; TeX output 1997.03.13:0917iԍ,\9Ǎn\9XQ ff cmr12W4elcome/totheR6ff cmss12deleqpack7xage!Y9K`y 3 cmr10ThisxisashortdoMcumen!ttodemonstratetheuseofthem#R 3 cmss10deleqpackdDageanditscom- 9mands.eItӶusesdeleqv!ersion4.41(Feebruary22, 1997).deleqw!aswrittenbyMatsDahlgren9( 3 cmmi10 yL+ncosz2N = 1@(1)9Thew rstexamplewillbMetomak!euseofthedeqnenvironmenttogetapartiallynumbMered9equation:Xsin>(!", 3 cmsy10 `) =1sin (2a)9Thisfequationhasitscosinecompanion,herewrittenintheddeqnen!vironment:YLcos( `) =cos +F(2b)9Notfsoexciting,sofar.:{) 9Infthenextexamplew!eintroMducethedeqarrenvironmentforwritingequations:sin@( yL+n )=|Wsin> ݑcosY ޹+nsin g#cos (3a)sin@( yLn )=|Wsin> ݑcosY nsin g#cos +G(3b)9where!w!ealsohaveputinthelabMelDemo1inthesecondequation.Next,Onoticehowthe9en!vironmentfddeqarusesthesamemainequationn!umbMerfasthepreviousequations:3#cosP( yL+n )ɓ=cosp ݑcosY nsin ݑsin"x b(3c)3#cosP( yLn )ɓ=cosp ݑcosY ޹+nsin ݑsin"x +F(3d)9Inthe rstoftheseequations, xan\arrlabelcommandwiththelabMelDemo2isincluded.9No!w,fwewillmakeanothereqnarray-likestructure,againintheddeqarenvironment:ysin`2 ҝ=!21sin ݑcosY @(4)cos`2 ҝ=!cosz2^8 yLnsin࢟z2s (5a)9orҝ=!21cos|^z2 yLn1+F(5b)Y9Thisexamplesho!wstheuseof\heqnointhe rstequation,?whichproMducesanordinary9equationn!umbMer.The rstequationisalsolabelled, withthelabelDemo3.Thenextequa-9tion'sn!umbMerwasproMducedbythecommand\nydeqno.KAlso,>noticetheuseof\rem{or},9whic!hLresultsinthetext\or"withoutchangingthealignment. oTeoillustratetheuseof9\arrlabel{Demo2}۹abMo!ve, weheremakeareferencetoit:~.3..pinequations3...whic!hwas9createdfb!ytyping`\ldots{}inequations\ref{Demo2}\ldots'.9Teosteptheequationn!umbMercounter,wewantthefollowingequationstypMesetinordinary9eqnarrayfen!vironment:䱍jtan< z2? չ=. sinڇ22 NȉfeG tcos-02 b(6c)9Also,fthemiddleformofequation6gotalabMel,Demo5.Inthelastexample,theconstructG\ddeqreqno[-\jotbaseline]{Demo4}>\nonumber9infadeqrarren!vironmentfisused,toobtainfleqncompatibilit!ye.9Therefisstilloneequationtowrite.Thistimew!eagainusethedeqarrenvironment:?2cotӟ &=bcos bȉfe tsin (9a)9wherev㍍&=1bȉfeڟ ttanD +G(9b)9ThisYexamplealsosho!wstheuseofthe\wherecommand,hwhichisaspMecialcaseofthe\rem9command.[No!w,theLinterestingthingofreferringtotherecycledequationsisahead.[Ifone9writes\ref{Demo5},OthisiswhatLپAGT,[wEB Xwillreturn:b.BtThatisnottoMoinstructiv!e,since9thepartialequationn!umbMersarequitecommoninthisdocumen!t.~Teomakethecompletek2ziԍ,\9Ǎn\99reference,use\ref{Demo4}\ref{Demo5}.ܘThereference6bism!uchmorecomprehensible, 9righ!t?(Iffyougetbadline-breaksatsuchreferences,puttheminan\mbox{...}.)9No!wAYwewillshowtheuseofthecommandstorecycleequationnumbMersineqnarray-like9structures.Thesecommandsare\eqreqno{FOO},k\deqreqno{FOO},and\ddeqreqno{FOO}.9Weefstartb!yrepMeatingequation3binandeqrarrenvironment:sin@( yLn )=|Wsin> ݑcosY nsin g#cos +G(3b)-sinr2 =|W21sin ݑcosY 9Thesecondequationheresho!wshowthealignmentoftheequationsispreserved.Next,we9canfusetheequation4forsomevdDariations:P)sin2 @=21sin ݑcosY (4a)P)sin4 @=21sin2 ݑcosY2 @=21u cmex1021sin ݑcosY ݑucosz2 yLnsin࢟z2s `R+G(4b) @=41sin ݑcosY ݑucosz2 yLnsin࢟z2s `Rb(4c)9Theڲfeaturesusedhereare\deqreqno{Demo3}onthe rstline,Ž\ddeqreqno{Demo3}onthe 9secondline,and\deqreqno[-\jotbaseline]{Demo3}onthethird.Noteho!wtheinclusion9of[-\jotbaseline]onthethirdlineprev!entsLپAGT,[wEB Xfrominsertinganextrablankline.The9secondflineendswith`\\',andhasth!usnoequationnumbMeratall.9Thelastpartsho!wshowyoumayuse\eqreqnoanditsrelativesindeqarrenvironment:sin ;=œsinh ݑcosY0n+sin01cosO Mh(10a)E$sin 2 ;=œ21sin ݑcosY @(4)E$sin 3 ;=œsinh2 ݑcosY yL+nsin ݑcos2 (10b)E$sin 4 ;=œ21sin2 ݑcosY2 $(10c)E$sin 5 ;=œsinh3 ݑcosY2 yL+nsin2 ݑcos3 +F(4d)E$sin 6 ;=œ21sin3 ݑcosY3 (10d)9Thein!terestingparthereisan`\eqreqno{Demo3}'attheendofthesecondlineanda 9`\ddeqreqno{Demo3}'attheendofthe fthline.Noticeho!wthepartialequationnum-9bMerfcoun!terinuna ectedbytheeneteringofthedeqarrenvironment.9Finallye,@the&~ENDA!;If&~y!ouwantyourequationnumbMersleft-aligned,@justspecifytheleqno9option'forthedocumentclassy!ouareusing.b3Itshouldwork!b3Ifyouhaveanysuggestions,9correctionsforcon!tributions,pleasecontactme.EnjoyLپAGT,[wEB X!9': 3 cmti10matsd.k3;i>| ': 3 cmti10!", 3 cmsy10 b> 3 cmmi10|{Ycmr8