÷ƒ’À;è TeX output 1997.03.13:0917‹ÿÿÿÿ ˜‚ ýs}ü n‚ ýÞ}þ‘åóÖÆG®G®cmss17ºdeleq–7tóDÓítG®G®cmr17¹{“a“LŸüdú‘úKGóX«Q cmr12»AŽŽ‘¹”¹T‘ý[™Ÿ¸-EŽ‘;gX“Macro“for“PšŒqartial“Num˜bsŽering“of“EquationsŸùº¯ó!",š cmsy10¿ŽŽŽŸ’½Ræ»Mats‘ê¨DahlgrenŽŽŸ’­§(ó߆µT cmtt12Æmatsd@homenet.se»)ŽŽŽŽŽŸ&37’Æ?R1997/02/22ŽŸ+ÊË’Ï@ˆót ‰: cmbx9ÉAbstractŽŸ’6‘5ïóo´‹Ç cmr9ÈT‘ÿ:«o–¥enable“a“more“ exible“equation“n•¾9um“b•AÇering,‘»†esp“ecially–¥\partial"“equation“n•¾9um“bAÇers‘¥(`3a',Ž¤ ‘'9õ`3b'–ìAó¼j‘¹ cmti9Êetc.È),‘!üthe“ó ÒoÇw cmss9Ëdeleq“Èpacš¾9k‘ÿ|rage“has“bAÇeen“dev˜elopšAÇed.‘¡8It“can“pro˜duce“partial“equation“n•¾9um“b˜ersŽ¡‘'9õinš¾9termixed–c6with“ordinary“equation“n˜um˜bAÇers“also“in“an“ó!ߤN cmtt9ÌeqnarrayÈ-lik˜e“en˜vironmen˜t,‘v®the“in˜ter-Ž¡‘'9õmixing–{­can“ošAÇccur“within“one“en•¾9vironmen“t.‘é8References–{­to“a“partially“n•¾9um“b˜ered–{­equation“can“b˜eŽ¡‘'9õbšAÇoth–Xïthe“complete“equation“n•¾9um“b˜er–Xï(`3b')“or“only“the“main“equation“n•¾9um“b˜er‘Xï(`3').‘ç@F‘ÿ:«urther-Ž¡‘'9õmore,‘‹`equation›sÄn•¾9um“b•AÇers˜can˜b“e˜recycled˜without˜disturbing˜the˜ordinary˜equation˜n•¾9um“bAÇers.Ž¡‘'9õThe–àHpacš¾9k‘ÿ|rage“also“pro˜vides“commands“for“putting“commen˜tatory“text“in“an“Ìeqnarray“Èen˜viron-Ž¡‘'9õmenš¾9t.‘pBoth–Tstandard“LŸýó5‘ü«‡ó¹Aa¨cmr6ÁAŽŽ‘© ÈT‘þuAŸïÿEŽ‘˜ŸX“class“options“Ìleqno“Èand“ÌfleqnŸü-=Á1ŽŽ‘?ûÈw˜ork“with“ËdeleqÈ.Ž¡‘'9õThis–T le“and“the“pacš¾9k‘ÿ|rage:“Cop˜yrigh˜t‘§žºŽcŽŽŽ“ó#©±Ê cmsy9Î ŽŽŽ‘j¤È1994-1997“b˜y“Mats“Dahlgren.‘pAll“righ˜ts“reserv˜ed.ŽŸ á‘9óó&ÂÖN ff cmbx12Ñ1Ž‘&†¾InŒÌtros3ductionŽŸç‘9óó'm#½R cmss10Òdeleq–ŸÔóKñ`y cmr10²is“a“LŸýó5‘üffóÙ“ Rcmr7±AŽŽ‘͉²T‘þU>Ÿ'EŽ‘ãxX“pacš¸ãk‘ÿqÇage“whic˜h“mak˜es“partial“n˜um˜bšGering“of“equations“p˜ossible.‘QEIt“is“mean¸ãt“to“b˜eŽ¤ ‘9óused–±_when“n•¸ãum“bGering›±_suc“h˜as˜3a,–Èa3b,“ó(ý': cmti10Óetc.–…ä²is˜desired.“The˜default˜is˜to˜giv•¸ãe˜an˜equation˜n“um“bGerŽ¡‘9ólikš¸ãe–Ou`3a'“without“p•Gerio“d–Ouand“with“the“`a'“t˜ypGeset“in“roman“fon˜t.‘`'It“can“bGe“used“in“ó)ßê²class“option.‘æEquations“can“bšGe“n•¸ãum“b˜ered–|>either“3,–Åø3a,“3b,“ó  b> cmmi10µ:–ª¨:“:Ž›pŸ²,“or‘|>2,“3a,“3b,“µ:–ª¨:“:Ž˜².‘æAlso,Ž¡‘9óequation›´n•¸ãum“bGers˜within˜Ôeqnarray²-lik“e˜en“vironmen“ts˜can˜bGe˜n“um“bGered˜3,–Þ 3a,“3b,“µ:–ª¨:“:Ž‘Kg²or˜startingŽ¡‘9óat–†,3a,‘Òbwhicš¸ãh“can“follo˜w“bGoth“after“equation“2b“or“3.‘MAn“Ôeqnarray²-lik˜e“en˜vironmen˜t“can“ha˜v˜eŽ¡‘9óits–ëÄ 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cmbx12Õ1.1Ž‘,ùóHistoryŽŸuT‘9óÔdeleq.sty–r²wš¸ãas“originally“written“for“LŸýó5‘üff±AŽŽ‘͉²T‘þU>Ÿ'EŽ‘ãxX“2.09,‘yPand“con˜tained“sev˜eral“commands“whic˜h“bGecameŽ¡‘9óobsolete–with“the“inš¸ãtroGduction“of“LŸýó5‘üff±AŽŽ‘͉²T‘þU>Ÿ'EŽ‘ãxX‘ü2Ÿÿµ"ŽŽ‘(W¿².‘V²These“commands“ha˜v˜e“bGeen“remo˜v˜ed.‘V²The“ rst“releaseŽ‘9óŸw‰ffª¶ÄŸ @‘ ÷ˆŸý-:óq¡% cmsy6ÅŽŽ‘LÜó|{Ycmr8ÀThis–ÕXdoš‘ "5Ÿý-:Á1ŽŽŽ‘LÜÀNot–ÕXall“commands“of‘wÇdeleq“ÀwÃŽork“with“the“ó$ßCÊscmtt8Ïfleqn“Àoption.ŽŽŸ’á=²1ŽŽŒ‹* ˜‚ ýs}ü n‚ ý´}ü‘9ó²for‘ú¦LŸýó5‘üff±AŽŽ‘͉²T‘þU>Ÿ'EŽ‘ãxX‘ü2Ÿÿµ"ŽŽ‘-Hö²w¸ãas–ú¦v.4.0,›#úof“Oct.“14,˜1994.‘a¹The“Decem¸ãbGer“1994“release“(v.4.1,˜Dec.“27,˜1994)“w¸ãasŽ¤ ‘9óthe–a 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3.02“is“the“last“(non-suppGorted)“v¸ãersion“for“LŸýó5‘üff±AŽŽ‘͉²T‘þU>Ÿ'EŽ‘ãxX2.09.‘YX(Command“names“are“a“mixture“ofŽ¡‘9óLŸýó5‘üff±AŽŽ‘͉²T‘þU>Ÿ'EŽ‘ãxX,–UUSwš¸ãedish“and“a“bit“of“the“author's“fan˜tasyµ:–ª¨:“:Ž‘ ª§²)ŽŸí>‘9óÕ1.2Ž‘,ùóKno wn‘€ProblemsŽ©uT‘9ôó !",š cmsy10¸ŽŽŽ‘'9õ²When–ú—using“Ô\eqreqno²,–#çÔ\deqreqno²,“and–ú—Ô\ddeqreqno“²on“the“last“line“in“a“Ôdeqarr²,‘#çÔddeqar²,Ž‘ÝmCÌ\eqreqnoŽŽŽŽ¡‘س­\deqreqnoŽŽŽŽŸ‘Óú\ddeqreqnoŽŽŽŽŸ$‘æàodeqarrŽŽŽŽŸ0‘æàoddeqarŽŽŽŽŸ<‘ʆë\jotbaselineŽŽŽŽ¡‘'9õÔeqnarray²,–T[or›TÔeqnarray*²,“there˜will˜bGe˜an˜extra˜blank˜line˜with˜an˜equation˜n•¸ãum“bGer˜(not˜inŽ¡‘'9õthe–UUÔ*“²form)“at“the“end“of“the“en•¸ãvironmen“t.‘qÇT‘ÿ*ªo›UUa“v“oid˜this˜problem,˜useŽ¡‘1¹ïÔ\eqreqno[-\jotbaseline]{FOO}‘?ý\nonumberŽ¡‘'9õ²instead–UUof“Ô\eqreqno{FOO}“²(the“analogues“for“Ô\deqreqno“²and“Ô\ddeqreqno“²are“ob¸ãvious).ŽŸ!Ì‘9óÑ2Ž‘&†¾UserguideŽŸç‘9óÕ2.1Ž‘,ùóRequiremen tsŽ¦‘9ó²The–‡ã le“Ôdeleq.sty“²mš¸ãust“bGe“a˜v‘ÿqÇailable“in“the“user's“ÔTEXINPUTS‘‡Ö²directories.‘ pIt“requires“LŸýó5‘üff±AŽŽ‘͉²T‘þU>Ÿ'EŽ‘ãxX‘ü2Ÿÿµ"ŽŽ‘,cp²ofŽ¡‘9ó1995/06/01–UU(or“new¸ãer).ŽŸí>‘9óÕ2.2Ž‘,ùóUsageŽ¦‘9ó²The–UUpacš¸ãk‘ÿqÇage“is“included“b˜y“statingŽ¡‘¹íÔ\usepackage{deleq}Ž¡‘9ó²In–ó¡the“doGcumenš¸ãt“pream˜ble.‘LªThe“doGcumen˜tclass“option“Ôleqno“²is“fully“suppGorted,‘3and“the“optionŽ¡‘9óÔfleqn–§ð²is“recognized“bš¸ãy“the“en˜vironmen˜ts“de ned“in“Òdeleq².‘i—Other“class“or“pac˜k‘ÿqÇage“options“do“notŽ¡‘9óha•¸ãv“e›UUan“y˜e ect˜on˜Òdeleq².ŽŸí>‘9óÕ2.3Ž‘,ùóEn• vironmen“tsŽ¦‘9ó²The–UUpacš¸ãk‘ÿqÇage“de nes“the“follo˜wing“ v˜e“en˜vironmen˜ts:ŽŸ±/‘9óÔdeqn–UU²is“an“equation“en•¸ãvironmen“t–UUfor“automatic“n•¸ãum“bšGering–UUof“the“ 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"5Ÿý-:Á2ŽŽŽ‘LÜÏfleqn–ÕXÀincompatibilitšÃŽy“w˜as“pŸ'EŽ‘ãxX“if“this“happGends.‘*ûIf“y˜ou“w˜an˜t“blank“lines“and“then“a“Ô\heqno²'edŽ¡‘'9õequation›£]follo•¸ãw“ed˜b“y˜partially˜n“um“bGered˜equations,‘öÞuse˜the˜Ôddeqar˜²en“vironmen“t˜instead.Ž¡‘'9õThe–UUsame“is“true“for“Ô\nydeqno²'ed“equations.Ž¦‘9óÔ\begin{ddeqar}–?ý...“\end{ddeqar}Ž‘æàoÌddeqarŽŽŽŽ¡‘'9õ²Tš¸ãypGesets–ò«an“equation“arra˜y“just“lik˜e“Ô\begin{eqnarray}–?ý...“\end{eqnarray}‘ò«²doGes,‘YÿbutŽ¡‘'9õgivš¸ães–ëhthe“equation“n˜um˜bGers“suc˜h“as“`3a'“if“follo˜wing“after“an“equation“n˜um˜bGered“`3'“(ordinaryŽ¡‘'9õequation›W9n•¸ãum“bGer)˜and˜n“um“bGers˜suc“h˜as˜`3c'˜if˜follo“wing˜after˜a˜partially˜n“um“bGered˜equationŽ¡‘'9õ`3b'.‘ÎCan–½bšGe“made“to“pro˜duce“the“result“of“Ôdeqarr“²en•¸ãvironmen“t›½b“y˜the˜use˜of˜Ô\nydeqno².Ž¡‘'9õÔddeqar–Ûv²doGes“not“step“the“main“equation“counš¸ãter.‘I(The“Ô\nonumber“²command“w˜orks“lik˜e“in“theŽ¡‘'9õÔdeqarr‘UU²en•¸ãvironmen“t.Ž¦‘9óÔ\begin{deqrarr}–?ý...“\end{deqrarr}Ž‘â&ÙÌdeqrarrŽŽŽŽ¡‘'9õ²This›ç[en•¸ãvironmen“t˜is˜mean“t˜to˜host˜recycled˜equations˜and˜has˜Ôeqnarray˜²structure.‘ 'ØByŽ¡‘'9õdefault,‘]it–õissues“no“equation“n•¸ãum“bGer–õat“all“on“a“line“whic¸ãh“ends“with“Ô\\².‘ Q The“use“ofŽ¡‘'9õÔ\label{FOO}–P|²within“Ôdeqrarr“²returns“the“presenš¸ãt“partial“equation“n˜um˜bGer“of“recycled“equa-Ž¡‘'9õtions–g`(just“lik¸ãe“with“Ô\rndeqno“²and“Ô\rdeqno²).‘§éNote“that“neither“Ô\heqno“²nor“Ô\nydeleqnoŽ¡‘'9õ²giv•¸ães›UUan“y˜equation˜n“um“bGers˜at˜all˜in˜the˜Ôdeqrarr˜²en“vironmen“t.Ž¦‘9óÔ\nydeqnoŽ‘ÝmCÌ\nydeqnoŽŽŽŽ¡‘'9õ²Used–éåwithin“Ôdeqarr“²and“Ôddeqar“²en•¸ãvironmen“ts–éåto“step“the“main“equation“n•¸ãum“bGer›éåb“y˜one˜andŽ¡‘'9õreset–öðthe“partial“equation“n•¸ãum“bGer–öðto“`a';‘G½thš¸ãus,‘VÔ\nydeqno“²giv˜es“equation“n˜um˜bGer“`4a'“whenŽ¡‘'9õfollo¸ãwing–UUafter“equation“`3c'.Ž¦‘9óÔ\heqnoŽ‘æàoÌ\heqnoŽŽŽŽ¡‘'9õ²Used–éåwithin“Ôdeqarr“²and“Ôddeqar“²en•¸ãvironmen“ts–éåto“step“the“main“equation“n•¸ãum“bGer›éåb“y˜one˜andŽ¡‘'9õto–B prošGduce“an“ordinary“equation“n•¸ãum“b˜er;‘¹Fth“us,‘}ógiv“es–B equation“n•¸ãum“b˜er–B `4'“when“follo¸ãwingŽ¡‘'9õequation–qß`3c'.‘%õEquations“folloš¸ãwing“the“Ô\heqno²-ed“will“bGe“partially“n˜um˜bGered“with“the“Ô\heqno²-Ž¡‘'9õed–Hµequation's“n•¸ãum“bšGer–Hµas“the“main“n•¸ãum“b˜er,›~oÓe.g.–Hµ²`4a'“(unless“it“has“a“Ô\nydeqno“²command,˜whic¸ãhŽ¡‘'9õin–UUthis“case“wš¸ãould“proGduce“the“equation“n˜um˜bGer“`5a').Ž¦‘9óÔ\reqno{FOO}Ž‘æàoÌ\reqnoŽŽŽŽ¡‘'9õ²Is–6zused“when“repšGeating“an“equation“with“its“original“n•¸ãum“b˜er,‘<¦\recycling"–6zthe“eqaution“n¸ãum-Ž¡‘'9õbGer.‘‡Ô\reqno–Š@²takš¸ães“the“argumen˜t“ÔFOO²,“whic˜h“has“to“bGe“de ned“b˜y“a“Ô\label{FOO}“²in“theŽ¡‘'9õoriginal–*equation.›ïúIt“can“only“bGe“used“within“Ô$$–?ý...“$$².˜It–*doGes“not“a ect“the“equationŽ¡‘'9õn•¸ãum“bGer›Õcoun“ter,‘õnor˜the˜ordinary˜partial˜equation˜n“um“bGer˜coun“ter.‘ðýHo“w“ev“er,‘õit˜resets˜theŽ¡‘'9õpartial– ïequation“n•¸ãum“bGer› ïcoun“ter˜for˜the˜Ô\rndeqno²,–8UÔ\rdeqno²,“Ô\deqreqno²,“and˜Ô\ddeqreqnoŽ¡‘'9õ²commands.‘iGIf–;Õused“with“a“Ô\label{FOOO}“²command,‘@ïthe“Ô.aux²- le“will“only“con¸ãtain“the“pageŽ¡‘'9õn•¸ãum“bšGer–Báof“lab˜el“ÔFOOO².“This“command“is“not“compatible“with“the“class“option“Ôfleqn².‘:kIn-Ž¡‘'9õstead–téof“Ô$$–?ý...“\reqno{FOO}“$$²,‘|Îuse–téa“one-line“Ôdeqrarr“²en•¸ãvironmen“t–téwith“the“commandsŽ¡‘'9õÔ\eqreqno[-\jotbaseline]{FOO}‘?ý\nonumber–UU²at“the“end.ŽŽŸ’á=4ŽŽŒ‹- ˜‚ ýs}ü n‚ ý´}ü‘9óÔ\rndeqno{FOO}Ž‘ÝmCÌ\rndeqnoŽŽŽŽ¤ ‘'9õ²Adds–éða“partial“equation“n•¸ãum“bšGer–éðto“an“old“equation“n•¸ãum“b˜er,‘sp˜eci ed›éðb“y˜the˜ÔFOO‘éʲlabGel.‘/™IfŽ¡‘'9õÔFOO–U²refers“to“equation“`4',‘UÔ\rdeqno{FOO}“²will“result“in“equation“n•¸ãum“bGer–U`4a'“(alw•¸ãa“ys‘U`a').‘q°ItŽ¡‘'9õcan–/only“bšGe“used“within“Ô$$–?ý...“$$².‘]It–/do˜es“not“a ect“the“equation“n•¸ãum“b˜er›/coun“ter,‘#nor˜theŽ¡‘'9õordinary–ìdpartial“equation“n•¸ãum“bGer›ìdcoun“ter.‘6óHo“w“ev“er,‘'it˜resets˜the˜partial˜equation˜n“um“bGerŽ¡‘'9õcounš¸ãter–'Zfor“the“Ô\rndeqno²,–0ŒÔ\rdeqno²,“Ô\deqreqno²,“and–'ZÔ\ddeqreqno“²commands.‘bsThe“argumen˜tŽ¡‘'9õof–Ä:Ô\rndeqno“²follo¸ãws“the“same“rules“as“that“of“Ô\reqno².‘¾wWhen“used“with“the“Ô\label{FOOO}Ž¡‘'9õ²command,‘‹a–âMreference“to“ÔFOOO‘â)²will“only“return“the“partial“equation“n•¸ãum“bGer–âM(and“the“pageŽ¡‘'9õn•¸ãum“bGer).‘PzT‘ÿ*ªo›ñlmak“e˜a˜complete˜reference˜to˜an˜equation˜whic“h˜has˜a˜Ô\rndeqno˜²command,‘hsa“yŽ¡‘'9õÔ\ref{FOO}\ref{FOOO}².›ÖThis–Ìcommand“is“not“compatible“with“the“class“option“Ôfleqn².˜In-Ž¡‘'9õstead–dof“Ô$$–?ý...“\rndeqno{FOO}“$$²,‘”Tuse–da“one-line“Ôdeqrarr“²en•¸ãvironmen“t–dwith“the“commandsŽ¡‘'9õÔ\deqreqno[-\jotbaseline]{FOO}‘?ý\nonumber–UU²at“the“end.Ž©‘9óÔ\rdeqno{FOO}Ž‘â&ÙÌ\rdeqnoŽŽŽŽ¡‘'9õ²Same–Ù†as“Ô\rndeqno{FOO}“²but“without“resetting“anš¸ãy“equation“n˜um˜bGer“coun˜ter“and“givingŽ¡‘'9õconsecutivš¸ãe–4¶partial“equation“n˜um˜bGers“(`4b',–¬`4c',“Óetc.²).‘ éó+ò"V cmbx10ÖNote:‘›‰²There–4¶is“nothing“pre-Ž¡‘'9õv•¸ãen“ting–-Xthe“repšGeated“use“of“Ô\rndeqno{FOO}“²and“Ô\rdeqno{FOO}“²for“the“same“lab˜el“ÔFOO².Ž¡‘'9õThis–PÙwill“result“in“n•¸ãum“bGering›PÙsuc“h˜as˜`3a'˜(if˜ÔFOO‘PV²refers˜to˜equation˜`3')˜oGccuring˜sev-Ž¡‘'9õeral–àtimes.› ÂiThis“command“is“not“compatible“with“the“class“option“Ôfleqn².˜InsteadŽ¡‘'9õof›»6Ô$$–?ý...“\rdeqno{FOO}“$$²,‘T­use˜a˜one-line˜Ôdeqrarr˜²en•¸ãvironmen“t˜with˜the˜commandsŽ¡‘'9õÔ\ddeqreqno[-\jotbaseline]{FOO}‘?ý\nonumber–UU²at“the“end.Ž¦‘9óÔ\eqreqno[Ólen‘ÄcÔ]{FOO}Ž‘ÝmCÌ\eqreqnoŽŽŽŽ¡‘'9õ²This–Žtcommand“is“the“arra•¸ãy-lik“e›Žtv“ersion˜of˜Ô\reqno{FOO}˜²and˜is˜used˜in˜m“uc“h˜the˜same˜w“a“y‘ÿ*ª.Ž¡‘'9õThe–ïVoptional“argumenš¸ãt“Ólen‘³¹²is“a“length“whic˜h“is“added“bGet˜w˜een“consecutiv˜e“ro˜ws“in“the“arra˜y-Ž¡‘'9õlik¸ãe–û¿structure.‘eWhen“using“Ô\eqreqno“²no“`Ô\\²'“should“bGe“issued“at“the“end“of“the“line,‘%Yit“isŽ¡‘'9õem¸ãbšGedded–{.in“the“command.‘ãQThis“is“giving“a“strange“app˜earance“if“Ô\eqreqno“²is“used“on“theŽ¡‘'9õlast–hÊline“of“the“arra•¸ãy-lik“e–hÊsturcture,‘m§namely“an“extra“blank“line“(with“equation“n•¸ãum“bGer).‘¬%T‘ÿ*ªoŽ¡‘'9õa•¸ãv“oid–\this“problem,›(spGecify“a“negativ¸ãe“length“for“Ólen²,˜preferably“`Ô-\jotbaseline²'“(se“bGelo¸ãw),Ž¡‘'9õand–UUissue“a“`Ô\nonumber²'“afterw¸ãards.Ž¦‘9óÔ\deqreqno[Ólen‘ÄcÔ]{FOO}Ž‘س­Ì\deqreqnoŽŽŽŽ¡‘'9õ²This–«Ùis“the“`Ô\rndeqno²'“v¸ãersion“of“`Ô\eqreqno²'“and“is“used“as“the“former“with“the“latter'sŽ¡‘'9õabilities–UUat“the“end“of“a“line.Ž¦‘9óÔ\ddeqreqno[Ólen‘ÄcÔ]{FOO}Ž‘ÓúÌ\ddeqreqnoŽŽŽŽ¡‘'9õ²This–•ÿis“the“`Ô\rdeqno²'“v¸ãersion“of“`Ô\eqreqno²'“and“is“used“as“the“former“with“the“latter's“abilitiesŽ¡‘'9õat–UUthe“end“of“a“line.Ž¦‘9óÔ\arrlabel{FOO}Ž‘س­Ì\arrlabelŽŽŽŽ¡‘'9õ²This–OŠcommand“is“a“vš¸ãersion“of“LŸýó5‘üff±AŽŽ‘͉²T‘þU>Ÿ'EŽ‘ãxX's“ordinary“Ô\label{FOO}“²command“mean˜t“to“bGe“used“inŽ¡‘'9õÔdeqarr–^º²and“Ôddeqar“²en•¸ãvironmen“ts.‘÷In–^ºthese“en•¸ãvironmen“ts,‘aa–^ºÔ\label{FOO}“²command“giv¸ães“aŽ¡‘'9õreference–oêto“the“spGeci c“equation,›ÌÓe.g.“²3b,˜whereas“Ô\arrlabel{FOO}“²in“the“same“pGosition“giv¸ãesŽ¡‘'9õa–ȹreference“conš¸ãtaining“only“the“main“equation“n˜um˜bGer,‘å’3“in“this“example.‘ËôF‘ÿ*ªor“restrictions,Ž¡‘'9õsee–¿5the“section“\Notice"“abGo•¸ãv“e.‘?½The–¿5four“commands“Ô\eqreqno²,–Ý;Ô\deqreqno²,“Ô\ddeqreqno²,“andŽ¡‘'9õÔ\arrlabel–UU²w¸ãere“created“after“inspiration“from“Larry“Jones“(Ôschnuff@mit.edu²).Ž¦‘9óÔ\whereŽ‘æàoÌ\whereŽŽŽŽ¡‘'9õ²The–ãJcommand“Ô\where“²tš¸ãypsets“the“text“\where"“(in“the“default“LR-fon˜t)“ ush“left“on“aŽ¡‘'9õsepGerate–;roš¸ãw“in“Ôeqnarray²,–2uÔdeqarr²,“Ôddeqar²,“and–;Ôdeqrarr“²en˜vironmen˜ts,‘2uand“preserv˜es“theŽ¡‘'9õen•¸ãvironmen“t's›UUalignmen“t˜for˜ro“ws˜to˜come.ŽŽŸ’á=5ŽŽŒ‹>¾ ˜‚ ýs}ü n‚ ý´}ü‘9óÔ\rem{Ótext‘òØÔ}Ž‘ÝmCÌ\remtextŽŽŽŽ¤ ‘'9õ²The–O‰command“Ô\rem{Ótext›òØÔ}“²t¸ãypsets“the“text“\Ótext˜²"“(in“the“default“LR-fon¸ãt)“ ush“left“on“aŽ¡‘'9õsepGerate–;roš¸ãw“in“Ôeqnarray²,–2uÔdeqarr²,“Ôddeqar²,“and–;Ôdeqrarr“²en˜vironmen˜ts,‘2uand“preserv˜es“theŽ¡‘'9õen•¸ãvironmen“t's›UUalignmen“t˜for˜ro“ws˜to˜come.‘qÇÔ\where˜²is˜equiv‘ÿqÇalen“t˜to˜Ô\rem{where}².Ž©‘9óÔ\nydeleqnoŽ‘ÓúÌ\nydeleqnoŽŽŽŽ¡‘'9õ²Givš¸ães–Ûa“new“partial“equation“n˜um˜bGer“when“used“within“Ô$$–?ý...“$$².‘üTh˜us,‘ü€writing‘ÛÔ$$“...Ž¡‘'9õ\nydeleqno›?ý$$–…]²is“equiv‘ÿqÇalen¸ãt“to“writing“Ô\begin{deqn}˜...˜\end{deqn}².‘ÞThis“command“isŽ¡‘'9õnot–UUcompatible“with“the“class“option“Ôfleqn²,“use“Ô\begin{deqn}–?ý...“\end{deqn}‘UU²instead.Ž¦‘9óÔ\deleqnoŽ‘ÝmCÌ\deleqnoŽŽŽŽ¡‘'9õ²Givš¸ães–rOa“partial“equation“n˜um˜bGer“when“used“within“Ô$$–?ý...“$$².‘ ȶTh˜us,‘ùwriting‘rOÔ$$“...Ž¡‘'9õ\deleqno–­š$$“²is“equiv‘ÿqÇalen¸ãt“to“writing“Ô\begin{ddeqn}–?ý...“\end{ddeqn}².‘z•This–­šcommand“isŽ¡‘'9õnot–=„compatible“with“the“class“option“Ôfleqn²,‘BHuse“Ô\begin{ddeqn}–?ý...“\end{ddeqn}‘=„²instead.Ž¦‘9óÔ\jotbaselineŽ‘ʆëÌ\jotbaselineŽŽŽŽ¡‘'9õ²This–ïåis“a“rubbšGer“length“whic¸ãh“is“set“to“b˜e“the“sum“of“Ô\baselinsekip“²and“Ô\jot“²eac¸ãh“timeŽ¡‘'9õa›XšÔdeqarr²,–™kÔddeqar²,“or˜a˜Ôdeqrarr˜²en•¸ãvironmen“t˜is˜en“terd.‘{–It˜is˜mean“t˜to˜bGe˜used˜with˜theŽ¡‘'9õÔ\eqreqno–úó²command“and“its“relativ¸ães“to“eliminate“the“problems“when“these“commands“areŽ¡‘'9õused–‰ion“the“last“line“of“the“en•¸ãvironmen“t.‘(The–‰ilength“Ô\baselineskip“²+“Ô\jot“²is“the“lengthŽ¡‘'9õLŸýó5‘üff±AŽŽ‘͉²T‘þU>Ÿ'EŽ‘ãxX–Óskips“bGet•¸ãw“een›Ót“w“o˜empt“y˜lines˜in˜an˜`Ôeqnarray²'˜en“vironmen“t˜and˜its˜deriv‘ÿqÇates˜de nedŽ¡‘'9õin‘UUÒdeleq².)Ž©!Ä‘9óÑ4Ž‘&†¾ExampleŽŸç‘9ó²After–Ghrunning“LŸýó5‘üff±AŽŽ‘͉²T‘þU>Ÿ'EŽ‘ãxX“on“Ôdeleq.ins²,›ƒíthere“is“an“example“a¸ãv‘ÿqÇaliable“in“the“ le“Ôdelex.tex²,˜whic¸ãhŽ¡‘9ómakš¸ães–jtuse“of“all“the“en˜vironmen˜ts“and“commands“de ned“in“the“Òdeleq“²pac˜k‘ÿqÇage.‘±$T˜ypset“it“and“seeŽ¡‘9ówith–UUyš¸ãour“o˜wn“ey˜es“what“the“results“are!Ž¦‘9óÑ5Ž‘&†¾Sending–ffa“Bug“Reps3ortŽŸç‘9óÒdeleq–L²is“most“likš¸ãely“to“con˜tain“bugs.‘¨¬RepGorts“of“bugs“in“the“pac˜k‘ÿqÇage“are“most“w˜elcome.‘¨¬BeforeŽ¡‘9ó ling–UUa“bug“repGort,“please“takš¸ãe“the“follo˜wing“actions:Ž¤‘r×1.ŽŽŽ‘'9õEnsure–UUyš¸ãour“problem“is“not“due“to“y˜our“input le;Ž¡‘r×2.ŽŽŽ‘'9õEnsure–UUyš¸ãour“problem“is“not“due“to“y˜our“o˜wn“pac˜k‘ÿqÇage(s)“or“class(es);Ž¡‘r×3.ŽŽŽ‘'9õEnsure–UUyš¸ãour“problem“is“not“co˜v˜ered“in“the“section“"Kno˜wn“Problems"“abGo˜v˜e;Ž¡‘r×4.ŽŽŽ‘'9õT‘ÿ*ªry–:to“loGcate“the“problem“bš¸ãy“writing“a“minimal“LŸýó5‘üff±AŽŽ‘͉²T‘þU>Ÿ'EŽ‘ãxX“input“ le“whic˜h“reproGduces“the“problem.Ž¤ ‘'9õInclude–UUthe“commandŽ¡‘1¹ïÔ\setcounter{errorcontextlines}{999}Ž¡‘'9õ²in–UUy¸ãour“input;Ž¤‘r×5.ŽŽŽ‘'9õRun–UUy¸ãour“ le“through“LŸýó5‘üff±AŽŽ‘͉²T‘þU>Ÿ'EŽ‘ãxX;Ž¡‘r×6.ŽŽŽ‘'9õSend–UUa“description“of“y¸ãour“problem,“the“input“ le“and“the“log“ le“via“e-mail“to:Ž© ‘8É=Ômatsd@homenet.se².Ž¡‘9óÓEnjoy–“çyour“LŸý雑üQíó,t}\Êcmti7×AŽŽ‘ÙÓT‘þKß'EŽ‘Í-X!¦mats“d.ŽŽŽŽŸ’á=²6ŽŽŒ‹P  ˜‚ ýs}ü n‚ ý´}ü‘9óÑ6Ž‘&†¾The‘ffCos3deŽŸç‘9ó²F‘ÿ*ªor–UUthe“in¸ãterested“reader(s),“here“is“a“short“description“of“the“coGde.Ž© ‘9óFirst,–UUthe“pacš¸ãk‘ÿqÇage“is“to“iden˜tify“itself.ŽŸ‘6f±1Ž‘ä¡Ì\NeedsTeXFormat{LaTeX2e}[1995/06/01]Ž¤ ‘6f±2Ž‘ä¡Ì\ProvidesPackage{deleq}[1997/02/22–¹–v.4.41“Partial“equation“numbering]Ž¡‘6f±3Ž‘ä¡Ì\def\deleqver{\textsf{deleq}–¹–version“4.41“(February~22,“1997)}ŽŸ‘9ó²Then,‘ 5wš¸ãe–ç¢need“to“de ne“the“coun˜ters“used“for“the“partial“part“of“the“equation“n˜um˜bGer.‘(­TheŽ¦‘9ócounš¸ãter–¯"ÔDeleq“²is“used“for“\recycled"“equation“n˜um˜bšGers,‘Ð`hence“no“dep˜endence“on“anš¸ãy“other“coun˜ter.ŽŸ‘6f±4Ž‘ä¡Ì\newcounter{deleq}[equation]Ž¡‘6f±5Ž‘ä¡Ì\newcounter{Deleq}Ž¡‘6f±6Ž‘ä¡Ì\newlength{\jotbaseline}Ž¡‘6f±7Ž‘ä¡Ì\renewcommand{\thedeleq}{\ensuremath{\theequation\mathrm{\alph{deleq}}}}Ž¡‘6f±8Ž‘ä¡Ì\renewcommand{\theDeleq}{\ensuremath{\mathrm{\alph{Deleq}}}}Ž¡‘6f±9Ž‘ä¡Ì\def\@deleqnnum{(\thedeleq)}Ž¡‘9ó±10Ž‘ä¡Ì\def\@deleqrnum#1{(\ref{#1}\theDeleq)}Ž¡‘9ó±11Ž‘ä¡Ì\def\@eqrnum#1{(\ref{#1})}ŽŸ‘9ó²The–_Qparts“making“up“the“Ô\\“²command“in“the“mš¸ãultiline“en˜vironmen˜ts“are“similar“to“those“used“b˜yŽ¦‘9óthe–UUstandard“en•¸ãvironmen“ts–UU(at“least“hoš¸ãw“they“loGok˜ed“some“time“ago):ŽŸ‘9ó±12Ž‘ä¡Ì\def\@deqncr{{\ifnum0=`}\fi\@ifstar{\global\@eqpen\@MŽ¡‘9ó±13Ž‘+ÊùÌ\@ydeqncr}{\global\@eqpen\interdisplaylinepenalty‘¹–\@ydeqncr}}Ž¡‘9ó±14Ž‘ä¡Ì\def\@ydeqncr{\@ifnextchar‘¹–[{\@xdeqncr}{\@xdeqncr[\z@]}}Ž¡‘9ó±15Ž‘ä¡Ì\def\@xdeqncr[#1]{\ifnum0=`{\fi}\@@deqncrŽ¡‘9ó±16Ž‘'cÌ\noalign{\penalty\@eqpen\vskip\jot\vskip‘¹–#1\relax}}Ž¡‘9ó±17Ž‘ä¡Ì\def\@@deqncr{\let\@tempa\relaxŽ¡‘9ó±18Ž‘+ÊùÌ\ifcase\@eqcnt–¹–\def\@tempa{&“&“&}\or“\def\@tempa{&“&}%Ž¡‘9ó±19Ž‘5>%Ì\else‘¹–\def\@tempa{&}\fiŽ¡‘9ó±20Ž‘0„Ì\@tempa‘¹–\if@eqnsw\@deleqnnum\stepcounter{deleq}\fiŽ¡‘9ó±21Ž‘0„Ì\global\@eqnswtrue\global\@eqcnt\z@\cr}Ž¡‘9ó±22Ž‘ä¡Ì\newcommand{\@xeqrcr}[2]{\ifnum0=`{\fi}\@@eqrcr{#2}Ž¡‘9ó±23Ž‘'cÌ\noalign{\penalty\@eqpen\vskip\jot\vskip‘¹–#1\relax}}Ž¡‘9ó±24Ž‘ä¡Ì\def\@@eqrcr#1{\let\@tempa\relaxŽ¡‘9ó±25Ž‘+ÊùÌ\ifcase\@eqcnt–¹–\def\@tempa{&“&“&}\or“\def\@tempa{&“&}%Ž¡‘9ó±26Ž‘5>%Ì\else‘¹–\def\@tempa{&}\fiŽ¡‘9ó±27Ž‘0„Ì\@tempa‘¹–\if@eqnsw\@eqrnum{#1}\fiŽ¡‘9ó±28Ž‘0„Ì\global\@eqnswtrue\global\@eqcnt\z@\cr}Ž¡‘9ó±29Ž‘ä¡Ì\newcommand{\@xdeqrcr}[2]{\ifnum0=`{\fi}\@@deqrcr{#2}Ž¡‘9ó±30Ž‘'cÌ\noalign{\penalty\@eqpen\vskip\jot\vskip‘¹–#1\relax}}Ž¡‘9ó±31Ž‘ä¡Ì\def\@@deqrcr#1{\let\@tempa\relaxŽ¡‘9ó±32Ž‘+ÊùÌ\ifcase\@eqcnt–¹–\def\@tempa{&“&“&}\or“\def\@tempa{&“&}%Ž¡‘9ó±33Ž‘5>%Ì\else‘¹–\def\@tempa{&}\fiŽ¡‘9ó±34Ž‘0„Ì\@tempa‘¹–\if@eqnsw\@deleqrnum{#1}\fiŽ¡‘9ó±35Ž‘0„Ì\global\@eqnswtrue\global\@eqcnt\z@\cr}Ž¡‘9ó±36Ž‘ä¡Ì\def\@deqrarcr{{\ifnum0=`}\fi\@ifstar{\global\@eqpen\@MŽ¡‘9ó±37Ž‘+ÊùÌ\@ydeqrarcr}{\global\@eqpen\interdisplaylinepenalty‘¹–\@ydeqrarcr}}Ž¡‘9ó±38Ž‘ä¡Ì\def\@ydeqrarcr{\@ifnextchar‘¹–[{\@xdeqrarcr}{\@xdeqrarcr[\z@]}}Ž¡‘9ó±39Ž‘ä¡Ì\def\@xdeqrarcr[#1]{\ifnum0=`{\fi}\@@deqrarcrŽ¡‘9ó±40Ž‘'cÌ\noalign{\penalty\@eqpen\vskip\jot\vskip‘¹–#1\relax}}Ž¡‘9ó±41Ž‘ä¡Ì\def\@@deqrarcr{\let\@tempa\relaxŽ¡‘9ó±42Ž‘+ÊùÌ\ifcase\@eqcnt–¹–\def\@tempa{&“&“&}\or“\def\@tempa{&“&}%Ž¡‘9ó±43Ž‘5>%Ì\else‘¹–\def\@tempa{&}\fiŽ¡‘9ó±44Ž‘0„Ì\@tempa‘¹–\global\@eqnswtrue\global\@eqcnt\z@\cr}ŽŽŸ’á=²7ŽŽŒ‹]  ˜‚ ýs}ü n‚ ý´}ü‘9ó²Here–UUthe“de nitions“of“the“user“commands“are.Ž©‘9ó±45Ž‘ä¡Ì\newcommand{\nydeleqno}{\stepcounter{equation}\stepcounter{deleq}Ž¤ ‘9ó±46Ž‘"WÍÌ\let\@currentlabel\thedeleq–¹–\eqno“(\thedeleq)}Ž¡‘9ó±47Ž‘ä¡Ì\newcommand{\deleqno}{\refstepcounter{deleq}‘¹–\let\@currentlabel\thedeleqŽ¡‘9ó±48Ž‘"WÍÌ\eqno‘¹–(\thedeleq)}Ž¡‘9ó±49Ž‘ä¡Ì\newcommand{\reqno}[1]{\setcounter{Deleq}{-1}\refstepcounter{Deleq}Ž¡‘9ó±50Ž‘'cÌ\eqno–¹–(\ref{#1})“}Ž¡‘9ó±51Ž‘ä¡Ì\newcommand{\rdeqno}[1]{\refstepcounter{Deleq}Ž¡‘9ó±52Ž‘'cÌ\eqno‘¹–(\ref{#1}\theDeleq)}Ž¡‘9ó±53Ž‘ä¡Ì\newcommand{\rndeqno}[1]{\setcounter{Deleq}{0}\refstepcounter{Deleq}Ž¡‘9ó±54Ž‘'cÌ\eqno‘¹–(\ref{#1}\theDeleq)}Ž¡‘9ó±55Ž‘ä¡Ì\newcommand{\eqreqno}[2][0pt]{{\ifnum0=`}\fi\@ifstar{\global\@eqpen\@MŽ¡‘9ó±56Ž‘+ÊùÌ\@xeqrcr{#1}{#2}}{\global\@eqpen\interdisplaylinepenaltyŽ¡‘9ó±57Ž‘+ÊùÌ\@xeqrcr{#1}{#2}}}Ž¡‘9ó±58Ž‘ä¡Ì\newcommand{\deqreqno}[2][0pt]{\setcounter{Deleq}{0}\refstepcounter{Deleq}Ž¡‘9ó±59Ž‘+ÊùÌ{\ifnum0=`}\fi\@ifstar{\global\@eqpen\@MŽ¡‘9ó±60Ž‘+ÊùÌ\@xdeqrcr{#1}{#2}}{\global\@eqpen\interdisplaylinepenaltyŽ¡‘9ó±61Ž‘+ÊùÌ\@xdeqrcr{#1}{#2}}}Ž¡‘9ó±62Ž‘ä¡Ì\newcommand{\ddeqreqno}[2][0pt]{\refstepcounter{Deleq}Ž¡‘9ó±63Ž‘+ÊùÌ{\ifnum0=`}\fi\@ifstar{\global\@eqpen\@MŽ¡‘9ó±64Ž‘+ÊùÌ\@xdeqrcr{#1}{#2}}{\global\@eqpen\interdisplaylinepenaltyŽ¡‘9ó±65Ž‘+ÊùÌ\@xdeqrcr{#1}{#2}}}Ž¡‘9ó±66Ž‘ä¡Ì\newcommand{\arrlabel}[1]{\let\@currentlabel\theequation‘¹–\label{#1}}Ž¡‘9ó±67Ž‘ä¡Ì\newcommand{\nydeqno}{\stepcounter{equation}\stepcounter{deleq}}Ž¡‘9ó±68Ž‘ä¡Ì\newcommand{\heqno}{\stepcounter{equation}}ŽŸ‘9ó²And–UUthe“t•¸ãw“o–UUcommands“Ô\where“²and“Ô\rem“²follo¸ãw“suit:Ž¦‘9ó±69Ž‘ä¡Ì\def\where{\let\@tempa\relax–¹–\def\@tempa{&“&“&}Ž¡‘9ó±70Ž‘0„Ì\@tempa–¹–{\hbox“to“.01\p@{}\rlap{\hskip“-\displaywidth“where}}\cr}Ž¡‘9ó±71Ž‘ä¡Ì\def\rem#1{\let\@tempa\relax–¹–\def\@tempa{&“&“&}Ž¡‘9ó±72Ž‘0„Ì\@tempa–¹–{\hbox“to“.01\p@{}\rlap{\hskip“-\displaywidth“#1}}\cr}ŽŸ‘9ó²The–ùç vš¸ãe“en˜vironmen˜ts“are“sligh˜t“mošGdi cations“of“the“corresp˜onding“LŸýó5‘üff±AŽŽ‘͉²T‘þU>Ÿ'EŽ‘ãxX“standard“en¸ãviron-Ž¤ ‘9ómenš¸ãts.‘àËThe–%main“di erence“lies“in“whic˜h“coun˜ter(s)“is“steppGed“and“whic˜h“in˜ternals“are“used“toŽ¡‘9ó nish–uo “the“lines.‘ÑThree“of“them“ha•¸ãv“e–ularge“parts“in“common,‘} parts“whic¸ãh“are“put“in“one“macroŽ¡‘9ó`Ô\@dlqnv²':Ž¦‘9ó±73Ž‘ä¡Ì\def\@dlqnv{\setlength{\jotbaseline}{\baselineskip}%Ž¤ ‘9ó±74Ž‘"WÍÌ\addtolength{\jotbaseline}{\jot}‘ s,\global\@eqnswtrue\m@thŽ¡‘9ó±75Ž‘"WÍÌ\global\@eqcnt\z@\tabskip\@centeringŽ¡‘9ó±76Ž‘"WÍÌ$$\halign‘¹–to\displaywidth\bgroup\@eqnsel\hskip\@centeringŽ¡‘9ó±77Ž‘"WÍÌ$\displaystyle\tabskip\z@{##}$&\global\@eqcnt\@neŽ¡‘9ó±78Ž‘"WÍÌ\hskip–¹–2\arraycolsep“\hfil${##}$\hfilŽ¡‘9ó±79Ž‘"WÍÌ&\global\@eqcnt\tw@–¹–\hskip“2\arraycolsepŽ¡‘9ó±80Ž‘ä¡Ì$\displaystyle\tabskip\z@{##}$\hfilŽ¡‘9ó±81Ž‘'cÌ\tabskip\@centering&\llap{##}\tabskip\z@\cr}Ž¡‘9ó±82Ž‘ä¡Ì\newenvironment{deqarr}{\stepcounter{equation}\stepcounter{deleq}Ž¡‘9ó±83Ž‘"WÍÌ\let\@currentlabel\thedeleq– s,\let\\\@deqncr“\@dlqnv}Ž¡‘9ó±84Ž‘ä¡Ì{\@@deqncr\egroupŽ¡‘9ó±85Ž‘5>%Ì\global\advance\c@deleq\m@ne$$\global\@ignoretrue}Ž¡‘9ó±86Ž‘ä¡Ì\newenvironment{ddeqar}{\stepcounter{deleq}Ž¡‘9ó±87Ž‘"WÍÌ\let\@currentlabel\thedeleq– s,\let\\\@deqncr“\@dlqnv}Ž¡‘9ó±88Ž‘ä¡Ì{\enddeqarr}Ž¡‘9ó±89Ž‘ä¡Ì\newenvironment{deqn}{$$\refstepcounter{equation}\stepcounter{deleq}Ž¡‘9ó±90Ž‘'cÌ\let\@currentlabel\thedeleq}ŽŽŸ’á=²8ŽŽŒ‹ j ˜‚ ýs}ü n‚ ý´}ü‘9ó±91Ž‘"WÍÌ{\eqno–¹–\hbox{\@deleqnnum}“$$\global\@ignoretrue}Ž¤ ‘9ó±92Ž‘ä¡Ì\newenvironment{ddeqn}{$$\refstepcounter{deleq}‘¹–\let\@currentlabel\thedeleq}Ž¡‘9ó±93Ž‘"WÍÌ{\enddeqn}Ž¡‘9ó±94Ž‘ä¡Ì\newenvironment{deqrarr}{\let\@currentlabel\theDeleqŽ¡‘9ó±95Ž‘"WÍÌ\let\\\@deqrarcr‘,Â\@dlqnv}Ž¡‘9ó±96Ž‘ä¡Ì{\@deqrarcr‘,Â\egroup‘ s,$$\global\@ignoretrue}Ž©‘9ó²If–‡Ñthe“user“w•¸ãan“ts–‡Ñthe“equation“n•¸ãum“bGers–‡Ñto“the“left,‘”pwš¸ãe“ha˜v˜e“to“moGdify“some“of“the“commandsŽ¤ ‘9óand–ÀJinš¸ãternals“de ned“abGo˜v˜e.‘²¥This“is“done“in“a“Ô\DeclareOption²-call,‘Ûbut“ rst“w˜e“set“a“switc˜h“toŽ¡‘9ótest–¡ for“the“Ôleqno“²option.‘TâInitially‘ÿ*ª,‘³õit“is“set“to“ÔF› õ²and“then“c¸ãhanged“to“ÔT˜²if“the“Ôleqno“²option“is“inŽ¡‘9óe ect.ŽŸ‘9ó±97Ž‘ä¡Ì\newif\ifl@qn‘¹–\l@qnfalseŽ¤ ‘9ó±98Ž‘ä¡Ì\DeclareOption{leqno}{%Ž¡‘9ó±99Ž‘ä¡Ì\global\l@qntrue%Ž¡‘ =€±100Ž‘ä¡Ì\renewcommand{\@deleqnnum}{\hbox–¹–to“.01\p@{}\rlap{\reset@font\rmfamilyŽ¡‘ =€±101Ž‘"WÍÌ\hskip‘¹–-\displaywidth(\thedeleq)}}Ž¡‘ =€±102Ž‘ä¡Ì\renewcommand{\nydeleqno}{\stepcounter{equation}\stepcounter{deleq}Ž¡‘ =€±103Ž‘"WÍÌ\let\@currentlabel\thedeleq–¹–\leqno“(\thedeleq)}Ž¡‘ =€±104Ž‘ä¡Ì\renewcommand{\deleqno}{\refstepcounter{deleq}‘¹–\let\@currentlabel\thedeleqŽ¡‘ =€±105Ž‘"WÍÌ\leqno‘¹–(\thedeleq)}Ž¡‘ =€±106Ž‘ä¡Ì\renewcommand{\reqno}[1]{\setcounter{Deleq}{-1}\refstepcounter{Deleq}Ž¡‘ =€±107Ž‘'cÌ\leqno–¹–(\ref{#1})“}Ž¡‘ =€±108Ž‘ä¡Ì\renewcommand{\rdeqno}[1]{\refstepcounter{Deleq}Ž¡‘ =€±109Ž‘'cÌ\leqno‘¹–(\ref{#1}\theDeleq)}Ž¡‘ =€±110Ž‘ä¡Ì\renewcommand{\rndeqno}[1]{\setcounter{Deleq}{0}\refstepcounter{Deleq}Ž¡‘ =€±111Ž‘'cÌ\leqno‘¹–(\ref{#1}\theDeleq)}Ž¡‘ =€±112Ž‘ä¡Ì\renewcommand{\@eqrnum}[1]{\hbox–¹–to“.01\p@{}\rlap{\reset@font\rmfamilyŽ¡‘ =€±113Ž‘>±QÌ\hskip‘¹–-\displaywidth(\ref{#1})}}Ž¡‘ =€±114Ž‘ä¡Ì\renewcommand{\@deleqrnum}[1]{\hbox–¹–to“.01\p@{}\rlap{\reset@font\rmfamilyŽ¡‘ =€±115Ž‘>±QÌ\hskip‘¹–-\displaywidth(\ref{#1}\theDeleq)}}Ž¡‘ =€±116Ž‘"WÍÌ}Ž¦‘9ó²The–\KÔfleqn“²option“is“mainly“a“`Òdeleq²-i cation'“of“the“LŸýó5‘üff±AŽŽ‘͉²T‘þU>Ÿ'EŽ‘ãxX‘ü2Ÿÿµ"ŽŽ‘* @² le“Ôfleqn.clo“²(1995/06/26“v1.3g).Ž¤ ‘9óIf–ANbšGoth“Ôleqno“²and“Ôfleqn“²options“are“in“use,‘EPthe“length“Ô\mathindent“²should“b˜e“increased“to“allo¸ãwŽ¡‘9óspace–8âfor“the“letters“of“the“partial“equation“n•¸ãum“bGers.‘hLF‘ÿ*ªor–8âthe“mš¸ãultiline“en˜vironmen˜ts,‘>“it“is“enoughŽ¡‘9óto–UUmakš¸ãe“c˜hanges“to“the“in˜ternal“Ô\@dlqnv².ŽŸ‘ =€±117Ž‘ä¡Ì\DeclareOption{fleqn}{%Ž¤ ‘ =€±118Ž‘ä¡Ì\ifl@qn–¹–\AtBeginDocument{\addtolength{\mathindent}{1em}}“\fiŽ¡‘ =€±119Ž‘ä¡Ì\renewenvironment{deqn}%Ž¡‘ =€±120Ž‘"WÍÌ{\@beginparpenalty\predisplaypenaltyŽ¡‘ =€±121Ž‘'cÌ\@endparpenalty\postdisplaypenaltyŽ¡‘ =€±122Ž‘'cÌ\refstepcounter{equation}\stepcounter{deleq}Ž¡‘ =€±123Ž‘'cÌ\let\@currentlabel\thedeleq%Ž¡‘ =€±124Ž‘'cÌ\trivlist‘¹–\item[]\leavevmodeŽ¡‘ =€±125Ž‘0„Ì\hb@xt@\linewidth\bgroup–¹–$\m@th%“$Ž¡‘ =€±126Ž‘0„Ì\displaystyleŽ¡‘ =€±127Ž‘0„Ì\hskip\mathindent}%Ž¡‘ =€±128Ž‘+ÊùÌ{$\hfil–¹–%“$Ž¡‘ =€±129Ž‘0„Ì\displaywidth\linewidth\hbox{\@deleqnnum}%Ž¡‘ =€±130Ž‘0„Ì\egroupŽ¡‘ =€±131Ž‘'cÌ\endtrivlist}Ž¡‘ =€±132Ž‘ä¡Ì\renewenvironment{ddeqn}%Ž¡‘ =€±133Ž‘"WÍÌ{\@beginparpenalty\predisplaypenaltyŽ¡‘ =€±134Ž‘'cÌ\@endparpenalty\postdisplaypenaltyŽŽŸ’á=²9ŽŽŒ‹ x£ ˜‚ ýs}ü n‚ ý´}ü‘ =€±135Ž‘'cÌ\refstepcounter{deleq}Ž¤ ‘ =€±136Ž‘'cÌ\let\@currentlabel\thedeleq%Ž¡‘ =€±137Ž‘'cÌ\trivlist‘¹–\item[]\leavevmodeŽ¡‘ =€±138Ž‘0„Ì\hb@xt@\linewidth\bgroup–¹–$\m@th%“$Ž¡‘ =€±139Ž‘0„Ì\displaystyleŽ¡‘ =€±140Ž‘0„Ì\hskip\mathindent}%Ž¡‘ =€±141Ž‘+ÊùÌ{\enddeqn}Ž¡‘ =€±142Ž‘ä¡Ì\renewcommand{\@dlqnv}{%Ž¡‘ =€±143Ž‘"WÍÌ\setlength{\jotbaseline}{\baselineskip}Ž¡‘ =€±144Ž‘"WÍÌ\addtolength{\jotbaseline}{\jot}Ž¡‘ =€±145Ž‘"WÍÌ\global\@eqcnt\z@Ž¡‘ =€±146Ž‘"WÍÌ\tabskip\mathindentŽ¡‘ =€±147Ž‘"WÍÌ\setlength\abovedisplayskip{\topsep}%Ž¡‘ =€±148Ž‘"WÍÌ\ifvmodeŽ¡‘ =€±149Ž‘+ÊùÌ\addtolength\abovedisplayskip{\partopsep}%Ž¡‘ =€±150Ž‘"WÍÌ\fiŽ¡‘ =€±151Ž‘"WÍÌ\addtolength\abovedisplayskip{\parskip}%Ž¡‘ =€±152Ž‘"WÍÌ\setlength\belowdisplayskip{\abovedisplayskip}%Ž¡‘ =€±153Ž‘"WÍÌ\setlength\belowdisplayshortskip{\abovedisplayskip}%Ž¡‘ =€±154Ž‘"WÍÌ\setlength\abovedisplayshortskip{\abovedisplayskip}%Ž¡‘ =€±155Ž‘"WÍÌ$$\everycr{}\halign–¹–to\linewidth%“$$Ž¡‘ =€±156Ž‘"WÍÌ\bgroupŽ¡‘ =€±157Ž‘+ÊùÌ\hskip\@centeringŽ¡‘ =€±158Ž‘+ÊùÌ$\displaystyle\tabskip\z@skip{##}$\@eqnsel&%Ž¡‘ =€±159Ž‘+ÊùÌ\global\@eqcnt\@ne–¹–\hskip“\tw@\arraycolsep“\hfil${##}$\hfil&%Ž¡‘ =€±160Ž‘+ÊùÌ\global\@eqcnt\tw@–¹–\hskip“\tw@\arraycolsepŽ¡‘ =€±161Ž‘+ÊùÌ$\displaystyle{##}$\hfil‘¹–\tabskip\@centering&%Ž¡‘ =€±162Ž‘+ÊùÌ\global\@eqcnt\thr@@Ž¡‘ =€±163Ž‘+ÊùÌ\hb@xt@\z@\bgroup\hss##\egroup\tabskip\z@skip\cr}Ž¡‘ =€±164Ž‘ä¡Ì}Ž©‘9ó²If–´wother“options“wš¸ãere“ask˜ed“for,‘Ì@the“pac˜k‘ÿqÇage“should“mak˜e“these“options“`un˜used'.‘.Then,–Ì@last,“theŽŸ ‘9óoption(s)–UUis“(are)“proGcessed.ŽŸ‘ =€±165Ž‘ä¡Ì\DeclareOption*{\OptionNotUsed}Ž¡‘ =€±166Ž‘ä¡Ì\ProcessOptionsŽ¦‘9ó²That–UUis“all.‘qÇHapp¸ãy“T‘þU>Ÿ'EŽ‘ãxX-ing!Ž È%“’*@s±Cop•Èãyrigh“t‘çžÉýcŽŽŽ‘±Èó O!â…cmsy7· ŽŽŽ‘ \u±1994-97›±Èb“y˜Mats˜Dahlgren.ŽŽŸ’ÞŸ=²10ŽŽŒø†ƒ’À;蘂¹ˆ ó,t}\Êcmti7ó+ò"V cmbx10ó*ÂÖN  cmbx12ó)ßê cmmi10óKñ`y cmr10óÙ“ Rcmr7ù¼ßßßßßß