU(x10)>\lCeil>ܲleftUUdoubleceilingbracketUU(x10)>\ldouble4leftUUdoubling(x10)>\leftD?ٲleftUUmoGdi er(x10)>\lfloor9߲leftUU oGorbracketUU(x10)>\lFloor9߲leftUUdouble oGorbracketUU(x10)>\lnull>ܲleftUUinvisiblefence(x10)>\ltNӲlessUUthansign(x10)>\ltriple4leftUUtripling(x10)>\lvert>ܲleftUUverticalline(x10)>\lVert>ܲleftUUdoubleverticalline(x10)>\mapsto9߲sizeableUU`7I=ÎÎ! /'(x14)>\mathop9߲seeUUx11>\mathstrut)seeUU[3]>\midIֲmiddleUUverticalline(x10)>\MidIֲmiddleUUdoubleverticalline(x10)>\middle9߲middleUUmoGdi er(x10)>\NathD?ٲlogo>\nathstyle)loGcalUUoptions(x4)>\nivIֲtheUUsymbGol`pB!B!N8'(x14)>\nonumber/?suppressesUUequationnumbGerUU(x22)>\numbered/?forcesUUequationnumbGerUU(x22)>\oldIֲseeUUthebGeginningofthissection>\otNӲsizeableUUleftarrow(x14)>\ottoD?ٲsizeableUUleft-rightarrow(x14)>\overbrace)horizontalUUbracesoverunbalancedmathmaterial>\overleftarrowleftUUarrowoveranexpression>\overleftrightarrow left-rightUUarrowoveranexpression>\overline/?overlineUUanexpression(x16)>\overrightarrowrightUUarrowoveranexpression>\padded9߲likeUUawall,witheverynextlinepadded(x20)>\paritem4numbGeredUUstatement(x23)>\punctpenalty?pGenaltyUUinsertedafterpunctuationinmath(x24)>\quadD?ٲ1emUUspace(x19)>\qquad>ܲ2emUUspace(x19)>\qqquad9߲3emUUspace(x19)>\rangle9߲rightUUanglebracket(x10)>\rAngle9߲rightUUdoubleanglebracket(x10)>\rbrace9߲rightUUbrace(x10)>\rbrack9߲rightUUbracket(x10)>\rBrack9߲rightUUdoublebracket(x10)17*y?>\rceil>ܲrightUUceilingbracket(x10) >\rCeil>ܲrightUUdoubleceilingbracket(x10)>\rdouble4rightUUdoubling(x10)>\return9߲ends?\walland\padded(x20)>\right>ܲrightUUmoGdi er(x10)>\rfloor9߲rightUU oGorbracket(x10)>\rFloor9߲rightUUdouble oGorbracket(x10)>\rnull>ܲrightUUinvisiblefence(x10)>\rootD?ٲarbitraryUUroGot(x13)>\rtriple4rightUUtripling(x10)>\rvert>ܲrightUUverticalline(x10)>\rVert>ܲrightUUdoubleverticalline(x10)>\scriptscriptstyle settingUUsizetosecondnextlevelscriptsize>\scriptstylesettingUUsizetonextlevelscriptsize>\sqrtD?ٲsquareUUroGot(x13)>\stackrel/?asUUinL5ffA͉TU>'ExX>\textD?ٲtextUUwithinmath>\tilde>ܲattachingUUtildeaccent(x16)>\toNӲsizeableUUrightarrow(x14)>\triple9߲triplingUUadelimiter(x10)>\underbrace$horizontalUUbracesunderunbalancedmathmaterial>\underleftarrowleftUUarrowunderanexpression>\underleftrightarrow left-rightUUarrowunderanexpression>\underline)underlineUUanexpression>\underrightarrow rightUUarrowunderanexpression>\vinIֲtheUUsymbGol`n:B!N8B!t'(x14)>\wallD?ٲbGeginUUawall/returnblock(x20)>Rede nedUUandnewenvironments:>arrayD?ٲseeUUx17 >casesD?ٲasUUinTU>'ExX>eqnsabc9eqns?withinsubabc>eqnarray4asUUinL5ffA͉TU>'ExX>eqnarray*/?asUUinL5ffA͉TU>'ExX>eqnarrayabc$eqnarray?withinsubabc>eqnsIֲaUUpileofequations(x22)>equation4asUUinL5ffA͉TU>'ExX>matrix>ܲseeUUx17>subabc>ܲsubnumbGeringUUbyletters(x22)>tightD?ٲtighterUUspacing(x25)>Thejfollowingcharactersareactive,retainingtheirpreviousmeaning:$,^,_.>OtherUUcharactersbGecomeactiveinmathmoGde:>(Y?ͲseeUUx10>)Y?ͲseeUUx1018ky?>[Y?ͲseeUUx10 >]Y?ͲseeUUx10>>Y?ͲseeUUx10>,Y?ͲseeUUx24>;Y?ͲseeUUx24>!Y?ͲseeUUx11>`Y?ͲseeUUx12͍>CommandsthatbGecameobsoletearestillpreservedinreducedformforback->wardUUcompatibility:>\BigIֲignored>\BiggD?ٲignored>\Biggl>ܲsameUUas?\left>\biggm>ܲsameUUas?\middle>\Biggm>ܲsameUUas?\middle>\biggr>ܲsameUUas?\right>\Biggr>ܲsameUUas?\right>\BiglD?ٲsameUUas?\left>\bigmD?ٲsameUUas?\middle>\BigmD?ٲsameUUas?\middle>\bigrD?ٲsameUUas?\right>\BigrD?ٲsameUUas?\right>\mathchoice$useless>\mathpaletteuseless>\textstyle)ignored>TheUUfollowingTU>'ExXcommandsaredisabled:>\atop>\over>\choose>TheUUfollowingL5ffA͉TU>'ExXenvironmentisdisabled:>math>NewUUifs(correspGondtolocaloptions):>\ifgeometry$seeUUx10>\ifleqno4seeUUx22>\ifsilent/?seeUUx5>\iftensors)seeUUx18>NewUUdimensionregisters:>\arraycolsepdimformer?\arraycolsep>\displaylineskiplimit>\mathindent$seeUUx19>\mexIֲaUUprorated?ex>\paritemwd)seeUUx2319)y?>NewUUskips(self-explanatory):>\displaybaselineskip >\displaylineskip>\interdisplayskip>\intereqnsskip>\beloweqnsskip>NewUUbGoxes:>\sizebox4delimitersUUmatchit(x10)>Moreover,UUNathtakesbGoxandtokenregistersonthe y*.6>x30.OFinalremarks. Nath:isascienti csoftwareintendedtoassistandease>theproGcessofscienti cpublication.Bydisburdeningtheencodingofmathemat->ics,iNathtriestoupholdTU>'ExX'spGositionasalanguagesuitableforbothscienti c>andUUtypGographicpurposes|especiallyifalternativesarestillelusive.MNathylisprovidedasitis;onlybugrepGortsandseriousdiscussionshouldgo>toUUM.Marvan@math.slu.cz.>x31. Release2003. Fixing@severalbugs,anewreleaseisavqailablesinceF*ebru->aryUU2003.MAsanewfeature,Nathtakescareoftheinterlinespacinginarrays.There>isbanewdimensionregister\arrayrowsepdimtoholdtheminimalinterline>space.pAlso,thedefaultsettingof\doublerulesepis\arrayrulewidth,so>that5horizontallinesproGducedbysuccessive\hline'sstickonetoanother,and>similarlyUUfortheverticallines:*iff//ffff//R{̈́ffff.ffff͟: 1ff 1ffz:Vpq$7r.: 1ff 1ff󋍍̈́ffff.ffffff//̈́ffff.ffff͟: 1ff 1ff~9V1?1$@0.: 1ff 1ff󋍍̈́ffff.ffff͟: 1ff 1ff~9V1?0$@0.: 1ff 1ff̈́ffff.ffffr̍͟r˄ ff ffA1&fes2?1$@0.r˄ ff ff+̈́ffff.ffffffff//ff//*>TheseUUchangesdonota ectthetabularenvironment.MThe=ܹ\paddedcommandnowappliestocontinuationlinesonly*.ForexamplenJl1U["=Jl1c𳍍qȸ8Jl1nN;ύnJl1qϟ▷=Jl1*ێqȸ8Jl1+Vd6; {nJl18ώ=(Jl18ώ?v;0Jl18ώ8Ϟ)<^:c+>isUUproGducedbyasingle\padded{\returnpair:20Jy?>\padded{\qquad} =stu X?=<stu \\b-<stu ?,?\\=stu X?=<stu \\b-<stu ?,?\\=stu X?=?(stu ,\\b-stu ).>\return>(CommasUUthatoGccurwithindelimitersdonotstartanewequation.)MSome@errorsstillsurvive.Inparticular,doubleaccentsdonotworkwith>MathTimeUUfonts.!č>References>ʱ[1]M;j cmti9AIPNʱ[2]M;M.TDo9wnes,Breakingequations,TUGboatT18(1997)182{194.>ʱ[3]M;D.E.TKn9uth,TheNʱ[4]M;M.Marv|ran,NaturalTuAEXnotationinmathematics,in:ProAc.Conf.EuroTlEX2001,M;Kerkrade,T23{27Septem9bAer2001;online ߤN cmtt9www.ntg.nl/eurotex/marvan-3.pdf.21`;y ߤN cmtt9j cmti9o cmr9': cmti10Ɍ cmbsy10"V cmbx10XQ cmr12DtGGcmr17 cmmi10 0ercmmi7K`y cmr10ٓRcmr7Zcmr5u cmex10