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les“bš¸ãy“Andreas“Sc˜hrell“(1994),‘ˆnamely“Øpictexwd.sty“²(for“LŸýó5‘üff±AŽŽ‘͉²T‘þU>Ÿ'EŽ‘ãxX“users)“andŽ¡‘k"Øpictexwd.tex–UU²(for“plain“T‘þU>Ÿ'EŽ‘ãxX“users).Ž©Ùü‘k"ó1ÂÖN  cmbx12Ü2.1Ž‘!+"The‘€programŽŸuT‘k"Ømpic21.exe‘ÿô(rename–?ýto“mathspic.exe)ŽŸ-¥‘k"²The–¶executable“program“Ømpic21.exe“²w¸ãas“compiled“on“an“MS-DOS‘š6.2“platform.‘¹éIt“is“compatibleŽ¡‘k"with›ãçWINDO¸ãWS‘ã9x,–G‹2000,“NT.˜F‘ÿ*ªor˜the˜purpGoses˜of˜this˜man¸ãual˜it˜is˜suggested˜that˜Ømpic21.exeŽ¡‘k"²bšGe–…renamed“to“Ømathspic.exe².‘VThe“executable“program“m¸ãust“b˜e“either“in“the“same“directory“as“theŽ¡‘k"¾mathsPIC–UU²input- le,“or“in“the“directory“path.Ž¦‘k"Ü2.2Ž‘!+"Optional‘€utilitiesŽŸuT‘k"Øshow.com‘ÿô(a–?ýDOS“textviewer)Ž¡‘k"clean.exe‘¿÷(a–?ýDOS“tool“for“deleting“comment“lines)ŽŸ-¥‘k"²These›“!t•¸ãw“o˜ les˜should˜bGe˜placed˜in˜the˜same˜directory˜as˜Ømathspic.exe².‘+*Øclean.exe˜²is˜a˜programŽ¡‘k"for–¯¯remoš¸ãving“all“the“commen˜ted“lines“from“the“output- 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le“is“a“large“one.Ž¡‘k"This–Lêcan“bGe“easily“done“using“the“included“ó2Œ-ø cmcsc10Ýclean.exe“²utilit•¸ãy‘ÿ*ª,‘N™whic“h–Lêwill“strip“out“all“lines“startingŽ¡‘k"with–ÎTthe“double“commenš¸ãt“sym˜bGol“Ø%%².‘ÜÄThe“/s“switc˜h“can“also“bGe“used“with“Ýclean.exe².‘ÜÄExamples“ofŽ¡‘k"the–UUsynš¸ãtax“are“as“follo˜ws.Ž©‘k"Øclean.exe‘?ý/?Ž¡‘k"clean.exe‘ úinputfilenameŽ¡‘k"clean.exe– ú/s“inputfilenameŽ¡‘k"clean.exe– ú/s“inputfilename‘?ýoutputfilenameŽ¦‘k"²If–X‡no“output“ lename“is“supplied,‘YSthen“Ýclean.exe“²will“use“the“same“ lename“but“add“the“ lenameŽ¡‘k"extension–l=Ø.mtc².‘¶F‘ÿ*ªor“example,›q÷the“follo¸ãwing“command“will“clean“the“output- le“Ømyfile.mt²,˜generatingŽ¡‘k"the–UU le“Ømyfile.mtc“²as“the“cleaned“ le,“and“then“view“the“`cleaned'“output- le“using“Øshow.com².Ž¦‘k"Øclean.exe– ú/s“myfile.mtŽŸþ6‘k"Ü3.3Ž‘!+"Batc h‘€pro`cessingŽŸuT‘k"²In–üaddition“to“running“the“program“from“the“command-line,‘ î¾mathsPIC‘ûþ²can“also“bGe“run“from“a“batc¸ãh- leŽ¡‘k"(some–'familiaritš¸ãy“with“the“MS-DOS‘batc˜h- le“language“is“assumed;‘ Œnote“that“the“batc˜h- les“need“to“bGeŽ¡‘k"tailored–_qto“the“particular“command-line“sequence.)‘F‘ÿ*ªor“example,‘aøthe“folloš¸ãwing“command“line“with“ v˜eŽ¡‘k"parameters›UU(t•¸ãw“o˜switc“hes˜and˜three˜ lenames)Ž¦‘k"Ømathspic– ú/b‘?ý/s“testpic.m“testpic.mt“testpic.dviŽ¦‘k"²will–Þ!bGe“executed“bš¸ãy“the“follo˜wing“MS-DOS‘Þbatc˜h- le“(written“for“the“EmT‘þU>Ÿ'EŽ‘ãxXŸü^ÿ±3ŽŽ‘Z”²implemen˜tation“of“LŸýó5‘üff±AŽŽ‘͉²T‘þU>Ÿ'EŽ‘ãxXŽ¡‘k"for–>PCs“using“MS-DOS),“whic¸ãh“ rst“runs“¾mathsPIC‘>²on“the“input- le“Øtestpic.m²;‘EÍthen“calls“LŸýó5‘üff±AŽŽ‘͉²T‘þU>Ÿ'EŽ‘ãxX‘ü2Ÿÿµ"ŽŽ‘+Ϻ²toŽ¡‘k"proGcess–ª‰the“output- le;‘Õ#and“ nally“calls“the“EmT‘þU>Ÿ'EŽ‘ãxX“screen“view¸ãer“Ødviscrs.exe“²(via“Øvs.bat²)“to“viewŽ¡‘k"the–UU le“Øtestpic.dvi“²(Ø%5²).Ž¦‘k"ØREM‘ úmathsPIC.bat–?ý(MS-DOS“6.0“and“greater)Ž¡‘k"@ECHO‘?ýOFFŽ¡‘k"mathspic.exe–?ý%1“%2“%3“%4“%5Ž¡‘k"CALL–?ýlatex2e“%4Ž¡‘k"CALL–?ývs.bat“/s3“%5Ž¦‘k"²Note–ç0that“care“needs“to“bGe“takš¸ãen“to“mak˜e“sure“that“the“parameters“used“in“the“batc˜h- le“correspGondŽ¡‘k"to–óthe“command-line“parameters.‘LJF‘ÿ*ªor“example,‘ if“the“t•¸ãw“o›óswitc“hes˜are˜run˜together˜without˜a˜spaceŽ¡‘k"(e.g.–“¨Ø/b/s²)“they“will“bšGe“p˜erceivš¸ãed“b˜y“MS-DOS‘“˜as“a“single“en˜tit˜y‘ÿ*ª,‘£=in“whic˜h“case“the“Ø.dvi“² le“w˜ould“bGeŽ¡‘k"represen•¸ãted›%„b“y˜Ø%4˜²in˜the˜batc“h- le˜instead˜of˜Ø%5².‘a×F‘ÿ*ªor˜example,‘/the˜follo“wing˜four-parameter˜command-Ž¡‘k"lineŽ¦‘k"Ømathspic– ú/b/s“testpic.m“testpic.mt“testpic.dviŽ¦‘k"²wš¸ãould–UUrequire“the“follo˜wing“MS-DOS“batc˜h- le.Ž¦‘k"Ø@ECHO‘?ýOFFŽ¡‘k"mathspic.exe‘ ú%1–?ý%2“%3“%4Ž¡‘k"CALL–?ýlatex2e.bat“%3Ž¡‘k"CALL–?ývs.bat‘ ú/s3“%4Ž‘k"Ÿ;»‰ff³?çŸ J=‘ "5Ÿý-:Ë3ŽŽŽ‘LÜÊThe–ÕXEmT‘þ•AŸ¸ãEŽ‘MX“screen“viewšÃŽer“is“×dviscrs.exe“Êand“is“usually“called“via“the“batc˜h- le“×vs.batÊ.ŽŽŸŽŒ‹   Åf¢ ý=´}Ÿ35ŸûÌÊ‘k"ÚmathsPIC‘꨼2.1ŽŽŽ’½Œ¤²9ŽŽŽŽ‘k"Ÿ™œ‰ffÀ!ƒŽŽŽŽ ¤Kƒ ý~´}‘k"As–\§a“ nal“example“(again“based“on“the“EmT‘þU>Ÿ'EŽ‘ãxX“implemenš¸ãtation),‘ž{suppGose“y˜ou“wish“to“use“y˜ourŽ¤ ‘k"o•¸ãwn›ùtext-view“er˜(sa“y‘ÿ*ª,–!ìØmyTextViewer.exe²)˜to˜view˜the˜output- le,“with˜the˜Ø/b˜²switc¸ãh˜(enables˜error-Ž¡‘k"bGeep),‘D%and›bha•¸ãv“e˜conditional˜branc“hing|i.e.˜ha“v“e˜the˜option˜to˜either˜(a)˜quit˜(select˜the˜`ØN²'‘0option)Ž¡‘k"and–ù¿return“to“the“text-editor“after“viewing“the“output- le,‘"Ùor“(b)“proGceed“(select“the“`ØY²'‘ù”option)“andŽ¡‘k"proGcess–À¶the“output- le“Øtestpic.mt“²(Ø%3²)“and“then“view“the“Ø.dvi“² le“(Ø%4²).‘@=In“this“example,‘Þpthe“follo¸ãwingŽ¡‘k"four-parameter‘UUcommand-lineŽ¤‘k"Ømathspic– ú/b“testpic.m“testpic.mt“testpic.dviŽ¡‘k"²could–UUbGe“run“using“the“folloš¸ãwing“batc˜h- le.Ž¡‘k"ØREM‘ úmPIC.bat–?ý(MS-DOS“6.0“and“greater)Ž¤ ‘k"@ECHO‘?ýOFFŽ¡‘k"mathspic.exe–?ý%1“%2“%3“%4Ž¡‘k"CALL–?ýmyTextViewer.exe“%3Ž¡‘k"CHOICE–?ý/C:YN‘ úView“figure?:Ž¡‘k"IF–?ýERRORLEVEL“1“IF“NOT“ERRORLEVEL“2“GOTO“yesŽ¡‘k"GOTO‘ únoŽ¡‘k":yesŽ¡‘k"CALL–?ýlatex2e“%3Ž¡‘k"CALL–?ývs.bat“/s3“%4Ž¡‘k":noŽŸ!Ä‘k"Ç4Ž‘·íThe–ffÛmathsPIC“Ç le“and“scriptŽŸç‘k"²The–’‰idea“underlying“the“¾mathsPIC‘’X² le“(input- le)“is“that“it“should“bGe“able“to“conš¸ãtain“ev˜erything“requiredŽ¡‘k"to–/Ùgenerate“the“propGosed“ gure“(i.e.“all“¾mathsPIC‘/¡²commands,–fzcommen¸ãts,“T‘þU>Ÿ'EŽ›ãxX–/Ùand“LŸýó5‘üff±AŽŽ‘͉²T‘þU>Ÿ'EŽ˜X“commandsŽ¡‘k"including–´\headers“and“foGoters,›ÌP‘þÌП'IŽ‘©DC‘þæfT‘þU>Ÿ'EŽ‘ãxX“commands,˜as“wš¸ãell“as“lines“to“bGe“copied“v˜erbatim)“so“that“theŽ¡‘k"output- le–LÁcan“bšGe“immediately“T‘þU>Ÿ'EŽ‘ãxXed“to“generate“the“graphic.‘X Some“general“p˜oin¸ãts“relating“to“theŽ¡‘k"¾mathsPIC–UU² le“are“as“follo¸ãws.ŽŸ‘k#¸ŽŽŽ‘k$¾mathsPIC‘«z²commands–«¥are“Ùnot‘ž}²pre xed“bš¸ãy“bac˜kslashes.‘97They“are“therefore“easily“distinguished“fromŽ¡‘k$T‘þU>Ÿ'EŽ›ãxX–UUand“P‘þÌП'IŽ‘©DC‘þæfT‘þU>Ÿ'EŽ˜X“commands.Ž©‘k#¸ŽŽŽ‘k$²Eacš¸ãh––ù¾mathsPIC‘–é²command“m˜ust“bšGe“on“a“separate“line.‘6´This“is“b˜ecause“¾mathsPICŽ‘0¢²frequen¸ãtly“addsŽ¡‘k$data–UUto“the“end“of“a“line“in“the“output- le“(see“bGelo¸ãw).Ž¦‘k#¸ŽŽŽ‘k$²As–>Šwith“T‘þU>Ÿ'EŽ‘ãxX,‘Cspaces“can“bGe“used“to“enhance“readabilit¸ãy‘ÿ*ª.‘j.This“is“particularly“useful“when“writingŽ¡‘k$lists–¼of“pšGoin¸ãts.‘§oF‘ÿ*ªor“example“the“command“Ødrawpoint(a1a22a34a4)“²can“b˜e“made“easier“to“readŽ¡‘k$b¸ãy–UUwriting“it“as“Ødrawpoint(a1–?ýa22“a34“a4)².Ž¦‘k#¸ŽŽŽ‘k$¾mathsPIC‘™/²commands–™^and“pGoinš¸ãt-names“are“Ùnot‘Œ6²case“sensitiv˜e.‘3 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Ïù Åf¢ ý=´}Ÿ35ŸûÌÊ‘k"ÚmathsPIC‘꨼2.1ŽŽŽ’¸Œ£²10ŽŽŽŽ‘k"Ÿ™œ‰ffÀ!ƒŽŽŽŽ ¤Kƒ ý~´}‘k#¸ŽŽŽ‘k$²Lines–žñhaš¸ãving“a“leading“bac˜kslash“command“(i.e.“where“there“is“Ùno‘@‰²in˜ter-w˜ord“space“immediatelyŽ¤ ‘k$folloš¸ãwing–‚ the“bac˜kslash,‘9e.g.“Ø\setdashes“²or“Ø\begin{document}²)“are“copied“v˜erbatim“through“toŽ¡‘k$the–r output- le.‘ÇèConsequen¸ãtly‘ÿ*ª,›y8all“T‘þU>Ÿ'EŽ–ãxX,˜LŸýó5‘üff±AŽŽ‘͉²T‘þU>Ÿ'EŽ“X–r and“P‘þÌП'IŽ‘©DC‘þæfT‘þU>Ÿ'EŽ‘ãxX“commands“can“bGe“used“in“the“normalŽ¡‘k$w•¸ãa“y›{epro“viding˜the˜command˜is˜restricted˜to˜a˜single˜line.‘ãøHo“w“ev“er,‘„éif˜suc“h˜commands˜do˜run˜onŽ¡‘k$to–·”the“subsequenš¸ãt“lines,‘Ð#these“lines“will“need“to“bGe“prev˜en˜ted“from“bšGeing“pro˜cessed“as“¾mathsPICŽ¡‘k$²commands,‘{Dbš¸ãy–DÀpre xing“them“with“¸nØ “²(see“bGelo˜w)|unless“of“course“they“also“start“with“a“bac˜kslashŽ¡‘k$command–UU(see“Sections“4.1“and“4.2).Ž©‘k#¸ŽŽŽ‘k$²Lines–,Àhaš¸ãving“a“leading‘PM¸nØ “²(i.e.“where“the“¸n“²is“follo˜w˜ed“immediately“b˜y“one“or“more“in˜ter-w˜ordŽ¡‘k$spaces–FÛØ “²e.g.‘UUØ\– 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ècommands“and/or“cošGordinate“data;‘$bfor“example,‘˜a“list“of“data“p˜oin¸ãts“as“part“of“a“P‘þÌП'IŽ‘©DC‘þæfT‘þU>Ÿ'EŽ‘ãxXŽ¡‘k$Ø\plot–UU²command)|see“example“in“Section“7.6.1ŽŸþ6‘k"Ü4.1Ž‘!+"P‘þaLŸªªIŽ‘e9C‘þƒ×T‘ý¿áŸªªEŽ‘ìSX‘€commandsŽŸuT‘k"²Note–dthat“P‘þÌП'IŽ‘©DC‘þæfT‘þU>Ÿ'EŽ‘ãxX“commands“can“Ùonly‘F…²bGe“used“within“the“Ø\beginpicture“²...‘!YØ\endpicture“²en•¸ãvironmen“t,Ž¡‘k"as–UUdescribGed“in“the“P‘þÌП'IŽ‘©DC‘þæfT‘þU>Ÿ'EŽ‘ãxX“Man•¸ãualŸü^ÿ±4ŽŽ‘ÑȲ(Wic“h“ura,‘UU1992).Ž¡‘k"Most–ÍuP‘þÌП'IŽ‘©DC‘þæfT‘þU>Ÿ'EŽ‘ãxX“commands“are“short“one-line“commands“starting“with“a“leading“bac•¸ãkslash.‘Ú'Suc“hŽ¡‘k"commands– can“bGe“used“in“the“normal“w•¸ãa“y– as“¾mathsPIC‘ŸÆ²will“automatically“cop¸ãy“lines“starting“withŽ¡‘k"a–Ÿ'EŽ‘ãxX“Ø\setdashes“²command,‘Rand“this“w¸ãould“bGe“expressed“in“theŽ¡‘k"¾mathsPIC–UU² le“as“follo¸ãws.Ž¤‘k"Ø\setdashesŽ¡‘k"²Ho•¸ãw“ev“er,‘ãsome–ñÇP‘þÌП'IŽ‘©DC‘þæfT‘þU>Ÿ'EŽ‘ãxX“commands“are“vš¸ãery“long.‘GIt“is“therefore“sometimes“necessary“to“ha˜v˜e“theŽ¤ ‘k"initial–Z—part“of“a“P‘þÌП'IŽ‘©DC‘þæfT‘þU>Ÿ'EŽ‘ãxX“command“on“one“line,‘[çwith“the“rest“of“the“command“con•¸ãtin“uing›Z—on“to˜the˜nextŽ¡‘k"line,‘Ž³sucš¸ãh–] that“the“second“and“subsequen˜t“lines“ma˜y“w˜ell“not“ha˜v˜e“a“leading“bac˜kslash“command.‘In“orderŽ¡‘k"to–:`protect“sucš¸ãh“subsequen˜t“lines“from“bšGeing“pro˜cessed“as“¾mathsPIC‘:Z²commands,‘?Åthey“m¸ãust“b˜e“protectedŽ¡‘k"bš¸ãy– |a“leading“bac˜kslash“Ùfol‘‚Ølowe›ÿ}'d–cIby“one“or“mor˜e“sp˜ac˜es‘ò²(e.g.› |Ø\ ².–ªª.“.“)‘`*as˜this˜instruction˜tells˜¾mathsPIC‘ o²toŽ¡‘k"copš¸ãy–Ì[the“rest“of“the“line“unc˜hanged“(Ùwithout‘¿3²the“leading“bac˜kslash)“through“in˜to“the“output- le.‘ÖÚF‘ÿ*ªorŽ¡‘k"example,‘è¿the–ËDP‘þÌП'IŽ‘©DC‘þæfT‘þU>Ÿ'EŽ‘ãxX“cošGde“for“plotting“data-p˜oinš¸ãts“for“a“curv˜e“could“bGe“spread“across“sev˜eral“lines“inŽ¡‘k"the–UU¾mathsPIC“² le“as“follo¸ãws.Ž©‘k"Ø\setquadraticŽ¡‘k"\plot‘ ú1.15‘ÿô-0.67Ž¡‘k"\‘î1.25‘?ñ0.02Ž¡‘k"\‘î1.35‘?ñ1.24Ž¡‘k"\‘î1.45‘?ñ3.13‘?ý/Ž¡‘k"\setlinearŽ¦‘k"²When–ÛÞthese“commands“are“prošGcessed“b¸ãy‘ÿk¾mathsPIC²,“they“will“app˜ear“in“the“output“T‘þU>Ÿ'EŽ‘ãxX“ le“(Ø.mt“² le)Ž¡‘k"as‘UUfollo¸ãws.Ž¦‘k"Ø\setquadraticŽ¡‘k"\plot‘ ú1.15‘ÿô-0.67Ž¡‘'+ 1.25‘?ñ0.02Ž¡‘'+ 1.35‘?ñ1.24Ž¡‘'+ 1.45‘?ñ3.13‘?ý/Ž¡‘k"\setlinearŽ‘k"Ÿ;¹‰ff³?çŸ J=‘ "5Ÿý-:Ë4ŽŽŽ‘LÜÊSee–ÕXSection“9.5“for“information“regarding“the“P‘þú䟸ãIŽ‘gZC‘ÿ£T‘þ•AŸ¸ãEŽ‘MX“manÃŽual.ŽŽŸŽŒ‹ ÞK Åf¢ ý=´}Ÿ35ŸûÌÊ‘k"ÚmathsPIC‘꨼2.1ŽŽŽ’¸Œ£²11ŽŽŽŽ‘k"Ÿ™œ‰ffÀ!ƒŽŽŽŽ ¤Kƒ ý~´}‘k"Ü4.2Ž‘!+"T‘ý¿áŸªªEŽ›ìSX–€and“LŸýAl‘û#×ó82Ç@Écmbx8ãAŽŽ~/ÜT‘ý¿áŸªªEŽ˜X“commandsŽ¤uT‘k"È4.2.1Ž‘%Ž¤Headers–ÕTand“foQÇotersŽ¡‘k"²It–Áis“particularly“useful“to“include“in“the“¾mathsPIC‘² le“an¸ãy“T‘þU>Ÿ'EŽ›ãxX“or“LŸýó5‘üff±AŽŽ‘͉²T‘þU>Ÿ'EŽ˜X“headers“and“foGoters“whic¸ãhŽ¤ ‘k"wš¸ãould–ÒQotherwise“ha˜v˜e“to“bGe“added“man˜ually“to“the“output- le“bGefore“LŸýó5‘üff±AŽŽ‘͉²T‘þU>Ÿ'EŽ‘ãxXing“the“ le.‘è¼F‘ÿ*ªor“example,Ž¡‘k"when–ºdusing“LŸýó5‘üff±AŽŽ‘͉²T‘þU>Ÿ'EŽ‘ãxX“a“tš¸ãypical“format“for“a“¾mathsPIC‘ºJ² le“migh˜t“bGe“as“follo˜ws“(note“that“in“this“exampleŽ¡‘k"Andreas–UUScš¸ãhrell's“st˜yle“option“Øpictexwd.sty“²is“used|see“Section“9.2).Ž©‘k"Ø\documentclass[a4paper]{article}Ž¡‘k"\usepackage{pictexwd}Ž¡‘k"\begin{document}Ž¡‘k"\beginpictureŽ¡‘k"...Ž¡‘k"...Ž¡‘k"\endpictureŽ¡‘k"\end{document}Ž¦‘k"²F‘ÿ*ªor–UUusers“of“plain“T‘þU>Ÿ'EŽ‘ãxX“a“tš¸ãypical“format“migh˜t“bGe“as“follo˜ws“(see“Section“9).Ž¦‘k"Ø\input‘?ýlatexpic.texŽ¡‘k"\input‘?ýpictexwd.texŽ¡‘k"\font\tiny=cmr5‘î%%–?ýused“for“drawing“linesŽ¡‘k"\font\large=cmr12‘ÿô%%–?ýused“for“drawing“thicklinesŽ¡‘k"\beginpictureŽ¡‘k"...Ž¡‘k"...Ž¡‘k"\endpictureŽ¡‘k"\byeŽ¦‘k"²If–͹it“is“necessary“(or“just“simply“con•¸ãv“enien“t)–͹to“extend“a“T‘þU>Ÿ'EŽ›ãxX“or“LŸýó5‘üff±AŽŽ‘͉²T‘þU>Ÿ'EŽ˜X“command“across“sev¸ãeral“lines,Ž¡‘k"then–ueacš¸ãh“additional“line“m˜ust“bGe“protected“within“the“¾mathsPIC‘E² le“using“a“leading“Ø\ ².–ªª.“.‘»sequenceŽ¡‘k"(see–CÉSection“4.1)“unless“a“line“actually“starts“with“a“T‘þU>Ÿ'EŽ‘ãxX“command.‘kîA‘CÅtš¸ãypical“example“is“the“follo˜wingŽ¡‘k"macro–R(used“in“Figure“9)“whicš¸ãh“de nes“a“`displa˜y'“maths“form˜ula.‘ƽThe“macro“is“split“across“sev˜eralŽ¡‘k"lines,–UUas“follo¸ãws.Ž¦‘k"Ø\newcommand{\formula}{%Ž¡‘k"\‘?ñ$\displaystyle–?ý\sum_{p\ge0}“\Delta_{jp}“z^{(p+1)}$%Ž¡‘k"\‘?ñ}%Ž¡‘k"text(\formula){B1}Ž¦‘k"²Note–¤œthat“when“using“T‘þU>Ÿ'EŽ›ãxX“or“LŸýó5‘üff±AŽŽ‘͉²T‘þU>Ÿ'EŽ˜X“commands“Ùwithin‘hÿ²the“P‘þÌП'IŽ‘©DC‘þæfT‘þU>Ÿ'EŽ˜X“picture“en•¸ãvironmen“t,‘¸mit–¤œis“v¸ãeryŽ¡‘k"impGortanš¸ãt–^Mto“include“the“commen˜t“Ø%“²sym˜bGol“at“the“end“of“suc˜h“lines,‘`‹to“prev˜en˜t“P‘þÌП'IŽ‘©DC‘þæfT‘þU>Ÿ'EŽ‘ãxX“accum˜ulatingŽ¡‘k"additional–{>space“c¸ãharacters“from“the“ends“of“non-P‘þÌП'IŽ›©DC‘þæfT‘þU>Ÿ'EŽ‘ãxX“commands,‘„¸since“otherwise“P‘þÌП'IŽ˜C‘þæfT‘þU>Ÿ'EŽ‘ãxX“incorpGo-Ž¡‘k"rates–Ýsucš¸ãh“space“c˜haracters“in˜to“the“horizon˜tal“distance“used“for“represen˜ting“µx²-coGordinates,‘ÿwith“theŽ¡‘k"e ect–UUthat“all“subsequenš¸ãt“picture“elemen˜ts“ma˜y“bGe“displaced“sligh˜tly“to“the“righ˜t.ŽŸþ6‘k"È4.2.2Ž‘%Ž¤Other–ÕTT‘þ<Ÿ8ãEŽ‘3sX“commandsŽŸuT‘k"²A‘e»vš¸ãery–fuseful“command“is“the“Ø\typeout{}“²command,‘ª,whic˜h“will“mak˜e“T‘þU>Ÿ'EŽ‘ãxX“prin˜t“commen˜ts“to“theŽ¡‘k"screen–kówhile“the“output- le“is“bšGeing“pro˜cessed.‘µ¡F‘ÿ*ªor“example,‘q›the“follo¸ãwing“commands“in“the“¾mathsPICŽ¡‘k"² le–UUwill“prin¸ãt“a“message“to“the“screen“just“bšGefore“pro˜cessing“a“data- le“for“a“curv¸ãe.Ž¦‘k"Ø\typeout{processing–?ýthe“data-file“now}%Ž¡‘k"inputfile*(curve.dat)ŽŽŸŽŒ‹ ï, Åf¢ ý=´}Ÿ35ŸûÌÊ‘k"ÚmathsPIC‘꨼2.1ŽŽŽ’¸Œ£²12ŽŽŽŽ‘k"Ÿ™œ‰ffÀ!ƒŽŽŽŽ ¤Kƒ ý~´}‘k"This–pcommand“is“also“useful“is“when“a“ le“is“Øinput“²sev¸ãeral“times“in“a“loGop“using“the“¾mathsPICŽ¤ ‘k"ØinputFile{..}[]–ª²command.‘^9In“suc¸ãh“cases“it“is“quite“useful“to“include“the“line“Ø\typeout{...}%“²at“theŽ¡‘k"bšGeginning–n)of“the“ le“b˜eing“input,‘t^as“this“results“in“T‘þU>Ÿ'EŽ‘ãxX“prinš¸ãting“Ø...“²to“the“screen“eac˜h“time“the“ le“isŽ¡‘k"input.Ž¡‘k"Note–kÌthe“impGortance“of“including“the“commenš¸ãt“Ø%“²sym˜bGol“at“the“end“of“the“line“when“the“Ø\typeout{}%Ž¡‘k"²command–UUis“used“within“the“P‘þÌП'IŽ‘©DC‘þæfT‘þU>Ÿ'EŽ‘ãxX“picture“en•¸ãvironmen“t.ŽŸþ6‘k"Ü4.3Ž‘!+"The–€plotting“areaŽ¤uT‘k"È4.3.1Ž‘%Ž¤AxesŽ¡‘k"²When–ôÐdraš¸ãwing“a“new“ gure“it“is“often“useful“to“ha˜v˜e“a“graduated“ruled“frame“to“guide“placemen˜t“ofŽ¤ ‘k"picture–¦Telemenš¸ãts.‘dÃThis“task“is“greatly“simpli ed“b˜y“using‘Éá¾mathsPIC²'s“one-line“Øpaper“²command,‘º“whic˜hŽ¡‘k"has–XZoptional“Øaxes“²and“Øticks“²parametersŸü^ÿ±5ŽŽ‘|s².‘zÖThe“axes-coGdes“used“in“the“Øaxes()“²option“are“ØL“²(Left),Ž¡‘k"ØR–x²(Righ¸ãt),›>ØT“²(T‘ÿ*ªop),˜ØB“²(Bottom),˜ØX“²(X-axis),˜ØY“²(Y-axis).‘ 0F‘ÿ*ªor“example,˜the“follo¸ãwing‘3Øpaper“²commandŽ¡‘k"generates–UUa“draš¸ãwing“area“5“cm“x“5“cm“with“a“ruled“frame“on“four“sides“as“sho˜wn“in“Figure“2a.Ž¤‘k"Øpaper{units(mm),xrange(0,50),yrange(0,50),axes(LRTB),ticks(10,10)}Ž¡‘k"²This–particular“Øpaper“²command“is“con•¸ãv“erted›b“y‘8¥¾mathsPIC‘ç²in“to˜the˜follo“wing˜P‘þÌП'IŽ‘©DC‘þæfT‘þU>Ÿ'EŽ‘ãxX˜coGde˜in˜theŽ© ‘k"output- le–UU(Ø.mt“² le).Ž¡‘k"Ø\setcoordinatesystem–?ýunits“<1mm,1mm>Ž¦‘k"\setplotarea–?ýx“from› ú0“to˜50“,“y“from˜0“to˜50Ž¦‘k"\axis–?ýleft“ticks“numbered“from› ú0“to˜50“by“10“/Ž¦‘k"\axis–?ýright“ticks“numbered“from› ú0“to˜50“by“10“/Ž¦‘k"\axis–?ýtop“ticks“numbered“from› ú0“to˜50“by“10“/Ž¦‘k"\axis–?ýbottom“ticks“numbered“from› ú0“to˜50“by“10“/Ž ú”Ÿ‚¸›Ÿ8’ê‘>4‰ŽCVffŽŽŽŽŽ‘9jŸž33„ffÌÈŽŽŽŽŽ‘9jŸŸã¿U„ffÌÈŽŽŽŽŽ‘9jŸŸÇKw„ffÌÈŽŽŽŽŽ‘9jŸŸª×™„ffÌÈŽŽŽŽŽ‘9jŸŸŽc»„ffÌÈŽŽŽŽŽ‘9jŸ ÿqïÝ„ffÌÈŽŽŽŽŽ‘1jžŸ8ã²0Ž‘,jŸæÅ10Ž‘,jŸÊQ'20Ž‘,jŸ­ÝI30Ž‘,jŸ‘ik40Ž‘,j ÿtõ50ŽŽŽŽŽ’ÌGŠ‰ŽCVffŽŽŽŽŽ’Ìz½ž33„ffÌÈŽŽŽŽŽ’Ìz½Ÿã¿U„ffÌÈŽŽŽŽŽ’Ìz½ŸÇKw„ffÌÈŽŽŽŽŽ’Ìz½Ÿª×™„ffÌÈŽŽŽŽŽ’Ìz½ŸŽc»„ffÌÈŽŽŽŽŽ’Ìz½ ÿqïÝ„ffÌÈŽŽŽŽŽ’ÙG†Ÿ8ã0Ž’ÔG…ŸæÅ10Ž’ÔG…ŸÊQ'20Ž’ÔG…Ÿ­ÝI30Ž’ÔG…Ÿ‘ik40Ž’ÔG… ÿtõ50ŽŽŽŽŽ‘>7g ÿqïÝ„ffŽCVŽŽŽŽŽ‘>4 ÿq¼ª‰ÌÈffŽŽŽŽŽ‘Zx ÿq¼ª‰ÌÈffŽŽŽŽŽ‘vëð ÿq¼ª‰ÌÈffŽŽŽŽŽ’“_Πÿq¼ª‰ÌÈffŽŽŽŽŽ’¯Ó¬ ÿq¼ª‰ÌÈffŽŽŽŽŽ’ÌGŠ ÿq¼ª‰ÌÈffŽŽŽŽŽ‘;·g ÿiïâ0Ž‘U«D ÿiïâ10Ž‘r" ÿiïâ20Ž’Ž“ ÿiïâ30Ž’«Þ ÿiïâ40Ž’Çz¼ ÿiïâ50ŽŽŽŽŽ‘>7gž33„ffŽCVŽŽŽŽŽ‘>4ŸÌȉÌÈffŽŽŽŽŽ‘ZxŸÌȉÌÈffŽŽŽŽŽ‘vëðŸÌȉÌÈffŽŽŽŽŽ’“_ΟÌȉÌÈffŽŽŽŽŽ’¯Ó¬ŸÌȉÌÈffŽŽŽŽŽ’ÌGŠŸÌȉÌÈffŽŽŽŽŽ‘;·gŸ>0Ž‘U«DŸ>10Ž‘r"Ÿ>20Ž’Ž“Ÿ>30Ž’«ÞŸ>40Ž’Çz¼Ÿ>50ŽŽŽŽŽŽŽŸ$jI‘K{»a.‘qÇUsing‘UUØ...axes(LRTB)ŽŽŸüy’@~BŸ8çΉŽCƒffŽŽŽŽŽ’;ä­Ÿ9„ffÌÈŽŽŽŽŽ’;ä­Ÿ§„ffÌÈŽŽŽŽŽ’;ä­Ÿã¿L„ffÌÈŽŽŽŽŽ’;ä­ŸÇKe„ffÌÈŽŽŽŽŽ’;ä­Ÿª×~„ffÌÈŽŽŽŽŽ’,ŽŸ;¶¸²2Ž’,ŽŸB ¸²1Ž’3䬟æÄü1Ž’3䬟ÊQ2Ž’3䬟­Ý.3ŽŽŽŽŽ’ɧž33„ffŽCƒŽŽŽŽŽ’–tŸÌȉÌÈffŽŽŽŽŽ’$ [ŸÌȉÌÈffŽŽŽŽŽ’\ò)ŸÌȉÌÈffŽŽŽŽŽ’yfŸÌȉÌÈffŽŽŽŽŽ’•Ù÷ŸÌȉÌÈffŽŽŽŽŽ’fŸ>¸²2Ž’ÙÿŸ>¸²1Ž’Z¥\Ÿ>1Ž’wCŸ>2Ž’“*Ÿ>3ŽŽŽŽŽŽŽŸ`ñ ’6#b.‘qÇUsing‘UUØ...axes(XY)ŽŽŽŸ{Už’Êí¨²Figure‘UU2:ŽŽŽŸÇ‘k"F‘ÿ*ªor–i—graphs“it“is“more“usual“for“the“axes“to“bGe“cenš¸ãtered“on“the“origin“(0µ;‘ª¨²0),‘n¨and“this“is“pro˜vided“forŽ¦‘k"bš¸ãy–UUthe“ØXY“²options.‘qÇF‘ÿ*ªor“example,“Figure“2b“w˜as“generated“using“the“follo˜wing“Øpaper“²command,Ž¡‘k"Øpaper{units(cm),xrange(-2,3),yrange(-2,3),axes(XY),ticks(1,1)}Ž‘k"ŸŸJ‰ff³?çŸ J=‘ "5Ÿý-:Ë5ŽŽŽ‘LÜÊSince–ÕXP‘þú䟸ãIŽ‘gZC‘ÿ£T‘þ•AŸ¸ãEŽ‘MX“uses“the“name“`axis',“ÖmathsPIC“Êrecognises“bšŸ'EŽ‘ãxX“coGde“in“the“output- le.Ž©‘k"Ø\setcoordinatesystem–?ýunits“<1cm,“1cm>Ž¤ ‘k"\setplotarea–?ýx“from“-2“to› ú3,“y“from“-2“to˜3Ž¡‘k"\axis–?ýleft“shiftedto“x=0“ticks“numbered“from“-2“to“-1“by‘ ú1Ž¡‘!ëfrom– ú1›?ýto“3˜by“1“/Ž¡‘k"\axis–?ýbottom“shiftedto“y=0“ticks“numbered“from“-2“to“-1“by‘ ú1Ž¡‘!ëfrom– ú1›?ýto“3˜by“1“/Ž¦‘k"²The–‹jtic¸ãk-marks“assošGciated“with“an“axis“can“b˜e“prev•¸ãen“ted›‹jb“y˜using˜a˜*˜after˜the˜axes-coGde˜(e.g.Ž¡‘k"Øaxis(LBT*R*)–^i²givš¸ães“four“axes“but“generates“tic˜k-marks“only“on“the“Left“and“Bottom“axes).‘Note“thatŽ¡‘k"an•¸ãy›8ãcom“bination˜of˜axes-co•Gdes˜can˜b“e˜used.‘÷F‘ÿ*ªor˜example,‘qÇthe˜options˜...Øaxes(LRTBX*Y*),‘?ýticks(10,10)Ž¡‘k"²will–UUgenerate“a“rectangular“axes“frame“(with“ticš¸ãks)“con˜taining“the“µX‘ÈâY‘Ž9²axes“(without“tic˜ks).Ž¡‘k"The–©¶line-thicš¸ãkness“of“axes“and“tic˜k-marks“is“con˜trolled“b˜y“the“P‘þÌП'IŽ‘©DC‘þæfT‘þU>Ÿ'EŽ‘ãxX‘?ýØ\linethickness“²commandŽ¡‘k"(see–UUSection“4.6.1,“and“also“Figure“14).Ž¡‘k"Once–õthe“ gure“is“ nished,‘Mthen“the“frame“or“axes“can“bGe“easily“adjusted“or“evš¸ãen“remo˜v˜ed.‘ŨTheŽ¡‘k" gure–Ušcan“also“bGe“scaled“in“size“simply“b¸ãy“altering“the“Øunits“²parameters.‘r—F‘ÿ*ªor“example,‘•¬the“optionŽ¡‘k"Øunits(3cm,1cm)– ²will“generate“an“µX‘Èâ²-axis“ha¸ãving“three“times“the“scale“as“the“µY‘8ä²-axis“(see“Figure“14).Ž¡‘k"If–ð*complicated“or“more“demanding“axis“con gurations“are“required,‘Vßthen“the“P‘þÌП'IŽ‘©DC‘þæfT‘þU>Ÿ'EŽ‘ãxX“Man¸ãual“(seeŽ¡‘k"Section–79.5)“will“need“to“bšGe“consulted.‘U½See“also“Section“8“for“details“on“p˜ositioning“ gures“within“LŸýó5‘üff±AŽŽ‘͉²T‘þU>Ÿ'EŽ‘ãxXŽ¡‘k"doGcumen¸ãts.ŽŸþ6‘k"È4.3.2Ž‘%Ž¤UnitsŽŸuT‘k"²In–•oaddition“to“the“usual“units“Ømm²,–¥vØcm²,“and›•oØpt²,“P‘þÌП'IŽ‘©DC‘þæfT‘þU>Ÿ'EŽ–ãxX˜accomoGdates˜the˜other˜six˜units˜used˜b¸ãy˜T‘þU>Ÿ'EŽ“XŸü^ÿ±6ŽŽ‘|s²,Ž¡‘k"and–03also“uses“the“same“t•¸ãw“o-letter–03coGdes,›fënamely“Øpc“²(pica),˜Øin“²(inc¸ãh),˜Øbp“²(big“pGoin¸ãt),˜Ødd“²(didot),˜ØccŽ¡‘k"²(cicero),‘øïØsp–Ø6²(scaled“pGoinš¸ãt).‘úkThe“a˜v‘ÿqÇailable“units“th˜us“en˜brace“the“Metric“system“(mm,–øïcm),“the‘Ø6DidotŽ¡‘k"system–UU(didot,“cicero),“and“the“UK“system“(pšGoin¸ãt,“big“p˜oinš¸ãt,“pica,“inc˜h).Ž¡‘k"Note–Ÿ‡that“if“only“Ùone›_â²unit“is“indicated“in“the“Øunits“²option,‘²then“¾mathsPIC‘Ÿt²uses“the“Ùsame˜²unit“forŽ¡‘k"bGoth–‡°the“µx“²and“µy‘㉲axes.‘ÙThš¸ãus“the“option“Øunits(mm)“²in“the“Øpaper“²command“is“translated“b˜y‘«=¾mathsPICŽ¡‘k"²inš¸ãto–UUthe“follo˜wing“P‘þÌП'IŽ‘©DC‘þæfT‘þU>Ÿ'EŽ‘ãxX“command“in“the“output- le.Ž¦‘k"Ø\setcoordinatesystem–?ýunits“<1mm,1mm>Ž¦‘k"²Note–Öthat“v‘ÿqÇariables“can“also“bGe“used“to“conš¸ãtrol“the“µx“²and“µy‘1è²units,‘ïƒas“sho˜wn“in“the“follo˜wing“example,Ž¡‘k"where–kÊthe“radius“(Ør²)“and“the“distance“(Øs²)“bšGet•¸ãw“een–kÊthe“lab˜el“µA“²and“its“p˜oin¸ãt-lo˜cation“are“ xed“irresp˜ectiv¸ãeŽ¡‘k"of–D_scaling“(i.e.“with“cš¸ãhanges“in“the“v‘ÿqÇalue“of“Øu²)“b˜y“dividing“the“relev‘ÿqÇan˜t“v‘ÿqÇariables“b˜y“the“scaling“v‘ÿqÇalue“Øu².Ž¦‘k"Øvariable(u){1.5}Ž¡‘k"paper{units(u–?ýmm),“xrange(0,100),“yrange(0,100)}Ž¡‘k"...Ž¡‘k"variable(r){2}Ž¡‘k"variable*(r){r,‘?ýdivide(u)}Ž¡‘k"point(A){30,20}[circle,r]Ž¡‘k"variable(s){4}Ž¡‘k"variable*(s){s,‘?ýdivide(u)Ž¡‘k"text($A$){A,‘?ýshift(-s,s)}Ž¦‘k"²If–di erenš¸ãt“scales“are“required“(most“commonly“when“dra˜wing“curv˜es“and“equations|see“Figure“14)Ž¡‘k"then–VÕbšGoth“need“to“b˜e“sp˜eci ed“in“the“¾mathsPIC“Øunits“²option.‘vGF‘ÿ*ªor“example,‘W5if“units“of“1“cm“and“2“mmŽ¡‘k"are–°required“for“the“µx“²and“µy‘ è²axes“respšGectiv¸ãely‘ÿ*ª,‘Ñthen“this“will“b˜e“implemenš¸ãted“b˜y“the“mathsPIC‘¯åcommandŽ¡‘k"Øunits(1cm,2mm)².‘FHo•¸ãw“ev“er,‘ìKwhen–Òthe“µx“²and“µy‘-á²scales“Ùar‘ÿ}'e‘’c²di eren¸ãt“strange“e ects“can“ošGccasionally“o˜ccur,Ž¡‘k"particularly–•8if“draš¸ãwing“ellipses“or“circular“arcs.‘1pIn“view“of“this“¾mathsPIC‘•'²writes“a“w˜arning“note“to“theŽ¡‘k"output- le–ºÙand“log- le“when“di erenš¸ãt“units“are“bGeing“used.‘¢SThe“dra˜wing“of“complete“circles“will“onlyŽ‘k"ŸX-‰ff³?çŸ J=‘ "5Ÿý-:Ë6ŽŽŽ‘LÜÊThese–ÕXare“describŸ'EŽ‘ãxX“sometimes“giv˜es“un-Ž¡‘k"predictable–éresults“if“decimals“are“used“with“the“Øxrange“²and“Øyrange“²options“in“conjunction“with“theŽ¡‘k"Øticks–زoption.‘ùôIn“general“P‘þÌП'IŽ‘©DC‘þæfT‘þU>Ÿ'EŽ‘ãxX“givš¸ães“more“pleasing“axes“if“in˜tegers“are“used“throughout“the“ØpaperŽ¡‘k"²command.ŽŸ‚›‘k"Ü4.4Ž‘!+"P• oin“tsŽŸuT‘k"²Eac•¸ãh›ŠTpGoin“t˜is˜asso•Gciated˜with˜a˜p“oin•¸ãt-name˜whic“h˜is˜de ned˜using˜the˜Øpoint˜²command.‘ÄF‘ÿ*ªor˜example,Ž¡‘k"the–UUfollo¸ãwing“command“allošGcates“the“p˜oin¸ãt-name“µA“²to“the“co˜ordinates“(5,7).Ž¤2D‘k"Øpoint(A){5,7}Ž¡‘k"²Once–";de ned,‘,spšGoin¸ãts“can“b˜e“referred“to“bš¸ãy“name.‘`¾Consequen˜tly‘ÿ*ª,‘,spGoin˜ts“can“bGe“de ned“in“relation“toŽ© ‘k"other–UUpGoinš¸ãts“or“lines“simply“b˜y“using“pGoin˜t-names,“as“sho˜wn“b˜y“the“follo˜wing“commands.Ž¡‘k"Øpoint(C){midpoint(AB)}Ž¦‘k"point(E){intersection(AB,CD)}Ž¦‘k"point(J){Q,–?ýrotate(P,“25“deg)}‘ ú%%“J“=“Q“rotated“about“P“by“25“degŽ¡‘k"²P•¸ãoin“ts–Sare“inš¸ãterpreted“according“to“their“grouping“and“con˜text.‘rÂTh˜us“t˜w˜o“pGoin˜ts“represen˜t“eitherŽ¦‘k"a–x8line“or“its“Pythagorean“length.‘ÚpF‘ÿ*ªor“example,‘€ñthe“command“ØdrawCircle(P,AB)‘x/²means“dra¸ãw“a“circle,Ž¦‘k"cenš¸ãter–ÿuµP‘c²with“radius“the“length“of“line“µAB‘€q².‘p(A‘ÿJgroup“of“three“pGoin˜ts“represen˜ts“either“a“triangle,‘)ýanŽ¦‘k"angle,–UUor“a“line,“depGending“on“the“circumstances.ŽŸ‚›‘k"È4.4.1Ž‘%Ž¤P•®9oin“t-nameŽŸuT‘k"²A‘7Šp•Goin¸ãt-name›7‘Ùmust‘*i²b“egin˜with˜a˜Ùsingle‘÷ì²letter,‘=…and˜ma•¸ãy˜ha“v“e˜up˜to˜a˜Ùmaximum‘ûô²of˜t“w“o˜follo“wing˜digits.Ž¦‘k"The–'Åfolloš¸ãwing“are“v‘ÿqÇalid“pGoin˜t-names:‘ZÿµA;–ª¨B‘€q;“C‘·²3µ;“d²45.‘b—Since–'žmathsPIC‘'¹²is“not“case“sensitiv˜e“the“pGoin˜ts“µd²45Ž¦‘k"and–W$µDšG²45“are“regarded“as“b˜eing“the“same“p˜oin•¸ãt.‘w3P“oin“t-names–W$can“b˜e“either“separated“b¸ãy“spaces,‘——orŽ¦‘k"simply–UUrun“together.Ž¦‘k"Sometimes–Ùëit“is“necessary“to“re-allošGcate“new“co˜ordinates“to“an“existing“p˜oinš¸ãt-name,‘ûin“whic˜h“caseŽ¦‘k"the–$ÁØpoint*“²command“is“used.‘à This“is“often“used“during“recursivš¸ãe“opGerations“whereb˜y“the“¾mathsPICŽ¦‘k"² le–W6inputs“another“ le“(using“the“Øinputfile“²command)“conš¸ãtaining“commands“whic˜h“alter“the“v‘ÿqÇalue“ofŽ¦‘k"pre-existing–tÏpGoinš¸ãts.‘Ð6F‘ÿ*ªor“example,‘|®the“follo˜wing“command“incremen˜ts“the“µx²-cošGordinate“of“p˜oinš¸ãt“µA“²b˜y“5Ž¦‘k"units.Ž¤àè‘k"Øpoint*(A){A,‘?ýshift(5,0)}ŽŸ‚›‘k"È4.4.2Ž‘%Ž¤P•®9oin“t-sym“bQÇolŽŸuT‘k"²The–+¦default“pšGoin•¸ãt-sym“b˜ol–+¦is“¸“²(Ø$\bullet$²).‘ôºHo•¸ãw“ev“er,‘a:¾mathsPIC‘+o²allo“ws–+¦the“optional“use“of“an¸ãy“T‘þU>Ÿ'EŽ‘ãxXŽ¦‘k"cš¸ãharacter–Ú:or“string“of“c˜haracters“to“represen˜t“a“particular“pGoin˜t,‘ûsb˜y“including“it“in“a“follo˜wing“squareŽ¦‘k"brac•¸ãk“et.‘qÇF‘ÿ*ªor–UUexample,“the“pšGoin¸ãt“µA²(5,10)“can“b˜e“represenš¸ãted“b˜y“the“¸4“²sym˜bGol“b˜y“de ning“it“as“follo˜ws.Ž¡‘k"Øpoint(A){5,10}[$\triangle$]Ž¡‘k"²The–½default“pšGoin•¸ãt-sym“b˜ol–½can“also“b˜e“cš¸ãhanged“to“an˜y“T‘þU>Ÿ'EŽ‘ãxX“c˜haracter“or“string“of“c˜haracters“b˜yŽ¦‘k"using–Þ£the“¾mathsPIC‘Þ>ØPointSymbol“²command,‘@öand“putting“this“command“Ùb–ÿ}'efor“e‘žþ²an•¸ãy›Þ£relev‘ÿqÇan“t˜ØpointŽ¦‘k"²commands,‘¹^since–r)the“ØPointSymbol“²command“only“in uences“subsequen¸ãt“Øpoint“²commands.‘ÈDF‘ÿ*ªor“ex-Ž¦‘k"ample,‘ê#the–eûc¸ãharacter“¸ “²(Ø$\odot$²)“can“bšGe“made“the“new“global“p˜oin•¸ãt-sym“b˜ol›eûb“y˜using˜the˜com-Ž¦‘k"mand–+œØPointSymbol($\odot$)².‘ô›The“original“default“pšGoin•¸ãt-sym“b˜ol–+œ(¸²)“can“b˜e“reinstituted“(reset)“us-Ž¦‘k"ing–q£the“command“ØPointSymbol(default)².‘Æ°The“pšGoin•¸ãt-sym“b˜ol–q£is“dra¸ãwn“at“the“p˜oin¸ãt-lo˜cation“using“theŽ¦‘k"ØdrawPoint–UU²command;“for“example,“ØdrawPoint(A)²,“or“ØdrawPoint(ABCD)².ŽŽŸŽŒ‹ø Åf¢ ý=´}Ÿ35ŸûÌÊ‘k"ÚmathsPIC‘꨼2.1ŽŽŽ’¸Œ£²15ŽŽŽŽ‘k"Ÿ™œ‰ffÀ!ƒŽŽŽŽ ¤Kƒ ý~´}‘k"Since–gmost“T‘þU>Ÿ'EŽ‘ãxX“cš¸ãharacters“and“sym˜bGols“are“t˜ypGeset“asymmetrically“in“relation“to“the“baseline,‘%ctheyŽ¤ ‘k"will–~çnot“bšGe“p˜ositioned“symmetrically“o•¸ãv“er–~ça“p˜oin¸ãt-lo˜cation.‘î|Most“c¸ãharacters“are“therefore“not“idealŽ¡‘k"for–êuse“as“pšGoin•¸ãt-sym“b˜ols,‘2as–êthey“generally“require“some“slighš¸ãt“adjustmen˜t“in“order“to“pGosition“themŽ¡‘k"symmetrically›ÿ*ª.‘bÀIn–(>view“of“this,‘1CT˜able“1“lists“those“T‘þU>Ÿ'EŽ‘ãxX“cš¸ãharacters“whic˜h“Ùar‘ÿ}'e‘虲particularly“suitable,‘1CsinceŽ¡‘k"they–a¿are“automatically“pšGositioned“b¸ãy“T‘þU>Ÿ'EŽ‘ãxX“symmetrically“with“resp˜ect“to“a“p˜oin¸ãt-lo˜cation“(for“exampleŽ¡‘k"the–UU¸ “²c¸ãharacter“Ø$\odot$²),“and“are“therefore“ideal“for“use“with“P‘þÌП'IŽ‘©DC‘þæfT‘þU>Ÿ'EŽ‘ãxX.ŽŸþ6‘k"È4.4.3Ž‘%Ž¤Line-free‘ÕTzoneŽŸuT‘k"²When–²·lines“are“draš¸ãwn“to“a“pGoin˜t,‘Ó=the“line“will“(unless“otherwise“instructed)“extend“to“the“p•Goin˜t-lo“cation.Ž¡‘k"Ho•¸ãw“ev“er,‘¦this–üúcan“bGe“prev•¸ãen“ted›üúb“y˜allo•Gcating˜an˜optional˜circular˜line-free˜zone˜to˜a˜p“oin•¸ãt˜b“y˜spGecifyingŽ¡‘k"the–q¬line-free“radius“in“a“folloš¸ãwing“square“brac˜k˜et.‘ÆËF‘ÿ*ªor“example,‘xÁlines“to“a“¸4“²sym˜bšGol“at“p˜oin¸ãt“µA“²can“b˜eŽ¡‘k"prev•¸ãen“ted–·from“bGeing“draš¸ãwn“through“the“triangle“to“its“cen˜ter“b˜y“alloGcating“a“5“unit“line-free“zone“toŽ¡‘k"the–UUpGoinš¸ãt,“as“follo˜ws.Ž¤‘k"Øpoint(A){3,10}[$\triangle$,5]Ž¡‘k"²If–öponly“the“line-free“radius“is“to“bšGe“sp˜eci ed“then“a“preceding“comma“m¸ãust“b˜e“used“(e.g.“Ø[,10]²).‘R&F‘ÿ*ªorŽ¤ ‘k"example–vthe“folloš¸ãwing‘+¾mathsPIC‘c²command“w˜ould“c˜hange“the“line-free“radius“assošGciated“with“p˜oin¸ãt“µA“²toŽ¡‘k"10‘UUunits.Ž¤‘k"Øpoint*(A){A}[,10]Ž¡‘k"²T‘ÿ*ªable–ì 1“givš¸ães“a“list“of“useful“p•Goin˜t-sym˜b“ols–ì whic˜h“T‘þU>Ÿ'EŽ‘ãxX“places“symmetrically“o˜v˜er“a“p•Goin˜t-lo“cationŽ¤ ‘k"(note–-„that“Ø$\Box$“²and“Ø$\Diamond$“²are“not“placed“symmetrically“o•¸ãv“er–-„a“pšGoin¸ãt“lo˜cation,‘5{but“Ø$\square$Ž¡‘k"²and–qØ$\lozenge$“²are).‘ÅOther“useful“symš¸ãbGols“are“a˜v‘ÿqÇailable“from“the“Øtextcomp“²fon˜tsŸü^ÿ±7ŽŽ‘|s².‘ÅF‘ÿ*ªor“example,‘xtheŽ¡‘k"folloš¸ãwing– êcommands“will“dra˜w“lines“bGet˜w˜een“pGoin˜ts“ABC,“suc˜h“that“the“lines“just“touc˜h“the“edge“of“theŽ¡‘k"¸ ‘UU²pšGoin•¸ãt-sym“b˜ol–UU(line-free“radius“1.2“mm;“10pt“fon¸ãt).Ž©‘k"Øpoint(A){1,1}[$\odot$,1.2]Ž¡‘k"point(B){2,2}[$\odot$,1.2]Ž¡‘k"point(C){1,3}[$\odot$,1.2]Ž¡‘k"drawline(ABC)Ž¦‘k"²It–Nis“often“useful“to“adjust“the“line-free“radius“assošGciated“with“a“particular“p˜oin¸ãt“b˜efore“dra¸ãwingŽ¡‘k"lines–>$or“arroš¸ãws“to“it,‘BÇin“order“to“optimise“the“distance“bGet˜w˜een“an“ob‘Ž8ject“cen˜tered“at“the“pGoin˜t“and“theŽ¡‘k"line–„Ûor“arro¸ãw.‘ZF‘ÿ*ªor“example,‘½one“can“use“the“Øpoint*“²command“to“set“a“line-free“radius“of“2“units“for“aŽ¡‘k"pre-existing–UUpGoinš¸ãt“(µP‘c²),“as“follo˜ws.Ž¦‘k"Øpoint*(P){P}[,2]Ž¦‘k"²By›­”w•¸ãa“y˜of˜illustration,‘Ï!this˜command˜is˜used˜in˜dra“wing˜Figure˜3˜where˜arro“ws˜are˜bGeing˜dra“wn˜fromŽ¡‘k"v‘ÿqÇarious–Ädirections“(µB‘€q²,‘áµS‘“²)“to“a“text“bGoš¸ãx“cen˜tered“on“pGoin˜t“µP‘' ¸ “²(the“coGde“is“sho˜wn“bGelo˜w“as“Ømpicm03a.m²).Ž¡‘k"By–w¦setting“the“line-free“radius“(dashed“circles)“assošGciated“with“p˜oin¸ãt“µP‘Û5²b˜efore“draš¸ãwing“eac˜h“particularŽ¡‘k"arroš¸ãw,–UUone“can“easily“adjust“and“optimise“the“distance“bGet˜w˜een“the“arro˜whead“and“the“text“bGo˜x.Ž¦‘k"Ø%%–?ýmpicm03a.m“(Figure“3)Ž¡‘k"\beginpictureŽ¡‘k"paper{units(cm),xrange(0,6),yrange(0,3),axes(LBT*R*),ticks(1,1)}Ž¡‘k"point(P){4,2}[$\odot$]Ž¡‘k"point(B){2,0.5}Ž¡‘k"point(S){1,2}Ž¡‘k"drawPoint(PBS)Ž¡‘k"\setdashesŽ‘k"Ÿ;¹‰ff³?çŸ J=‘ "5Ÿý-:Ë7ŽŽŽ‘LÜÊSee–•Harald“Harders'“useful“ le“(×textcomp.texÊ)“whicšÃŽh“sho˜ws“the“c˜haracters“of“the“×textcomp“Êfon˜t“together“with“theirŽŸ €names.‘Ç It–ÕXcan“b‘wxŸ„ffŽ’ ñ ²|‘)¢(Ÿ„ffŽ’ßNamssym•¸ãb.st“y‘ ©@Ÿ„ffŽŽŸff‰ff$ãxŽŽŽŽŸ‘k"Ø\inboundscheckon‘)ÿè%%–?ýrestrict“circles“to“drawing“areaŽ¤ ‘k"drawcircle(P,1)Ž¡‘k"drawcircle(P,2)Ž¡‘k"\setsolidŽ¡‘k"point*(P){P}[,1]‘)ÿè%%–?ýset“line-free“radius“of“P“to“1“cmŽ¡‘k"drawArrow(BP)‘9¿ß%%–?ýdraw“arrow“from“B“(below)Ž¡‘k"point*(P){P}[,2]‘)ÿè%%–?ýchange“line-free“radius“of“P“to“2“cmŽ¡‘k"drawArrow(SP)‘9¿ß%%–?ýdraw“arrow“from“S“(side)Ž¡‘k"text($S$){S,‘?ýshift(-0.4,0)}Ž¡‘k"text($B$){B,‘?ýshift(-0.4,0)}Ž¡‘k"text(\textsc{p}){P,‘?ýshift(0.3,0)}Ž¡‘k"\newcommand{\textbox}{\fbox{text\hspace{17mm}box}}%Ž¡‘k"text(\textbox){P}Ž¡‘k"\endpictureŽŸ‘k"²Of–“Vcourse,‘º#sometimes“it“is“con•¸ãv“enien“t–“Vjust“to“draš¸ãw“the“arro˜ws“a“certain“length“from“one“pGoin˜t“to˜w˜ardsŽ¡‘k"another–ïŸpGoin¸ãt.‘OàF‘ÿ*ªor“example,›÷in“Figure“3,˜the“t•¸ãw“o–ïŸØpoint*“²commands“and“the“t•¸ãw“o–ïŸØdrawArrow“²commandsŽŽŸŽŒ‹@Ä Åf¢ ý=´}Ÿ35ŸûÌÊ‘k"ÚmathsPIC‘꨼2.1ŽŽŽ’¸Œ£²17ŽŽŽŽ‘k"Ÿ™œ‰ffÀ!ƒŽŽŽŽ ¤Kƒ ýùNÀŸÓúV’’`‰U[µffŽŽŽŽŽ’yËž33„ffÌÈŽŽŽŽŽ’yËŸã¿L„ffÌÈŽŽŽŽŽ’yËŸÇKe„ffÌÈŽŽŽŽŽ’yËŸª×~„ffÌÈŽŽŽŽŽ’…yÊŸ8ã0Ž’…yÊŸæÄü1Ž’…yÊŸÊQ2Ž’…yÊŸ­Ý.3ŽŽŽŽŽ’<ÊʉU[µffŽŽŽŽŽ’’F“Ÿª×~„ffª·jŽŽŽŽŽ’’F“ž33„ffª·jŽŽŽŽŽ’’`ŸÌȉÌÈffŽŽŽŽŽ’®‡GŸÌȉÌÈffŽŽŽŽŽ’Êû.ŸÌȉÌÈffŽŽŽŽŽ’çoŸÌȉÌÈffŽŽŽŽŽ’âüŸÌȉÌÈffŽŽŽŽŽ’ 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nes“the“pšGoin¸ãt“µD‘œr²as“b˜eing“23“units“Ùfr›ÿ}'om–“çµA“Ùin“the“dir˜e˜ction“of“µB‘€q².Ž¦‘k"È4.4.5Ž‘%Ž¤Num®9bšQÇer–ÕTof“p˜oin®9tsŽŸuT‘k"²The–1maximš¸ãum“com˜bined“n˜um˜bšGer“of“named“p˜oinš¸ãts“and“v‘ÿqÇariables“whic˜h“can“bGe“used“is“curren˜tly“set“b˜yŽ¡‘k"default–¿áat“50.‘±lThe“total“arraš¸ãy“space“for“pGoin˜ts“and“v‘ÿqÇariables“can“bGe“increased“b˜y“using“the“¾mathsPICŽ¡‘k"ØPointNumber()–V°²command.‘æF‘ÿ*ªor“example,‘‰žarraš¸ãy“space“for“a“total“of“75“pGoin˜ts/v‘ÿqÇariables“w˜ould“bšGe“allo˜catedŽ¡‘k"b¸ãy–UUthe“command“ØPointNumber(75)².Ž¡‘k"If–Öthe“comš¸ãbined“pGoin˜t/v‘ÿqÇariable“alloGcation“is“exceeded,‘/uthen“a“so-called“`fatal“error'“arises“and“theŽ¡‘k"program–‹ìterminates.‘.¥The“folloš¸ãwing“example“(from“an“output- le)“doGcumen˜ts“a“fatal“error“whic˜h“oGccuredŽ¡‘k"while–UUthe“program“wš¸ãas“trying“to“de ne“a“new“pGoin˜t“µZŸÿ±3Ž‘|s².ŽŸ‘k"Ø%%–?ý***“point(Z3){P,shift(2,5)}Ž¡‘k"%%–?ý...“FATAL“ERROR:“points“used“exceed“allocationŽ¡‘k"%%–?ý...“use“the“PointNumber()“command“to“increase“allocationŽŸþ6‘k"Ü4.5Ž‘!+"Scalar‘€v‘ÿ@ariablesŽŸuT‘k"²Numeric–æËscalar“v‘ÿqÇariables“are“de ned“using“the“Øvariable(Ùname–À[Ø){Ùvalue“Ø}–æ˲command.‘&*The“Ùvalue‘§&²in“theŽ¡‘k"braces–™µcan“bGe“either“a“n¸ãumeric“(e.g.“4.32;‘»ä2.6E-2),›ªÌa“v‘ÿqÇariable“name“(e.g.“r3),˜or“t•¸ãw“o›™µpGoin“ts˜(e.g.˜AB|Ž¡‘k"meaning–8ãthe“Pythagorean“distance“bšGet•¸ãw“een–8ãthe“t•¸ãw“o‘8ãp˜oin“ts›8ãµA;‘ª¨B‘€q²).‘÷Th“us˜the˜command˜Øvariable(r3){20}Ž¡‘k"²allošGcates–¤20“to“the“v‘ÿqÇariable“Ør3²,‘÷Ëwhic¸ãh“could“then“b˜e“used,›÷Ëfor“example,˜as“the“radius“in“the“circleŽ¡‘k"command–’Ødrawcircle(C3,r3)².‘Ð~New“v‘ÿqÇalues“can“bšGe“re-allo˜cated“to“existing“v‘ÿqÇariable-names“using“theŽ¡‘k"Øvariable*‘UU²command.Ž¡‘k"Ho•¸ãw“ev“er,‘+one›ßšm“ust˜bGe˜careful˜not˜to˜mistak“e˜v‘ÿqÇariables˜for˜pGoin“ts,‘+and˜vice˜v“ersa,‘+since˜they˜bGothŽ¡‘k"ha•¸ãv“e–Ñæthe“same“name“structure.‘çzWhen“bšGoth“are“necessary‘ÿ*ª,‘ñ using“upp˜er“case“for“p˜oinš¸ãts“and“lo˜w˜er“caseŽ¡‘k"for–½æv‘ÿqÇariables“is“a“con•¸ãv“enien“t–½æstrategy‘ÿ*ª.‘«zIf“yš¸ãou“inadv˜erten˜tly“use“a“pGoin˜t“instead“of“a“v‘ÿqÇariable“¾mathsPICŽ¡‘k"²will–UUgenerate“an“appropriate“error“message“(see“the“last“example“in“Section“5.1).Ž¦‘k"È4.5.1Ž‘%Ž¤ArithmeticŽŸuT‘k"²V‘ÿ*ªariables–àcan“bGe“manipulated“using“the“commands“Øadvance²,–÷†Ømultiply²,“Ødivide–à²and“Ømod².‘J±The“format“isŽ¡‘k"similar–°Œto“that“of“the“Øpoint“²commands.‘ƒkThš¸ãus“the“command“Øvariable(a1){a,advance(-r3)}“²mak˜esŽ¡‘k"the–†Ìv›ÿqÇariable“Øa1“²assume“the“v˜alue“Øa-r3“²(i.e.“µaŸÿ±1Ž‘•ü²=‘‰µa–YÚ¸“µrŸÿ±3Ž‘|s²).‘,Note–†Ìthat“although“¾mathsPIC‘†¿²allo¸ãws“the“useŽŽŸŽŒ‹Sò Åf¢ ý=´}Ÿ35ŸûÌÊ‘k"ÚmathsPIC‘꨼2.1ŽŽŽ’¸Œ£²18ŽŽŽŽ‘k"Ÿ™œ‰ffÀ!ƒŽŽŽŽ ¤Kƒ ý~´}‘k"of–ý6the“negativš¸ãe“sign“with“v‘ÿqÇariables“(e.g.“Ø-5.34²,–ÖØ-r3²),“the–ý6pGositiv˜e“sign“is“Ùnot‘ð²allo˜w˜ed.‘ThExamples“of“v‘ÿqÇalidŽ¤ ‘k"Øvariable–UU²commands“are“giv¸ãen“in“Section“6.ŽŸþ6‘k"È4.5.2Ž‘%Ž¤Scien®9ti c‘ÕTnotationŽŸuT‘k"²When›Ó‡n•¸ãum“bGers˜are˜either˜v“ery˜small˜or˜v“ery˜big˜they˜are˜generally˜written˜using˜the˜usual˜computer˜`E'Ž¡‘k"format–Õof“so-called“`scien¸ãti c“notation',›!¼for“example,˜1.243E{9“etc.‘\G¾mathsPIC‘Ųalloš¸ãws“the“use“of“scien˜ti cŽ¡‘k"notation–UUin“commands“wherevš¸ãer“decimals“are“normally“allo˜w˜ed,“as“follo˜ws.Ž©‘k"Øvariable(p2){3.78E3}Ž¡‘k"point(Z3){J,shift(1.3E-1,6)}Ž¦‘k"²Unfortunately‘ÿ*ª,‘æÆT‘þU>Ÿ'EŽ‘ãxX–Ë"došGes“not“pro˜cess“nš¸ãumeric“v‘ÿqÇalues“in“scien˜ti c“notation,‘æÆand“will“generate“an“errorŽ¡‘k"message–™Úwhenevš¸ãer“it“ nds“the“letter“ØE‘™ª²as“part“of“a“n˜um˜bGer.‘3IConsequen˜tly‘½g¾mathsPIC‘™ª²con˜v˜erts“all“n˜um˜bGersŽ¡‘k"whicš¸ãh–±zappGear“within“P‘þÌП'IŽ‘©DC‘þæfT‘þU>Ÿ'EŽ‘ãxX“commands“in“the“output- le“in˜to“con˜v˜en˜tional“decimal“format“(place-v‘ÿqÇalueŽ¡‘k"notation).‘SGIf–ùÔthe“v›ÿqÇalue“is“less“than“1.0E{7“(0.0000001)“then“¾mathsPIC‘ù½²simply“con•¸ãv“erts–ùÔthe“v˜alue“to“zero.Ž¡‘k"Ho•¸ãw“ev“er,›R¤since–ûthis“con•¸ãv“ertion–ûrequires“additional“c•¸ãhec“king,˜¾mathsPIC‘DzdošGes–ûnot“b˜other“to“do“thisŽ¡‘k"when–Ê)it“outputs“data“to“the“end“of“a“commenš¸ãted“line.‘ÐBF‘ÿ*ªor“example,‘ç]in“the“follo˜wing“extract“from“anŽ¡‘k"output- le–¾1the“v‘ÿqÇariables“µsŸÿ±4Ž›:¤²and“µsŸÿ±5Ž˜²appGear“in“scienš¸ãti c“notation“when“in“commen˜ted“lines,‘Ükbut“in“decimalŽ¡‘k"notation–.ˆin“the“P‘þÌП'IŽ‘©DC‘þæfT‘þU>Ÿ'EŽ‘ãxX“Ø\put...“²commands“(see“the“line“for“pGoin¸ãt“µJŸÿ±45Ž‘xæ²).‘dØNote“also“that“in“this“exampleŽ¡‘k"the–0]µy[Ù²-cošGordinate“of“µJŸÿ±45Ž‘ ©C²app˜ears“as“zero“in“the“Ø\put...“²command“(since“Øs5“²is“less“than“0.0000001),‘7ÂbutŽ¡‘k"as–UUØ2.3E-8“²in“the“Ø%%variable(s5){...“²line.Ž¦‘k"Ø%%–?ývariable(r){23}‘ ú(“23“)Ž¡‘k"%%–?ývariable(s1){r,divide(100000)}‘ ú(“.00023“)Ž¡‘k"%%–?ývariable(s2){r,divide(1000000)}‘ ú(“.000023“)Ž¡‘k"%%–?ývariable(s3){r,divide(10000000)}‘ ú(“.0000023“)Ž¡‘k"%%–?ývariable(s4){r,divide(100000000)}‘ ú(“2.3E-7“)Ž¡‘k"%%–?ývariable(s5){r,divide(1000000000)}‘ ú(“2.3E-8“)Ž¡‘k"%%‘?ýpoint(J12){s1,s2}Ž¡‘k"%%‘?ýpoint(J23){s2,s3}Ž¡‘k"%%‘?ýpoint(J34){s3,s4}Ž¡‘k"%%‘?ýpoint(J45){s4,s5}Ž¡‘k"%%–?ýdrawpoint(J12“J23“J34“J45)Ž¡‘k"\put–?ý{$\bullet$}“at‘ ú.00023–¿÷.000023“%%‘?ýJ12Ž¡‘k"\put–?ý{$\bullet$}“at‘ ú.000023–¿÷.0000023“%%‘?ýJ23Ž¡‘k"\put–?ý{$\bullet$}“at‘ ú.0000023–¿÷.00000023“%%‘?ýJ34Ž¡‘k"\put–?ý{$\bullet$}“at‘ ú.00000023–¿÷0“%%‘?ýJ45ŽŸþ6‘k"Ü4.6Ž‘!+"LinesŽŸuT‘k"¾mathsPIC‘b~²dra¸ãws–blines“using“its“ØdrawLine“²and“ØdrawThickline“²commands.‘™LF‘ÿ*ªor“example,‘eÌa“line“from“µPŸÿ±1ŽŽŽ¡‘k"²to‘ÒµPŸÿ±2ŽŽ‘Œ-²is–Òdraš¸ãwn“with“the“command“ØdrawLine(P1P2)².‘FIf“a“line“is“to“bGe“dra˜wn“through“sev˜eral“pGoin˜ts“(sa˜y‘ÿ*ª,Ž¡‘k"µJŸÿ±1Ž–|sµ;›ª¨JŸÿ±2Ž“µ;˜JŸÿ±3Ž“µ;˜JŸÿ±4Ž“µ;˜JŸÿ±5Ž“²)–1[and“can“bšGe“dra¸ãwn“without“`lifting“the“p˜en',‘8then“this“can“b˜e“ac•¸ãhiev“ed–1[using“the“singleŽ¡‘k"¾mathsPIC‘éÔ²command–éûØdrawLine(J1J2J3J4J5)².‘/¸Sevš¸ãeral“unconnected“lines“can“also“bGe“dra˜wn“using“oneŽ¡‘k"command–ã±bš¸ãy“separating“eac˜h“line“segmen˜t“with“a“comma;‘ ’for“example,‘úkØdrawLine(J1J2,J3J4J5,J1J3)².Ž¡‘k"A‘*êline–*ôcan“also“bšGe“dra¸ãwn“a“sp˜eci ed“distance“from“one“p˜oinš¸ãt“to˜w˜ards“(or“a˜w˜a˜y“from)“another“pGoin˜t,Ž¡‘k"using–™äthe“square-brac•¸ãk“et–™äoption.‘?tF‘ÿ*ªor“example,‘«the“folloš¸ãwing“command“dra˜ws“a“line“a“distance“µd“²unitsŽ¡‘k"from–UUpšGoin¸ãt“µA“Ùtowar‘ÿ}'ds‘'v²p˜oin¸ãt“µB‘€q².Ž¦‘k"Ødrawline(AB)[d]Ž¦‘k"²Note–}Úthat“in“this“particular“command“the“order“of“the“pGoin¸ãts“µAB‘þK²and“the“sign“of“the“distance“Ø[d]Ž¡‘k"²are–¢úimpGortanš¸ãt.‘ZµF‘ÿ*ªor“example,‘¶cthe“follo˜wing“command“will“dra˜w“a“line“a“distance“µd“²units“from“pGoin˜t“µBŽ¡‘k"Ùaway‘“çfr‘ÿ}'om‘¸²pGoin¸ãt‘UUµA².ŽŽŸŽŒ‹‰F Åf¢ ý=´}Ÿ35ŸûÌÊ‘k"ÚmathsPIC‘꨼2.1ŽŽŽ’¸Œ£²19ŽŽŽŽ‘k"Ÿ™œ‰ffÀ!ƒŽŽŽŽ ¤Kƒ ý~´}‘k"Ødrawline(BA)[-d]ŽŸHú‘k"²Since–³the“P‘þÌП'IŽ‘©DC‘þæfT‘þU>Ÿ'EŽ‘ãxX“Ø\putrule“²command“for“draš¸ãwing“horizon˜tal“or“v˜ertical“lines“is“m˜uc˜h“more“mem-Ž¤ ‘k"ory–epecienš¸ãt“than“the“Ø\plot“²command,‘©w¾mathsPIC‘e*²automatically“in˜v˜ok˜es“the“Ø\putrule“²command“forŽ¡‘k"horizonš¸ãtal–UUand“v˜ertical“lines“(see“also“ØPictex2.sty“²in“Section“9.3).Ž¡‘k"Ho•¸ãw“ev“er,‘>çthere–9Kare“some“oGccasions“when“it“is“necessary“to“draš¸ãw“using“the“Ø\plot“²command“ev˜en“forŽ¡‘k"horizonš¸ãtal–r…and“v˜ertical“lines“(eg.“when“using“Ø\setdots“²with“larger“than“usual“dots),‘yÒin“whic˜h“case“theŽ¡‘k"Ødrawline*–UU²command“(disables“the“use“of“Ø\putrule²)“should“bGe“used.Ž©.W‘k"È4.6.1Ž‘%Ž¤Line‘ÕTthic®9knessŽŸuT‘k"²P‘þÌП'IŽ‘©DC‘þæfT‘þU>Ÿ'EŽ‘ãxX–¥×draš¸ãws“lines“using“t˜w˜o“di eren˜t“methošGds“dep˜ending“on“whether“the“lines“are“(a)“horizon¸ãtalŽ¡‘k"or–þŒvš¸ãertical,‘(Ú(b)“an˜y“other“orien˜tation.‘mmThese“t˜w˜o“groups“use“di eren˜t“commands“for“con˜trolling“line-Ž¡‘k"thicš¸ãkness,–UUas“follo˜ws.Ž¦‘k"ÈHorizonš®9tal–ÕTand“v˜ertical“lines“(rules)ŽŸuT‘k"²Horizonš¸ãtal–ÕVand“v˜ertical“lines“are“dra˜wn“using“the“P‘þÌП'IŽ‘©DC‘þæfT‘þU>Ÿ'EŽ‘ãxX“Ø\putrule“²commandŸü^ÿ±8ŽŽ‘Qɲand“consequen˜tly“theŽ¡‘k"thicš¸ãkness–x of“suc˜h“lines“is“con˜trolled“b˜y“the“P‘þÌП'IŽ‘©DC‘þæfT‘þU>Ÿ'EŽ‘ãxX“Ø\linethickness“²command“(the“default“line-thic˜knessŽ¡‘k"is–UU0.4pt).‘qÇF‘ÿ*ªor“example,“the“folloš¸ãwing“P‘þÌП'IŽ‘©DC‘þæfT‘þU>Ÿ'EŽ‘ãxX“command“c˜hanges“the“thic˜kness“to“1pt.Ž¤Hú‘k"Ø\linethickness=1ptŽ¡‘k"²The–D²Ø\linethickness“²command“is“also“useful“for“adjusting“the“thicš¸ãkness“of“graph“axes,‘Htic˜k“marks.Ž© ‘k"F‘ÿ*ªor–UUexample,“the“folloš¸ãwing“commands“are“used“in“the“coGde“for“Figure“14“to“dra˜w“thic˜k“axes.Ž¡‘k"Ø\linethickness=2ptŽ¦‘k"paper{units(mm),xrange(0,50),yrange(0,50),axes(XY)}Ž¦‘k"\linethickness=0.4pt‘ÿô%%–?ýreset“to“defaultŽ¡‘k"²Note–M also“that“the“P‘þÌП'IŽ‘©DC‘þæfT‘þU>Ÿ'EŽ‘ãxX“Ø\linethickness“²command“can“also“bGe“reset“to“its“default“v‘ÿqÇalue“(0µ:²4pt)Ž¦‘k"bš¸ãy–‹ƒthe“P‘þÌП'IŽ‘©DC‘þæfT‘þU>Ÿ'EŽ‘ãxX“Ø\normalgraphs“²command,‘™whic˜h“resets“all“P‘þÌП'IŽ‘©DC‘þæfT‘þU>Ÿ'EŽ‘ãxX“graph-dra˜wing“parameters“to“theirŽ¦‘k"default–UUv‘ÿqÇalues“including“Ø\linethickness“²(see“Section“6.3).ŽŸ.W‘k"ÈOther–ÕTlines“and“curv®9esŽŸuT‘k"²All–²™other“lines“(non-horizonš¸ãtal“non-v˜ertical)“and“curv˜es“are“dra˜wn“using“the“P‘þÌП'IŽ‘©DC‘þæfT‘þU>Ÿ'EŽ‘ãxX“Ø\plot“²commandŽ¦‘k"whic•¸ãh›Ϊdra“ws˜a˜con“tin“uous˜line˜of˜dots.‘DäConsequen“tly˜the˜thic“kness˜of˜these˜lines˜is˜con“trolled˜b“y˜the˜sizeŽ¦‘k"of–7ñthe“dot,›=Òwhic¸ãh“is“de ned“using“the“P‘þÌП'IŽ‘©DC‘þæfT‘þU>Ÿ'EŽ‘ãxX“Ø\setplotsymbol“²command,˜the“default“size“of“dot“bGeingŽ¦‘k"Ø{\tiny‘?ý.}².›yLarger–W¿dots“therefore“generate“thic•¸ãk“er–W¿lines.˜F‘ÿ*ªor“example,‘XYthe“follo¸ãwing“P‘þÌП'IŽ‘©DC‘þæfT‘þU>Ÿ'EŽ‘ãxX“commandŽ¦‘k"sets–UUthe“dot“to“a“larger“size.Ž¡‘k"Ø\setplotsymbol({\Large‘?ý.})Ž¡‘k"²The–ȾmathsPIC‘’ØdrawLine“²command“uses“the“currenš¸ãt“dot“size.‘+CHo˜w˜ev˜er,‘¬the“¾mathsPIC‘’ØdrawThicklineŽ¦‘k"²command–2Öuses“the“Ø\large“²dot“size,›9¼but“then“resets“the“dot“size“to“Ø\tiny².‘fGF‘ÿ*ªor“example,˜the“commandsŽ¡‘k"Øpoint(A){5,5}Ž¦‘k"point(B){10,10}Ž¦‘k"drawThickline(AB)Ž¡‘k"²will–UUresult“in“the“follo¸ãwing“coGde“in“the“output- le.Ž¡‘k"Ø%%‘?ýpoint(A){5,5}‘?ñ(5,5)Ž¦‘k"%%–?ýpoint(B){10,10}‘¿÷(10,“10)Ž¦‘k"%%‘?ýdrawThickline(AB)Ž¦‘k"\setplotsymbol({\large‘?ý.})Ž¦‘k"\plot›?ý5– ú5‘¿÷10“10˜/˜%%˜ABŽ¦‘k"\setplotsymbol({\tiny‘?ý.})Ž‘k"Ÿ¼{‰ff³?çŸ J=‘ "5Ÿý-:Ë8ŽŽŽ‘LÜÊNote–ºXthat“the“P‘þú䟸ãIŽ‘gZC‘ÿ£T‘þ•AŸ¸ãEŽ›MX“ó#¾KÈ cmsy8În×putrule“Êcommand“emploÃŽys“the“T‘þ•AŸ¸ãEŽ˜X“and“LŸþ¢#‘üð¡ËAŽŽ‘ ïÊT‘þ•AŸ¸ãEŽ˜X“În×rule“Êcommand,‘ó˜and“so“is“only“used“forŽŸ €horizonšÃŽtal–ÕXand“v˜ertical“lines.ŽŽŸŽŒ‹š  Åf¢ ý=´}Ÿ35ŸûÌÊ‘k"ÚmathsPIC‘꨼2.1ŽŽŽ’¸Œ£²20ŽŽŽŽ‘k"Ÿ™œ‰ffÀ!ƒŽŽŽŽ ¤Kƒ ý~´}‘k"ÈRecommendationsŽŸuT‘k"²Since–HdP‘þÌП'IŽ‘©DC‘þæfT‘þU>Ÿ'EŽ‘ãxX“uses“t•¸ãw“o–Hdgroups“of“commands“for“conš¸ãtrolling“the“thic˜kness“of“lines“(i.e.“Ø\linethicknessŽ¤ ‘k"²and–ËØ\setplotsymbol²)“it“is“impGortanš¸ãt“to“use“pairs“of“equiv‘ÿqÇalen˜t“commands“for“`rules'“(horizon˜tal“andŽ¡‘k"vš¸ãertical–šXlines)“and“dots“(all“other“lines)“when“c˜hanging“line-thic˜kness.‘@ÑThese“are“sho˜wn“in“T‘ÿ*ªable“2“forŽ¡‘k"a–UU10-pGoinš¸ãt“fon˜t“(note“that“the“default“sizes“are“0.4-pGoin˜t“and“Ø\tiny²).Ž „$¥Ÿ™Ì‘b…ÑT‘ÿ*ªable–UU2:‘qÇEquiv‘ÿqÇalenš¸ãt“P‘þÌП'IŽ‘©DC‘þæfT‘þU>Ÿ'EŽ‘ãxX“commands“for“a“10-pGoin˜t“fon˜tŽŽ¡Ÿ+Ÿ‘K™ŸÖLljff.¸–¡Ìͤ™œ„™œff›ÌÍŸüfdrules‘UU(horizon•¸ãtal/v“ertical)˜¡„™œffŽ‘|pj¤™œ„™œff›;¸Ÿüfdall–UUother“lines˜¡„™œffŽŽ©‰ff.¸–¡Ìͤ™œ„™œff‘ÌΟüfdØ\linethickness=1.35pt‘0¨¡„™œffŽ’‚£ž\setplotsymbol({\Large‘?ý.})‘#bŸ™œ„™œffŽŽ¤™œÌͤ™œ„™œff‘ÌΟüfd\linethickness=1.1pt‘ p¥¡„™œffŽ’‚£ž\setplotsymbol({\large‘?ý.})‘#bŸ™œ„™œffŽŽ¡Ìͤ™œ„™œff‘ÌΟüfd\linethickness=0.9pt‘ p¥¡„™œffŽ’‚£ž\setplotsymbol({\normalsize‘?ý.})‘ ""Ÿ™œ„™œffŽŽ¡Ìͤ™œ„™œff‘ÌΟüfd\linethickness=0.4pt‘ p¥¡„™œffŽ’‚£ž\setplotsymbol({\tiny‘?ý.})‘(¢Ÿ™œ„™œffŽŽ¦‰ff.¸–ŽŽŽŽŸÿ ‘k"²The–iøauthor's“expšGerience“is“that“although“¾mathsPIC‘i°²do˜es“ha•¸ãv“e–iøcommands“for“draš¸ãwing“thic˜k“linesŽ¡‘k"and–å§thicš¸ãk“arro˜ws,‘ »it“is“generally“bGetter“to“con˜trol“the“line-thic˜kness“separately“using“the“t˜w˜o“P‘þÌП'IŽ‘©DC‘þæfT‘þU>Ÿ'EŽ‘ãxXŽ¡‘k"commands–ïœshoš¸ãwn“in“T‘ÿ*ªable“2,‘ôand“to“mak˜e“separate“macros“where“necessary–ÿ*ª.‘OßF“or–ïœexample,‘ôthe“follo˜wingŽ¡‘k"coGde–UUdraš¸ãws“a“medium-thic˜k“line“µAB‘ÕƲb˜y“in˜v˜oking“the“command“Ø\mediumthickline².ŽŸ?‘k"Ø\newcommand{\mediumthickline}{\linethickness=1.1pt\setplotsymbol({\large‘?ý.})}%Ž¡‘k"...Ž¡‘k"\mediumthickline%Ž¡‘k"drawline(AB)ŽŸX¹‘k"Ü4.7Ž‘!+"T‘þàextŽŸuT‘k"²T‘ÿ*ªext–ïis“tš¸ãypGeset“using“the“Øtext“²command“and,‘ˆb˜y“default,‘ˆis“cen˜tered“bGoth“horizon˜tally“and“v˜ertically“atŽ¡‘k"a–³Šde ned“pGoinš¸ãt.‘;ÙF‘ÿ*ªor“example,‘Óæthe“triangle“sym˜bGol“¸4“²w˜ould“bšGe“placed“at“the“p˜oin¸ãt“µZ‘j¦²using“the“commandŽ¡‘k"Øtext($\triangle$){Z}².Ž¡‘k"T‘ÿ*ªext–úcan“bšGe“lo˜cated“relativ¸ãe“to“a“p˜oin¸ãt-lo˜cation“using“the“Øshift(µdxØ,µdy[ÙØ)“²or“Øpolar(µr˜Ø,µ˜Ø)“²commands.Ž¡‘k"F‘ÿ*ªor–UUexample,“pGoinš¸ãts“µPŸÿ±1ŽŽ‘=VµPŸÿ±2ŽŽ‘%WµPŸÿ±3ŽŽ‘'b­²could“ha˜v˜e“their“labšGels“lo˜cated“4“units“from“eac¸ãh“p˜oinš¸ãt“as“follo˜ws.Ž©?‘k"Øvariable(d){4}Ž¡‘k"text($P_1$){P1,shift(-d,0)}Ž¡‘k"text($P_2$){P2,polar(d,10‘?ýdeg)}Ž¡‘k"text($P_3$){P3,polar(d,0.29088‘?ýrad)}Ž¦‘k"²Optionally‘ÿ*ª,‘ÚŸtext–¿÷can“bšGe“p˜ositioned“relativš¸ãe“to“a“giv˜en“pGoin˜t“using“appropriate“com˜binations“of“theŽ¡‘k"Ùc‘ÿ}'ase‘õÄsensitive‘i̲P‘þÌП'IŽ‘©DC‘þæfT‘þU>Ÿ'EŽ‘ãxX›©qoptions‘énØl–?ýt“r“B“b˜²to˜align˜the˜Èl²eft˜edge,–ËÒÈr²igh¸ãt˜edge,“Èt²op˜edge,“ÈB²aseline,“Èb²ottomŽ¡‘k"edge–]Fof“the“text“respšGectiv¸ãely‘ÿ*ª,‘_Bas“describ˜ed“in“the“P‘þÌП'IŽ‘©DC‘þæfT‘þU>Ÿ'EŽ‘ãxX“man¸ãual“(see“Section“9.5).‘‰šF‘ÿ*ªor“example“in“theŽŸ Ø‘k"diagram–ÉbšGelo¸ãw,‘åthe“text“b˜oš¸ãx“Ÿö㎉ff;L®Ÿ r„ rffŸý‘Øa–?ýnice“boxŽŽ‘:â„ rffŽžff‰ff;L®ŽŽŽ‘@ÞÒ²is“aligned“suc˜h“that“the“righ˜t“edge“of“the“text“bGo˜x“is“cen˜teredŽ¡‘k"vš¸ãertically–UUat“the“pGoin˜t“µP‘¸ä²using“the“Ø[r]“²option“as“follo˜ws.Ž¦‘k"Øpoint(P){25,5}Ž¡‘k"text(\fbox{a–?ýnice“box}){P}[r]ŽŸ'ˆ:ÁŸàŒ"‰ff´‚EŸ'DŒ„'DŒffŸø/R‘›öŸëM-‰ff3…µŸ ñÇ„ ñÇffŸý‘²a–UUnice“bGo¸ãxŽŽ‘2¸é„ ñÇffŽžff‰ff3…µŽŽŽŽ‘G¡«Ÿóþô¸Ž‘r<ŽŸÞç²this–UUis“pGoin¸ãt“PŽ‘káÜŸþºã°.Ž‘kVŸþ—Â.Ž‘k Пþt¡.Ž‘jÀJŸþQ€.Ž‘j_ÄŸþ._.Ž‘iÿ>Ÿþ >.Ž‘iž¸Ÿýè.Ž‘i>2ŸýÄü.Ž‘hݬŸý¡Û.Ž‘h}&Ÿý~º.Ž‘h Ÿý[™.Ž‘g¼Ÿý8x.Ž‘g[”ŸýW.Ž‘fûŸüò6.Ž‘fšˆŸüÏ.Ž‘f:Ÿü«ô.Ž‘eÙ|ŸüˆÓ.Ž‘exöŸüe².Ž‘epŸüB‘.Ž‘d·êŸüp.Ž‘dWdŸûüO.Ž‘cöÞŸûÙ..Ž‘c–XŸû¶ .Ž‘c5ÒŸû’ì.Ž‘bÕLŸûoË.Ž‘btÆŸûLª.Ž‘b@Ÿû)‰.Ž‘a³ºŸûh.Ž‘aS4ŸúãG.Ž‘`ò®ŸúÀ&.Ž‘`’(Ÿú.Ž‘`1¢Ÿúyä.Ž‘_ÑŸúVÃ.Ž‘_p–Ÿú3¢.Ž‘_Ÿú.Ž‘^¯ŠŸùí`.Ž‘^OŸùÊ?.Ž‘]î~Ÿù§.Ž‘]øŸùƒý.Ž‘]-rŸù`Ü.Ž‘\ÌìŸù=».Ž‘\lfŸùš.Ž‘\ àŸø÷y.Ž‘[«ZŸøÔX.Ž‘[JÔŸø±7.Ž‘ZêNŸøŽ.Ž‘Z‰ÈŸøjõ.Ž‘Z)BŸøGÔ.Ž‘YȼŸø$³.Ž‘Yh6Ÿø’.Ž‘Y°Ÿ÷Þq.Ž‘X§*Ÿ÷»P.Ž‘XF¤Ÿ÷˜/.Ž‘WæŸ÷u.Ž‘W…˜Ÿ÷Qí.Ž‘W%Ÿ÷.Ì.Ž‘VÄŒŸ÷ «.Ž‘VdŸöèŠ.Ž‘V€ŸöÅi.Ž‘U¢úŸö¢H.Ž‘UBtŸö'.Ž‘TáîŸö\.Ž‘ThŸö8å.Ž‘T âŸöÄ.Ž‘SÀ\Ÿõò£.Ž‘S_ÖŸõÏ‚.Ž‘RÿPŸõ¬a.Ž‘RžÊŸõ‰@.Ž‘R>DŸõf.Ž‘QݾŸõBþ.Ž‘Q}8ŸõÝ.Ž‘Q²Ÿôü¼.Ž‘P¼,ŸôÙ›.Ž‘P[¦Ÿô¶z.Ž‘Oû Ÿô“Y.Ž‘OššŸôp8.Ž‘O:ŸôM.Ž‘NÙŽŸô)ö.Ž‘NyŸôÕ.Ž‘NxÍŸô‰.Ž‘NÞPŸô‡.Ž‘OCüŸô%ã.Ž‘O©ÉŸô1«.Ž‘PµŸô:ì.Ž‘Pu¬ŸôAµ.Ž‘PÛ¶ŸôF.Ž‘QAÈŸôH.Ž‘Q§éŸôGÐ.Ž‘RŸôEH.Ž‘RtŸô@.Ž‘RÚ&Ÿô9².Ž‘S@Ÿô0¿.Ž‘S¦Ÿô%Å.Ž‘T ÑŸôÐ.Ž‘Tq‰Ÿô í.Ž‘NxÍŸô‰.Ž‘NÑ}Ÿô:Ä.Ž‘O(šŸôq.Ž‘O~)Ÿô©ˆ.Ž‘OÒ0Ÿôãô.Ž‘P$©Ÿõ L.Ž‘Pu£Ÿõ^‰.Ž‘PÅ Ÿõž™.Ž‘Q-Ÿõàv.Ž‘Q_Ÿö$.Ž‘QªíŸöiC.Ž‘Qô®Ÿö°.Ž‘R=Ÿöø….Ž‘R„Ÿ÷Bn.Ž‘RɸŸ÷Ê.Ž‘SŸ÷Ú“.ŽŽŽŽŽŽ’³µy„'DŒffŽžff‰ff´‚EŽŽŽŽŸö#‘k"²T‘ÿ*ªext–`can“also“bšGe“placed“at“a“p˜oin¸ãt-lo˜cation“(using“a“ØDrawPoint“²command),‘I"if“the“text“is“de nedŽ¡‘k"as–fùthe“optional“pšGoin•¸ãt-sym“b˜ol–fù(in“square“brac•¸ãk“ets)–fùasso˜ciated“with“a“Øpoint“²command.‘¦³Although“this“isŽ¡‘k"useful–áïin“certain“circumstances,›this“methoGd“is“somewhat“less“ exible“than“the“Øtext“²command,˜sinceŽ¡‘k"the–UUØdrawPoint“²command“cenš¸ãters“the“p•Goin˜t-sym˜b“ol–UUv˜ertically“and“horizon˜tally“o˜v˜er“the“p•Goin˜t-lo“cation.ŽŽŸŽŒ‹ª  Åf¢ ý=´}Ÿ35ŸûÌÊ‘k"ÚmathsPIC‘꨼2.1ŽŽŽ’¸Œ£²21ŽŽŽŽ‘k"Ÿ™œ‰ffÀ!ƒŽŽŽŽ ¤Kƒ ý~´}‘k"Ç5Ž‘·íError-messagesŽŸç‘k"²A‘|certain–|Lamounš¸ãt“of“syn˜tax“c˜hec˜king“is“pGerformed“b˜y‘ŸÙ¾mathsPIC².“Error-messages“appGear“in“the“output- leŽ¤ ‘k"(Ø.mt–UU² le)“and“also“in“the“log- le“(Ø.mlg“² le).ŽŸó·‘k"Ü5.1Ž‘!+"Output- leŽŸuT‘k"²A‘$Nline–$ƒconš¸ãtaining“an“error“is“pre xed“b˜y‘HØ***²;‘Œthe“assošGciated“error-message“app˜ears“on“the“next“lineŽ¡‘k"and–E×is“pre xed“bš¸ãy“dots“(Ø...²).‘lIf“the“Ø/b“²switc˜h“is“used“then“a“bšGeep“is“sounded“if“an“error“o˜ccurs“duringŽ¡‘k"proGcessing.Ž¡‘k"Runš¸ãtime–ƒYerrors“most“commonly“arise“when“an“argumen˜t“has“bGeen“omitted,‘ŽÚor“division“b˜y“zero“hasŽ¡‘k"bGeen–"þattempted.‘`ÿSyn¸ãtax“errors“are“where“the“¾mathsPIC‘"ñ²commands“are“written“incorrectly“(e.g.“missingŽ¡‘k"brac•¸ãk“et).‘ÃiA‘ÅÃt“ypical–Åàexample“migh¸ãt“bšGe“in“a“Ødraw“²command“if“a“p˜oin¸ãt“has“not“b˜een“previously“de nedŽ¡‘k"resulting–UUin“a“`pGoinš¸ãt-name'“error“as“follo˜ws.Ž©Ã‘k"Ø%%–?ý***“drawTriangle(T1T6T3)Ž¡‘k"%%–?ý...“?syntax“error:‘ úpoint“T6“is“not“definedŽ¦‘k"²If–Ómthe“maximš¸ãum“pGoin˜t/v‘ÿqÇariable“alloGcation“(default“is“50)“is“exceeded,‘òóthen“a“so-called“`fatal“error'Ž¡‘k"arises–®and“the“program“terminates.‘ÑIn“the“follo¸ãwing“example,‘›Äa“fatal“error“oGccured“while“the“programŽ¡‘k"wš¸ãas–UUtrying“to“de ne“a“new“pGoin˜t“µZŸÿ±3Ž‘|s².Ž¦‘k"Ø%%–?ý***“point(Z3){P,shift(2,5)}Ž¡‘k"%%–?ý...“FATAL“ERROR:“points“used“exceed“allocationŽ¡‘k"%%–?ý...“use“the“PointNumber()“command“to“increase“allocationŽ¦‘k"²Some–UUother“examples“of“error-messages“are“as“follo¸ãws.Ž¦‘k"Ø%%–?ý***“point(a2{5,6}Ž¡‘k"%%–?ý...“syntax“error:‘ úextra“or“missing“()Ž¡‘k"%%Ž¡‘k"%%–?ý***“point(B2){A,shift(,6)}Ž¡‘k"%%–?ý...“syntax“error:‘ úmissing“X“coordinate“in“shift()Ž¡‘k"%%Ž¡‘k"%%–?ý***“point(z2){}Ž¡‘k"%%–?ý...“runtime“error:‘ ú?syntax“errorŽ¡‘k"%%Ž¡‘k"%%–?ý***“pointt(z4){2,3}Ž¡‘k"%%–?ý...“?syntax“error:“statement“not“recognisedŽ¡‘k"%%Ž¡‘k"%%–?ý***“drawLine(AB)Ž¡‘k"%%–?ý...“?syntax“error:“points“A“and“B“are“the“sameŽ¡‘k"%%Ž¡‘k"%%–?ý***“variable(d){j,“advance(4)}Ž¡‘k"%%–?ý...“?syntax“error:“j“is“a“Point“not“a“VariableŽ¡Ÿó·‘k"Ü5.2Ž‘!+"Log- leŽŸuT‘k"¾mathsPIC‘ä²outputs–ä²).‘$aThe“format“w˜as“designed“to“matc˜h“that“of“a“standard“T‘þU>Ÿ'EŽ‘ãxX“log- le“in“orderŽ¡‘k"to–UUbGe“compatible“with“commonly“used“error-c•¸ãhec“king›UUutilities.‘qÇP“art˜of˜a˜t“ypical˜log- le˜is˜as˜follo“ws.Ž¦‘k"ØmathsPIC–?ýlog-file‘ÿô=“myfile.mlgŽ¡‘k"mathsPIC–?ýinput-file‘ ú=“myfile.mŽ¡‘k"mathsPIC–?ýoutput-file“=“myfile.mtŽŽŸŽŒ‹Àq Åf¢ ý=´}Ÿ35ŸûÌÊ‘k"ÚmathsPIC‘꨼2.1ŽŽŽ’¸Œ£²22ŽŽŽŽ‘k"Ÿ™œ‰ffÀ!ƒŽŽŽŽ ¤Kƒ ý~´}¤ ‘k"Ø!–?ýsyntax“error:“extra“or“missing“()“bracketŽ¡‘k"l.9‘ úpoint(A{10,5}Ž¡‘k"Ž¡¡‘k"!–?ý?syntax“error:‘ úpoint“A“is“not“definedŽ¡‘k"l.13‘ údrawpoint(ABC)Ž¡‘k"Ž¡¡‘k"!–?ýsyntax“error:“point“A“is“not“definedŽ¡‘k"l.22‘ úpoint(P){A,shift(5,0)}Ž¡‘k"Ž¡¡‘k"!–?ýstart“of“inputfile“Ž¡¡‘k"!–?ýsyntax“error:“point“X“is“not“definedŽ¡‘k"l.7‘ úpoint(Q){X,shift(5,0)}Ž¡‘k"Ž¡‘k"...Ž¡‘k"...ŽŸ ³‘k"Ç6Ž‘·íCommandsŽŸç‘k"Ü6.1Ž‘!+"ó:ñkAH cmssbx10åMathsPIC‘€ÜcommandsŽŸuT‘k"²Although–ƒæ¾mathsPIC‘ƒ±²commands“are“Ùnot‘v¾²case“sensitivš¸ãe,‘­Éit“is“recommended“(to“a˜v˜oid“confusion)“that“pGoin˜tsŽ¡‘k"are–UUrepresenš¸ãted“using“uppGer“case“letters,“and“v‘ÿqÇariables“are“represen˜ted“using“lo˜w˜er“case“letters.Ž¡‘k"The–:ùparameters“of‘¾mathsPIC‘:ò²commands“are“either“strings“(an¸ãy“legitimate“T‘þU>Ÿ'EŽ›ãxX“or“LŸýó5‘üff±AŽŽ‘͉²T‘þU>Ÿ'EŽ˜X“commandsŽ¡‘k"or–S¿cš¸ãharacters“whic˜h“are“suitable“for“an“Ø\hbox“²are“allo˜w˜ed),‘TpGoin˜t-names“(e.g.“A,B,C),“or“scalar“quan˜ti-Ž¡‘k"ties.‘Where–Zrappropriate,‘[¹¾MathsPIC‘Zq²alloš¸ãws“scalar“quan˜tities“in“commands“to“bGe“represen˜ted“b˜y“either“aŽ¡‘k"n¸ãumeric–;Êv‘ÿqÇalue“(e.g.“0.432,›@æor“4.32E-1“),˜a“v‘ÿqÇariable“name“(e.g.“r2),˜or“the“Pythagorean“distance“bGet•¸ãw“eenŽ¡‘k"t•¸ãw“o›pGoin“ts˜(e.g.˜µAB‘€q²).‘Z[F‘ÿ*ªor˜example,‘the˜structure˜of˜a˜ØDrawCircle(ó;ßêŸ'EŽ‘ãxXŽ¡‘k"are–UUdescribGed“in“Section“4.6.1.Ž¦‘k#¸ŽŽŽ‘k$Ÿõ€‰ff⟄ffŸú€‘nØ...ŽŽ‘M„ffŽžff‰ff⎎Ž‘O1ÚŸõ€‰ff$"Ÿ„ffŸú€‘¸nØ ...ŽŽ‘#UJ„ffŽžff‰ff$"ŽŽŽŽŸøm‘k$²A‘Äline–Ôhaš¸ãving“a“Ùle‘ÿ}'ading‘öQ²bac˜kslash“is“proGcessed“(copied“v˜erbatim)“sligh˜tly“di eren˜tly“depGending“onŽ¡‘k$whether–UUthe“cš¸ãharacter“follo˜wing“the“bac˜kslash“is“a“space“or“not.Ž©’‘k$A‘Ò;leading–Òžbac¸ãkslash“Ùfol‘‚Ølowe›ÿ}'d–ò¯by“a“non-sp˜ac˜e“char˜acter‘æ+²tells–Òž¾mathsPIC‘Ò;²to“cop¸ãy“the“whole“lineŽ¡‘k$vš¸ãerbatim–3G(Ùincluding‘IJthe“bac˜kslash)“through“to“the“output- le“(th˜us“a“line“leading“with“the“LŸýó5‘üff±AŽŽ‘͉²T‘þU>Ÿ'EŽ‘ãxXŽ¡‘k$command–UUØ\begin{document}“²will“bGe“copied“unc¸ãhanged).Ž¦‘k$Ho•¸ãw“ev“er,‘/$a–%—leading“bac¸ãkslash“Ùfol‘‚Ølowe›ÿ}'d–gûby“one“or“mor˜e“sp˜ac˜es²,‘/$(e.g.–%—¸nØ ...²)‘aÝtells“¾mathsPIC‘%‹²to“cop¸ãyŽ¡‘k$the–UUrest“of“the“line“vš¸ãerbatim“through“to“the“output- le,“but“Ùwithout‘H-²the“leading“bac˜kslash.ŽŸn‘k#¸ŽŽŽ‘k$Ÿö9‰fflIŸ*«„*«ffŸúÇ‘ØArrowshape(æL,–?ýB,“C‘¼rØ)ŽŽ‘k|9„*«ffŽžff‰fflIŽŽŽŽŸ#‘k$²This–j¢command“de nes“the“shapGe“of“an“arroš¸ãwhead,‘¯õand“allo˜ws“di eren˜t“arro˜wheads“to“bGe“cus-Ž¡‘k$tomised–™£(see“Section“7.3“for“details).‘>±The“default“arroš¸ãw“shapGe“is“equiv‘ÿqÇalen˜t“to“the“commandŽŽŸŽŒ‹ËÑ Åf¢ ý=´}Ÿ35ŸûÌÊ‘k"ÚmathsPIC‘꨼2.1ŽŽŽ’¸Œ£²23ŽŽŽŽ‘k"Ÿ™œ‰ffÀ!ƒŽŽŽŽ ¤Kƒ ý~´}‘k$ØArrowshape(2,30,40)².‘B$This–ðdefault“arro¸ãwhead“shapšGe“can“b˜e“reset“using“Ødefault“²as“the“argu-Ž¤ ‘k$menš¸ãt,–UUas“sho˜wn“in“the“follo˜wing“example.ŽŸÅö‘k$ØArrowshape(4,30,60)Ž¡‘k$drawArrow(AB)Ž¡‘k$ArrowShape(default)ŽŸå@‘k#¸ŽŽŽ‘k$Ÿõ€‰ffL8Ÿ„ffŸú€‘ØDrawAngleArc¸fØangle(),–?ýradius(),“internal,“clockwise¸gŽŽ’l„ffŽžff‰ffL8ŽŽŽŽŸ£Ö‘k$²This–ŸXcommand“dra¸ãws“an“arc“in“the“spGeci ed“angle,‘±Ùa“distance“Ùr‘ÿ}'adius‘qy²from“the“angle.‘OÐThe“angleŽ¡‘k$is–ˆ”either“Ùinternal›‘²(¸‘Ç*²180Ÿü^ÿó O!â…cmsy7·Ž‘˜ä²)“or“Ùexternal˜²(¸‘Ç*²180Ÿü^ÿ·Ž‘˜ä²).‘ …The“direction“of“the“arc“is“either“Ùclo‘ÿ}'ckwiseŽ¡‘k$²or–híÙanticlo‘ÿ}'ckwise²,‘­Òand“this“direction“m¸ãust“correspšGond“with“the“letter“sequence“sp˜eci ed“for“theŽ¡‘k$angle.‘¥[Strange–f†and“unexpšGected“results“will“b˜e“pro˜duced“if“the“four“parameters“are“not“in¸ãternallyŽ¡‘k$consisten¸ãt.ŽŸË©‘k$F‘ÿ*ªor–nexample,‘t2the“folloš¸ãwing“command“dra˜ws“a“cloGc˜kwise“arc,›t2radius“3“units,˜in“the“external“angleŽ¡‘k$µAB›€qC‘·²,–UUfrom“line“µAB‘ÕƲto“line“µB˜C‘·².ŽŸÅö‘k$ØDrawAngleArc{angle(ABC),–?ýradius(3),“external,“clockwise}ŽŸå@‘k#¸ŽŽŽ‘k$Ÿõ€‰ff!Ì2Ÿ„ffŸú€‘ØDrawAngleArrow¸fØangle(),–?ýradius(),“internal,“clockwise¸gŽŽ’ ÿf„ffŽžff‰ff!Ì2ŽŽŽŽŸ£Ö‘k$²This–íucommand“draš¸ãws“an“arro˜w“in“the“spGeci ed“angle,‘Ÿ'EŽ‘ãxX“draš¸ãws“circles“with“the“Ø\circulararc“²command,‘î£using“a“radius“equiv‘ÿqÇalen˜t“toŽ¤ ‘k$the–;distance“from“the“cenš¸ãter“to“the“pGoin˜t“at“whic˜h“it“starts“dra˜wing“the“arc.‘#Consequen˜tly‘ÿ*ª,‘tŒifŽ¡‘k$the–ÎUunits“of“the“µx“²and“µy‘*.²axes“are“di erenš¸ãt,‘ì•circles“ma˜y“bGe“dra˜wn“strangely‘ÿ*ª.‘ÜȾMathsPIC‘Î6²thereforeŽ¡‘k$generates–Baa“message“to“this“e ect“in“the“output- le“if“di erenš¸ãt“units“are“selected“for“the“t˜w˜o“axesŽ¡‘k$in–UUthe“Øunits“²command“(see“Section“4.3.2).ŽŸs‘k#¸ŽŽŽ‘k$Ÿö9‰ff|¿œŸ Ç„ ÇffŸü*­‘ØDrawCircumcircle(µAB‘€qC‘·Ø)ŽŽ‘{òЄ ÇffŽžff‰ff|¿œŽŽŽŽ¤Íy‘k$²This–UUcommand“draš¸ãws“the“circumcircle“of“the“triangle“de ned“b˜y“the“pGoin˜ts“A,“B,“C.ŽŸäæ‘k#¸ŽŽŽ‘k$Ÿö9‰ffR Ÿ Ç„ ÇffŸü*­‘ØDrawCurve(æABC‘¼rØ)ŽŽ‘QŸ'EŽ‘ãxX˜Ø\plot˜²command,‘êÃand˜so˜it˜is˜only˜recommended˜for˜threeŽ¡‘k$pšGoin¸ãts–+€(for“more“than“three“p˜oinš¸ãts“the“resulting“curv˜e“is“unlik˜ely“to“bšGe“`smo˜oth').‘cÕThis“commandŽ¡‘k$will–UUbGe“upgraded“in“the“next“vš¸ãersion“to“giv˜e“a“smoGoth“curv˜e“for“more“than“three“pGoin˜ts.Ž©Íy‘k$Note–þ\that“curvš¸ães“dra˜wn“using“this“command“do“Ùnot‘ñ4²break“to“a˜v˜oid“line-free“zones“assoGciated“withŽ¡‘k$the–UUpGoinš¸ãts“(the“ØdrawLine“²command“for“straigh˜t“lines“Ùdo‘ÿ}'es‘'v²ac˜kno˜wledge“line-free“zones).ŽŸs‘k#¸ŽŽŽ‘k$Ÿö9‰ff•ò”ŸUT„UTffŸûœs‘ØDrawExcircle(µAB–€qC‘·Ø,‘?ýµAB“Ø)[µ`ãrGØ]ŽŽ’•%È„UTffŽžff‰ff•ò”ŽŽŽŽ¦‘k$²This–›command“draš¸ãws“the“excircle“touc˜hing“side“µAB‘ ²of“the“triangle“µAB‘€qC‘·².‘Z4The“optional“argumen˜tŽ¡‘k$[µ`ãrG²]–•–is“a“ ne“adjustmenš¸ãt“to“the“radius“of“the“excircle“circle“to“facilitate“dra˜wing“the“ gure“in“certainŽ¡‘k$circumstances.Ž¦‘k$In–}the“folloš¸ãwing“t˜w˜o“examples,‘ÂBthe“ rst“dra˜ws“the“true“excircle,‘ÂBwhile“the“second“dra˜ws“the“excircleŽ¡‘k$with–UUits“radius“reduced“b¸ãy“0.2“units.Ž©ÐÖ‘k$ØdrawExcircle(T1T2T3,‘?ýT1T2)Ž¡‘k$drawExcircle(T1T2T3,‘?ýT1T2)[-0.2]Ž¦‘k#¸ŽŽŽ‘k$Ÿö9‰ff{Ü`Ÿ Ç„ ÇffŸü*­‘ØDrawIncircle(µAB‘€qC‘·Ø)[µ`ãrGØ]ŽŽ‘{”„ ÇffŽžff‰ff{Ü`ŽŽŽŽ©Íy‘k$²This–¢’command“draš¸ãws“the“incircle“of“a“triangle.‘Y}The“optional“argumen˜t“[µ`ãrG²]“is“a“ ne“adjustmen˜tŽ¡‘k$to–UUthe“radius“of“the“incircle“circle“to“facilitate“dra¸ãwing“the“ gure.Ž¦‘k$In–Ëthe“folloš¸ãwing“t˜w˜o“examples,‘æ¹the“ rst“dra˜ws“the“true“incircle,‘æ¹while“the“second“dra˜ws“the“incircleŽ¡‘k$with–UUits“radius“reduced“b¸ãy“0.2“units.Ž©ÐÖ‘k$ØdrawIncircle(T1T2T3)Ž¡‘k$drawIncircle(T1T2T3)[-0.2]Ž¦‘k#¸ŽŽŽ‘k$Ÿö9‰ffaÉ Ÿ Ç„ ÇffŸü*­‘Ødrawline(æABCD...‘¼rØ)ŽŽ‘`ü?„ ÇffŽžff‰ffaÉ ŽŽŽ’’ÌŸö9‰ffWIŸ Ç„ ÇffŸü*­‘drawline(æAB‘¼rØ)[6]ŽŽ‘V|E„ ÇffŽžff‰ffWIŽŽŽ’þFzŸö9‰ff†ˆöŸUT„UTffŸûœs‘drawline(æAB,CD,EFG,‘?ý...‘¼rØ)ŽŽ’…¼*„UTffŽžff‰ff†ˆöŽŽŽŽŸk$Ÿö9‰ffg Ÿ Ç„ ÇffŸü*­‘drawline*(æABCD...‘¼rØ)ŽŽ‘f<<„ ÇffŽžff‰ffg ŽŽŽŽ©Íy‘k$²This–ÀEcommand“draš¸ãws“a“line“joining“t˜w˜o“or“more“pGoin˜ts.‘²—Lines“are“dra˜wn“in“the“order“spGeci ed.Ž¡‘k$Lines–UUare“not“draš¸ãwn“within“line-free“zones“of“pGoin˜ts.Ž¦‘k$P•¸ãarameters›UUwhic“h˜con“trol˜line-thic“kness˜are˜describGed˜in˜Section˜4.6.1.ŽŽŸŽŒ‹é/ Åf¢ ý=´}Ÿ35ŸûÌÊ‘k"ÚmathsPIC‘꨼2.1ŽŽŽ’¸Œ£²25ŽŽŽŽ‘k"Ÿ™œ‰ffÀ!ƒŽŽŽŽ ¤Kƒ ý~´}‘k$Ødrawline(AB)Ž¤ ‘k$drawline(BCDE)Ž¡‘k$drawline(FG,–?ýHJK,“PQRST)Ž©‘k$²A‘¥fline–¥¼can“also“bšGe“dra¸ãwn“a“sp˜eci ed“distance“from“one“p˜oinš¸ãt“to˜w˜ards“another“pGoin˜t,‘ùÖusing“aŽ¡‘k$square-brac•¸ãk“et–I option.‘m¯F‘ÿ*ªor“example,‘Kthe“folloš¸ãwing“command“dra˜ws“a“line“a“distance“µd“²units“fromŽ¡‘k$pGoinš¸ãt–UUµA“²to˜w˜ards“pGoin˜t“µB‘€q².Ž¦‘k$Ødrawline(AB)[d]Ž¦‘k$²Note–ÿÛthat“some“restrictions“are“assošGciated“with“the“square“brac•¸ãk“et–ÿÛoption:‘G (a)“it“can“only“b˜e“usedŽ¡‘k$when–c¿dra¸ãwing“a“Ùsingle‘$²line;‘jô(b)“a“line-free“zone“assošGciated“with“the“second“p˜oin¸ãt“will“b˜e“ignored,Ž¡‘k$(c)–ÄÜthe“order“of“the“pšGoin¸ãts“µAB‘EM²is“imp˜ortanš¸ãt|the“line“is“dra˜wn“from“the“ rst“pGoin˜t“Ùtowar‘ÿ}'ds‘–ý²theŽ¡‘k$second–UUpGoin¸ãt“(see“Figure“11).ŽŸ‘k$Note–ƒ‘that“the“Ødrawline“²command“uses“the“P‘þÌП'IŽ‘©DC‘þæfT‘þU>Ÿ'EŽ‘ãxX“Ø\putrule“²command“for“horizonš¸ãtal“and“v˜erticalŽ¡‘k$lines,›SQand–RÐthe“Ø\plot“²command“for“all“other“lines.‘pðHo•¸ãw“ev“er,˜the–RÐuse“of“the“Ø\putrule“²command“isŽ¡‘k$disabled–ùƒwhen“using“the“¾mathsPIC‘ùlØdrawline*“²command,‘ àwhic¸ãh“uses“only“the“Ø\plot“²command“forŽ¡‘k$all–c“lines.‘!2Since“the“Ø\plot“²command“should“bGe“used“when“using“larger“than“normal“dots“(Ø\setdots²)Ž¡‘k$for–UUhorizonš¸ãtal“or“v˜ertical“lines,“then“this“is“ac˜hiev˜ed“with“the“Ødrawline*“²command.ŽŸIô‘k#¸ŽŽŽ‘k$Ÿö9‰ffÀHÕŸ*«„*«ffŸúÇ‘ØDrawPerpendicular(æpoint,line‘¼rØ)[foot]ŽŽ’¿| „*«ffŽžff‰ffÀHÕŽŽŽŽŸJ‘k$²This–Üìcommand“dra¸ãws“the“p•Gerp“endicular–Üìfrom“Ùp‘ÿ}'oint‘ÏIJto“the“Ùline².‘ŒIf“the“option“[fošGot]“is“sp˜eci ed,Ž¡‘k$then–¬kthis“command“also“draš¸ãws“the“curren˜t“Øpointsymbol()“²c˜haracter“(default“p•Goin˜t-sym˜b“ol‘¬kisŽ¡‘k$Ø$\bullet$²)–ü¤at“the“pšGoin¸ãt“where“the“p˜erp˜endicular“joins“the“line.‘T7The“folloš¸ãwing“example“dra˜ws“theŽ¡‘k$p•Gerp“endicular–UUfrom“the“pGoin¸ãt“µP‘¸ä²to“the“line“µAB‘€q².Ž¦‘k$ØdrawPerpendicular(P,AB)ŽŸ‘‘k#¸ŽŽŽ‘k$Ÿö9‰ffWIŸ*«„*«ffŸúÇ‘Ødrawpoint(æname‘¼rØ)ŽŽ‘V|E„*«ffŽžff‰ffWIŽŽŽ’‡˜ÒŸö9‰ff›ˆêŸ*«„*«ffŸúÇ‘drawpoint(æname1–?ýname2“...‘ H„*«ffŽžff‰ff— ŽŽŽ’ÇZÕŸö9‰ffq¾TŸ*«„*«ffŸúÇ‘inputFile*(µpictex:docØ)ŽŽ‘pñˆ„*«ffŽžff‰ffq¾TŽŽŽŽ¦‘k$²The–*„ØinputFile“²command“inputs“a“plain“text“ le“con¸ãtaining‘N¾mathsPIC‘*M²commands.‘ñUOptionally‘ÿ*ª,Ž¡‘k$the–ìw le“can“bGe“input“[Ùlo‘ÿ}'op‘¡˜²]“times,‘@in“whicš¸ãh“case“this“command“functions“lik˜e“a“DO{LOOP›ÿ*ª.“F˜orŽ¡‘k$example,–UUthe“follo¸ãwing“command“inputs“the“ le“Ønewfile.dat“²4“times“in“succession.Ž¤·{‘k$ØinputFile(newfile.dat)[4]Ž¡‘k$²The–·sØinputfile*“²command“is“used“to“input“a“ le“in“Ùverb‘ÿ}'atim²,‘Ïûi.e.“a“ le“with“Ùno‘Y ¾mathsPIC‘·Z²com-Ž¤ ‘k$mands.‘˜íF‘ÿ*ªor–bbexample,‘e¥a“ le“conš¸ãtaining“only“P‘þÌП'IŽ‘©DC‘þæfT‘þU>Ÿ'EŽ‘ãxX“commands“or“data-pGoin˜ts“for“plotting“etc.‘˜íAŽ¡‘k$tš¸ãypical–íÆexample“migh˜t“bGe“the“follo˜wing“ le“(curv˜e-A.dat)“whic˜h“w˜ould“bGe“input“v˜erbatim“usingŽ¡‘k$the–UUcommand“Øinputfile*(curve-A.dat)².Ž©·{‘k$Ø%%‘?ýcurve-A.datŽ¡‘k$\setquadraticŽ¡‘k$\plot‘?ý0‘?ñ0Ž¡‘:ë3.56‘ ú4.87Ž¡‘:ë8.45‘ ú9.45Ž¡‘:ë5‘?ñ7Ž¡‘:ë2.34‘ ú3.23‘?ý/Ž¡‘k$\setlinearŽ¦‘k$²Note–UUthat“the“Øinputfile*“²command“has“no“[µl2`oop²]“option.ŽŸN:‘k#¸ŽŽŽ‘k$Ÿõ€‰ffL8Ÿ„ffŸú€‘Øpaper¸fØunits(–?ý),xrange(“),yrange(“),axes(“),ticks(“)¸gŽŽ’l„ffŽžff‰ffL8ŽŽŽŽŸÀ‘k$Øunits(ÙunitØ)–ªª²or“Øunits(Ùxunit,yunitØ)Ž¤óê‘k$xrange(Ùxlow,xhighØ)Ž¡‘k$yrange(Ùylow,yhighØ)Ž¡‘k$axes(ÙXYLR‘ÿ;¼TBØ)Ž¡‘k$ticks(Ùx,yØ)Ž¡‘k$²The–€ÝØpaper{..}“²command“de nes“a“plot“area“with“optional“axes“and“tic¸ãk-marks“(see“Section“4.3.1).Ž¡‘k$F‘ÿ*ªor–Ñ example,‘ëthe“folloš¸ãwing“statemen˜t“sets“up“a“rectangular“dra˜wing“area“50mm“x“50mm“with“axesŽŸ ‘k$on–UUthe“ØL²eft“(y-axis)“and“ØB²ottom“(x-axis),“and“ticš¸ãk“marks“at“10mm“in˜terv‘ÿqÇals.Ž¦‘k$Øpaper{units(mm),xrange(0,50),yrange(0,50),axes(LB),ticks(10,10)}ŽŽŸŽŒ‹Ô Åf¢ ý=´}Ÿ35ŸûÌÊ‘k"ÚmathsPIC‘꨼2.1ŽŽŽ’¸Œ£²27ŽŽŽŽ‘k"Ÿ™œ‰ffÀ!ƒŽŽŽŽ ¤Kƒ ý~´}‘k$All–Öncomš¸ãbinations“of“the“axis-coGdes“(XYLR‘ÿ*ªTB)‘ÖMare“allo˜w˜ed,‘öµand“a“*“follo˜wing“an“axis-coGde“(e.g.Ž¤ ‘k$L*)–UUstops“ticš¸ãks“bGeing“dra˜wn“on“the“spGeci ed“axis.ŽŸ‘k$If–µˆit“is“necessary“to“ha•¸ãv“e–µˆÙdi er‘ÿ}'ent‘¨`²unit“scales“for“the“µx“²and“µy‘a²axes,‘Õ~saš¸ãy“1“cm“and“2“mm“respGectiv˜ely‘ÿ*ª,Ž¡‘k$then–ŒŸ'EŽ‘ãxX“will“use“the“last“de ned“units“(within“the“same“picture“en•¸ãvironmen“t),Ž¡‘k$the–ŒBdefault“units“bGeing“Ùxunit›òز=1pt“and“Ùyunit˜²=1pt“(see“the“P‘þÌП'IŽ‘©DC‘þæfT‘þU>Ÿ'EŽ‘ãxX“Manš¸ãual,‘Ùýpage“3;‘'¹Wic˜h˜ura,Ž¡‘k$1992).ŽŸff‘k#¸ŽŽŽ‘k$Ÿõ€‰ffá=Ÿ„ffŸú€‘Øpoint(æname›¼rØ)¸fØ...¸gØ[æsymbol,–?ýlinefree“radius˜Ø]ŽŽ’à8q„ffŽžff‰ffá=ŽŽŽŽŸÌÌ‘k$Ÿõ€‰ffæE:Ÿ„ffŸú€‘point*(æname›¼rØ)¸fØ...¸gØ[æsymbol,–?ýlinefree“radius˜Ø]ŽŽ’åxn„ffŽžff‰ffæE:ŽŽŽŽŸØ-‘k$²The–˜zØpoint“²command“is“used“to“de ne“pšGoin¸ãts.‘;6Note“that“a“p˜oin¸ãt-name“Ùmust‘‹R²b˜egin“with“a“ÙsingleŽ¡‘k$²letter–UU(either“uppGer“or“lo•¸ãw“er–UUcase),“and“maš¸ãy“ha˜v˜e“up“to“a“Ùmaximum‘¸²of“t˜w˜o“follo˜wing“digits.Ž©‘k$The–ó&default“pšGoin•¸ãt-sym“b˜ol–ó&is“the“Ø$\bullet$².‘K9An“optional“alternativ¸ãe“p˜oin•¸ãt-sym“b˜ol–ó&(or“string“ofŽ¡‘k$c¸ãharacters)–UUcan“bšGe“sp˜eci ed“within“square“brac•¸ãk“ets–UUe.g.“Ø[$\triangle$]“²(see“Section“4.4).Ž¦‘k$By–Tadefault“lines“are“draš¸ãwn“to“the“pGoin˜t“loGcation.‘nêHo˜w˜ev˜er,‘”#the“radius“of“an“optional“line-freeŽ¡‘k$zone–†hcan“bšGe“sp˜eci ed“within“an“optional“square“brac•¸ãk“et–†he.g.“Ø[$\triangle$,4]“²(see“Section“4.4).Ž¡‘k$If–ßa“line-free“radius“is“spšGeci ed“without“a“p˜oin•¸ãt-sym“b˜ol,‘ŸÂthen–ßthe“preceding“comma“m¸ãust“still“b˜eŽ¡‘k$included;–UUfor“example“Ø[,5]².Ž¦‘k$An– ]optional“`Øcircle²'“can“also“bGe“used“as“the“Ùsymb‘ÿ}'ol².‘RÞIf“a“radius“v‘ÿqÇalue“is“also“included,‘óe.g.Ž¡‘k$Ø[circle,‘?ý5]–m²then“a“circle“will“bGe“draš¸ãwn“ha˜ving“the“spšGeci ed“radius“(the“radius“v‘ÿqÇalue“will“also“b˜eŽ¡‘k$assumed–mÑto“bšGe“the“line-free“radius).‘»Ÿ'EŽ‘ãxXŽ¡‘k$Ùp‘ÿ}'osition‘Zo²options‘Ö Øl–?ýt“r“B“b–– ²to“align“the“Èl²eft“edge,›¦9Èr²igh¸ãt“edge,˜Èt²op“edge,˜ÈB²aseline,˜Èb²ottom“edgeŽ¡‘k$respšGectiv¸ãely–ðTof“the“text“b˜o¸ãx“with“the“p˜oin¸ãt-lo˜cation“(see“the“P‘þÌП'IŽ‘©DC‘þæfT‘þU>Ÿ'EŽ‘ãxX“Manš¸ãual,‘page“5;‘=ÓWic˜h˜ura,ŽŸ Ø‘k$1992).‘CzF‘ÿ*ªor–Êlexample,‘æ4the“text“bGoš¸ãx“Ÿö㎉ffUŒŸŸUV„UVffŸúÇ‘ØThis–?ýis“point“PŽŽ‘T¿Ó„UVffŽžff‰ffUŒŸŽŽŽ‘[!w²w˜ould“bGe“aligned“suc˜h“that“the“righ˜t“edge“ofŽŸ ‘‘k$the–Ltext“bGoš¸ãx“w˜ould“bGe“cen˜tered“v˜ertically“at“the“pGoin˜t“µP‘c²,‘Mêusing“Øtext(This–?ýis“point“P){P}[r]².Ž¦‘k$The–åJØtext“²command“can“bšGe“used“to“lab˜el“p˜oin¸ãts,‘û²or“to“simply“p˜osition“text“in“a“diagram,‘û²as“sho¸ãwnŽ¡‘k$in–UUthe“follo¸ãwing“examples.Ž©3‡‘k$Øtext(A){5,6}Ž¡‘k$text($A_1$){A1,–?ýshift(2,“2)}Ž¡‘k$text($Z2$){Z2,–?ýshift(5,“-5)}[tr]Ž¡‘k$text($Z3$){Z2,–?ýpolar(5,“20“deg)}[Br]Ž¡‘k$text($Z4$){Z2,–?ýpolar(5,“1.34“rad)}Ž¡‘k$text(\framebox{$Z5$}){Z3}Ž¦‘k#¸ŽŽŽ‘k$Ÿõ€‰ffxyŸ„ffŸú€‘Øvariable(æname–¼rØ)¸fævalue“¸gŽŽ‘w8­„ffŽžff‰ffxyŽŽŽŽŸª¸‘k$Ÿõ€‰ff}EvŸ„ffŸú€‘Øvariable*(æname–¼rØ)¸fævalue“¸gŽŽ‘|xª„ffŽžff‰ff}EvŽŽŽŽŸDR‘k$²The–"”Øvariable“²command“is“used“to“de ne“scalar“v›ÿqÇariables“(see“Section“4.5).‘`ÜNote“that“a“v˜ariable-Ž¡‘k$name–µ-Ùmust‘¨²bšGegin“with“a“Ùsingle‘uˆ²letter“(either“upp˜er“or“lo•¸ãw“er–µ-case),‘Õ5and“maš¸ãy“ha˜v˜e“up“to“a“ÙmaximumŽ¡‘k$²of›ët•¸ãw“o˜follo“wing˜digits.‘NVV‘ÿ*ªariables˜and˜pGoin“ts˜ha“v“e˜the˜same˜name˜structure,‘Fand˜a˜v‘ÿqÇariable˜cannotŽ¡‘k$ha•¸ãv“e–vthe“same“name“as“a“pGoinš¸ãt.‘Z}The“scalar“argumen˜t“in“the“braces“can“bGe“either“a“n˜umeric“v‘ÿqÇalue,Ž¡‘k$another–UUv‘ÿqÇariable,“or“t•¸ãw“o›UUpGoin“ts˜(implying˜the˜distance˜bGet“w“een˜the˜t“w“o˜pGoin“ts).Ž©Ýì‘k$New–»v‘ÿqÇalues“can“bšGe“re-allo˜cated“to“existing“v›ÿqÇariable-names“using“the“equiv˜alen¸ãt“Øvariable*“²com-Ž¡‘k$mand;‘—´th¸ãus–8ãthe“v‘ÿqÇariable“Ør3“²can“bšGe“re-allo˜cated“the“v‘ÿqÇalue“15“using“the“command“Øvariable*(r3){15}Ž¡‘k$²(if–UUthe“v‘ÿqÇariable-name“has“not“bšGeen“used“b˜efore“then“¾mathsPIC“²will“generate“an“error“message).Ž¦‘k$V‘ÿ*ªariables–UUcan“bGe“manipulated“using“the“commands“Øadvance²,“Ømultiply²,“Ødivide“²and“Ømod².Ž¦‘k$The–UUfollo¸ãwing“are“examples“of“v‘ÿqÇalid“Øvariable“²commands.ŽŸ3‡‘k$Øvariable(r3){20}Ž¡‘k$variable(z3){3.46E-2}Ž¡‘k$variable(r4){r1}Ž¡‘k$variable(r5){AB}Ž¡‘k$variable*(r5){6}Ž¡‘k$variable(x1){w,‘?ýadvance(-6)}Ž¡‘k$variable(x2){w2,‘?ýdivide(-p)}Ž¡‘k$variable(x3){AB,‘?ýmultiply(2)}Ž¡‘k$variable*(x1){x1,‘?ýmod(3)}Ž¡‘k$variable(g){angle(ABC)}Ž¡‘k$variable(g2){area(ABC)}Ž¡‘k$variable(x3){Xpoint(P3)}‘¿÷%–?ýgets“the“x-coordinate“of“a“pointŽ¡‘k$variable(y3){Ypoint(P3)}‘¿÷%–?ýgets“the“y-coordinate“of“a“pointŽ¡‘k$variable(p1){3.14159}‘î%–?ýuse“p1“to“represent“PiŽ¡‘k$variable(e){2.71828}ŽŽŸŽŒ‹2A Åf¢ ý=´}Ÿ35ŸûÌÊ‘k"ÚmathsPIC‘꨼2.1ŽŽŽ’¸Œ£²30ŽŽŽŽ‘k"Ÿ™œ‰ffÀ!ƒŽŽŽŽ ¤Kƒ ý~´}‘k"Ü6.2Ž‘!+"Summary–€of‘º«åmathsPIC“ÜcommandsŽŸuT‘k"²The–Üfolloš¸ãwing“list“sho˜ws“the“format“and“t˜ypical“usage“of“all“¾mathsPIC‘Ѳcommands.‘ñ\Although“¾mathsPICŽ¤ ‘k"²commands–4+are“Ùnot‘'²case“sensitivš¸ãe,‘kàin“this“summary“of“commands“pGoin˜ts“are“represen˜ted“using“uppGerŽ¡‘k"case–ºletters,‘Ó@and“v‘ÿqÇariables“are“represenš¸ãted“using“lo˜w˜er“case“letters.‘ŸüNote“that“a“leading‘Ýž¸nØ “²is“used“forŽ¡‘k"cop¸ãying–UUT‘þU>Ÿ'EŽ›ãxX“or“P‘þÌП'IŽ‘©DC‘þæfT‘þU>Ÿ'EŽ˜X“lines“v¸ãerbatim,“for“example“with“macros“or“cošGordinates“of“data“p˜oin¸ãts“etc.ŽŸ‘k"Ø\‘¿÷4.5‘ÿô6.3Ž¡‘k"\setdashesŽ¡‘k"\typeout{drawing–?ýcircle“C2“now}%Ž¡‘k"arrowShape(4,30,40)Ž¡‘k"arrowShape(default)Ž¡‘k"drawAngleArc{angle(ABC),–?ýradius(3),“internal,“clockwise}Ž¡‘k"drawAngleArrow{angle(ABC),–?ýradius(3),“internal,“clockwise}Ž¡‘k"drawArrow(AB)Ž¡‘k"drawArrow(AB)[d]‘9¿ß%%–?ýdraw“arrow“distance“d“from“A“towards“BŽ¡‘k"drawArrow(AB,CD)Ž¡‘k"drawCircle(J,12)Ž¡‘k"drawCircle(C,r2)Ž¡‘k"drawCircle(C,AB)‘9¿ß%%–?ýthe“radius“is“length“of“line“ABŽ¡‘k"drawCircumcircle(ABC)Ž¡‘k"drawCurve(ABC)‘D?Ù%%–?ýbest“for“only“three“pointsŽ¡‘k"drawExcircle(ABC)[-0.2]Ž¡‘k"drawIncircle(ABC)[-0.3]Ž¡‘k"drawLine(AB)Ž¡‘k"drawline*(AB,–?ýCDEF)‘?ñ%%“the“*“option“disables“use“of“\putruleŽ¡‘k"drawLine(AB)[d]‘/?å%%–?ýdraw“line“distance“d“from“A“towards“BŽ¡‘k"drawLine(ABCDE)Ž¡‘k"drawPerpendicular(P,AB)Ž¡‘k"drawPerpendicular(P,AB)[foot]‘?ñ%%–?ýdraws“pointSymbol“at“the“footŽ¡‘k"drawPoint(B)Ž¡‘k"drawPoint(ABP1P2)Ž¡‘k"drawRightAngle(ABC,‘?ý4)Ž¡‘k"drawThickArrow(AB)Ž¡‘k"drawThickArrow(AB)[d]‘ÿô%%–?ýdraw“thickarrow“distance“d“from“A“towards“BŽ¡‘k"drawThickArrow(AB,CD)Ž¡‘k"drawThickLine(PQ)Ž¡‘k"drawThickLine(RS,TU)Ž¡‘k"drawTriangle(ABC)Ž¡‘k"inputFile(mathspic.dat)Ž¡‘k"inputFile(mathspic.dat)[4]Ž¡‘k"inputfile*(fig2.dat)‘?ñ%%–?ýdisables“mathsPIC“processing“of“fileŽ¡‘k"paper{units(1mm,3mm),xrange(-5,50),yrange(-5,50),axes(LR)}Ž¡‘k"paper{units(cm),xrange(0,5),yrange(0,9),axes(X*Y),ticks(1,1)}Ž¡‘k"point(D1){20,2}Ž¡‘k"point(D4){6.3,8.9534E-1}Ž¡‘k"point(P){x1,y1}Ž¡‘k"point(P){AB,PQ}Ž¡‘k"point(D2){20,2}[circle]Ž¡‘k"point(D3){20,3}[circle,5]Ž¡‘k"point(D4){20,4}[$\Box$,4]Ž¡‘k"point(D5){20,7}[,4]‘?ñ%%–?ýset“the“line-free“radiusŽ¡‘k"point(E1){D1,‘?ýshift(5,6)}[$\Box$]Ž¡‘k"point(E5){D1,‘?ýshift(r2,6)}Ž¡‘k"point(E2){D2,–?ýpolar(8,45)}‘?ñ%%“deg“is“the“defaultŽŽŸŽŒ‹Aå Åf¢ ý=´}Ÿ35ŸûÌÊ‘k"ÚmathsPIC‘꨼2.1ŽŽŽ’¸Œ£²31ŽŽŽŽ‘k"Ÿ™œ‰ffÀ!ƒŽŽŽŽ ¤Kƒ ý~´}‘k"Øpoint(E2){D2,–?ýpolar(8,45“deg)}Ž¤ ‘k"point(E6){D2,–?ýpolar(r4,45“deg)}Ž¡‘k"point(E5){D2,–?ýpolar(AB,45“deg)}[,5]Ž¡‘k"point(D32){midpoint(AB)}Ž¡‘k"point(D2){intersection(AB,CD)}Ž¡‘k"point(F){PointOnLine(AB,5.3)}Ž¡‘k"point(G){perpendicular(P,AB)}Ž¡‘k"point(G){perpendicular(P,AB)}Ž¡‘k"point(G2){Q,–?ýrotate(P,“23“deg)}‘ ú%%“rotate“Q“about“P“by“23“degŽ¡‘k"point(H){circumcircleCenter(ABC)}Ž¡‘k"point(J){incircleCenter(ABC)}Ž¡‘k"point(K){excircleCenter(ABC,BC)}Ž¡‘k"point*(D1){20,3}Ž¡‘k"point*(E1){D1,‘?ýshift(3,0)}Ž¡‘k"point*(E1){E1}[,6]‘D?Ù%%–?ýchange“the“line-free“radiusŽ¡‘k"pointNumber(67)‘4â%%–?ýdefault“is“50“pointsŽ¡‘k"pointSymbol($\odot$)Ž¡‘k"pointSymbol($\odot$,3)Ž¡‘k"pointSymbol(,4)Ž¡‘k"pointSymbol(default)Ž¡‘k"show(P3)Ž¡‘k"show(m)Ž¡‘k"showAngle(ABC)Ž¡‘k"showArea(ABC)Ž¡‘k"showIntersection(AB,CD)Ž¡‘k"showLength(AB)Ž¡‘k"text(P){5,7}Ž¡‘k"text($A$){A}Ž¡‘k"text($K$){K}[r]Ž¡‘k"text($B$){B,‘?ýshift(5,5)}Ž¡‘k"text(\framebox{$C$}){C,–?ýpolar(5,62“deg)}[Br]Ž¡‘k"variable(r1){15}Ž¡‘k"variable(z3){4.875E-2}Ž¡‘k"variable(d){AB}Ž¡‘k"variable(d2){d1}Ž¡‘k"variable(x1){w,‘?ýadvance(6)}Ž¡‘k"variable(x1){w,‘?ýadvance(-23.55)}Ž¡‘k"variable(x2){w2,‘?ýdivide(-p)}Ž¡‘k"variable(x3){AB,‘?ýmultiply(2)}Ž¡‘k"variable(g){angle(ABC)}Ž¡‘k"variable(g2){area(ABC)}Ž¡‘k"variable(x3{Xpoint(P3)}‘¿÷%–?ýgets“the“x-coordinate“of“a“pointŽ¡‘k"variable(y3){Ypoint(P3)}‘ ú%–?ýgets“the“y-coordinate“of“a“pointŽ¡‘k"variable(p1){3.14159}‘?ñ%–?ýuse“p1“to“represent“PiŽ¡‘k"variable(e){2.71828}Ž¡‘k"variable*(r1){20}Ž¡‘k"variable*(x1){x1,‘?ýmod(3)}ŽŸ‘k"²Note–jƒthat“the“old“Ølatex{...}“pictex{...}“²and“Øtex{...}“²`wrappGer'“commands“(for“cop¸ãying“theirŽ¡‘k"argumen•¸ãt›Ïunc“hanged˜in“to˜the˜output˜ le)˜ha“v“e˜b•Geen˜sup“erseded˜b•¸ãy˜the˜more˜con“v“enien“t˜¸n˜²and˜¸nØ Ž¡‘k"²commands,–UUbut“are“still“aš¸ãv‘ÿqÇailable“to“allo˜w“do˜wn˜w˜ards“compatibilit˜y“with“earlier“v˜ersions“of‘r¾mathsPIC².ŽŽŸŽŒ‹ L% Åf¢ ý=´}Ÿ35ŸûÌÊ‘k"ÚmathsPIC‘꨼2.1ŽŽŽ’¸Œ£²32ŽŽŽŽ‘k"Ÿ™œ‰ffÀ!ƒŽŽŽŽ ¤Kƒ ý~´}‘k"Ü6.3Ž‘!+"Useful–€P‘þaLŸªªIŽ‘e9C‘þƒ×T‘ý¿áŸªªEŽ‘ìSX“commandsŽŸuT‘k"²The–8folloš¸ãwing“is“a“list“of“P‘þÌП'IŽ‘©DC‘þæfT‘þU>Ÿ'EŽ‘ãxX“commands“whic˜h“are“particularly“useful“for“including“in“the“¾mathsPICŽ¤ ‘k"² le,‘–Hmainly–f„for“conš¸ãtrolling“the“thic˜kness“of“lines“and“axes,‘–Hcustomising“dash“patterns“and“sym˜bGol“spacing,Ž¡‘k"and–for“plotting“and“rotation.‘stNote“that“there“is“a“section“on“P‘þÌП'IŽ‘©DC‘þæfT‘þU>Ÿ'EŽ‘ãxX“in“Alan“HošGenig's“recen¸ãt“b˜o˜okŽ¡‘k"óŸ'EŽ‘ãxX›5YUn•¸ãbGoundd¿Ÿü^ÿ±9ŽŽ‘‹²whic“h˜also˜includes˜a˜brief˜list˜of˜commands.‘gNote˜that˜where˜small˜angle˜brac“k“ets˜areŽ¡‘k"shoš¸ãwn–UU(e.g.“Ø<²)“then“these“m˜ust“bGe“used“exactly“as“sho˜wn.ŽŸ=Þ‘k"Ø\grid–?ý{cols}“{rows}‘ ú%%“eg“\grid“{5}“{10}Ž¡‘k"\setdashpattern–?ý<4pt,“2pt>Ž¡‘k"\setdashes–?ý<7pt>› ú%%“equivalent“to˜\setdashpattern“<7pt,“7pt>Ž¡‘k"\setdashes‘)ÿè%%–?ýdefault“is‘ ú\setdashes“<5pt>Ž¡‘k"\setdots‘?ý<4pt>Ž¡‘k"\setdots‘4â%%–?ýdefault“is‘ ú\setdots“<5pt>Ž¡‘k"\setsolid‘/?å%%–?ýsets“solid-line“mode“(ie“not“dashes/dots)Ž¡‘k"\setlinear‘)ÿè%%–?ýsets“straight-line“plotting“mode“(ie“not“quadratic)Ž¡‘k"\setquadratic‘?ñ%%–?ýsets“curved“plotting“for“graphs“etcŽ¡‘k"\setplotsymbol({\large‘?ý.})Ž¡‘k"\setplotsymbol({\tiny–?ý.})‘¿÷%%“default“size“for“curves“(used“by“\plot)Ž¡‘k"\plotsymbolspacing=2pt‘ ú%%–?ýsets“spacing“between“plot“symbols“(used“by“\plot)Ž¡‘k"\plotheading{..}‘)ÿè%%–?ýeg“\plotheading{This“is“a“quadratic“curve}Ž¡‘k"\headingtoplotskip=1cm‘ ú%%–?ýseparation“between“plotheading“and“graphŽ¡‘k"\linethickness=2pt‘î%%–?ýfor“horiz“&“vert“lines:“default“0.4ptŽ¡‘k"\frame–?ý“{text}‘9¿ß%%“eg‘ ú\frame“<5pt>“HelloŽ¡‘k"\rectangle–?ý‘¿÷%%“eg‘ ú\rectangle“<2cm>“<1cm>Ž¡‘k"\putrectangle–?ýcorners“at“5“10‘ ú30“5‘¿÷%%“corners“at“Top-left“Bottom-rightŽ¡‘k"\inboundscheckon‘)ÿè%%–?ýrestricts“plotting“to“plotting“areaŽ¡‘k"\inboundscheckoff‘$¿ë%%Ž¡‘k"\normalgraphs‘9¿ß%%–?ýrestores“default“values“for“graph“parametersŽ¡‘k"\circulararc–?ý30“degrees“from“3.5‘ ú4.5“center“at“5“5Ž¡‘k"\ellipticalarc–?ýaxes“ratio“2:1‘ ú360“degrees“from“3“3“center“at“5“5Ž¡‘k"(axes–?ýratio“is› úmajor-axis:minor-axis,“ie˜a:b)ŽŸ=Þ‘k"²Note–‘Ãthat“P‘þÌП'IŽ‘©DC‘þæfT‘þU>Ÿ'EŽ‘ãxX“also“has“an“excellenš¸ãt“rotation“facilit˜y‘ÿ*ª.‘0—P‘þÌП'IŽ‘©DC‘þæfT‘þU>Ÿ'EŽ‘ãxX“will“rotate“abGout“a“giv˜en“pGoin˜t,‘¸áb˜y“aŽ¡‘k"givš¸ãen–ÿ¦angle,‘Éall“picture“elemen˜ts“(but“not“text)“whic˜h“are“detailed“bGet˜w˜een“its“Ø\startrotation...“²andŽ¡‘k"Ø\stoprotation›\²commands.‘ˆHo•¸ãw“ev“er˜the˜decimal˜v‘ÿqÇalue˜of˜the˜Sine˜and˜Cosine˜angle˜m“ust˜bGe˜suppliedŽ¡‘k"(see–dbšGelo¸ãw).‘žIf“the“p˜oin¸ãt“is“not“sp˜eci ed“then“rotation“is“p˜erformed“ab˜out“the“origin.‘žThe“format“is“asŽ¡‘k"follo¸ãws.Ž©=Þ‘k"Ø\startrotation–?ýby“cos(t)“sin(t)“[about“x“y]Ž¡‘k"...Ž¡‘k"\stoprotationŽ¦‘k"²This–'Ûcommand“is“particularly“useful“for“rotating“curvš¸ães.‘éYF‘ÿ*ªor“example,‘\|to“rotate“an“ellipse“b˜y“30Ž¡‘k"degrees–UUabšGout“the“p˜oinš¸ãt“(5,5)“one“w˜ould“writeŽ¦‘k"Ø\startrotation‘?ýby– ú0.86602“0.5“about“5“5Ž¡‘k"\ellipticalarc.....Ž¡‘k"\stoprotationŽ¦‘k"²A‘{kP‘þÌП'IŽ‘©DC‘þæfT‘þU>Ÿ'EŽ‘ãxX–{¶error-bar“facilitš¸ãy“is“also“a˜v‘ÿqÇailable“b˜y“loading“the“ le“Øerrorbar.tex“²(see“Section“9.4).Ž¡‘k"Note–VÝthat“P‘þÌП'IŽ‘©DC‘þæfT‘þU>Ÿ'EŽ‘ãxX“doGes“alloš¸ãw“more“sophisticated“graph“axes“and“tic˜k-marks“to“bGe“setup,‘—>as“w˜ell“asŽ¡‘k"shading–Ý5of“enclosed“areas.‘ hHo•¸ãw“ev“er,‘ÿ-these–Ý5are“complicated“and“require“access“to“the“P‘þÌП'IŽ‘©DC‘þæfT‘þU>Ÿ'EŽ‘ãxX“Man¸ãualŽ¡‘k"(see–UUSection“9.5),“and“are“curren¸ãtly“outside“the“scopGe“of‘r¾mathsPIC².Ž‘k"Ÿ˜¿‰ff³?çŸ J=‘ "5Ÿý-:Ë9ŽŽŽ‘LÜÊHoš¡8)Ïcmsl8éAŽŽp¨èT‘þ•AŸ¸ãEŽ›MX“and“T‘þ•AŸ¸ãEŽ˜X“strategies“for“fonšÃŽts,–EÕgraphics,“&–/Vmore.‘ÕÊ(Oxford“Univ˜ersit˜y“Press,ŽŸ €UK)–ÕXpp“580.–Ç ó?Œ-ø cmcsc10êisbnÊ:“0-19-509685-1–ÕX(hardbacšÃŽk),“0-19-509686-X“(papŸ'EŽ‘ãxX“commands“to“Ø\input“²the“ le“and“pGosition“the“graphic“on“the“page“areŽ¡‘k"describGed–UUin“Section“8.ŽŸþ6‘k"Ü7.1Ž‘!+"Input-–€and“output- lesŽŸuT‘k"²The–ëˆfolloš¸ãwing“example“¾mathsPIC‘ëb² le“(input- le)“illustrates“ho˜w“some“of“these“commands“are“used“toŽ¡‘k"draš¸ãw–c½Figure“4.‘œÿNote“that“the“dashed“line“µAD‘ªÚ²is“dra˜wn“after“the“P‘þÌП'IŽ‘©DC‘þæfT‘þU>Ÿ'EŽ‘ãxX“Ø\setdashes“²command“isŽ¡‘k"in•¸ãv“ok“ed;‘O follo“wing–¦xthis“Ø\setsolid“²is“used“bGefore“draš¸ãwing“the“righ˜t-angle“sym˜bšGol.‘e/Also,‘úÀthe“p˜oin¸ãtsŽ¡‘k"µA;–ª¨B‘€q;“C‘M¹²are––de ned“using“the“T‘þU>Ÿ'EŽ‘ãxX“Ø\odot“²sym¸ãbGol“¸ ²,‘¦ïin“conjunction“with“a“line-free“zone“of“1.2“mm“inŽ¡‘k"order–>xto“makš¸ãe“the“lines“go“to“the“edge“of“the“sym˜bGol|the“v‘ÿqÇalue“of“the“radius“of“suc˜h“T‘þU>Ÿ'EŽ‘ãxX“sym˜bGols“hasŽ¡‘k"to–UUbGe“determined“b¸ãy“trial“and“error|see“T‘ÿ*ªable“1“(Section“4.4.3).Ž ãŸÓúV‘~³( ÿt‰CVff Œ ÿ~‰ffŽ¤ ‰ffŽ¡‰ffŽ¡‰ffŽ¡‰ffŽ¡‰ffŽ¡‰ffŽ¡‰ffŽ¡‰ffŽ¡‰ffŽ¡‰ffŽ¡‰ffŽ¡‰ffŽ¡‰ffŽŽŽŽŽŽŽ‘z“ž33„ffÌÈŽŽŽŽ‘z“Ÿã¿U„ffÌÈŽŽŽŽ‘z“ŸÇKw„ffÌÈŽŽŽŽ‘z“Ÿª×™„ffÌÈŽŽŽŽ‘z“ŸŽc»„ffÌÈŽŽŽŽ‘z“ ÿqïÝ„ffÌÈŽŽŽŽ‘r’Ÿ8ã0Ž‘m‘ŸæÅ10Ž‘m‘ŸÊQ'20Ž‘m‘Ÿ­ÝI30Ž‘m‘Ÿ‘ik40Ž‘m‘ ÿtõ50ŽŽŽŽŽ’EÞ: ÿt‰CVff Œ ÿ~‰ffŽ¤ ‰ffŽ¡‰ffŽ¡‰ffŽ¡‰ffŽ¡‰ffŽ¡‰ffŽ¡‰ffŽ¡‰ffŽ¡‰ffŽ¡‰ffŽ¡‰ffŽ¡‰ffŽ¡‰ffŽŽŽŽŽŽŽ’Fmž33„ffÌÈŽŽŽŽ’FmŸã¿U„ffÌÈŽŽŽŽ’FmŸÇKw„ffÌÈŽŽŽŽ’FmŸª×™„ffÌÈŽŽŽŽ’FmŸŽc»„ffÌÈŽŽŽŽ’Fm ÿqïÝ„ffÌÈŽŽŽŽ’RÞ6Ÿ8ã0Ž’MÞ5ŸæÅ10Ž’MÞ5ŸÊQ'20Ž’MÞ5Ÿ­ÝI30Ž’MÞ5Ÿ‘ik40Ž’MÞ5 ÿtõ50ŽŽŽŽŽ ÿqïÝ‘~æ[„ffŽ– „ffŽ“„ffŽ“„ffŽ“„ffŽ“„ffŽ“„ffŽ“„ffŽ“„ffŽ“„ffŽ“„ffŽ“„ffŽ“„ffŽ“„ffŽ“„ffŽ“„ffŽ“„ffŽ“„ffŽ“„ffŽŽ’<æ[ ÿqïÝ„ffŽŽŽŽ‘~³( ÿq¼ª‰ÌÈffŽŽŽŽŽ’›' ÿq¼ª‰ÌÈffŽŽŽŽŽ’·šä ÿq¼ª‰ÌÈffŽŽŽŽŽ’Ô ÿq¼ª‰ÌÈffŽŽŽŽŽ’ð‚  ÿq¼ª‰ÌÈffŽŽŽŽŽ’ 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le“bš¸ãy“remo˜ving“all“the“Ø%%“²commen˜t“linesŽ¡‘k"(using–ôthe“Ýclean.exe“²utilitš¸ãy|see“Section“3.2),‘as“w˜ell“as“some“of“the“header“and“foGoter“lines“whic˜h“areŽ¡‘k"not–UUnoš¸ãw“required,“as“follo˜ws.Ž¦‘k"Ø%–?ýmPICm04.pic“(Figure“4)Ž¡‘k"%------------Ž¡‘k"\beginpictureŽ¡‘k"\setcoordinatesystem–?ýunits“<“1mm,“1mm>Ž¡‘k"\setplotarea–?ýx“from› ú0“to˜70,“y“from˜0“to˜50Ž¡‘k"\axis–?ýleft“ticks“numbered“from› ú0“to˜50“by˜10˜/Ž¡‘k"\axis–?ýbottom“ticks“numbered“from› ú0“to˜70“by˜10˜/Ž¡‘k"\put–?ý{$\odot$}“at– ú10“10“%%‘?ýAŽ¡‘k"\put–?ý{$\odot$}“at– ú35.7115“40.64178“%%‘?ýBŽ¡‘k"\put–?ý{$\odot$}“at– ú59.24039“18.68241“%%‘?ýCŽ¡‘k"\put–?ý{$\bullet$}“at– ú40.17626“15.32089“%%‘?ýDŽ¡‘k"\plot‘¿÷10.77135– ú10.91925‘?ñ34.94016“39.72252›?ý/“%%˜ABŽ¡‘k"\plot‘¿÷36.58879– ú39.82301‘?ñ58.3631“19.50117›?ý/“%%˜BCŽ¡‘k"\plot‘¿÷58.05862– ú18.47403‘?ñ11.18177“10.20838›?ý/“%%˜CAŽ¡‘k"\setdashesŽ¡‘k"\plot‘¿÷35.91988– ú39.46001‘?ñ40.17626“15.32089›?ý/“%%˜BDŽ¡‘k"\setsolidŽ¡‘k"\plot›¿÷42.63828– ú15.75501‘?ñ42.20416“18.21703˜/Ž¡‘k"\plot›¿÷39.74214– ú17.78291‘?ñ42.20416“18.21703˜/Ž¡‘k"\put–?ý{$B$}“at– ú34.7115“44.64178Ž¡‘k"\put–?ý{$A$}“at– ú6“8Ž¡‘k"\put–?ý{$C$}“at– ú63.24039“17.68241Ž¡‘k"\put–?ý{$D$}“at– ú41.17626“11.32089Ž¡‘k"\endpictureŽ¡‘k"%----------ŽŽŸŽŒ‹$²: Åf¢ ý=´}Ÿ35ŸûÌÊ‘k"ÚmathsPIC‘꨼2.1ŽŽŽ’¸Œ£²36ŽŽŽŽ‘k"Ÿ™œ‰ffÀ!ƒŽŽŽŽ ¤Kƒ ý~´}‘k"Note–íãthat“the“remaining“commenš¸ãts“at“the“end“of“the“Ø\plot“²and“Ø\put“²lines“are“generally“sucien˜t“toŽ¤ ‘k"understand–Ûwhat“eacš¸ãh“line“relates“to.‘$YNote“also“that“the“Ýclean.exe“²utilit˜y“only“remo˜v˜es“lines“ha˜vingŽ¡‘k"a–UUleading“Ø%%“²pair“of“cš¸ãharacters,“so“commen˜t“lines“pre xed“with“only“a“single“Ø%“²c˜haracter“will“remain.ŽŸÁ‘k"Ü7.2Ž‘!+"Line‘€mo`desŽŸuT‘k"²When–È8draš¸ãwing“ gures“with“bGoth“solid“and“dashed“lines“it“is“necessary“to“switc˜h“bGet˜w˜een“the“P‘þÌП'IŽ‘©DC‘þæfT‘þU>Ÿ'EŽ‘ãxXŽ¡‘k"commands–ÒsØ\setdashes“²and“Ø\setsolid“²(see“Section“6.3),‘1ºas“in“the“folloš¸ãwing“coGde“for“dra˜wing“theŽ¡‘k"rectangular–UUbGoš¸ãx“sho˜wn“in“Figure“5.Ž¡‘k"The–Ðdefault“Ø\setdashes“²givš¸ães“alternating“lines“and“spaces,‘@îeac˜h“of“width“5pt.‘§8More“fancy“dash-Ž¡‘k"patterns–Ü/(see“Figure“5)“can“bGe“easily“generated“using“the“P‘þÌП'IŽ‘©DC‘þæfT‘þU>Ÿ'EŽ‘ãxX“Ø\setdashpattern“²command“whic¸ãhŽ¡‘k"de nes–q}Ž¡‘k"...Ž¡‘k"\fancydashesŽ¦‘k"²Note–dbthat“in“Figure“5“all“the“pGoin¸ãts“are“de ned,›h%directly“or“indirectly‘ÿ*ª,˜relativš¸ãe“to“pGoin˜t“µA²,‘h%with“theŽ¡‘k"e ect–^gthat“the“pšGosition“of“the“whole“ 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‘k"this–‚Kprogram.‘øªThe“author“is“grateful“to“ApšGostolos“Syrop˜oulos,›͉Bob“Sc•¸ãh“umac“her,˜F‘ÿ*ªran“tisek‘‚KCh“v‘ÿqÇala,Ž¡‘k"Orlando–Ÿ'EŽ›ãxX“and“LŸýó5‘üff±AŽŽ‘͉²T‘þU>Ÿ'EŽ˜X“commands“and“for“copš¸ãying“lines“v˜erbatim.‘x/The“follo˜wingŽ¡‘k$commands›UUha•¸ãv“e˜also˜bGeen˜added/extended.Ž©À‘k$ØdrawCurve(ABC)Ž¡‘k$drawline(AB)[d]‘^Ê%%–?ýadded“the“[]“optionŽ¡‘k$drawline*(AB)‘hÿÄ%%–?ýdisables“use“of“\putruleŽ¡‘k$point(S){Q,–?ýrotate(P,“23“deg)}‘¿÷%%“added“the“rotate()“optionŽ¡‘k$pointsymbol(char,lineFreeRadius)–?ý%%“added“the“line-free“radius“optionŽ¦‘k#¸ŽŽŽ‘k$²1.9b–UU(Ma¸ãy“2000):Ž¤õU‘k$Fixed–UUa“bug“assoGciated“with“the“ØdrawAngleArc“²and“ØdrawAngleArrow“²commands.Ž©ꪑk#¸ŽŽŽ‘k$²1.9a–UU(Jan¸ãuary“2000):Ž¡‘k$Added–±the“options“X›°îand“Y˜to“the“Øaxes“²option“in“the“Øpaper“²command,‘Ññwhicš¸ãh“allo˜ws“X›°îand“Y˜axesŽ¤ ‘k$to–ª3bGe“draš¸ãwn.‘pbAlso“added“the“option“of“follo˜wing“an˜y“of“the“Øaxes“²options“b˜y“a“*“whic˜h“prev˜en˜tsŽ¡‘k$ticš¸ãks–UUbGeing“dra˜wn“on“that“particular“axis.Ž¦‘k#¸ŽŽŽ‘k$²1.8f–UU(OctobGer“1999):ŽŸõU‘k$Fixed– wproblem“with“scienš¸ãti c“notation;‘#ladded“curren˜t“loGop“n˜um˜bGer“indicator;‘#ladded“the“follo˜wingŽ¡‘k$new‘UUcommands:Ž©À‘k$Øvariable(){area()}Ž¡‘k$variable(){angle()}Ž¡‘k$variable(){Xpoint()}Ž¡‘k$variable(){Ypoint()}Ž¡‘k$inputfile*()Ž¡‘k$PointSymbol(default)Ž¦‘k#¸ŽŽŽ‘k$²1.7u–UU(Septem¸ãbGer“1999):‘qÇFirst“release.ŽŸ!•‘k"Ç13Ž‘"цReferencesŽŸç‘k#¸ŽŽŽ‘k$²Cameron–UUP‘ÿ*ª.“J.“(1992).›qÇGeometric“diagrams“in“LŸýó5‘üff±AŽŽ‘͉²T‘þU>Ÿ'EŽ‘ãxX.˜ÙTUGb–ÿ}'o“at‘H-È13–UU²(No.“2),“215{216.ŽŸꪑk#¸ŽŽŽ‘k$²F‘ÿ*ªeruglio–UUG.“V.“(1994).‘qÇTš¸ãypGesetting“comm˜utativ˜e“diagrams.‘qÇÙTUGb–ÿ}'o“at‘H-È15–UU²(No.“4),“466{484.ŽŽŸŽŒ‹7'™ Åf¢ ý=´}Ÿ35ŸûÌÊ‘k"ÚmathsPIC‘꨼2.1ŽŽŽ’¸Œ£²55ŽŽŽŽ‘k"Ÿ™œ‰ffÀ!ƒŽŽŽŽ ¤Kƒ ý~´}‘k#¸ŽŽŽ‘k$²Nic¸ãk‘ÿqÇalls–UUR‘þãWD“(1999a).‘qǾMathsPIC²:“a“ lter“program“for“use“with“P‘þÌП'IŽ‘©DC‘þæfT‘þU>Ÿ'EŽ‘ãxX.Ž¤ ‘k$ÙEur–ÿ}'oT‘þKß'EŽ‘Í-X'99‘“çPr“o“c“e“e“dings‘Ò!²;–UU197{210.‘qÇ(HeidelbGerg,“German¸ãy;“August“1999).Ž©‘k#¸ŽŽŽ‘k$²Nic¸ãk‘ÿqÇalls–UUR‘þãWD“(1999b).‘qǾMathsPIC²:“a“ lter“program“for“use“with“P‘þÌП'IŽ‘©DC‘þæfT‘þU>Ÿ'EŽ‘ãxX.Ž¡‘k$ÙEutup‘ÿ}'on‘ÄcŸü^ÿ±16ŽŽ‘ ’ž²[the–UUGreek“T‘þU>Ÿ'EŽ‘ãxX“F‘ÿ*ªriends'“journal];“No.“3“(OctobGer,“1999),“33{49“(English).Ž¡‘k$[This–UUis“an“upGdated“vš¸ãersion“of“Nic˜k‘ÿqÇalls“(1999a)].Ž¦‘k#¸ŽŽŽ‘k$²Salomon–UUD.“(1992).‘qÇArroš¸ãws“for“tec˜hnical“dra˜wing.‘qÇÙTUGb–ÿ}'o“at‘H-È13–UU²(No.“2),“146{149.Ž¦‘k#¸ŽŽŽ‘k$²SyropšGoulos–)A.“and“Nic¸ãk‘ÿqÇalls“R.“W.“D.“(2000).‘cA–(üPERL“p˜orting–)of“the“¾mathsPIC‘(ü²graphics“pac¸ãk‘ÿqÇage.Ž¡‘k$ÙTUG2000‘“çConfer–ÿ}'enc“e‘°²(Oxford,–UUUK);“August“13{16,“2000.Ž¦‘k#¸ŽŽŽ‘k$²Wic•¸ãh“ura–€/M.“J.“(1992).›òUThe“P‘þÌП'IŽ‘©DC‘þæfT‘þU>Ÿ'EŽ‘ãxX“man•¸ãual.˜Pub:‘Ç{P“ersonal–€/T‘þU>Ÿ'EŽ‘ãxX“Inc.,›Šå12“Madrona“Av•¸ãen“ue,˜MillŽ¡‘k$V–ÿ*ªalley“,–UUCA“94941,“USA.“Ùtexsales@p–ÿ}'ctex.c“om‘o 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