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::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::bC :vY:::::::::::J\\CkdB:jysy^VLFC@:nTjy;::::::::::::C`>=Je;yA::::::::::Z ::xI::::::::::::::bMnCJA;W\\Hlysy:::::::::::::::::::::::vPt>W:RlvYxI:::::::::::::::::::::::i?nCjysy:ZqryvY::::::::::::::::: ::tBbMnGxIyA:vPJa:yay=::::::::::::::::::::::::::t@W\\H;:::::JqryvY:::: :::::::::::::::::::::::::::::::::::::::::::::::::::tBbMnGjy;:::::::::: :::::::W>nCt@ry::vPJa:yay=:::::::::::::::::::::::::::::::::::::::::::: :::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: :::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: :::::::::::::::<:ry::::::::::::::ZZ@NbM:Zymy;:::::::::::::::::::::::i? nCjysy:ZqryvY:::::::::::::::::::XGi_ql^;yA:vPt>W:::::b]vYxI::::::::::::::::::::::::::::::::::::::::: ::::::::::::::roZql^;yA:::::::::::::::::vTjUSlZy=:jUcMnCjysy:::::::::: :::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: :::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: :::::::::::::::::::::::::::::::::::::::::::::::::Z::xI:::::::::::::::W \\H;JqryvY:::::::::::::::::::::::jU;W:1:" }{TEXT -1 0 "" }}{PARA 259 "" 0 "" {TEXT -1 11 "CHAPITRE 3:" }{TEXT 389 1 "\n" }{TEXT -1 16 "LA PROGRAMMATION" }}{PARA 19 "" 0 "" {TEXT -1 39 "\251 Apprendre Maple. Alain Le Stang. 2006" }}{PARA 19 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }{TEXT 256 0 "" }{TEXT -1 0 "" }}{EXCHG {PARA 0 "" 0 "" {TEXT 257 20 "Remarque importante:" }{TEXT -1 121 " pour pouvoir \+ entrer plusieurs lignes d'instructions Maple successives,\nsans ex\351 cution \340 la fin de chaque ligne, presser " }{TEXT 258 13 "Shift+Ent r\351e " }{TEXT -1 90 "\340 la fin de chaque ligne.\nPuis, pour valide r l'ensemble des lignes ainsi \351crites, presser " }{TEXT 259 6 "Entr \351e" }{TEXT -1 64 " en pla\347ant le curseur par\nexemple sur la der ni\350re ligne \351crite." }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 326 26 "LES STRUCTURES D E CONTR\324LE" }{TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "" 0 "" {TEXT 260 33 "Structu re de contr\364le if .. then:" }}}{EXCHG {PARA 256 "" 0 "" {TEXT 261 2 "if" }{TEXT -1 1 " " }{TEXT 268 10 "condition1" }{TEXT -1 1 " " } {TEXT 262 4 "then" }{TEXT -1 1 " " }{TEXT 269 14 "instruction 1 " } {TEXT -1 34 " " }}{PARA 256 "" 0 "" {TEXT -1 4 " " }{TEXT 263 4 "elif" }{TEXT -1 2 " " }{TEXT 274 11 " condition2 " }{TEXT 264 4 "then" }{TEXT -1 1 " " }{TEXT 270 14 "instru ction2 " }{TEXT -1 26 " " }{TEXT 273 1 "(" } {TEXT -1 5 "elif " }{TEXT 271 3 "et " }{TEXT -1 5 "else " }{TEXT 272 16 "sont optionnels)" }}{PARA 256 "" 0 "" {TEXT -1 4 " " }{TEXT 265 4 "elif" }{TEXT -1 2 " " }{TEXT 275 10 "condition3" }{TEXT -1 1 " " }{TEXT 266 4 "then" }{TEXT -1 17 " instruction3 ..." }}{PARA 256 " " 0 "" {TEXT -1 4 " " }{TEXT 267 4 "else" }{TEXT -1 1 " " }{TEXT 276 13 "instructionN\n" }{TEXT -1 7 "end if;" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 46 "Effectue un test selon certaine s conditions: " }{TEXT 333 40 "condition1, condition2, ..., condition N." }}{PARA 0 "" 0 "" {TEXT 334 5 "elif " }{TEXT -1 83 "signifie \"aut rement si\" . La derni\350re instruction \340 ex\351cuter doit \352tre pr\351c\351d\351e de " }{TEXT 335 4 "else" }{TEXT -1 1 "." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 277 10 "Exemple 1:" } {TEXT -1 43 " r\351solution de l'\351quation du premier degr\351 " } {XPPEDIT 18 0 "ax+b=0" "6#/,&%#axG\"\"\"%\"bGF&\"\"!" }{TEXT -1 28 " . \nModifiez les valeurs de " }{TEXT 327 1 "a" }{TEXT -1 7 " et de " } {TEXT 328 1 "b" }{TEXT -1 36 ", puis validez les lignes suivantes:" }} }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "a:=7:b:=3:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 129 "if a<>0 then print(`Une solution : x `=-b/a)\n elif b=0 then print(`Tout x est solution`)\n else print (`Pas de solution`)\nend if;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/%2Une ~solution~:~x~G#!\"$\"\"(" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "" 0 "" {TEXT 278 34 "Structure de contr\364le while .. do:" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 279 5 "w hile" }{TEXT -1 11 " condition " }{TEXT 280 2 "do" }{TEXT -1 5 " ... \+ " }{TEXT 281 8 "end do; " }{TEXT -1 83 " \nEx\351cute une suite d'instructions, tant que la condition est vraie. " }}{PARA 0 " " 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 282 10 "Exemple 2:" } {TEXT -1 53 " calcul de la somme des 100 premiers entiers naturels" }} {PARA 0 "> " 0 "" {MPLTEXT 1 0 76 "somme:=0:k:=-1:\nwhile k<100 do k:= k+1:somme:=somme+k end do:\n`somme `=somme;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/%'somme~G\"%]]" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }} {PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "" 0 "" {TEXT 283 32 "S tructure de contr\364le for .. to:" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 284 4 " for" }{TEXT -1 10 " variable " }{TEXT 285 4 "from" }{TEXT -1 10 " initiale " }{TEXT 286 2 "to" }{TEXT -1 8 " finale " }{TEXT 332 2 "by" }{TEXT -1 5 " pas " }{TEXT 287 2 "do" }{TEXT -1 5 " ... " }{TEXT 288 7 "end do;" }}{PARA 0 "" 0 "" {TEXT -1 86 "Ex\351cute une boucle p our une variable allant d'une valeur initiale \340 une valeur finale, " }}{PARA 0 "" 0 "" {TEXT -1 18 "avec un pas donn\351." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 289 11 " from , by " } {TEXT -1 56 "peuvent \352tre omises ou \351crites dans un ordre quelco nque." }}{PARA 0 "" 0 "" {TEXT -1 14 "Si l'on omet " }{TEXT 290 4 "fr om" }{TEXT -1 36 " , initiale vaut 1. Si l'on omet " }{TEXT 291 2 " by" }{TEXT -1 14 " , pas vaut 1." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }} {PARA 0 "" 0 "" {TEXT 292 10 "Exemple 3:" }{TEXT -1 53 " calcul de la \+ somme des 100 premiers entiers naturels" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 71 "somme:=0:\nfor k from 0 to 100 do somme:=somme+k end do:\n`som me `=somme;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/%'somme~G\"%]]" }}} {PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "" 0 "" {TEXT 293 10 "E xemple 4:" }{TEXT -1 71 " calcul de la somme des entiers impairs inf \351rieurs \340 100\nIci, on omet " }{TEXT 330 4 "from" }{TEXT -1 27 " donc la premi\350re valeur de" }{TEXT 329 2 " k" }{TEXT -1 37 " est \+ 1. La derni\350re valeur prise par " }{TEXT 331 1 "k" }{TEXT -1 9 " se ra 99." }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 69 "somme:=0:\nfor k to 100 b y 2 do somme:=somme+k end do:\n`somme `=somme;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/%'somme~G\"%+D" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }} {EXCHG {PARA 0 "" 0 "" {TEXT 361 3 "for" }{TEXT -1 10 " variable " } {TEXT 362 2 "in" }{TEXT -1 12 " expression " }{TEXT 363 2 "do" }{TEXT -1 4 " .. " }{TEXT 364 7 "end do;" }{TEXT -1 10 " " }}} {EXCHG {PARA 0 "" 0 "" {TEXT 294 10 "Exemple 5:" }{TEXT -1 55 " donner les nombres premiers de la liste [31,39,47,105]" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 85 "for k in [31,39,47,105] do\n if isprime(k) then prin t(k,`est premier`) end if\nend do;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$ \"#J%,est~premierG" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$\"#Z%,est~premie rG" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" } }{PARA 0 "" 0 "" {TEXT 295 15 "LES PROC\311DURES:" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 66 "Un programme MAPLE peut \352tre organis\351 en sous-programmes appel\351es " }{TEXT 336 10 "proc\351dures" }{TEXT -1 25 ". \nUne proc\351dure, de type" } {TEXT 392 10 " procedure" }{TEXT -1 30 ", est d\351finie par le mot-c l\351 " }{TEXT 337 4 "proc" }{TEXT -1 82 " et peut \352tre assign\351e \340\nun nom de variable. Pour d\351finir une proc\351dure intitul \351e " }{TEXT 338 3 "nom" }{TEXT -1 36 " , on utilisera la syntaxe su ivante:" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 339 3 "nom" }{TEXT -1 2 ":=" }{TEXT 296 4 "proc" }{TEXT -1 20 "(param\350t res_formels)" }}{PARA 0 "" 0 "" {TEXT -1 3 " " }{TEXT 297 7 "global \+ " }{TEXT -1 58 "variables_globales; (la li gne " }{TEXT 298 6 "global" }{TEXT -1 17 " est optionnelle)" }}{PARA 0 "" 0 "" {TEXT -1 2 " " }{TEXT 299 7 " local " }{TEXT -1 61 " variab les_locales; (la ligne " }{TEXT 300 5 " local" }{TEXT -1 21 " est optionnelle)\n " }{TEXT 344 11 "descriptio n" }{TEXT -1 47 " cha\356ne_de_description; (la ligne " } {TEXT 345 11 "description" }{TEXT -1 18 " est optionnelle) " }}{PARA 0 "" 0 "" {TEXT -1 3 " " }{TEXT 301 7 "option " }{TEXT -1 59 "nom_op tion; (la ligne " }{TEXT 302 7 "o ption " }{TEXT -1 16 "est optionnelle)" }}{PARA 0 "" 0 "" {TEXT -1 3 " " }{TEXT 341 5 ". . ." }{TEXT -1 13 " instructions" }{TEXT 340 6 " \+ . . ." }{TEXT -1 60 " (corps de la proc\351dure)" }}{PARA 0 "" 0 "" {TEXT 303 9 "end proc;" }}{PARA 0 " " 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 " " {TEXT -1 0 "" }{TEXT 304 10 "Exemple 6:" }}{PARA 0 "" 0 "" {TEXT -1 23 "La proc\351dure intitul\351e " }{TEXT 343 4 "maxi" }{TEXT -1 81 " \+ calcule le plus grand de 2 entiers positifs.\nElle comporte 2 param \350tres formels " }{TEXT 346 1 "u" }{TEXT -1 4 " et " }{TEXT 347 1 "v " }{TEXT -1 82 ". Leur type peut \352tre omis, mais si on le veut le p r\351ciser,\nbien noter la syntaxe " }{TEXT 349 1 "u" }{TEXT 348 1 " \+ " }{TEXT 352 2 "::" }{TEXT 351 1 " " }{TEXT 350 6 "posint" }{TEXT -1 3 " , " }{TEXT 359 1 "v" }{TEXT 355 1 " " }{TEXT 358 2 "::" }{TEXT 357 1 " " }{TEXT 356 6 "posint" }{TEXT -1 20 " pour signifier que " } {TEXT 353 1 "u" }{TEXT -1 4 " et " }{TEXT 360 1 "v" }{TEXT -1 14 " son t de type " }{TEXT 354 6 "posint" }{TEXT -1 94 ".\nElle ne comporte ni variables globales, ni variables locales, mais une cha\356ne de descr iption" }}{PARA 0 "" 0 "" {TEXT -1 44 "de la proc\351dure et une optio n de copyright.\n" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 172 "maxi:=proc(u: :posint,v::posint)\ndescription \"calcule le plus grand de 2 entiers p ositifs\";\noption `Copyright (c) 2001 A.Le Stang`;\n if u%%maxiGf *6$'%\"uG%'posintG'%\"vGF)6\"6#%?Copyright~(c)~2001~~A.Le~StangGF,@%29 $9%F2F16#QLcalcule~le~plus~grand~de~2~entiers~positifsF,F,F," }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "maxi(5,9);maxi(1.2,Pi);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"*" }}{PARA 8 "" 1 "" {TEXT -1 95 " Error, invalid input: maxi expects its 1st argument, u, to be of type \+ posint, but received 1.2\n" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 4 "Une " }{TEXT 305 15 "variable locale" } {TEXT -1 70 " est une variable qui n'est reconnue qu'\340 l'int\351rie ur de la proc\351dure," }}{PARA 0 "" 0 "" {TEXT -1 20 "contrairement \+ \340 une " }{TEXT 306 16 "variable globale" }{TEXT -1 39 " accessible \+ en dehors de la proc\351dure. " }}{PARA 0 "" 0 "" {TEXT -1 0 "" } {TEXT 365 10 "Exemple 7:" }{TEXT 366 0 "" }{TEXT -1 2 " " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 116 "messages:=proc()\nglobal message1; \nlocal message2;\n message1:=\"Hello, world!\";\n message2:=\"How a re you?\";\nend proc;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%)messagesGf *6\"6#%)message2GF&F&C$>%)message1GQ.Hello,~world!F&>8$Q-How~are~you?F &F&6#F+F&" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "messages();" } }{PARA 11 "" 1 "" {XPPMATH 20 "6#Q-How~are~you?6\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "message1,message2; " }}{PARA 11 "" 1 "" {XPPMATH 20 "6$Q.Hello,~world!6\"%)message2G" }}}{EXCHG {PARA 0 "" 0 " " {TEXT -1 32 "La valeur de la variable locale " }{TEXT 369 8 "message 2" }{TEXT -1 69 " n'a pas \351t\351 reconnue, contrairement \340 celle de la \nvariable globale " }{TEXT 368 8 "message1" }{TEXT -1 2 ". " } }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "" 0 "" {TEXT 388 21 "Remarque importante:\n" }{TEXT 371 95 "Un param\350tre formel pass \351 \340 une proc\351dure ne peut \352tre modifi\351 \340 l'int\351ri eur de cette proc\351dure" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "" 0 "" {TEXT 367 10 "Exemple 8 :" }{TEXT 370 1 " " }{TEXT -1 27 "Diviser un entier positif " }{TEXT 482 1 "x" }{TEXT -1 27 " par 2 tant qu'il est pair." }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 69 "div:=proc(x::posint)\n while type(x,even) do x:=x /2 end do;\nend proc;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$divGf*6#'% \"xG%'posintG6\"F*F*?(F*\"\"\"F,F*-%%typeG6$9$%%evenG>F0,$F0#F,\"\"#F* F*F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "div(48);" }}{PARA 8 "" 1 "" {TEXT -1 50 "Error, (in div) illegal use of a formal parameter \n" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 45 "La tentative d'affecter au \+ param\350tre formel " }{TEXT 372 1 "x" }{TEXT -1 99 " sa valeur divis \351e par 2 provoque une erreur.\nOn peut modifier la proc\351dure de \+ la mani\350re suivante:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 88 " div:=proc(x::posint)\n local y;\n y:=x;\n while type(y,even) do y:=y/2 end do;\n y\nend proc;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$divGf*6# '%\"xG%'posintG6#%\"yG6\"F,C%>8$9$?(F,\"\"\"F2F,-%%typeG6$F/%%evenG>F/ ,$F/#F2\"\"#F/F,F,F," }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "div( 48);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"$" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 50 "On obtient en effet successivement : 48,24,12,6,3." }} }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "div(45);" }}{PARA 11 "" 1 " " {XPPMATH 20 "6#\"#X" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "" 0 "" {TEXT 342 8 " return " }{TEXT -1 47 "met fin \340 la p roc\351dure en donnant un r\351sultat.\n" }{TEXT 374 5 " next" }{TEXT -1 59 " permet de passer \340 la valeur suivante dans une it\351ration .\n" }{TEXT 376 6 " break" }{TEXT -1 42 " permet de sortir de la struc ture de contr" }{TEXT 375 1 "\364" }{TEXT -1 13 "le en cours. " }} {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 373 10 "Exemple \+ 9:" }{TEXT -1 234 " On parcourt une liste de nombres. Au premier entie r positif trouv\351, on sort de la proc\351dure\navec pour r\351sultat cet entier, sinon si ce nombre est n\351gatif, on sort de la boucle a vec pour r\351sultat -1,\nsinon on passe au nombre suivant. " }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 188 "liste:=proc(L::list(numeric ))\nlocal k;\nfor k in L do\n print(`lecture de`,k);\n if type(k,non negint) then return k\n elif k<0 then break;\n else next;\n end if \nend do;\nreturn -1;\nend proc;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>% &listeGf*6#'%\"LG-%%listG6#%(numericG6#%\"kG6\"F/C$?&8$9$%%trueGC$-%&p rintG6$%+lecture~deGF2@'-%%typeG6$F2%*nonnegintGOF22F2\"\"![\\O!\"\"F/ F/F/" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "liste([12.56,8.9,7, 3.14]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$%+lecture~deG$\"%c7!\"#" }} {PARA 11 "" 1 "" {XPPMATH 20 "6$%+lecture~deG$\"#*)!\"\"" }}{PARA 11 " " 1 "" {XPPMATH 20 "6$%+lecture~deG\"\"(" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "liste([12.56 ,-8.9,7,3.14]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$%+lecture~deG$\"%c7 !\"#" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$%+lecture~deG$!#*)!\"\"" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#!\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "liste([12.56,8.9,7.1,3.14]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$%+lecture~deG$\"%c7!\"#" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$%+lecture~deG$\"#*)!\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$%+le cture~deG$\"#r!\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$%+lecture~deG$ \"$9$!\"#" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#!\"\"" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 308 12 "R\351cursivit\351:" }}{PARA 0 "" 0 "" {TEXT -1 82 "Une proc\351dure qui fait r\351f\351rence \340 elle m\352me dans s a d\351finition est une proc\351dure " }{TEXT 309 9 "r\351cursive" } {TEXT -1 2 " ." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 307 11 "Exemple 10:" }{TEXT -1 16 " factorielle de " }{TEXT 310 13 "n " }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 91 "factorielle := proc(n::nonnegint)\n if n>0 then n*factorielle(n-1) else 1 end if;\n end proc;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%,factorielleGf*6#'%\"nG %*nonnegintG6\"F*F*@%2\"\"!9$*&F.\"\"\"-F$6#,&F.F0F0!\"\"F0F0F*F*F*" } }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "factorielle(12);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"*+;+z%" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" } }{EXCHG {PARA 0 "" 0 "" {TEXT 459 9 "Fonction " }{TEXT 460 5 "error" } {TEXT 461 1 ":" }{TEXT -1 12 "\nLa fonction" }{TEXT 387 6 " error" } {TEXT -1 57 " permet de d\351finir des messages d'erreur personnalis \351s. \n" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 385 11 "Exemple 11:" } {TEXT -1 18 " racine carr\351e de " }{TEXT 386 1 "x" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 97 "racine := proc (x)\n if x<0 then error \" invalide x: %1\", x else simplify(x^(1/2)) end if\nend proc;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%'racineGf*6#%\"xG6\"F(F(@%29$\"\"!Y6$Q/inv alide~x:~%1F(F+-%)simplifyG6#*$-%%sqrtG6#F+\"\"\"F(F(F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "racine(144);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"#7" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "raci ne(-144);" }}{PARA 8 "" 1 "" {TEXT -1 36 "Error, (in racine) invalide \+ x: -144\n" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 390 13 "LES MODULES: " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 3 "Un " }{TEXT 391 6 "module" }{TEXT -1 48 " est un e collection de proc\351dures et de donn\351es." }}{PARA 0 "" 0 "" {TEXT -1 18 "Un module, de type" }{TEXT 395 7 " module" }{TEXT -1 29 " , est d\351fini par le mot-cl\351 " }{TEXT 393 6 "module" }{TEXT -1 76 " et peut \352tre assign\351 \340 un\nnom de variable. Pour d\351fi nir un module intitul\351 " }{TEXT 394 3 "nom" }{TEXT -1 37 " , on uti lisera la syntaxe suivante:\n" }}{PARA 0 "" 0 "" {TEXT 404 3 "nom" } {TEXT -1 2 ":=" }{TEXT 396 6 "module" }{TEXT -1 2 "()" }}{PARA 0 "" 0 "" {TEXT -1 3 " " }{TEXT 397 7 "global " }{TEXT -1 58 "variables_glo bales; (la ligne " }{TEXT 398 6 "global" } {TEXT -1 17 " est optionnelle)" }}{PARA 0 "" 0 "" {TEXT -1 2 " " } {TEXT 399 7 " local " }{TEXT -1 61 " variables_locales; \+ (la ligne " }{TEXT 400 5 "local" }{TEXT -1 20 " est o ptionnelle)\n " }{TEXT 409 0 "" }{TEXT 410 8 " export " }{TEXT 411 0 "" }{TEXT -1 52 "variables_locales_export\351es; (la lign e " }{TEXT 412 6 "export" }{TEXT -1 21 " est optionnelle)\n " } {TEXT 407 11 "description" }{TEXT -1 47 " cha\356ne_de_description; \+ (la ligne " }{TEXT 408 11 "description" }{TEXT -1 18 " est \+ optionnelle) " }}{PARA 0 "" 0 "" {TEXT -1 3 " " }{TEXT 401 7 "option " }{TEXT -1 59 "nom_option; (la \+ ligne " }{TEXT 402 7 "option " }{TEXT -1 16 "est optionnelle)" }} {PARA 0 "" 0 "" {TEXT -1 3 " " }{TEXT 406 5 ". . ." }{TEXT -1 13 " i nstructions" }{TEXT 405 6 " . . ." }{TEXT -1 54 " \+ (corps du module)" }}{PARA 0 "" 0 "" {TEXT 403 11 "end module;" }}{PARA 0 "" 0 "" {TEXT -1 38 "\nContrairement au cas des pr oc\351dures, " }{TEXT 413 45 "le module ne peut avoir de param\350tres formels" }{TEXT -1 87 " .\nOn retrouve les notions de variables globa les et locales, comme pour les proc\351dures," }}{PARA 0 "" 0 "" {TEXT -1 5 "mais " }{TEXT 415 50 "les modules peuvent exporter des var iables locales" }{TEXT -1 21 " (celles de la ligne " }{TEXT 414 6 "exp ort" }{TEXT -1 3 "), " }}{PARA 0 "" 0 "" {TEXT -1 80 "auxquelles on a \+ acc\350s de l'ext\351rieur du module en utilisant la syntaxe suivante: " }{TEXT 423 2 " \n" }{TEXT 428 3 "nom" }{TEXT 429 4 " :- " }{TEXT 430 3 "var" }{TEXT 431 2 " " }{TEXT -1 47 "permet d'acc\351der \340 l a variable locale export\351e " }{TEXT 433 3 "var" }{TEXT 432 1 " " } {TEXT -1 10 "du module " }{TEXT 435 3 "nom" }{TEXT -1 3 ". \n" }} {PARA 0 "" 0 "" {TEXT -1 88 "En utilisant la terminologie de la progra mmation orient\351e objet, les variables d\351clar\351es" }}{PARA 0 " " 0 "" {TEXT -1 13 "dans la ligne" }{TEXT 425 7 " local " }{TEXT -1 28 "s'apparentent \340 des membres " }{TEXT 426 6 "priv\351s" }{TEXT -1 54 " du module, tandis que celles\nd\351clar\351es dans la ligne " }{TEXT 424 7 "export " }{TEXT -1 28 "s'apparentent \340 des membres " }{TEXT 427 8 "publics " }{TEXT -1 10 "du module." }}{PARA 0 "" 0 "" {TEXT -1 3 " " }}}{EXCHG {PARA 0 "" 0 "" {TEXT 416 11 "Exemple 12:" }{TEXT -1 34 " Anneau Z/4Z des entiers modulo 4." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 177 "Z4:=module()\n description \"Arithm\351tiq ue modulo 4\";\n export add,mult,opp;\n add := (x,y)-> (x+y) mod 4 ;\n mult := (x,y)-> (x*y) mod 4;\n opp := x-> (-x) mod 4;\nend mod ule;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#Z4G`6%%$addG%%multG%$oppGb6 #%+thismoduleG6\"F-6%F'%%multG%$oppGF-6#Q6Arithm|dytique~modulo~4F-F-F -6\"6\"" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 49 "Le module comporte 3 v ariables locales export\351es " }{TEXT 434 3 "add" }{TEXT -1 2 ", " } {TEXT 436 4 "mult" }{TEXT -1 2 ", " }{TEXT 437 3 "opp" }{TEXT -1 61 ". \nV\351rifions que: (2+3) mod 4 = 1 , que (2*3) mod 4 = 2 et " } {TEXT 438 3 "opp" }{TEXT -1 22 "(1) = -1 mod 4 = 3 :\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "Z4:-add(2,3);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "Z4 :-mult(2,3);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"#" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "Z4:-opp(1);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"$" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "" 0 "" {TEXT 417 11 "Exemple 13:" } {TEXT -1 10 " Anneau Z/" }{TEXT 418 1 "n" }{TEXT -1 21 "Z des entiers \+ modulo " }{TEXT 419 1 "n" }{TEXT -1 84 ".\nOn d\351sire modifier le pr ogramme pr\351c\351dent pour effectuer de l'arithm\351tique modulo " } {TEXT 420 1 "n" }{TEXT -1 1 "," }}{PARA 0 "" 0 "" {TEXT -1 5 "avec " } {XPPEDIT 18 0 "0 < n;" "6#2\"\"!%\"nG" }{TEXT -1 90 " entier quelconqu e.\nUn module n'acceptant pas de param\350tre formel, \351crivons une \+ proc\351dure " }{TEXT 421 13 "Construire_Zn" }}{PARA 0 "" 0 "" {TEXT -1 20 "de param\350tre formel " }{TEXT 422 1 "n" }{TEXT -1 35 " , rend ant pour r\351sultat un module:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 223 "Construire_Zn:=proc(n::posint)\n module()\n description \+ \"Arithm\351tique modulo n\";\n export add,mult,opp;\n add := (x ,y)-> (x+y) mod n;\n mult := (x,y)-> (x*y) mod n;\n opp := x-> ( -x) mod n;\n end module;\nend proc;" }}{PARA 12 "" 1 "" {XPPMATH 20 " 6#>%.Construire_ZnGf*6#'%\"nG%'posintG6\"F*F*b6#%+thismoduleGF*F*6%%$a ddG%%multG%$oppGC%>8$f*6$%\"xG%\"yGF*6$%)operatorG%&arrowGF*-%$modG6$, &9$\"\"\"9%FAT$F*F*6$F(FC>8%f*F6F*F9F*-F=6$*&F@FAFBFAFCF*F*FD>8&f*6#F7 F*F9F*-F=6$,$F@!\"\"FCF*F*FD6#Q6Arithm|dytique~modulo~nF*F*6$F(F@F*F*F *F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "Z7:=Construire_Zn(7) ;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#Z7G`6%%$addG%%multG%$oppGb6#%+ thismoduleG6\"F-6%F'%%multG%$oppGF-6#Q6Arithm|dytique~modulo~nF-F-6$% \"nG\"\"(6\"6\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "Z7:-add( 6,5);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"%" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 14 "Z7:-mult(5,3);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "Z7:-opp(3); " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"%" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 43 "On peut utiliser la stru cture de contr\364le " }{TEXT 439 4 "use " }{TEXT 440 3 "nom" }{TEXT 441 16 " in ... end use\n" }{TEXT -1 54 "pour acc\351der aux variables locales export\351es du module" }{TEXT 443 1 " " }{TEXT 442 3 "nom" } {TEXT 444 1 " " }{TEXT -1 18 "sans avoir recours" }{TEXT 446 1 "\n" } {TEXT -1 18 "\340 l'utilisation de" }{TEXT 447 1 " " }{TEXT 445 4 ":- \+ \n" }{TEXT 448 8 "Exemple:" }{TEXT -1 85 " (opp(3) mod 7) = (4 mod 7) = 4 ( (opp(3) mod 7)*5 ) mod 7 = (4*5) mod 7 = 6" }}{PARA 0 " " 0 "" {TEXT -1 70 " (2 + ( (opp(3) mod 7)*5 ) mod 7 \+ ) = (2+6) mod 7 = 1 " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 48 "use Z7 in\n add( 2, mult( opp(3), 5) )\nend use;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"\"" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 12 "La fonction \+ " }{TEXT 481 6 "member" }{TEXT -1 59 " permet de savoir si une express ion est membre d'un module:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "member(mult,Z7) , member(prod,Z7);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$%%trueG%&falseG" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "" 0 "" {TEXT 449 23 "Le constructeur Record:" }{TEXT 450 0 " " }{TEXT 451 1 "\n" }{TEXT -1 16 "Le constructeur " }{TEXT 452 6 "Reco rd" }{TEXT -1 9 " cr\351e un " }{TEXT 453 14 "enregistrement" }{TEXT -1 35 " Maple. Un enregistrement, de type " }{TEXT 456 6 "record" } {TEXT -1 83 ", est\nd\351fini par les noms de ses champs (appel\351s \+ \"slots\" ou \"fields\" en anglais).\n\n" }{TEXT 454 12 "Exemple 14: \+ " }{TEXT -1 89 "On veut cr\351er un enregistrement pour mod\351liser l es nombres complexes.\nUn nombre complexe " }{TEXT 457 1 "z" }{TEXT -1 68 " est d\351fini par 2 champs: sa partie r\351elle et sa partie i maginaire. " }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "z := Record( 're', 'im' );" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"zG`6$%#reG%#imGb6#%+thismoduleG6\"6#%'recordG6$%#re G%#imGF,F,F,F,6\"6\"" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 72 "On voit q u'un enregistrement est un module particulier, qui a l'option " } {TEXT 455 6 "record" }{TEXT -1 1 "." }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 27 "On d\351finit un nouveau type " }{TEXT 458 8 "complexe" }{TEXT -1 52 " associ\351 et la fonction modul e d'un nombre complexe:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 89 " `type/complexe` := 'record( re, im )':\n Mon_module:=(z::complexe)->sq rt(z:-re^2+z:-im^2);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%+Mon_moduleG f*6#'%\"zG%)complexeG6\"6$%)operatorG%&arrowGF*-%%sqrtG6#,&*$)_9$%#reG \"\"#\"\"\"F8*$)_F5%#imGF7F8F8F*F*F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 36 "z:-re:=1 : z:-im:=2 :Mon_module(z); " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*$-%%sqrtG6#\"\"&\"\"\"" }}}{EXCHG {PARA 0 "" 0 " " {TEXT -1 92 "On peut aussi initialiser les valeurs des parties r\351 elle et imaginaire de la fa\347on suivante:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 47 "z:= Record( 're' = 1, 'im' = 2 ):Mon_module(z);" } }{PARA 11 "" 1 "" {XPPMATH 20 "6#*$-%%sqrtG6#\"\"&\"\"\"" }}}{PARA 11 "" 1 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 311 28 "LES LIBRAIRIES E T PACKAGES: " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "" 0 " " {TEXT -1 91 "Pour obtenir le listing de certaines fonctions des libr airies MAPLE, comme ici la fonction " }{TEXT 377 8 "ithprime" }}{PARA 0 "" 0 "" {TEXT -1 9 "utiliser:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 41 "interface(verboseproc=2);print(ithprime);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#f*6#%\"iG6\"6#%fnCopyright~(c)~1999~Waterloo~Maple~Inc. ~All~rights~reserved.GF&@'-%%typeG6$9$.%'posintG@'1F-\"#D-%#opG6$F-7; \"\"#\"\"$\"\"&\"\"(\"#6\"#8\"#<\"#>\"#B\"#H\"#J\"#P\"#T\"#V\"#Z\"#`\" #f\"#h\"#n\"#r\"#t\"#z\"#$)\"#*)\"#(*2F-% " 0 "" {MPLTEXT 1 0 14 "?index,package" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 11 "La fonction" }{TEXT 313 6 " with " }{TEXT -1 54 "permet de charger toute ou partie d'un package choisi:" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 63 "with(studen t); \n#charge toutes les fonctions du package student" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#7@%\"DG%%DiffG%*DoubleintG%$IntG%&LimitG%(LineintG %(ProductG%$SumG%*TripleintG%*changevarG%/completesquareG%)distanceG%' equateG%*integrandG%*interceptG%)intpartsG%(leftboxG%(leftsumG%)makepr ocG%*middleboxG%*middlesumG%)midpointG%(powsubsG%)rightboxG%)rightsumG %,showtangentG%(simpsonG%&slopeG%(summandG%*trapezoidG" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 26 "Chargement de la fonction " }{TEXT 378 8 "binomial" }{TEXT -1 12 " du package " } {TEXT 379 10 "combinat :" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "with(combinat,binomial);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7#%)binom ialG" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 44 "Cette fonction retourne l e nombre binomial(" }{XPPEDIT 18 0 "n,p" "6$%\"nG%\"pG" }{TEXT -1 4 " ) = " }{XPPEDIT 18 0 "n!/(p!*(n-p)!)" "6#*&-%*factorialG6#%\"nG\"\"\"* &-F%6#%\"pGF(-F%6#,&F'F(F,!\"\"F(F0" }{TEXT -1 16 " appel\351 aussi C( " }{XPPEDIT 18 0 "n,p" "6$%\"nG%\"pG" }{TEXT -1 2 ")." }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 257 "" 0 "" {TEXT -1 19 "Exercice corrig \351 3:" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "" 0 "" {TEXT 462 6 "Ex 3.1" }{TEXT -1 77 "\nEcrire une proc\351dure calculant le plus grand de 3 entiers naturels non nuls " }{TEXT 382 1 "a" } {TEXT -1 1 "," }{TEXT 383 1 "b" }{TEXT -1 1 "," }{TEXT 384 1 "c" } {TEXT -1 1 "." }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 169 "max3:=proc(a::pos int,b::posint,c::posint)\n local max2;\n max2:=proc(x::posint,y::pos int)\n if x>y then x else y end if;\n end proc;\n max2(a,max2( b,c));\n end proc;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%max3Gf*6%'%\" aG%'posintG'%\"bGF)'%\"cGF)6#%%max2G6\"F0C$>8$f*6$'%\"xGF)'%\"yGF)F0F0 F0@%29%9$F=F " 0 " " {MPLTEXT 1 0 17 "max3(5!,5^3,123);" }}{PARA 11 "" 1 "" {XPPMATH 20 " 6#\"$D\"" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 380 4 "max3" }{TEXT -1 30 " \+ comporte une variable locale " }{TEXT 381 4 "max2" }{TEXT -1 94 " \340 laquelle est affect\351e une proc\351dure calculant le\nplus grand de 2 entiers naturels non nuls." }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }} {EXCHG {PARA 0 "" 0 "" {TEXT 463 6 "Ex 3.2" }{TEXT -1 21 "\n1\260 \311 crire un module " }{TEXT 466 3 "pnt" }{TEXT -1 74 " permettant de mod \351liser un point du plan, d\351fini par ses coordonn\351es\n " } {TEXT 464 1 "x" }{TEXT -1 1 "," }{TEXT 465 1 "y" }{TEXT -1 116 ". Ce m odule comportera des variables locales export\351es rendant comme r \351sultat l'abscisse\n et l'ordonn\351e du point." }}{PARA 0 "" 0 "" {TEXT -1 21 "\n2\260 \311crire un module " }{TEXT 467 6 "cercle" } {TEXT -1 237 " permettant de mod\351liser un cercle du plan, d\351fini par son centre et \n son rayon. Ce module comportera des variables locales export\351es rendant comme r\351sultat le\n centre, le ray on, le diam\350tre, l'aire, et la circonf\351rence du cercle." }}} {PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 30 "1 \260 D\351finition de la proc\351dure " }{TEXT 468 3 "pnt" }{TEXT -1 34 " rendant pour r\351sultat un module: " }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 120 "pnt:=proc(x,y)\n module()\n export abscisse,or donnee;\n abscisse:=()->x;\n ordonnee:=()->y;\n end module\nend proc;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$pntGf*6$%\"xG%\"yG6\"F)F) b6#%+thismoduleGF)F)6$%)abscisseG%)ordonneeGC$>8$f*F)F)6$%)operatorG%& arrowGF)T$F)F)6$F'F7>8%f*F)F)F4F)F7F)F)6$F(T&F)F)6&F'9$F(9%F)F)F)F)" } }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 22 " D\351finition d'un point " }{TEXT 475 1 "A" }{TEXT -1 17 " de coordonn \351es (" }{TEXT 469 1 "a" }{TEXT -1 1 "," }{TEXT 470 1 "b" }{TEXT -1 3 ") :" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "A:=pnt(a,b);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"AG`6$%)abscisseG%)ordonneeGb6#%+th ismoduleG6\"F,6$%)abscisseG%)ordonneeGF,F,F,6&%\"xG%\"aG%\"yG%\"bG6\"6 \"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "A:-abscisse(), A:-ord onnee();" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$%\"aG%\"bG" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 30 "2\260 D\351fi nition de la proc\351dure " }{TEXT 471 6 "cercle" }{TEXT -1 34 " renda nt pour r\351sultat un module: " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 230 "cercle:=proc(c,r)\n module()\n export centre,rayon,diamet re,aire,circonference;\n centre:=()->c;\n rayon:=()->r;\n dia metre:=()->2*rayon();\n aire:=()->Pi*r^2;\n circonference:=()->P i*diametre();\n end module\nend proc;" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%'cercleGf*6$%\"cG%\"rG6\"F)F)b6#%+thismoduleGF)F)6'%'centreG%& rayonG%)diametreG%%aireG%.circonferenceGC'>8$f*F)F)6$%)operatorG%&arro wGF)T$F)F)6$F'F:>8%f*F)F)F7F)F:F)F)6$F(T&>8&f*F)F)F7F),$-T#F)\"\"#F)F) 6$F/F=>8'f*F)F)F7F)*&%#PiG\"\"\")F:FGFNF)F)F?>8(f*F)F)F7F)*&FMFNFEFNF) F)6$F0FBF)F)6&F'9$F(9%F)F)F)F)" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }} {EXCHG {PARA 0 "" 0 "" {TEXT -1 23 "D\351finition d'un cercle " } {TEXT 472 1 "C" }{TEXT -1 11 " de centre " }{TEXT 473 1 "A" }{TEXT -1 10 " de rayon " }{TEXT 474 1 "R" }{TEXT -1 1 ":" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 15 "C:=cercle(A,R);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"CG`6'%'centreG%&rayonG%)diametreG%%aireG%.circonferenceGb6#% +thismoduleG6\"F/6'%'centreG%&rayonG%)diametreG%%aireG%.circonferenceG F/F/F/6&%\"cG%\"AG%\"rG%\"RG6\"6\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 70 "C:-centre(), C:-rayon(), C:-diametre(), C:-aire(), C: -circonference();" }}{PARA 11 "" 1 "" {XPPMATH 20 "6'%\"AG%\"RG,$F$\" \"#*&%#PiG\"\"\")F$F&F),$*&F(F)F$F)F&" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 74 "Utilisation des deux structures pour obtenir les coordonn \351es du centre de " }{TEXT 476 1 "C" }{TEXT -1 1 ":" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 50 "C:-centre():-abscisse(), C:-centre( ):-ordonnee(); " }}{PARA 11 "" 1 "" {XPPMATH 20 "6$%\"aG%\"bG" }}} {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 257 "" 0 "" {TEXT -1 17 "Travail dirig\351 3:" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "" 0 " " {TEXT 314 7 "TD 3.1:" }}{PARA 0 "" 0 "" {TEXT -1 21 "\311crire une p roc\351dure " }{TEXT 316 19 "second_degr\351(a,b,c)" }{TEXT -1 40 " qu i r\351sout l'\351quation du second degr\351 \340" }}{PARA 0 "" 0 "" {TEXT -1 20 "coefficients r\351els: " }{XPPEDIT 18 0 "a*x^2+b*x+c = 0; " "6#/,(*&%\"aG\"\"\"*$%\"xG\"\"#F'F'*&%\"bGF'F)F'F'%\"cGF'\"\"!" } {TEXT -1 53 " en distinguant 3 cas selon le signe du discriminant." }} }{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "" 0 "" {TEXT 315 7 "T D 3.2:" }}{PARA 0 "" 0 "" {TEXT -1 21 "\311crire une proc\351dure " } {TEXT 317 8 "somme(n)" }{TEXT -1 11 " calculant " }{TEXT 318 13 "r\351 cursivement" }{TEXT -1 25 " la somme des entiers de " }{TEXT 319 1 "0 " }{TEXT -1 3 " \340 " }{TEXT 320 1 "n" }{TEXT -1 7 " , pour" }}{PARA 0 "" 0 "" {TEXT 321 1 "n" }{TEXT -1 22 " entier naturel donn\351." }}} {PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "" 0 "" {TEXT 322 7 "TD 3.3:" }}{PARA 0 "" 0 "" {TEXT -1 21 "\311crire une proc\351dure " } {TEXT 323 12 "renverser(n)" }{TEXT -1 40 " , qui , \351tant donn\351 u n entier naturel " }{TEXT 324 1 "n" }{TEXT -1 21 " ne comportant pas \+ de" }}{PARA 0 "" 0 "" {TEXT -1 86 "0 dans son \351criture d\351cimale \+ , rend pour r\351sultat l'\351criture renvers\351e de cet entier ." }} {PARA 0 "" 0 "" {TEXT -1 62 "Pr\351voir un message d'erreur si l'entie r comporte le chiffre 0." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 325 8 "Exemple:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "renverser(122564);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6 #\"'@_Y" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "renverser(120325 );" }}{PARA 8 "" 1 "" {TEXT -1 54 "Error, (in renverser) le chiffre 0 \+ n'est pas autoris\351." }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "" 0 "" {TEXT 477 7 "TD 3.4:" }}{PARA 0 "" 0 "" {TEXT -1 17 " \311crire un module " }{TEXT 478 7 "segment" }{TEXT -1 290 " permettan t de mod\351liser un segment du plan, d\351fini par ses deux\npoints e xtr\351mit\351s.Ce module comportera des variables locales export\351e s rendant comme\nr\351sultat la premi\350re et la seconde extr\351mit \351 du segment, sa longueur, et son milieu. \nOn pourra utiliser le \+ module d\351fini par la proc\351dure " }{TEXT 480 3 "pnt" }{TEXT -1 23 " de l'exercice corrig\351 " }{TEXT 479 3 "3.2" }{TEXT -1 1 "." }}} {PARA 0 "" 0 "" {TEXT -1 0 "" }}}{MARK "2 0" 39 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }