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:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: ::::::::::::::::::::::::::::::::::::::::<:J\\;E_>L<;:E_ymy;:::::::::::BsZ>W=vY::::::::::::::::::::::::::::: ::t@W\\HKAsyvY:::XGW\\H;jUsyvY:::::::::::::::::::::::::::::::::::::::: ::::::::::::::tBW\\HKqryvY:::::::::::::::::JA;W\\h;xI::::::::::::::::: :::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::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 260 "" 0 "" {TEXT 368 24 "CHAPITR E 2: LES \311L\311MENTS" }{TEXT 450 1 "\n" }{TEXT 449 16 "DE BASE DE M APLE" }}{PARA 19 "" 0 "" {TEXT -1 39 "\251 Apprendre Maple. Alain Le S tang. 2006" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 256 14 "LES VARIABLES:" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 4 "Une " }{TEXT 257 8 "variable" }{TEXT -1 80 " informatique est l'adresse , dans la m \351moire de l'ordinateur , d'un emplacement" }}{PARA 0 "" 0 "" {TEXT -1 49 "permettant de stocker un objet d'un type donn\351 . " }}{PARA 0 "" 0 "" {TEXT 258 9 "Exemples:" }{TEXT -1 62 " AB, aB , X1, _var , \+ x[a] sont des noms de variables MAPLE . " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 65 "Si l'on affecte \340 une variable \+ une valeur , la variable est dite " }{TEXT 259 8 "assign\351e" }{TEXT -1 1 "." }}{PARA 0 "" 0 "" {TEXT -1 62 "Si elle n'est associ\351e \340 aucune valeur , la variable est dite " }{TEXT 260 12 "non assign\351e " }{TEXT -1 1 "." }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 " " 0 "" {TEXT -1 12 "La fonction " }{TEXT 261 7 "restart" }{TEXT -1 70 " permet de r\351initialiser toutes les variables de la feuille de cal cul." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart;" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "" 0 "" {TEXT 262 4 "var " } {TEXT -1 49 "est une variable assign\351e, dont la valeur est 3 :" }} {PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "var:=3;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$varG\"\"$" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 11 "La variable" }{TEXT 264 3 " a " }{TEXT -1 22 "et la variable indic\351e " }{TEXT 265 1 " " }{XPPEDIT 18 0 "x[a]" "6#&%\"xG6#%\"aG" }{TEXT 263 1 " " }{TEXT -1 20 "sont non assign\351es :" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "a,x[a];" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$%\"aG&%\"xG 6#F#" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 82 "Une autre mani\350re d'af fecter une valeur \340 une variable est d'utiliser la fonction " } {TEXT 436 6 "assign" }{TEXT -1 1 ":" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "assign(nom,10-var);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 4 "n om;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"(" }}}{EXCHG {PARA 0 "" 0 " " {TEXT -1 93 "Pour d\351saffecter une variable assign\351e, lui affec ter son nom \351crit entre deux accents aigus :" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "nom:='nom':nom;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%$ nomG" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 35 "On peut aussi utiliser la fonction " }{TEXT 437 5 "evaln" }{TEXT -1 22 " (\351valuer en un nom) :" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "var:=evaln(var):var;" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#%$varG" }}}{PARA 6 "" 1 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 266 15 "LES CONSTANTES:" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "" 0 " " {TEXT 267 4 "true" }{TEXT -1 3 " , " }{TEXT 268 5 "false" }{TEXT -1 36 " (valeurs bool\351ennes vrai , faux) , " }{TEXT 269 2 "I " }{TEXT 272 1 " " }{TEXT -1 25 "(complexe de carr\351 -1) , " }{TEXT 270 2 "Pi " }{TEXT -1 14 " (nombre pi) ," }}{PARA 0 "" 0 "" {TEXT 271 9 "infinit y " }{TEXT -1 43 " (plus l'infini) sont des constantes MAPLE." }} {PARA 0 "" 0 "" {TEXT 273 1 "E" }{TEXT -1 74 " (base des logarithmes \+ n\351p\351riens) n'est pas une constante MAPLE : faire " }{TEXT 274 7 "exp(1)." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "eval(exp(1))= evalf(exp(1));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/-%$expG6#\"\"\"$\"+ G=G=F!\"*" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "" 0 "" {TEXT 275 17 "LES EXPRESSIONS :" }}} {PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 90 "El les sont \351valu\351es de la gauche vers la droite , avec la priorit \351 usuelle des op\351rateurs." }}{PARA 0 "" 0 "" {TEXT -1 53 "Pour a fficher une expression, utiliser les fonctions " }{TEXT 276 6 "lprint " }{TEXT -1 4 " ou " }{TEXT 277 5 "print" }{TEXT -1 2 " :" }}{PARA 0 " " 0 "" {TEXT -1 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "lprint(1-2/a +(a+1)/(a-5));" }}{PARA 6 "" 1 "" {TEXT -1 17 "1-2/a+(a+1)/(a-5)" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "print(1-2/a+(a+1)/(a-5));" } }{PARA 11 "" 1 "" {XPPMATH 20 "6#,(\"\"\"F$*&\"\"#F$%\"aG!\"\"F(*&,&F' F$F$F$F$,&F'F$\"\"&F(F(F$" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 22 "Tout e expression a un " }{TEXT 278 4 "type" }{TEXT -1 43 " que l'on peut o btenir gr\342ce \340 la fonction " }{TEXT 279 8 "whattype" }{TEXT -1 2 " :" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 100 "Parmi les types possibles figurent : + (somme) , * (produit) , ^ (pui ssance) , = (\351galit\351) , <> (non" }}{PARA 0 "" 0 "" {TEXT -1 106 "\351galit\351) , < , <= (in\351galit\351 au sens strict ou large) , a nd , or , not (et,ou,non) , integer (nb entier) ," }}{PARA 0 "" 0 "" {TEXT -1 96 "fraction (nb rationnel) , float (nb r\351el en virgule fl ottante) , complex (nb complexe) , numeric" }}{PARA 0 "" 0 "" {TEXT -1 182 "(num\351rique) , symbol (symbole), string (cha\356ne de carac t\350res) , list (liste) , set (ensemble) ,\n table (table) , array(ta bleau) , function (fonction) , name (nom) , .. (intervalle)." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 92 "whattype( a+b),whattype(a>b),whattype(-1.2245),whattype(a^7),whattype((a and b) \+ or (c or d));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6'%\"+G%\" " 0 "" {MPLTEXT 1 0 82 "whattype(x-2/y), whattype(a/b),whattype(`MAPLE`),whattype(\"MAPLE\"),whattype(\{a,b\}); " }}{PARA 11 "" 1 "" {XPPMATH 20 "6'%\"+G%\"*G%'symbolG%'stringG%$setG " }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 74 "On peut tester si une expression a un type donn\351 en utilisant l a fonction " }{TEXT 280 4 "type" }{TEXT -1 2 " :" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "type(x,name),type(a+3*x-7/5,list);" }}{PARA 11 "" 1 " " {XPPMATH 20 "6$%%trueG%&falseG" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 281 18 "Autres fonctions :" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "expr:=x-3 *y+5/(x+y);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%exprG,(%\"xG\"\"\"*& \"\"$F'%\"yGF'!\"\"*&\"\"&F',&F&F'F*F'F+F'" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 282 16 "nops(expression)" }{TEXT -1 45 " donne le nombre d'op \351randes de l'expression:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "nops(expr);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"$" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 283 16 "op(i,expression)" }{TEXT -1 41 " donne l e i-\350me op\351rande de l'expression:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "op(2,expr);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$%\"y G!\"$" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 284 19 "op(i..j,expression)" } {TEXT -1 56 " donne les op\351randes de l'expression, du i-\350me au j -\350me:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "op(2..3,expr); \+ " }}{PARA 11 "" 1 "" {XPPMATH 20 "6$,$%\"yG!\"$,$*&\"\"\"F(,&%\"xGF(F $F(!\"\"\"\"&" }}}{PAGEBK }{PARA 0 "" 0 "" {TEXT 285 32 "Transformatio n des expressions :" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 64 "Regrouper certains termes selon une ou plusieurs \+ variables avec " }{TEXT 286 22 "collect(expression,v) " }{TEXT -1 2 "; " }{TEXT 287 1 "v" }{TEXT -1 20 " est une variable ou" }}{PARA 0 "" 0 "" {TEXT -1 24 "une liste de variables :" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 52 "expr:=x^3*ln(x)+3*x^2+ln( x)*x-x:collect(expr,ln(x));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,(*&,&* $)%\"xG\"\"$\"\"\"F*F(F*F*-%#lnG6#F(F*F**&F)F*)F(\"\"#F*F*F(!\"\"" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 56 "expr:=x^2+5*x-25*y+48*(x-2*y +7)+y^3:collect(expr,[x,y]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,,*$)% \"xG\"\"#\"\"\"F(*&\"#`F(F&F(F(*&\"$@\"F(%\"yGF(!\"\"\"$O$F(*$)F-\"\"$ F(F(" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 34 "Transformer en un seul terme avec " }{TEXT 288 24 "combine(expr ession,noms)" }{TEXT -1 3 " : " }}{PARA 0 "" 0 "" {TEXT -1 13 "Le para m\350tre " }{TEXT 289 4 "noms" }{TEXT -1 73 " est optionnel et \340 ch oisir par exemple parmi : exp , ln , trig , power ." }}{PARA 0 "" 0 " " {TEXT -1 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 43 "combine(2*Sum(i^2 ,i=1..n)+Sum(i^3,i=1..n));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%$SumG6 $,&*$)%\"iG\"\"#\"\"\"F**$)F)\"\"$F+F+/F);F+%\"nG" }}}{EXCHG {PARA 0 " > " 0 "" {MPLTEXT 1 0 58 "combine(exp(sin(a)*cos(b))/exp(cos(a)*sin(b) ),[trig,exp]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%$expG6#-%$sinG6#,& %\"aG\"\"\"%\"bG!\"\"" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 31 "Simplifier une expression avec " }{TEXT 290 18 "normal(expression)" }{TEXT -1 42 " , simplifier une expression contenant des" }}{PARA 0 "" 0 "" {TEXT -1 13 "radicaux avec" }{TEXT 291 20 " radsimp(expression)" }{TEXT -1 3 " : " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "normal( 1/x+x/(x+1) );" }{TEXT -1 0 "" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*(,(%\"xG\"\"\"F &F&*$)F%\"\"#F&F&F&F%!\"\",&F%F&F&F&F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 32 "normal( 1/x+x/(x+1), expanded );" }{TEXT -1 0 "" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#*&,(%\"xG\"\"\"F&F&*$)F%\"\"#F&F&F&,&F 'F&F%F&!\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 37 "radsimp((x- 1)*sqrt(x*x-2*x+1)*(x+1));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*&),&%\" xG\"\"\"F'!\"\"\"\"#F',&F&F'F'F'F'" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" } }{EXCHG {PARA 0 "" 0 "" {TEXT -1 29 "Ordonner une expression avec " } {TEXT 369 18 "sort(expression,v)" }{TEXT -1 2 "; " }{TEXT 370 1 "v" } {TEXT -1 45 " est une variable ou une liste de variables :" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "sort(expr,y);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,,*$)%\"yG\"\"$\"\"\"F(*&\"$@\"F(F&F(!\"\"*&\"#`F(%\"xG F(F(\"$O$F(*$)F.\"\"#F(F(" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 31 "Ordo nner selon un crit\350re avec " }{TEXT 292 21 "sort(liste,param\350tre )" }{TEXT -1 3 " ; " }{TEXT 293 5 "liste" }{TEXT -1 27 " est une liste de valeurs ," }}{PARA 0 "" 0 "" {TEXT 294 9 "param\350tre" }{TEXT -1 92 " = `<` ou `>` (ordre croissant, d\351croissant) , lexorder ou str ing (ordre lexicographique) ." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }} {PARA 0 "> " 0 "" {MPLTEXT 1 0 56 "liste1:=[12,-2,5,1]:liste2:=[s,q,a, g,h,p,z,j,l,m,o,b,i]:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 39 "so rt(liste1,`>`),sort(liste2,lexorder);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$7&\"#7\"\"&\"\"\"!\"#7/%\"aG%\"bG%\"gG%\"hG%\"iG%\"jG%\"lG%\"mG%\"o G%\"pG%\"qG%\"sG%\"zG" }}}{PAGEBK }{PARA 0 "" 0 "" {TEXT -1 0 "" }} {EXCHG {PARA 0 "" 0 "" {TEXT -1 54 "Transformer une expression selon l e mod\350le forme avec " }{TEXT 295 25 "convert(expression,forme)" } {TEXT -1 2 " :" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 31 "sin(2*x)= convert(sin(2*x),tan);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/-%$sinG6#,$ %\"xG\"\"#,$*&-%$tanG6#F(\"\"\",&F/F/*$)F,F)F/F/!\"\"F)" }}}{PARA 0 " " 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 29 "Faire des s ubstitutions avec " }{TEXT 296 33 "subs(eq1,eq2,...,eqn,expression):" }{TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 38 "expr;\nsub s(x=lambda,y=2*t,expr);\nexpr;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,,*$ )%\"yG\"\"$\"\"\"F(*&\"$@\"F(F&F(!\"\"*&\"#`F(%\"xGF(F(\"$O$F(*$)F.\" \"#F(F(" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,,*$)%\"tG\"\"$\"\"\"\"\")* &\"$U#F(F&F(!\"\"*&\"#`F(%'lambdaGF(F(\"$O$F(*$)F/\"\"#F(F(" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,,*$)%\"yG\"\"$\"\"\"F(*&\"$@\"F(F&F(!\"\"*& \"#`F(%\"xGF(F(\"$O$F(*$)F.\"\"#F(F(" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 16 "On constate que " }{TEXT 371 4 "expr" }{TEXT -1 16 " n'a pas ch ang\351." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "subsop(1=w,2=-t ,4=mu,expr); " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,,%\"wG\"\"\"%\"tG! \"\"*&\"#`F%%\"xGF%F%%#muGF%*$)F*\"\"#F%F%" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 34 "L'op\351rande n\2601 a \351t\351 remplac\351 par " } {TEXT 297 1 "w" }{TEXT -1 36 ", l'op\351rande n\2602 a \351t\351 rempl ac\351 par " }{XPPEDIT 18 0 "-t;" "6#,$%\"tG!\"\"" }{TEXT -1 15 " et l e n\2604 par " }{XPPEDIT 18 0 "mu;" "6#%#muG" }{TEXT -1 1 "." }}} {PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 27 "On peut \351galement utiliser " }{TEXT 451 21 "use ... in .. end use" } {TEXT -1 2 " :" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 49 "use x=4*r ho, y=h, z=mu in \n (x+y-z+3)^7\nend use;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*$),*%$rhoG\"\"%%\"hG\"\"\"%#muG!\"\"\"\"$F)\"\"(F)" }} }{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 49 "A ppliquer une fonction \340 tous les op\351randes avec " }{TEXT 298 24 "map(fonction,expression)" }{TEXT -1 1 ";" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 17 "map(x->x^2,expr);" }}{PARA 11 "" 1 "" {XPPMATH 20 " 6#,,*$)%\"yG\"\"'\"\"\"F(*&\"&TY\"F()F&\"\"#F(F(*&\"%4GF()%\"xGF,F(F( \"''*G6F(*$)F0\"\"%F(F(" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 45 "Isoler une expression dans une \351quatio n avec " }{TEXT 299 28 "isolate(equation,expression)" }{TEXT -1 1 ";" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 48 "expr:=-x^3+2*(sqrt(y-sin( x))+1):isolate(expr,y);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/%\"yG,&*$) ,&*$)%\"xG\"\"$\"\"\"#F-\"\"#F-!\"\"F/F-F--%$sinG6#F+F-" }}}{PARA 0 " " 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 53 "Obtenir le \+ membre gauche ou droit d'une \351galit\351 avec " }{TEXT 372 16 "lhs(e xpression);" }{TEXT -1 4 " ou " }{TEXT 373 16 "rhs(expression);" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "lhs(%);rhs(%%);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%\"yG" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,&*$), &*$)%\"xG\"\"$\"\"\"#F+\"\"#F+!\"\"F-F+F+-%$sinG6#F)F+" }}}{PAGEBK } {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 431 14 "LES FONC TIONS:" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 17 "Pour d\351finir une " }{TEXT 435 8 "fonction" }{TEXT -1 34 " , on peut utiliser les syntaxes :" }}{PARA 0 "" 0 "" {TEXT -1 0 " " }}{PARA 0 "" 0 "" {TEXT -1 57 "nom := var -> expr; pour une fonctio n d'une variable var" }}{PARA 0 "" 0 "" {TEXT -1 92 "nom := (var1,var2 ,...,varN) -> expr; pour une fonction de N variables var1,var2,...,v arN ." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "f:=x->exp(x)-x;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"fGf*6#%\" xG6\"6$%)operatorG%&arrowGF(,&-%$expG6#9$\"\"\"F0!\"\"F(F(F(" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "f:=(x,y,z,t)->x^2-3*y+4*z-t; " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"fGf*6&%\"xG%\"yG%\"zG%\"tG6\"6 $%)operatorG%&arrowGF+,**$)9$\"\"#\"\"\"F4*&\"\"$F49%F4!\"\"*&\"\"%F49 &F4F49'F8F+F+F+" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 12 "La fonction " }{TEXT 432 7 "unapply" }{TEXT -1 73 "( expr,var1,var2,...,varN) permet de transformer l'expression expr en u ne" }}{PARA 0 "" 0 "" {TEXT -1 44 "fonction des N variables var1,var2, ...,varN:" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 43 "expr:=u^2-3*v+4*w : f:=unapply(expr,u,v,w);" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"fGf*6%% \"uG%\"vG%\"wG6\"6$%)operatorG%&arrowGF*,(*$)9$\"\"#\"\"\"F3*&\"\"$F39 %F3!\"\"*&\"\"%F39&F3F3F*F*F*" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }} {EXCHG {PARA 0 "" 0 "" {TEXT 433 26 "Composition des fonctions:" } {TEXT -1 32 " l'op\351rateur @ , l'op\351rateur de " }{TEXT 434 18 "co mposition it\351r\351e" }{TEXT -1 3 " @@" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 42 "f:=u->u^3:g:=t->2*t+1: \n(f@ g)(a);(g@f)(a);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*$),&%\"aG\"\"#\"\" \"F(\"\"$F(" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,&*$)%\"aG\"\"$\"\"\"\" \"#F(F(" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 45 "f@@N correspond \340 f o f o . . . o f (N fois)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "(f@@3)(u);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*$)%\"uG\"#F\"\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 45 "(D@@2)(f); # fonction \+ d\351riv\351e seconde de f" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#f*6#%\"u G6\"6$%)operatorG%&arrowGF&,$9$\"\"'F&F&F&" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 300 18 "LES TYPES DE BASE:" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 386 20 "LES TYPES NUM\311RIQUES" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 29 "On peut utiliser la fonc tion " }{TEXT 452 6 "assume" }{TEXT -1 29 " pour imposer une condition :\n" }{TEXT 453 8 "Exemple:" }{TEXT -1 13 " on impose \340 " }{TEXT 454 1 "r" }{TEXT -1 14 " la condition " }{XPPEDIT 18 0 "0 < r;" "6#2\" \"!%\"rG" }{TEXT -1 5 " ( " }{TEXT 459 1 "r" }{TEXT -1 39 " est alor s affich\351 suivi d'une tilde: " }{TEXT 458 1 "r" }{TEXT 455 1 " " } {TEXT -1 3 "~ )" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "assume(r ,positive);r;\nsign(r);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%#r|irG" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"\"" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 12 "La fonction " }{TEXT 456 5 "a bout" }{TEXT -1 51 " permet d'obtenir une information sur une variable :" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "about(r);" }}{PARA 6 " " 1 "" {TEXT -1 25 "Originally r, renamed r~:" }}{PARA 6 "" 1 "" {TEXT -1 47 " is assumed to be: RealRange(Open(0),infinity)" }}{PARA 6 "" 1 "" {TEXT -1 0 "" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "" 0 "" {TEXT 301 11 "LES ENTIERS " }{TEXT -1 28 " : ce sont des objets de typ" }{TEXT 303 2 "e " } {TEXT -1 7 "integer" }{TEXT 302 3 " . " }}{PARA 0 "" 0 "" {TEXT -1 19 "Un entier peut \352tre" }{TEXT 304 17 " positive (>0) , " }{TEXT -1 1 " " }{TEXT 305 8 "negative" }{TEXT -1 8 " (<0), " }{TEXT 306 6 "non neg" }{TEXT -1 10 " (>=0) , " }{TEXT 307 7 " posint" }{TEXT -1 14 " ( entier>0) , " }}{PARA 0 "" 0 "" {TEXT 308 6 "negint" }{TEXT -1 14 " (e ntier<0) , " }{TEXT 309 10 "nonnegint " }{TEXT -1 14 "(entier>=0) , " }{TEXT 310 4 "even" }{TEXT -1 10 " (pair) , " }{TEXT 311 3 "odd" } {TEXT -1 12 " (impair) , " }{TEXT 312 9 "primeint " }{TEXT -1 10 "(pre mier)." }}{PARA 0 "" 0 "" {TEXT -1 28 "Ce que l'on peut tester avec" } {TEXT 313 6 " type" }{TEXT -1 4 " ou " }{TEXT 314 3 " is" }{TEXT -1 1 "." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "type(-15,negint), is(13,even);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$%%trueG%&falseG" }}}{EXCHG {PARA 6 "" 1 "" {TEXT -1 0 " " }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 75 "On peut s\351lectionner des \351l\351ments r\351pondant \340 une c ondition bool\351enne avec " }{TEXT 374 21 "select(condition,v);\n" } {TEXT 375 8 "Exemple:" }{TEXT -1 64 " s\351lectionner dans une liste d e nombres ceux qui sont entiers >0" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 55 "select(x->type(x,posint),[-1/2,-7,Pi,3/4,0.25,18,2^5] );" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7$\"#=\"#K" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "" 0 "" {TEXT 315 41 "Quelques fonction s utilisant les entiers:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 33 "q:=iquo(89,-12);r:=irem(89,-12); " }}{PARA 11 "" 1 "" {XPPMATH 20 "6# >%\"qG!\"(" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"rG\"\"&" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 93 "( quotient et reste de la division euclid ienne de a par b : a =bq +r , avec |r|<|b| , ici" }}{PARA 0 "" 0 " " {TEXT -1 24 " 89 = (-12) (-7) + 5 )" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 18 "54 est-il premier?" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "isprime(54); " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%&falseG" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 50 "nombre premier sui vant , nombre premier pr\351c\351dent:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "nextprime(215),prevprime(215);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$\"$B#\"$6#" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 25 "Le 1 7 \350me nombre premier:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "ithprime(17);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"#f" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 35 "D\351composition en facteurs premiers:" } }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "ifactor(117208);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#**)-%!G6#\"\"#\"\"$\"\"\")-F&6#\"\"(F(F*-F&6 #\"#8F*-F&6#\"#BF*" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 40 "Le ppcm et \+ le pgcd de plusieurs entiers:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "ilcm(20,25,15);igcd(20,25,15);" }}{PARA 11 "" 1 "" {XPPMATH 20 " 6#\"$+$" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"&" }}}{EXCHG {PARA 0 " " 0 "" {TEXT -1 31 "Le plus petit ou le plus grand:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 46 "min(712,56,100,25,125),max(712,56,100,25, 125);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$\"#D\"$7(" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 376 3 "mod" }{TEXT 425 1 " " }{TEXT -1 2 " (" }{TEXT 426 1 "a" }{TEXT -1 8 " modulo " }{TEXT 427 1 "n" }{TEXT -1 34 " donne le reste de la division de " }{TEXT 428 1 "a" }{TEXT -1 4 " par" } {TEXT 429 2 " n" }{TEXT -1 18 ", ici 31=4*7+3 ) :" }}}{EXCHG {PARA 0 " > " 0 "" {MPLTEXT 1 0 9 "31 mod 4;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6# \"\"$" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 316 7 "rand(n)" }{TEXT -1 76 " \+ rend une fonction (appel\351e ici hasard) calculant un entier al\351at oire entre " }{TEXT 317 1 "0" }{TEXT -1 4 " et " }{XPPEDIT 18 0 "n-1; " "6#,&%\"nG\"\"\"F%!\"\"" }{TEXT -1 1 "." }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 31 "hasard:=rand(100):h:=hasard(); " }}{PARA 11 "" 1 " " {XPPMATH 20 "6#>%\"hG\"#\")" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 9 "F onction " }{TEXT 377 4 "sign" }{TEXT -1 30 ": cette fonction rend : -1 si " }{XPPEDIT 18 0 "n < 0;" "6#2%\"nG\"\"!" }{TEXT -1 8 " , 1 si " } {XPPEDIT 18 0 "0 <= n;" "6#1\"\"!%\"nG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "n:=-7;sign(n);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>% \"nG!\"(" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#!\"\"" }}}{EXCHG {PARA 0 " " 0 "" {TEXT -1 24 "Fonction valeur absolue:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "abs(n); " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"( " }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "" 0 "" {TEXT 318 14 "LES RATIONNELS" }{TEXT -1 30 " : ce sont des objets de type " } {TEXT 319 8 "fraction" }{TEXT -1 5 " (ou " }{TEXT 320 8 "rational" } {TEXT -1 3 ") ." }}{PARA 0 "" 0 "" {TEXT -1 23 "Un rationnel peut \352 tre " }{TEXT 321 8 "positive" }{TEXT -1 8 " (>0) , " }{TEXT 322 10 " n egative " }{TEXT -1 8 "(<0) , " }{TEXT 323 6 "nonneg" }{TEXT -1 36 " \+ (>=0) , ce qui peut \352tre test\351 par" }}{PARA 0 "" 0 "" {TEXT 324 4 "type" }{TEXT -1 4 " ou " }{TEXT 325 3 "is " }{TEXT -1 26 "(comm e pour les entiers). " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 326 44 "Quelques fonctions utilisant les rationnels:" }} {PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "q:=21*(144/124);numer(q);denom(q); " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"qG#\"$c(\"#J" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"$c(" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"#J" }}} {EXCHG {PARA 0 "" 0 "" {TEXT -1 50 "Comme pour les entiers , on a auss i les fonctions " }{TEXT 327 6 "assume" }{TEXT -1 3 " , " }{TEXT 328 3 "min" }{TEXT -1 3 " , " }{TEXT 329 3 "max" }{TEXT -1 3 " , " }{TEXT 330 4 "sign" }{TEXT -1 3 " , " }{TEXT 331 4 "abs." }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "" 0 "" {TEXT 332 9 "LES REELS" }{TEXT -1 19 " : un r\351el de type " }{TEXT 333 5 "float" }{TEXT -1 9 " , a \+ une " }{TEXT 334 8 "mantisse" }{TEXT -1 7 " et un " }{TEXT 335 8 "expo sant" }{TEXT -1 1 "." }}{PARA 0 "" 0 "" {TEXT 336 8 "Exemple:" }{TEXT -1 30 " 1234567=0.1234567*10^7 . La " }{TEXT 337 8 "mantisse" }{TEXT -1 20 " est 0.1234567 , et " }{TEXT 338 10 "l'exposant" }{TEXT -1 4 " \+ 7 ." }}{PARA 0 "" 0 "" {TEXT -1 37 "Le nombre s'\351crit Float(0.12345 67,7);" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "evalf(Float(0.1234567,7));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6# $\"(nXB\"\"\"!" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 23 "L'utilisation d u point " }{TEXT 430 1 "." }{TEXT -1 64 " d\351clenche l'affichage en \+ calcul flottant dans le second membre:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "1/9=1.0/9; " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/#\"\" \"\"\"*$\"+66666!#5" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }{TEXT 339 7 "Digits " }{TEXT -1 95 "est une variable d'environnement repr \351sentant le nombre de d\351cimales affich\351es (10 par d\351faut). " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "Digits:=30:evalf(exp(1) );" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"?NruGg`BX!f%G=G=F!#H" }}} {PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "" 0 "" {TEXT 340 39 "Q uelques fonctions utilisant les r\351els:" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 341 4 "abs " }{TEXT -1 2 ", " }{TEXT 342 4 "sqrt" }{TEXT -1 19 " (racine carr\351e) , " }{TEXT 343 4 "exp " } {TEXT -1 1 "," }{TEXT 344 3 " ln" }{TEXT -1 3 " , " }{TEXT 345 5 "log1 0" }{TEXT -1 3 " , " }{TEXT 346 6 "log[a]" }{TEXT -1 26 " (logarithme \+ de base a) , " }{TEXT 347 21 "sin , cos , tan , cot" }{TEXT -1 1 " " } }{PARA 0 "" 0 "" {TEXT -1 26 "(fonctions circulaires) , " }{TEXT 348 25 "sinh , cosh , tanh , coth" }{TEXT -1 29 " (fonctions hyperboliques ) , " }{TEXT 349 14 "arcsin ,arccos" }{TEXT -1 3 " , " }}{PARA 0 "" 0 "" {TEXT 350 15 "arctan , arccot" }{TEXT -1 39 " (fonctions circulaire s r\351ciproques) , " }{TEXT 366 37 "arcsinh , arccosh , arctanh , arc coth" }}{PARA 0 "" 0 "" {TEXT -1 38 "(fonctions hyperboliques r\351cip roques)." }}{PARA 0 "" 0 "" {TEXT -1 12 "La fonction " }{TEXT 353 14 " partie enti\350re" }{TEXT -1 3 ": " }{TEXT 352 8 "floor(x)" }{TEXT -1 46 " est le plus grand entier inf\351rieur ou \351gal \340 " } {TEXT 351 3 "x. " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 32 "sqrt(1250);ln(exp(7));arctan(1);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$*$-%%sqrtG6#\"\"#\"\"\"\"#D" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"(" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$%#PiG#\"\"\" \"\"%" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "floor(-7.98);floor (7.98);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#!\")" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"(" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 457 25 "La fonct ion Gamma d'Euler" }{TEXT -1 1 ":" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 44 "GAMMA(x)=Int(t^(x-1)*exp(-t),t=0..infinity);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#/-%&GAMMAG6#%\"xG-%$IntG6$*&)%\"tG,&F' \"\"\"F/!\"\"F/-%$expG6#,$F-F0F//F-;\"\"!%)infinityG" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "" 0 "" {TEXT 354 13 "LES COMPLEXES " }{TEXT -1 11 " : de type " }{TEXT 355 7 "complex" }{TEXT -1 64 " , s ont constitu\351s de deux r\351els , la partie r\351elle et la partie " }}{PARA 0 "" 0 "" {TEXT -1 12 "imaginaire ." }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 31 "z:=1-5*I*sqrt(2):z,Re(z),Im(z);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%,&\"\"\"F$*&^#!\"&F$-%%sqrtG6#\"\"#F$F$F$,$*$F(F$F'" }} }{EXCHG {PARA 0 "" 0 "" {TEXT 460 5 "evalc" }{TEXT -1 46 " : fonction \+ d'\351valuation des nombres complexes" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 36 "z:=evalc((1+exp(1)^(I*Pi/6))/(1-I));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"zG,(#\"\"\"\"\"%F'*&F&F'-%%sqrtG6#\"\"$F'F'*&, &#F-F(F'*&F&F'F*F'F'F'^#F'F'F'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "Digits:=10:evalf(z);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#^$$\"+ ?q7Io!#5$\"+-F,$=\"!\"*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 " map(evalc,polar(a+I*b));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%&polarG6 $*$-%%sqrtG6#,&*$)%\"aG\"\"#\"\"\"F/*$)%\"bGF.F/F/F/-%'arctanG6$F2F-" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 356 43 "Quelques fonctions utilisant l es complexes:" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 357 37 "abs(z) , argument(z) , conjugate(z) " }{TEXT -1 27 " : \+ module , argument dans " }{TEXT 358 8 "]-Pi,Pi]" }{TEXT 367 1 " " } {TEXT -1 17 ", conjugu\351 de z ." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 47 "z:=1+sqrt(3)*I:abs(z),argument(z),conjugate(z);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6%\"\"#,$%#PiG#\"\"\"\"\"$,&F'F'*&^#!\" \"F'-%%sqrtG6#F(F'F'" }}}{PARA 0 "" 0 "" {TEXT -1 1 "\n" }{TEXT 387 13 "AUTRES TYPES:" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 388 17 "LE TYPE BOOLEAN :" }{TEXT -1 0 "" }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 26 "Les bool\351ens sont de type " }{TEXT 378 7 "boolean" }{TEXT -1 32 " et peuvent prendre 2 valeurs : " }{TEXT 379 6 "false " }{TEXT -1 3 "et " }{TEXT 380 4 "true" }{TEXT -1 2 " ." }}{PARA 0 "" 0 "" {TEXT -1 77 "Si MAPLE ne parvient pas \340 r\351soudre un probl\350 me , il peut rendre le r\351sultat " }{TEXT 381 4 "FAIL" }{TEXT -1 2 " ." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 33 "Les op\351rateurs logiques sont : " }{TEXT 382 4 "not " }{TEXT -1 8 "(n on) , " }{TEXT 383 2 "or" }{TEXT -1 8 " (ou) , " }{TEXT 384 4 "and " } {TEXT -1 7 "(et) , " }{TEXT 390 3 "xor" }{TEXT -1 17 " (ou exclusif) , " }{TEXT 389 8 "implies " }{TEXT -1 14 "(implication)." }}{PARA 0 "" 0 "" {TEXT -1 59 "Une expression bool\351enne peut \352tre \351valu \351e par la fonction " }{TEXT 385 5 "evalb" }{TEXT -1 2 " :" }}{PARA 0 "" 0 "" {TEXT -1 1 " " }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 46 "t:=10:\n evalb(t*t>0),evalb(isprime(t) and t>0);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$%%trueG%&falseG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 31 "ev alb(evalf(exp(1)) " 0 "" {MPLTEXT 1 0 21 "type(a[x],`ind exed`);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%%trueG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "type(nom_var,`indexed`);" }}{PARA 11 "" 1 " " {XPPMATH 20 "6#%&falseG" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 16 "Un nom, de type " }{TEXT 415 4 "name" } {TEXT -1 162 ", est une expression Maple d\351finie \340 partir d'une \+ lettre, suivie d'autres lettres\nou de chiffres, ou d'autres symboles, comme _ ,ou si elle est de type index\351. " }}{PARA 0 "" 0 "" {TEXT -1 98 "Un nom peut aussi \352tre form\351 en entourant une s\351 quence de caract\350res par des accents graves ` `. \n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "type(a[x],`name`);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%%trueG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "type(nom_var,`name`);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%%trueG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "type(a/b,`name`);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#%&falseG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "type(`12345`,`name`);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%%trueG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "type(12345 ,`name`);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%&falseG" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 20 "Un symbole, d e type " }{TEXT 414 7 "symbol," }{TEXT -1 72 " est une expression Mapl e qui est un nom, mais n'est pas de type index\351." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "type(a[x],`symbol`);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%&falseG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 " type(nom_var,`symbol`);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%%trueG" }} }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "type(a/b,`symbol`);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#%&falseG" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "" 0 "" {TEXT 417 39 "Quelques fonctions utilisa nt ces types:" }}{PARA 0 "" 0 "" {TEXT 418 6 "length" }{TEXT -1 1 "(" }{TEXT 419 1 "c" }{TEXT -1 26 ") retourne la longueur de " }{TEXT 420 1 "c" }{TEXT -1 3 " ( " }{TEXT 421 1 "c" }{TEXT -1 31 " \351tant un no m ou un symbole ) ." }}{PARA 0 "" 0 "" {TEXT -1 15 "L'op\351rateur de \+ " }{TEXT 422 18 "concat\351nation || " }{TEXT -1 16 " ou la fonction \+ " }{TEXT 423 3 "cat" }{TEXT -1 45 " permettent de rassembler 2 noms ou symboles." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 16 "length(nom_var);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6 #\"\"(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "nom_var || a;" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#%)nom_varaG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "cat(nom_var,a);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6 #%)nom_varaG" }}}{PARA 0 "" 0 "" {TEXT 411 1 " " }}{PARA 0 "" 0 "" {TEXT 424 37 "LE TYPE CHA\316NE DE CARACT\310RES (string)" }}{PARA 0 " " 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 35 "Les cha\356 nes de caract\350res, de type " }{TEXT 416 6 "string" }{TEXT -1 119 ", se notent entre guillemets \" \" :\npar exemple , \"MAPLE \" et \"7 \+ pour Linux et Windows\" sont 2 cha\356nes de caract\350res . " }} {PARA 0 "" 0 "" {TEXT -1 15 "L'op\351rateur de " }{TEXT 391 18 "concat \351nation || " }{TEXT -1 47 " permet de rassembler 2 cha\356nes de c aract\350res :" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 42 "ch:=\"MAPLE \" || \"7 pour Linux et Windows\";" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%#chGQ>MAPLE~7~pour~Linux~et~Windows6 \"" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 35 "On peut aussi utiliser la f onction " }{TEXT 392 3 "cat" }{TEXT -1 2 " :" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 44 "ch:=cat(\"MAPLE \",\"7 pour Linux et Windows\"); " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#chGQ>MAPLE~7~pour~Linux~et~Wind ows6\"" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "" 0 "" {TEXT 393 55 "Quelques fonctions utilisant les cha\356nes de caract \350res:" }}{PARA 0 "" 0 "" {TEXT 396 6 "length" }{TEXT -1 1 "(" } {TEXT 395 6 "chaine" }{TEXT -1 50 ") retourne la longueur de la cha \356ne de caract\350res " }{TEXT 394 6 "chaine" }{TEXT -1 1 "." }} {PARA 0 "" 0 "" {TEXT 397 9 "substring" }{TEXT -1 1 "(" }{TEXT 398 11 "chaine,a..b" }{TEXT -1 59 ") retourne la sous-cha\356ne constitu\351e par les caract\350res de " }{TEXT 399 6 "chaine" }{TEXT -1 13 " situ \351s entre" }}{PARA 0 "" 0 "" {TEXT -1 14 "les positions " }{TEXT 400 1 "a" }{TEXT -1 4 " et " }{TEXT 401 1 "b" }{TEXT -1 1 "." }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "length(ch);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"#H" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "substring(ch,9..18);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#Q+pour~Linux6 \"" }}}{PARA 256 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "" 0 "" {TEXT 409 35 "\300 propos des guillemets et accents:" }{TEXT -1 38 "\nNe pas confondre , pour une variable " }{TEXT 402 1 "x" }{TEXT -1 4 " , `" } {TEXT 403 1 "x" }{TEXT -1 6 "` et '" }{TEXT 404 1 "x" }{TEXT -1 6 "' : " }{TEXT 405 1 "x" }{TEXT -1 5 " et `" }{TEXT 406 1 "x" }{TEXT -1 41 "` d\351signent le m\352me nom de variable alors" }}{PARA 0 "" 0 " " {TEXT -1 5 "que '" }{TEXT 407 1 "x" }{TEXT -1 45 "' repr\351sente la variable non assign\351e de nom " }{TEXT 408 1 "x" }{TEXT -1 1 "." }} {PARA 0 "" 0 "" {TEXT -1 106 "\300 ne pas, bien s\373r, confondre avec \"x\" qui est la cha\356ne de caract\350res ne comportant qu'un\ncara ct\350re: x. " }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "x:=3: x+1,`x`+ 1,'x'+1;\n\"x\";" }{TEXT -1 0 "" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\" \"%F#,&%\"xG\"\"\"F&F&" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#Q\"x6\"" }}} {PARA 256 "" 0 "" {TEXT -1 0 "" }}{PARA 256 "" 0 "" {TEXT -1 19 "Exerc ice corrig\351 2:" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 " " 0 "" {TEXT -1 20 "Ecrire une fonction " }{TEXT 359 1 "F" }{TEXT -1 7 " qui \340 " }{TEXT 360 1 "n" }{TEXT -1 49 " entier naturel non nul \+ , associe le produit des " }{TEXT 361 1 "n" }{TEXT -1 17 " premiers no mbres" }}{PARA 0 "" 0 "" {TEXT -1 9 "premiers." }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 34 "F:=n->product(ithprime(k),k=1..n);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"FGf*6#%\"nG6\"6$%)operatorG%&arrowGF(-%( productG6$-%)ithprimeG6#%\"kG/F2;\"\"\"9$F(F(F(" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 5 "F(5);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"%5B " }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 35 "En effet, F(5) = 2.3.5.7.11 = 2310." }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 256 "" 0 "" {TEXT -1 17 "Travail dirig\351 2:" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "" 0 "" {TEXT 362 7 "TD 2.1:" }}{PARA 0 "" 0 "" {TEXT -1 20 "E crire une fonction " }{TEXT 363 1 "F" }{TEXT -1 7 " qui \340 " }{TEXT 364 1 "n" }{TEXT -1 47 " entier naturel non nul , associe la somme des " }{TEXT 365 1 "n" }{TEXT -1 17 " premiers entiers" }}{PARA 0 "" 0 " " {TEXT -1 18 "naturels non nuls." }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }} {EXCHG {PARA 257 "" 0 "" {TEXT -1 7 "TD 2.2:" }}{PARA 0 "" 0 "" {TEXT -1 18 "Soit l'expression " }{TEXT 438 5 "expr " }{TEXT -1 13 "d\351fin ie par :" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/%%exprG*(,(%\"xG\"\"\"%\" yG!\"$%\"zG\"\"#F(,(F'F(F)F(!\"\"F(F(,(F(F(F)F.F+F(F(" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 38 "1\260 De quel type est cette expression ?" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 " " {TEXT -1 14 "2\260 D\351velopper " }{TEXT 439 4 "expr" }{TEXT -1 1 " ." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 12 "3 \260 Ordonner " }{TEXT 440 5 "expr " }{TEXT -1 40 "suivant les puissan ces d\351croissantes de " }{TEXT 441 1 "x" }{TEXT -1 2 " ." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 19 "4\260 Substituer \+ dans " }{TEXT 442 4 "expr" }{TEXT -1 3 " : " }{TEXT 443 3 "x+1" } {TEXT -1 3 " \340 " }{TEXT 444 1 "x" }{TEXT -1 3 " , " }{TEXT 445 3 "y -2" }{TEXT -1 3 " \340 " }{TEXT 446 1 "y" }{TEXT -1 3 " , " }{TEXT 448 2 "z\262" }{TEXT -1 3 " \340 " }{TEXT 447 1 "z" }{TEXT -1 2 " ." } }}{PARA 0 "" 0 "" {TEXT -1 0 "" }{TEXT 461 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "" 0 " " {TEXT 467 7 "TD 2.3:" }}{PARA 0 "" 0 "" {TEXT -1 31 "1\260 D\351fini r la fonction P qui \340 " }{TEXT 463 1 " " }{TEXT 462 1 "x" }{TEXT -1 10 " associe :" }{XPPEDIT 18 0 "x^4+(3-4*a)*x^3+(-9*a+6*a^2+2)*x^2+ (-4*a^3-4*a+9*a^2)*x+2*a^2-3*a^3+a^4;" "6#,0*$%\"xG\"\"%\"\"\"*&,&\"\" $F'*&F&F'%\"aGF'!\"\"F'*$F%F*F'F'*&,(*&\"\"*F'F,F'F-*&\"\"'F'*$F,\"\"# F'F'F6F'F'*$F%F6F'F'*&,(*&F&F'*$F,F*F'F-*&F&F'F,F'F-*&F2F'*$F,F6F'F'F' F%F'F'*&F6F'*$F,F6F'F'*&F*F'*$F,F*F'F-*$F,F&F'" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 14 "2\260 Factoriser " } {XPPEDIT 18 0 "P(x);" "6#-%\"PG6#%\"xG" }{TEXT -1 25 " et calculer ses racines " }{TEXT 464 1 "x" }{TEXT -1 2 " ." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 14 "3\260 D\351velopper " } {XPPEDIT 18 0 "P(x);" "6#-%\"PG6#%\"xG" }{TEXT -1 66 " et regrouper se s termes suivant les puissances d\351croissantes de " }{TEXT 465 1 "a " }{TEXT -1 2 " ." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 24 "4\260 On prend d\351sormais " }{XPPEDIT 18 0 "a = -1;" "6#/%\"aG,$\"\"\"!\"\"" }{TEXT -1 2 ": " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 41 " a) repr\351senter graphiquement P pour " }{TEXT 466 1 "x" }{TEXT -1 7 " entre " }{XPPEDIT 18 0 "-1;" "6#,$\"\"\"!\"\"" }{TEXT -1 6 " et 1." }}{PARA 0 "" 0 "" {TEXT -1 0 " " }}{PARA 0 "" 0 "" {TEXT -1 28 " b) calculer l'image de " } {XPPEDIT 18 0 "1+sqrt(3)" "6#,&\"\"\"F$-%%sqrtG6#\"\"$F$" }{TEXT -1 8 " par P ." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 43 "5\260 Calculer l'int\351grale de P entre -1 et 1." }}}}{MARK "0 0 " 0 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 1 1 1 33 1 1 }