; TeX output 1999.10.22:1101soDtGGcmr17The7tpacqkage-G cmcsc10easyeqn!ɍXQ cmr12EnricoBertolazzi;LabSoratoriodiMatematicaApplicataeMeccanicaComputazionaleb$DipartimenrtodiIngegneriaMeccanicaeStrutturaleDUnivrersit adegliStudidiTVrentoMesiano,TVrenrto,Italy˭(R6 cmss12enrico.bSertolazzi@ing.unitn.it~US22ndOctobSer1999#3!K*t : cmbx9Abstract>ꍑ[)o cmr9TheOpac9k|rage+- cmcsc10easyeqnintroAducessomeequationenvironmentsthat Nsimplifyc writingofequations.Itusesasyn9taxsimilartothearrayenvi-Nronmen9t^tode nethecolumnalignment.ThelabAel eldisfullycustomiz-Nable.^mAJpac9k|rageoptionpAermitstonumbAeronlythoseequationsthatNw9ere',j cmti9labeled_,andreferenced.SSomeadditionalmacrosarealsoincludedtoNfacilitateTt9ypingofformulae.%ʹ5.Nff cmbx12Contentsɍ5/"V cmbx101DSomeTexampleswitheasy9eqn352DUseTofthe0kAH cmssbx10EQen9vironment353DTheT1 cmmi10xn<wfe (֍:y=zC8(1)<$ԵaԟwfeI0 (֍CbJO=cIUUwillreferonlyto(1)qor,intheoldstyle,1.SĚffffffS̎t[5NotethatthereferenceisdonebyV\eqrefor\refeq.G#Thecommand\refeq 5proGducesUUthesameoutputas\ref,while\eqrefuses(?)fortheoutput.ȍ5Remark:Duetothealgorithmimplementation,(inordertoobtaintheright5cross;reference,ٵyouneedtorecompilethe le3times.zTheuse\labelisnot5pGermittedsinsideAEQ*environmentssandifyouuse\refforreferencingequations5theUUresultsareunpredictable^2|s.5ThisUUisanotherexample:h [7ffS̠̍ffffGffF34fffd fffd\begin{EQ}[rcll]3d ff fffd\nabla\cdot(\rho\nabla?u)&=&f\qquadvs ff ff"fd&\mbox{on?$\Omega$}\\3 ff fffdu&=&u_{0}&\mbox{on?$A\subset\partial\Omega$}\\<ʡ ff fffd(\rho\nabla?u)\cdotn&=&u_{1}3 ff ff"fd&\mbox{on?$B\subset\partial\Omega$}k󯡄 ff fffd\end{EQ}3L ff ffF34 ffffF34ffffffG%e%z !", cmsy10r8(ru)0=|Nfu6onUU u0=|Nu0u6onUUA@8 gz7(ru)8n0=|Nu1u6onUUBG@8 SffffffS̎5NoteHthatbGetweenH[...]youcanspecifythecolumnalignmentinthesame5wayMsasintheAarrayqorMsAtabularenvironment^3|s.Z!TheMspGermittedalignmentarel5forXleftalignment,Yrforrightalignmentandcforcentering.mThereisalsothe5character\."thatusedbGetweende nitionoftwocolumnsdisablethespacing5ffffv J= "5-:2LܼTheXpreviousreleasetolab "5-:3LܼInapreviousreleaseof&@easyeqnmÎulticolumnalignmentwasimplementedinaEs6cmss8EEQSмenvi-ronmenÎt. HoweverXtomainÎtainbackwardcompatibilitysuchanenvironmentaremaintainedsfd5Thepackageeasyeqn5o5bGetween_columnsasinthefollowingexampletakenfromthedoGcumentationof 5F- cmcsc10FeqnarraUTyofUURolandWinkler;q7)ffS̠¬΍¬ff)ffGffF34fffd fffd\begin{EQ}[rcl.l]g ff ff fd\phi?&=&\sum\bigg(&\frac{xxxxxxxxxx}{\phi}\\23С ff ff'fd&?&&+\frac{yyyyyyyyyy}{\phi}\bigg)\\Ls ff ff'fd&?=&\eqmulticol{2}{l} ff ffG?ٟfd{\frac{zzzzzzzzzz}{\phi}}{ ff fffd\end{EQ}3L ff ffF34 ffffF34ffffffG7poрyֲ=u cmex10Xe^<$: xxxxxxxxxx: wfe9' (֍ ٲ+<$33y[yyyyyyyyy33wfe4 (֍T-7^yֲ=<$'zpzzzzzzzzz'wfe2, (֍xS¬ffffffS̎5inthisexamplewehaveusedalsothecommand\eqmulticolthesyntaxisthe5followingzD\eqmulticol{ncol}{align}{body}5where{78ncolNisUUthenumbGerUUofcolumntofuse.Z3alingNisUUthealignment,itcanbGel,r,c.35bGodyNisUUthethingtoputacrossthecolumn.%m卍53MLTheffG߆Tff cmtt12G\yesnumbercommand㍑5IfyouwanttonumbGeranequationwithoutreferenceit,Hjusethe\yesnumber 5commandUUasthisexampleshows:V<7݊ffS̠D썄Dff݊CffGffF34fffd fffd\begin{EQ}[rcl]\yesnumber ff fffda?&=&\frac{1}{23}\\ ff fffdb?&=&\sqrt{\frac{1}{23}} ff fffd\end{EQ}3L ff ffF34 ffffF34ffffffG'yĥa ղ=<$'1&wfe  (֍23_o+b ղ=IdrIdfe fh<$4133wfe  (֍23C8(2)SDffffffS̎sfd5Thepackageeasyeqn6o54MLUseffofCEQAenvironmentE͍7|YffS̠L̍LffYffGffF34fffd fffd\begin{EQA}[rcll]g ff  fffd\nabla\!\cdot\!(\rho\nabla?u)&=&f\qquadas ff ff"fd&\mbox{on?$\Omega$} ff fffd\yesnumber?\\3d ff fffdu&=&u_{0}&\mbox{on?$A\subset\partial\Omega$}Ls ff ff7fd\label{eq:3}?\\ ff fffd(\rho\nabla?u)\!\cdot\!n&=&u_{1}s ff ff'fd&\mbox{on?$B\subset\partial\Omega$}f ff ff7fd\label{eq:4}ϳv ff fffd\end{EQA}O ff fffdit?isreferencedonly\eqref{eq:4}!!3 ff ffF34 ffffF34ffffffG"f"r8(ru) =ѦfʎonUU C8(3)Q u =Ѧu0ʎonUUA@8 i$(ru)8n =Ѧu1ʎonUUBG@8 C8(4)itUUisreferencedonly(4)t!!SLffffffS̎[5Notethatonlythereferencedlinesorthelineswith\yesnumberarenumbGered.%ތ55MLTheffG\labelcommand㍑5ItispGossibletousecustomlabelby >\labelcommand.LThesyntaxisoneofthe 5following:ȍ?\label{labelname}?\label[eqnum]?\label[eqnum]{labelname}?\label(eqnum)?\label(eqnum){labelname}5whereD\[eqnum]"isanoptionalargumentthatifde ned,(equationdisplays5\eqnum"insteadof\(equation?number)".ITheequationcounterisnotad-5vqancedUUand\labelname"ifpresentwillreferto\eqnum".ȍ5If8Nweusewhere\(eqnum)"isanoptionalargumentthatifde ned,q equation5displaysg!\(eqnum)"insteadof\(equation?number)".*Theequationcounteris5notUUadvqancedand\labelname"ifpresentwillreferto\eqnum".5LoGokUUatthisexample:')sfd5Thepackageeasyeqn7o( ̍7YffS̠L̍LffYffGffF34fffd fffd\begin{EQA}[c]^ ff  fffd\nabla\cdot(\rho\nabla?u)=03 ff ff'fd\label(eq.1){eq:custom:a}?\\s ff fffd\nabla\cdot(\rho\nabla?u)=03 ff ff'fd\label[eq.2]{eq:custom:b}?\\s ff fffd\nabla\cdot(\rho\nabla?u)=03 ff ff'fd\label[***1***]ϳv ff fffd\end{EQA}O ff fffdI?willreferto\eqref{eq:custom:a}s ff fffdand?\eqref{eq:custom:b}sy ff ffF34 ffffF34ffffffG" ~r8(ru)=06(eq.1) ~r8(ru)=0>eq.2 ~r8(ru)=0,***1***IUUwillreferto(eq.1)and(eq.2)SLffffffS̎>5NoticeUUthatcustomlabGelarealwaysUUdisplayedalsoiftheyarenotreferenced.%R56MLLabs3elffpositioning㍑5ItN6ispGossibletochangethedefaultpositionosasinglelabelbythecommands:@]DN\eqlabeltopʍDN\eqlabelbotDN\eqlabelcenter@^5F*orUUexample:c>񍍍7YffS̠L̍LffYffGffF34fffd fffd\eqlabeltop sU ff  fffd\begin{EQ}R ff fffd\nabla\cdot(\rho\nabla?u)=0\\s ff fffd\nabla\cdot(\rho\nabla?u)=0\\s ff fffd\nabla\cdot(\rho\nabla?u)=0\label[TOP]\3 ff fffd\end{EQ}3L ff ffF34 ffffF34ffffffG ~r8(ru)=0 ~r8(ru)=0 ~r8(ru)=0:1TOPSLffffffS̎0sfd5Thepackageeasyeqn8o57MLSub-numbs3ering㍑5T*oUUsub-numbGerequationinsteadofusesomethinglikeȍ?\begin{subequations} ?\begin{EQ}...?\end{EQ}?\end{subequations}5Iprefertouse\labelcommandwiththecharacter~asashortcutforthe5commandUU\theequation.qThefollowingexampleshowstheusedx7YffS̠L̍LffYffGffF34fffd fffd\begin{EQA}[c]\yesnumber3| ff fffd\nabla\cdot(\rho\nabla?u)=0\label(~.A)\\Ls ff fffd\nabla\cdot(\rho\nabla?u)=0\label(~.B)\\Ls ff fffd\nabla\cdot(\rho\nabla?u)=0\label(~.C)\3 ff fffd\end{EQA}O ff ffF34 ffffF34ffffffG" ~r8(ru)=08(5.A) ~r8(ru)=09\n(5.B) ~r8(ru)=098(5.C)SLffffffS̎c[5ther|\yesnumbercommandisnecessarytoenforceadvqancingofequationcounter.%ތ58MLUseffofC eqnandCleqnooption㍑5Y*oucanuseA eqnto uxlefttheequationsorAleqnotonumbGerequationsonthe5left.qIfUUforexamplewehaveused?\documentclass{article}?.?.?\usepackage[fleqn,leqno]{easyeqn}?.?.5theUUe ectwiththisexample: :msfd5Thepackageeasyeqn9o( ̍7YffS̠L̍LffYffGffF34fffd fffd\begin{EQA}[rcll]g ff  fffd\nabla\cdot(\rho\nabla?u)&=&f\qquadvs ff ff"fd&\mbox{on?$\Omega$}\yesnumber\\{ ff fffdu&=&u_{0}&\mbox{on?$A\subset\partial\Omega$}Ls ff ff"fd\yesnumber\\j ff fffd(\rho\nabla?u)\!\cdot\!n&=&u_{1}s ff ff"fd&\mbox{on?$B\subset\partial\Omega$}k󯡄 ff ff,fd\label{eq:5}3p ff fffd\end{EQA}O ff fffdit?isreferencedonly\eqref{eq:5}!!3 ff ffF34 ffffF34ffffffG"r8(ru)J=VVֵftOonUU (6)@:uJ=VVֵu0tOonUUA@8 (7)!(ru)8nJ=VVֵu1tOonUUBG@8 (8)itUUisreferencedonly(8)t!!SLffffffS̎[5The8samee ectcanbGeobtainedeverywhereusingthecommands\equationleft 5and'\numberleftbGeforede ningtheequation.T*orestorethedefaultvqalues5useUUthecommands\equationcenterand\numberrightaftertheequation.%ތ59MLCosmeticffchanges㍑5ItٖispGossibletomodifyalittletheappearanceoftheequations.HTherearethree5parameterUUthatitispGossibletochangeȍleftUUindentNWhen2Rtheequationsare uxedleft,9StheleftindentcanbGechangedbytheNcommandUU\eqleftmargin.]\eqleftmargin{new?indent}NforUUexampleX\eqleftmargin{1cm}NTheUUdefaultvqaluefortheleftmarginis\leftmargini.equationUUspacingNThe:@8y[@ SyffffffS̎P15noticeؤthatsingleitemofderivqativemustbGeasingleletter(oramacro)ormust 5bGeinsideagroup{?...}.nIfyouuse\ParDerwithpackqageFeasyvector5remembGerUUtoputmacrosinbracewhenuse\[]"asfollows:C髍7ɃffS̟alalffɃ/鍑ffGffF34fffd fffd\[?\xx,\xx[i,j]=g ff fffd\ParDer[\xx\xx{\xx[i,j]}\yy]{f(x,y,z)}?\]\3 ff ffF34 ffffF34ffffffG 絍|x;Bx 0ercmmi7i;j 2=<$K@8^4 f(x;y[;zp)Kwfe1 (֍O@8xr2|s@Bxi;j@ySalffffffS̎C[r5otherwiseUUyouobtainstrangethinklikethefollowing=-:7ffS̟UUff^!ffGffF34fffd fffd\[?\ParDer[\xx\xx\xx[i,j]\yy]{f(x,y,z)}\]f ff ffF34 ffffF34ffffffG 絍<$wٵ@8^7 yy(wfe5ӟ (֍@8xr3|s@[UU@i@;@j.]f(x;y[;zp)SUffffffS̎5TheUUmacros\DIV,\GRADand\LAPLAarede ned,thee ectisthefollowing7?7ؠffS̟IIffݠffGffF34fffd fffd\[?\DIV{A},\qquad\GRAD{B},\qquad\LAPLA{C}\]G3ġ ff ffF34 ffffF34ffffffG u8Er8A;rBq;CSIffffffS̎7>5TheUUmacro\SUMisde ned,thee ectisthefollowingb5sfd5Thepackageeasyeqn14ot7ffS̟ff±󍍟XffGffF34fffd fffd\[8: ff  ff fd\SUM{i=1}{100}a_{i},\quads ff ff fd\SUM[10]{i=1}{100}a_{i} ff fffd\]8: ff ffF34 ffffF34ffffffG ۍE100  X tʴi=1~aiTL; 100  X t ifi=1rq(10)'U`aiSffffffS̎Rs5TheUUmacro\PRODisde ned,thee ectisthefollowingRs7ffS̟ff±󍍟XffGffF34fffd fffd\[8: ff  ff fd\PROD{i=1}{100}a_{i},\quad3 ff ff fd\PROD[10]{i=1}{100}a_{i} ff fffd\]8: ff ffF34 ffffF34ffffffG ۍ100 Z Y tCi=1~aiTL; *$100  BY t i=1q(10)%aiSffffffS̎5TheenvironmentAARRA*YVisde ned,#0isasimplesubsetoftheenvironmentAarray 5withUUadi erentspacing;loGokthefollowingexample~Uf7ϏffS̠`ፄ`ffϐ5ffGffF34fffd fffd\[8: ff ff fd\left(\begin{array}{cc} ff fffd1)&?\frac{1}{2}\\󋡄 ff ff,fd\sqrt{3}?&\frac{2}{\sqrt{3}}󣡄 ff ff fd\end{array}\right),?\qquad3 ff ff fd\left(\begin{ARRAY}{cc} ff fffd1)&?\frac{1}{2}\\󋡄 ff ff,fd\sqrt{3}?&\frac{2}{\sqrt{3}}󣡄 ff ff fd\end{ARRAY}\right),s ff fffd\]8: ff ffF34 ffffF34ffffffG $ _n^ o 1 ͱ1͟&fes2 k]Ppt PfeE3 ͱ2S&fe <č3 O!cmsy7pɟ3W sM3W^s;X0Bfi@k"W1<$;1;wfe (֍2j=Vp&=Vfeª3<$;266wfe UX EPpUWPfeE3XE{1E{CfiE{AOj;S`ffffffS̎~Ue5TheZenvironmentAMA*TRIXZisde ned,\ isasimplereplacementof!\matrixcom-5mandUUwithadi erentspacing;loGokthefollowingexamplemDsfd5Thepackageeasyeqn15o%7eAffS̠5}5}ffeB˧ffGffF34fffd fffd\[8: ff  ff fd\matrix{R ff fffd1)&?\frac{1}{2}\cr ff fffd\sqrt{3}?&\frac{2}{\sqrt{3}}󗡄 ff ff fd},?\qquad sU ff ff fd\begin{MATRIX}3d ff fffd1)&?\frac{1}{2}\cr ff fffd\sqrt{3}?&\frac{2}{\sqrt{3}}󗡄 ff ff fd\end{MATRIX},sa ff fffd\]8: ff ffF34 ffffF34ffffffG 4YE z1 \1\&fes2 EuPp~DBPfeE3 \2ww&fe <č3pɟ3W sM3 𠎒㎵;>s1 3&ñ13&ß&fes2 EURPpPfeE3 3&ñ2/ޟ&fe <č3pɟ3W sM3=I;S5}ffffffS̎y;G߆Tff cmtt12F- cmcsc10Es6cmss8DCscmtt8CkAHff cmssbx10B': cmti10Am#R cmss10@- cmcsc101 cmmi10 0ercmmi7K`y cmr10ٓRcmr7Zcmr5u cmex10Y