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{SECT 0 {EXCHG {PARA 256 "" 0 "" {TEXT 256 20 "Introduction a Maple" }
}{PARA 259 "" 0 "" {TEXT -1 0 "" }}{PARA 259 "" 0 "" {TEXT -1 12 "Feli
ce Ronga" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 262 "" 0 "" {TEXT 
-1 24 "Version du 10 avril 2002" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}
{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 257 "" 0 "" {TEXT 286 50 "Clique
z sur les boutons \"+\" pour deployer le texte" }}{PARA 0 "" 0 "" 
{TEXT -1 0 "" }}}{SECT 1 {PARA 3 "" 0 "" {TEXT 263 13 "Mode d'emploi" 
}}{PARA 0 "" 0 "" {TEXT -1 193 "J'ai  essaye de rassembler dans cette \+
feuille de travail quelques elements de base de Maple, qui est un prog
ramme permettant de faire des manipulations mathematiques symboliques \+
et numeriques. " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" 
{TEXT -1 21 "Vous etes invites a :" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}
{PARA 0 "" 0 "" {TEXT -1 95 "1 - creer votre propre feuille de travail
 (\"worksheet\"), par la commande \"new\" du menu fichier." }}{PARA 0 
"" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 212 "2 - lire les not
es de la feuille presente , en faisant au fur et a mesure vos propres \+
experiences sur votre feuille a vous. Vous pouvez copier de cette feui
lle et coller sur la votre, puis modifier a votre guise." }}{PARA 0 "
" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 74 "3 - faire au moins
 les exercices qui vous sont proposes sur votre feuille." }}{PARA 0 "
" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 78 "Les caracteres acc
entues ont ete supprimes pour des raisons d'incompatibilite." }}}
{SECT 1 {PARA 3 "" 0 "" {TEXT 264 9 "1. Depart" }}{PARA 0 "" 0 "" 
{TEXT -1 397 "Dans Maple, les commandes se terminent avec un point vir
gule et sont envoyees en appuyant sur la touche Carriage Return. Une l
igne de commandes doit commencer par le signe \"plus grand\" > . Pour \+
engendrer une ligne susceptible de contenir une commande (plutot que d
u texte), cliquez sur le symbole \"[>\" dans la barre de menu; sur une
 nouvelle feuille de travail ce n'est en principe pas necessaire." }}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 4 "2+3;" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#\"\"&" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }{TEXT 
290 33 "Assignation de valeurs et egalite" }}}{EXCHG {PARA 0 "" 0 "" 
{TEXT -1 204 "L'assignation de valeurs aux variables se fait avec le s
ymbole \":=\", comme en Pascal; si on veut supprimer l'impression du r
esultat, on on termine la commande par deux points a la place du point
 virgule :" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "x:=2:y:=x^2;y
+x;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"yG\"\"%" }}{PARA 11 "" 1 "
" {XPPMATH 20 "6#\"\"'" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 120 "Le sym
bole \"=\" est utilise pour exprimer une equation; la commande \"solve
(\"equation\")\" retourne la liste des solutions :" }}}{EXCHG {PARA 0 
"> " 0 "" {MPLTEXT 1 0 13 "solve(z^2=2);" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6$*$-%%sqrtG6#\"\"#\"\"\",$F#!\"\"" }}}{EXCHG {PARA 0 "" 0 "" 
{TEXT -1 51 "Si on a oublie que l'on a assigne la valeur 2 a x :" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "solve(x^2=2);" }}}{EXCHG 
{PARA 0 "" 0 "" {TEXT -1 109 "on n'obtient aucune solution! Evidemment
, puisque x vaut 2 et qu'il n'y a pas de solution a l'equation 2^2=2.
" }}{PARA 0 "" 0 "" {TEXT -1 96 "Si on veut de nouveau utiliser x comm
e variable, il faut lui assigner la valeur symbolique 'x' :" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "x:='x';" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%\"xGF$" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "
solve(x^2=2);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$*$-%%sqrtG6#\"\"#\"\"
\",$F#!\"\"" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 32 "et voila! De meme,
 si on ecrit :" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "solve(1=2
);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 42 "on n'obtient rien en retour
, evidemment.  " }}{PARA 0 "" 0 "" {TEXT -1 21 "On peut meme ecrire :
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "z:=x^2=2;" }}{PARA 11 "
" 1 "" {XPPMATH 20 "6#>%\"zG/*$)%\"xG\"\"#\"\"\"F)" }}}{EXCHG {PARA 0 
"" 0 "" {TEXT -1 60 "et z a pour valeur l'expression x^2=2; on peut do
nc ecrire :" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "solve(z);" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6$*$-%%sqrtG6#\"\"#\"\"\",$F#!\"\"" }}}
{EXCHG {PARA 0 "" 0 "" {TEXT -1 12 "Si l'on pose" }}}{EXCHG {PARA 0 ">
 " 0 "" {MPLTEXT 1 0 7 "z:=x=2;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%
\"zG/%\"xG\"\"#" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 127 "on aura assig
ne a z une expression booleenne, dont on peut connaitre la valeur par \+
la commande \"evalb\" (evaluation booleenne) :" }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 14 "x:=1:evalb(z);" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6#%&falseG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "x:=2:eval
b(z);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%%trueG" }}}{EXCHG {PARA 0 "
" 0 "" {TEXT -1 0 "" }{TEXT 291 4 "Aide" }}}{EXCHG {PARA 0 "" 0 "" 
{TEXT -1 80 "Maple propose un systeme d'aide tres complet et qui fourn
it beaucoup d'exemples." }}{PARA 0 "" 0 "" {TEXT -1 121 " Si on veut d
e l'aide sur une commande ou une procedure, taper ?\"nom\" (ici il n'e
st pas necessaire de mettre un ; ou :) :" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 2 "?+" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 9 "ou encore" }
}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "?plot" }}}{EXCHG {PARA 0 "
" 0 "" {TEXT -1 70 "On peut aussi ecrire (notez la presence du point v
irgule cette fois) :" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "hel
p(plot);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 123 "Enfin, on peut utili
ser l'aide a partir de la barre de menu de Maple, par mot-cle ou par s
ujet. Essayez aussi la commande :" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 11 "help(help);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" 
}}{PARA 0 "" 0 "" {TEXT 265 8 "Remarque" }}{PARA 0 "" 0 "" {TEXT -1 
274 "Lorsqu'on ouvre une feuille de travail telle que celle-ci, Maple \+
n'evalue pas automatiquement les expressions qui s'y trouvent. Cela ve
ut dire que si on veut evaluer une commande, il faut au prealable eval
uer toutes les commandes precedentes qui sont utilisees. Par exemple \+
" }{TEXT 267 1 ":" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "a:=3;" 
}}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"aG\"\"$" }}}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 7 "b:=a+2;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"bG
,&%\"aG\"\"\"\"\"#F'" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 121 "Ici, la \+
commande a:=3 n'as pas encore ete evaluee (ce n'est pas visible, mais \+
il faut me croire!). Maintenant on evalue :" }}}{EXCHG {PARA 0 "> " 0 
"" {MPLTEXT 1 0 5 "a:=3;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"aG\"\"
$" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 2 "b;" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#\"\"&" }}}{EXCHG {PARA 266 "" 0 "" {TEXT -1 11 "Recomme
ncer" }{TEXT 292 0 "" }}{PARA 0 "" 0 "" {TEXT -1 85 "Maple vous offre \+
la possibilte de repartir a zero, mais pas tout-a-fait; la commande " 
}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart;" }}}{EXCHG {PARA 
0 "" 0 "" {TEXT -1 179 "efface les valeurs assignees aux variables et \+
les eventuelles librairies chargees en memoire (par exemple avec la co
mmande \"with(plots)\", utilisee au dernier paragraphe). Ainsi : " }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 2 "a;" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#%\"aG" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 50 "La variab
le \"a\" n'a plus qu'une valeur symbolique." }}{PARA 0 "" 0 "" {TEXT 
-1 84 "Cependant, cette commande ne remet pas a disposition la memoire
 utilisee jusque-la ." }}{PARA 0 "" 0 "" {TEXT -1 175 "Si le comportem
ent de Maple est bizarre, il faut repartir a zero en quittant l'applic
ation (apres avoir eventuellement sauve votre feuille de travail), et \+
la relancer ensuite." }}}}{SECT 1 {PARA 3 "" 0 "" {TEXT 257 27 "2. Cal
culs avec les nombres" }}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 8 "Exemples
" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 4 "2+2;" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#\"\"%" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 4 "2*4;
" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\")" }}}{EXCHG {PARA 0 "" 0 "" 
{TEXT -1 48 "Le signe % rappelle le dernier resultat obtenu :" }}
{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 4 "%+2;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"#5" }}}{EXCHG {PARA 0 "
" 0 "" {TEXT -1 36 "Le circonflexe precede en exposant :" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 4 "3^2;" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6#\"\"*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "2^(3+2);" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#\"#K" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 
-1 51 "Les fractions sont representees sous forme exacte :" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 4 "9/7;" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6##\"\"*\"\"(" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 148 "Si on veut \+
le resultat sous forme de nombre decimal, il faut utiliser la fonction
 \"evalf\" (\"f\" pour \"float\", i.e. nombre reel a virgule flottante
) :" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "evalf(%);" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#$\"+'G9dG\"!\"*" }}}{EXCHG {PARA 0 "" 0 "" 
{TEXT -1 33 "et si on veut plus de decimales :" }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 14 "evalf(9/7,20);" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6#$\"5Vr&G9dG9dG\"!#>" }}}{EXCHG {PARA 261 "" 1 "" {TEXT -1 73 "On
 remarque maintenant que les decimales ont une periode, de longueur 6.
 " }}{PARA 0 "" 0 "" {TEXT -1 132 "On peut forcer les nombres entiers \+
a etre traites come des \"float\" en ecrivant un 0 apres la virgule (q
ui est un point dans Maple) :" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "2.0/3;" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#$\"+nmmmm!#5" }}}{EXCHG {PARA 258 "" 0 "" {TEXT -1 47 "
Racine carree se dit \"square root\" en anglais :" }}}{EXCHG {PARA 0 "
> " 0 "" {MPLTEXT 1 0 8 "sqrt(2);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*
$-%%sqrtG6#\"\"#\"\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "ev
alf(%);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+iN@99!\"*" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "sqrt(2.0);" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#$\"+iN@99!\"*" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 213 "
On remarque ci-dessus que \"sqrt(2)\" est conserve sous forme symboliq
ue par Maple; par contre, si on ecrit \"sqrt(2.0)\"  le 2.0 force Mapl
e a travailler avec des representation decimales approchees de nombres
 reels." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 
66 "Si on veut d'autres racines, on utilise l'ecriture exponentielle :
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "2^(1/3);" }}{PARA 11 "" 
1 "" {XPPMATH 20 "6#*$)\"\"##\"\"\"\"\"$F'" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 9 "evalf(%);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+]5#
*f7!\"*" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 117 "Certains nombres sont
 predefinis, comme le nombre \"Pi\", qui est la moitie de la circonfer
ence du cercle  de rayon 1 :" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 3 "Pi;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%#PiG" }}}{EXCHG {PARA 0 "
> " 0 "" {MPLTEXT 1 0 10 "evalf(Pi);" }}{PARA 11 "" 1 "" {XPPMATH 20 "
6#$\"+aEfTJ!\"*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "evalf(Pi
,20);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"5&QKz*e`EfTJ!#>" }}}
{EXCHG {PARA 0 "" 0 "" {TEXT -1 90 "ou le nombre d'Euler \"e\", qui n'
a pas de nom particulier dans Maple (contrairement a Pi) :" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "exp(1);" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#-%$expG6#\"\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 12 "evalf(%,30);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"?NruGg`BX!f
%G=G=F!#H" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 97 "Maple est sensible a
ux majuscules-minuscules. Mais Maple n'est pas contrariant; si vous ec
rivez :" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 3 "pi;" }}{PARA 11 "
" 1 "" {XPPMATH 20 "6#%#piG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
10 "evalf(pi);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%#piG" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "Pi:=1;" }}{PARA 8 "" 1 "" {TEXT -1 
55 "Error, attempting to assign to `Pi` which is protected\n" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "pi:=1;" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%#piG\"\"\"" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 46 "Ma
ple pense que pi  est une nouvelle variable." }}{PARA 0 "" 0 "" {TEXT 
-1 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 42 "Pour assigner un nombre
 a une variable x :" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "x:=s
qrt(2);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"xG*$-%%sqrtG6#\"\"#\"\"
\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 4 "x^2;" }}{PARA 11 "" 1 
"" {XPPMATH 20 "6#\"\"#" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "
y:=sqrt(2.0);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"yG$\"+iN@99!\"*" 
}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 4 "y^2;" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#$\"+********>!\"*" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 
12 "Ha, ha, ha !" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "
" 0 "" {TEXT -1 81 "Decomposition en produit de facteurs premiers (\"i
factor=integer factorisation\") :" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 14 "ifactor(1998);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*(-
%!G6#\"\"#\"\"\")-F%6#\"\"$F,F(-F%6#\"#PF(" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 14 "ifactor(2003);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-
%!G6#\"%.?" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "isprime(2003)
;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%%trueG" }}}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 17 "isprime(6^5+5^6);" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6#%&falseG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "ifactor(6
^5+5^6);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*&-%!G6#\"\"(\"\"\"-F%6#\"
%VLF(" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{PARA 0 "" 0 "" {TEXT -1 0 
"" }}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 33 "Exercices (faites-en au moin
s 2!)" }}{SECT 1 {PARA 5 "" 0 "" {TEXT 259 102 "1. Ecrire sous forme d
e fraction le nombre x=2.123123123 (periodique). Indication : calculez
 1000*x-x." }}}{SECT 1 {PARA 5 "" 0 "" {TEXT 260 35 "2. Nombres premie
rs, factorisation." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" 
{TEXT -1 43 "a) Trouver le nombre premier qui suit 1003." }}{PARA 0 "
" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 242 "b) Soit F_n=2^(2^
n)+1. Pour quelles valeurs de n le nombre F_n est-il premier ? Si non,
 trouver sa factorisation. Essayez pour n<=6; ne vous laissez pas impr
essioner par Maple : il travaille avec des tables de nombres premiers \+
toutes faites. " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" 
{TEXT -1 172 "La factorisation de F_7 a ete trouvee en 1975 , celle de
  F_8 en 1981, celle de F_9 en 1993. On ne connait rien de plus. N'ess
ayez pas de factoriser ces nombres avec Maple!" }}{PARA 0 "" 0 "" 
{TEXT -1 0 "" }}}{SECT 1 {PARA 5 "" 0 "" {TEXT 276 41 "3. Testez le th
eoreme de Fermat suivant :" }}{PARA 0 "" 0 "" {TEXT -1 85 "b^(p-1) est
 congru a 1 modulo p, si p est un nombre premier et que b est premier \+
a p." }}{PARA 0 "" 0 "" {TEXT -1 83 "Utiliser la division sur les enti
ers (\"iquo\" donne le quotient et \"irem\" le reste)." }}}{SECT 1 
{PARA 5 "" 0 "" {TEXT 258 17 "4. Approximation." }}{PARA 5 "" 0 "" 
{TEXT 269 94 "Calculez quelques valeurs de (1+1/n)^n et comparez avec \+
la valeur donnee par Maple a exp(1).  " }}}}}{SECT 1 {PARA 3 "" 0 "" 
{TEXT 261 48 "3. Expressions symboliques, fonctions, equations" }}
{SECT 1 {PARA 4 "" 0 "" {TEXT -1 8 "Exemples" }}{SECT 1 {PARA 5 "" 0 "
" {TEXT -1 23 "Expressions symboliques" }}{PARA 0 "" 0 "" {TEXT -1 25 
"On commence par nettoyer:" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 
"restart;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "r:=(a+b)^2;" }
}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"rG*$),&%\"aG\"\"\"%\"bGF)\"\"#F)
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "er:=expand(%);" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#erG,(*$)%\"aG\"\"#\"\"\"F**(F)F*F(F
*%\"bGF*F**$)F,F)F*F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "r-e
r;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,**$),&%\"aG\"\"\"%\"bGF(\"\"#F(
F(*$)F'F*F(!\"\"*(F*F(F'F(F)F(F-*$)F)F*F(F-" }}}{EXCHG {PARA 0 "> " 0 
"" {MPLTEXT 1 0 15 "simplify(r-er);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6
#\"\"!" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 137 "L'exemple ci-dessus mo
ntre a quel point Maple respecte la volonte de l'utilisateur: les expr
essions ne sont simplifiees que sur demande. " }}}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 19 "s:=(a^2-b^2)/(a+b);" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%\"sG*&,&*$)%\"aG\"\"#\"\"\"F+*$)%\"bGF*F+!\"\"F+,&F)F
+F.F+F/" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "simplify(s);" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#,&%\"aG\"\"\"%\"bG!\"\"" }}}{EXCHG 
{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 158 "Maple co
nsidere r et s comme des expressions en les variables symboliques a et
 b. Pour remplacer les symboles par des valeurs on utilise la fonction
 \"subs\" : " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "subs(a=1,r)
;subs(a=2,b=1,r);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*$),&\"\"\"F&%\"b
GF&\"\"#F&" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"*" }}}{EXCHG {PARA 
0 "" 0 "" {TEXT -1 37 "Maple sait factoriser des polynomes:\n" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "factor(x^3-y^3);" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#*&,&%\"xG\"\"\"%\"yG!\"\"F&,(*$)F%\"\"#F&F&*
&F%F&F'F&F&*$)F'F,F&F&F&" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 36 "et me
me des quotients de polynomes:\n" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 28 "factor((x^4-y^4)/(x^3+y^3));" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#*(,&%\"xG\"\"\"%\"yG!\"\"F&,&*$)F'\"\"#F&F&*$)F%F,F&F&F
&,(F-F&*&F%F&F'F&F(F*F&F(" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 68 "et d
ans ce cas Maple a pris l'initiaitve de simplifier l'expression." }}}
{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{SECT 1 {PARA 5 "" 0 "" {TEXT -1 9 "F
onctions" }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 27 "Definition d'une fonct
ion :" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "f:=x->x^2-1;" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"fGf*6#%\"xG6\"6$%)operatorG%&arrow
GF(,&*$)9$\"\"#\"\"\"F1F1!\"\"F(F(F(" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 5 "f(1);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"!" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "g:=(x,y)->x^2+y^2-1;" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"gGf*6$%\"xG%\"yG6\"6$%)operatorG%&
arrowGF),(*$)9$\"\"#\"\"\"F2*$)9%F1F2F2F2!\"\"F)F)F)" }}}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 7 "g(2,1);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6
#\"\"%" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "g(1,0);" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#\"\"!" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}
{SECT 1 {PARA 5 "" 0 "" {TEXT -1 42 "Difference entre expressions et f
onctions." }}{PARA 0 "" 0 "" {TEXT -1 161 "Une expression est liee aux
 symboles utilises dans sa definition; dans une fonction, au contraire
, le nom du symbole representant la variable peut etre modifie :" }}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "f(u);" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#,&*$)%\"uG\"\"#\"\"\"F(F(!\"\"" }}}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 20 "h:=(x,y)->x^2-y^3+1;" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%\"hGf*6$%\"xG%\"yG6\"6$%)operatorG%&arrowGF),(*$)9$\"
\"#\"\"\"F2*$)9%\"\"$F2!\"\"F2F2F)F)F)" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 7 "h(y,x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,(*$)%\"yG
\"\"#\"\"\"F(*$)%\"xG\"\"$F(!\"\"F(F(" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 7 "h(u,v);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,(*$)%\"uG
\"\"#\"\"\"F(*$)%\"vG\"\"$F(!\"\"F(F(" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 9 "E:=x^2-1;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"EG,&*
$)%\"xG\"\"#\"\"\"F*F*!\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
12 "subs(x=1,E);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"!" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "subs(u=1,E);" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#,&*$)%\"xG\"\"#\"\"\"F(F(!\"\"" }}}}{SECT 1 {PARA 5 "" 
0 "" {TEXT -1 9 "Equations" }}{PARA 5 "" 0 "" {TEXT 281 28 "Pour resou
dre une equation :" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "solve(
x^2-1=0,x);" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6$\"\"\"!\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
21 "solve(x^2+y^2-1=0,x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$*$-%%sqrt
G6#,&\"\"\"F(*$)%\"yG\"\"#F(!\"\"F(,$F#F-" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 31 "solve(\{x^2+y^2-1=0,x=y\},\{x,y\});" }}{PARA 0 "" 
0 "" {TEXT -1 0 "" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#<$/%\"xG-%'RootOf
G6$,&*$)%#_ZG\"\"#\"\"\"F-F.!\"\"/%&labelG%$_L2G/%\"yGF&" }}}{EXCHG 
{PARA 0 "" 0 "" {TEXT -1 27 "et si on veut tout savoir :" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 42 "allvalues(solve(\{x^2+y^2-1=0,x=y\}
,\{x,y\}));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$<$/%\"xG,$*$-%%sqrtG6#
\"\"#\"\"\"#F,F+/%\"yGF&<$/F%,$F'#!\"\"F+/F/F2" }}}{PARA 0 "" 0 "" 
{TEXT -1 40 "On peut aussi utiliser d'autres formes :" }}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 17 "solve(x^2+x-1,x);" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6$,&#!\"\"\"\"#\"\"\"*&#F'F&F'-%%sqrtG6#\"\"&F'F',&F$F'*&
#F'F&F'*$F*F'F'F%" }}}{PARA 0 "" 0 "" {TEXT -1 59 "ce qui montre que l
e signe \"=0\" est facultatif; ou encore :" }}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 17 "solve(x^2+x=1,x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "
6$,&#!\"\"\"\"#\"\"\"*&#F'F&F'-%%sqrtG6#\"\"&F'F',&F$F'*&#F'F&F'*$F*F'
F'F%" }}}{PARA 0 "" 0 "" {TEXT -1 40 "Les solutions peuvent etre imagi
naires :" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "solve(x^2+x+1,x)
;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$,&#!\"\"\"\"#\"\"\"*&^##F'F&F'-%%
sqrtG6#\"\"$F'F',&F$F'*&^#F$F'F+F'F'" }}}{PARA 0 "" 0 "" {TEXT -1 37 "
ou \"I\" est la racine de -1.La preuve:" }}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 4 "I*I;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#!\"\"" }}}
{EXCHG {PARA 0 "" 0 "" {TEXT -1 55 "Il est donc interdit d'utilise I c
omme nom de variable:" }{TEXT 293 0 "" }{TEXT -1 0 "" }}}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 5 "I:=1;" }}{PARA 8 "" 1 "" {TEXT -1 42 "Erro
r, illegal use of an object as a name\n" }}}{PARA 0 "" 0 "" {TEXT -1 
102 "Les solutions sont donnees sous forme de liste. Voici comment acc
eder individuellement aux solutions :" }}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 36 "equat:=x^2-x+1;sols:=solve(equat,x);" }}{PARA 11 "" 
1 "" {XPPMATH 20 "6#>%&equatG,(*$)%\"xG\"\"#\"\"\"F*F(!\"\"F*F*" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%solsG6$,&#\"\"\"\"\"#F(*&^#F'F(-%%s
qrtG6#\"\"$F(F(,&F'F(*&^##!\"\"F)F(F,F(F(" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 11 "a:=sols[1];" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"
aG,&#\"\"\"\"\"#F'*&^#F&F'-%%sqrtG6#\"\"$F'F'" }}}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 16 "subs(x=a,equat);" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6#,(*$),&#\"\"\"\"\"#F(*&^#F'F(-%%sqrtG6#\"\"$F(F(F)F(F(F'F(*&^##!
\"\"F)F(F,F(F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "eval(%);" 
}}{PARA 11 "" 1 "" {XPPMATH 20 "6#,(*$),&#\"\"\"\"\"#F(*&^#F'F(-%%sqrt
G6#\"\"$F(F(F)F(F(F'F(*&^##!\"\"F)F(F,F(F(" }}}{EXCHG {PARA 0 "" 0 "" 
{TEXT -1 145 "Maple est minimaliste : il ne developpe pas les expressi
ons plus que necessaire. Pour voir si notre a est vraiment solution, i
l faut faire ainsi:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "expa
nd(subs(x=a,equat));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"!" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "expand(subs(x=sols[2],equat)
);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"!" }}}{EXCHG {PARA 264 "" 0 
"" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 260 "" 1 "" 
{TEXT -1 86 "Si on tient a avoir des solutions approchees, on utilise \+
\"fsolve\" (\"f\" pour \"float\") :" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 32 "fsolve(\{x^2+y^2-1=0,x=y\},\{x,y\});" }}{PARA 11 "" 
1 "" {XPPMATH 20 "6#<$/%\"yG$!+7y1rq!#5/%\"xGF&" }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 18 "solve(exp(x)=2,x);" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#-%#lnG6#\"\"#" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 19 "fsolve(exp(x)=2,x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+1=ZJp
!#5" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 17 "Controlons (??) :" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "evalf(ln(2),20);" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#$\"5U4`%*f0=ZJp!#?" }}}{EXCHG {PARA 0 "" 0 "
" {TEXT -1 131 "Lorsqu'on a 2 equations a 2 inconnues, les solutions s
ont donnees sous la forme de liste d'expression de la forme \"x=...,y=
.... \" :" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 46 "sols:=allvalues(solve(\{x^2+y-1=0,x=y\},\{x,y\}));
" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%solsG6$<$/%\"yG,&#!\"\"\"\"#\"
\"\"*&#F-F,F--%%sqrtG6#\"\"&F-F-/%\"xGF)<$/F5,&F*F-*&#F-F,F-*$F0F-F-F+
/F(F8" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 114 "Voici comment acceder a
ux solutions. La commande \"op\" donne acces aux \"operants\", ou comp
osantes d'une expression:" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "sols[1];op(sols[1]);" }}{PARA 11 "
" 1 "" {XPPMATH 20 "6#<$/%\"yG,&#!\"\"\"\"#\"\"\"*&#F*F)F*-%%sqrtG6#\"
\"&F*F*/%\"xGF&" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$/%\"yG,&#!\"\"\"\"#
\"\"\"*&#F)F(F)-%%sqrtG6#\"\"&F)F)/%\"xGF%" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 30 "op(sols[1])[1];op(sols[1])[2];" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#/%\"yG,&#!\"\"\"\"#\"\"\"*&#F)F(F)-%%sqrtG6#\"\"&F)F)" 
}}{PARA 11 "" 1 "" {XPPMATH 20 "6#/%\"xG,&#!\"\"\"\"#\"\"\"*&#F)F(F)-%
%sqrtG6#\"\"&F)F)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "evalf(
op(sols[1])[2]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/%\"xG$\"+!*)R.='!
#5" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 77 "On peut aussi utiliser la c
ommande \"rhs\" (=right hand side=membre de droite):" }}}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 20 "rhs(op(sols[1])[1]);" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#,&#!\"\"\"\"#\"\"\"*&#F'F&F'-%%sqrtG6#\"\"&F'F'" }}}
{EXCHG {PARA 0 "" 0 "" {TEXT -1 101 "Dans la commande \"fsolve\", on p
eut preciser un intervalle dans lequel on veut chercher les solutions:
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "fsolve(x^2-2,x,-2..0);
" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$!+iN@99!\"*" }}}{PARA 0 "" 0 "" 
{TEXT -1 0 "" }}}{SECT 1 {PARA 5 "" 0 "" {TEXT -1 11 "Derivations" }}
{EXCHG {PARA 0 "" 0 "" {TEXT -1 71 "Pour deriver une fonction (d'abord
 on aimerait se rappeler qui est g) :" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 9 "print(g);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#f*6$%\"xG
%\"yG6\"6$%)operatorG%&arrowGF',(*$)9$\"\"#\"\"\"F0*$)9%F/F0F0F0!\"\"F
'F'F'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "diff(g(x,y),x);" }
}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$%\"xG\"\"#" }}}{EXCHG {PARA 0 "" 0 
"" {TEXT -1 82 "On itere en repetant le nom des variables par rapport \+
auxquelles on veut deriver :" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 17 "diff(g(x,y),x,x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"#" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "diff(g(x,y),x,y);" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#\"\"!" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 
55 "Mais on peut changer le nom des variables, si on veut :" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "diff(g(u,v),u);" }}{PARA 11 
"" 1 "" {XPPMATH 20 "6#,$%\"uG\"\"#" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 
-1 39 "On peut aussi deriver une expression : " }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 29 "f:=x^2+x*y^3-x*y;diff(f,x,y);" }}{PARA 11 "" 
1 "" {XPPMATH 20 "6#>%\"fG,(*$)%\"xG\"\"#\"\"\"F**&F(F*)%\"yG\"\"$F*F*
*&F(F*F-F*!\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,&*$)%\"yG\"\"#\"\"
\"\"\"$F(!\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "diff(f,x,
y,y);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$%\"yG\"\"'" }}}{EXCHG 
{PARA 0 "" 0 "" {TEXT -1 19 "D'autres exemples :" }}}{EXCHG {PARA 0 ">
 " 0 "" {MPLTEXT 1 0 23 "diff(exp(x^2+y^2),x,y);" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#,$*(%\"xG\"\"\"%\"yGF&-%$expG6#,&*$)F%\"\"#F&F&*$)F'F.F
&F&F&\"\"%" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "diff(exp(x^2+
y^2),y,x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$*(%\"xG\"\"\"%\"yGF&-%
$expG6#,&*$)F%\"\"#F&F&*$)F'F.F&F&F&\"\"%" }}}{PARA 4 "" 0 "" {TEXT 
-1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "diff(sin(x^2+y^2),
x,y,y);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,&*(-%$cosG6#,&*$)%\"xG\"\"
#\"\"\"F-*$)%\"yGF,F-F-F-F/F-F+F-!\")*(\"\"%F--%$sinGF'F-F+F-!\"\"" }}
}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "diff(sin(x^2+y^2),y,x,y);" 
}}{PARA 11 "" 1 "" {XPPMATH 20 "6#,&*(-%$cosG6#,&*$)%\"xG\"\"#\"\"\"F-
*$)%\"yGF,F-F-F-F/F-F+F-!\")*(\"\"%F--%$sinGF'F-F+F-!\"\"" }}}{PARA 0 
"" 0 "" {TEXT -1 0 "" }}}}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 47 "Exercic
es (faites au moins les deux premiers !)" }}{SECT 1 {PARA 5 "" 0 "" 
{TEXT 270 23 "5. Approximation de Pi." }}{PARA 0 "" 0 "" {TEXT -1 101 
"Definir une fonction f(n)=4*(1-1/3+1/5-1/7...) et se convaincre que f
(n)->Pi si n tend vers l'infini." }}{PARA 0 "" 0 "" {TEXT -1 97 "Sugge
stion : utiliser la procedure de maple \"sum(...)\";  faites \"help(su
m)\" pour savoir comment. " }}}{SECT 1 {PARA 5 "" 0 "" {TEXT 266 99 "6
. Resoudre l'equation 2*x^3+x+7=0. Remplacer les solutions trouvees da
ns l'equation pour verifier." }}}{SECT 1 {PARA 5 "" 0 "" {TEXT 268 25 
"7. Dire si les polynomes " }{TEXT 271 19 "f:=x^3-6*x^2+11*x-6" }
{TEXT 272 4 " et " }{TEXT 273 21 "g:=x^4-15*x^2+10*x+24" }{TEXT 274 
50 " ont un facteur commun. Simplifier le quotient f/g" }{TEXT -1 1 ".
" }}}{SECT 1 {PARA 5 "" 0 "" {TEXT 275 8 "8. Soit " }{TEXT 277 33 "f(x
,y,z)=x^2*y^2*z^3-sin(y^2)*x*z" }{TEXT 278 85 ". Verifier l'independan
ce de l'ordre de derivation pour les derivees  d'ordre 2, 3..." }}}}}
{SECT 1 {PARA 3 "" 0 "" {TEXT 262 13 "4. Graphiques" }}{SECT 1 {PARA 
4 "" 0 "" {TEXT -1 24 "Fonctions d'une variable" }}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 8 "restart;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 12 "f:=x->x^3-x;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"fGf*6#%\"x
G6\"6$%)operatorG%&arrowGF(,&*$)9$\"\"$\"\"\"F1F/!\"\"F(F(F(" }}}
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{SECT 1 {PARA 5 "" 0 "" {TEXT 282 43 "Exercices (faites au moins le 10
 et le 11)." }}{SECT 1 {PARA 5 "" 0 "" {TEXT 280 10 "9. Graphes" }
{TEXT 287 1 "." }}{PARA 0 "" 0 "" {TEXT -1 215 "Tracer le graphe de si
n(x) et exp(x)-1 pour x variant dans un intervalle contenant 0.  Montr
er que si l'intervalle est assez petit les 2 graphes coincident ou pre
sque. Qu'est-ce qui permet de prevoir ce phenomene ? " }}}{PARA 0 "" 
0 "" {TEXT -1 0 "" }}{SECT 1 {PARA 263 "" 0 "" {TEXT 288 36 "10. Solut
ions d'\216quations et graphes" }}{PARA 0 "" 0 "" {TEXT -1 253 "On veu
t resoudre l'equation x^4-10*sin(x)+log(x^2+10)=0. Dessiner le graphe \+
du premier membre pour identifier les regions ou on risque de trouver \+
des racines, puis utiliser la commande fsolve(f(x),x=a..b), qui cherch
e une racine dans l'intervalle [a,b]." }}{PARA 0 "" 0 "" {TEXT -1 44 "
Meme question pour l'equation x^5-sin(3x+1)." }}{PARA 0 "" 0 "" {TEXT 
-1 0 "" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{SECT 1 {PARA 20 "" 0 "" 
{TEXT 283 34 "11. Graphe en coordonnees polaires" }{TEXT 289 1 "." }}
{EXCHG {PARA 0 "" 0 "" {TEXT -1 81 "Quelle est la fonction r(t) dont l
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}}{SECT 1 {PARA 5 "" 0 "" {TEXT 284 24 "Exercice 12 (a faire!). " }}
{PARA 0 "" 0 "" {TEXT -1 380 "Un exemple d'epicycloide : la cardioide.
 Prenons un cercle C, de centre (0,0), rayon 1 et faisons rouler sans \+
frottement sur l'exterieur de C un cercle C', de rayon 1 aussi. La cou
rbe decrite par un point fixe P de C' est appele cardioide. On suppose
 qu'au depart le cercle C' est centre en (2,0), de sorte que C et C' s
ont tangents en (1,0), et que ce meme point est le point P. " }}{PARA 
0 "" 0 "" {TEXT -1 362 "Trouver la parametrisation de cette courbe. Ci
-dessous, en bleu le cercle C, en brun le cercle C', en vert le point \+
P et en rouge la cardioide (c'est une animation: cliquez sur le dessin
; une barre de menu pour animation devrait apparaitre: cilquez sur le \+
bouton avec un signe \">\", ou bien sur \"play\" dans le sous-menu de \+
l'article \"animation\" du menu principal)" }}{PARA 0 "" 0 "" {TEXT 
-1 0 "" }}{EXCHG {PARA 13 "" 1 "" {TEXT -1 0 "" }{GLPLOT2D 301 289 
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45.000000 45.000000 0 0 "Curve 1" "Curve 2" "Curve 3" "Curve 4" "Curve
 5" }}}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}}{SECT 1 {PARA 4 "" 0 "" 
{TEXT -1 32 "Courbes donnee par une equation." }}{PARA 0 "" 0 "" 
{TEXT -1 53 "Il faut d'abord charger une librairie de procedures :" }}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "with(plots);" }}{PARA 7 "" 
1 "" {TEXT -1 50 "Warning, the name changecoords has been redefined\n
" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#7W%(animateG%*animate3dG%-animatec
urveG%&arrowG%-changecoordsG%,complexplotG%.complexplot3dG%*conformalG
%,conformal3dG%,contourplotG%.contourplot3dG%*coordplotG%,coordplot3dG
%-cylinderplotG%,densityplotG%(displayG%*display3dG%*fieldplotG%,field
plot3dG%)gradplotG%+gradplot3dG%-implicitplotG%/implicitplot3dG%(inequ
alG%-listcontplotG%/listcontplot3dG%0listdensityplotG%)listplotG%+list
plot3dG%+loglogplotG%(logplotG%+matrixplotG%(odeplotG%'paretoG%*pointp
lotG%,pointplot3dG%*polarplotG%,polygonplotG%.polygonplot3dG%4polyhedr
a_supportedG%.polyhedraplotG%'replotG%*rootlocusG%,semilogplotG%+setop
tionsG%-setoptions3dG%+spacecurveG%1sparsematrixplotG%+sphereplotG%)su
rfdataG%)textplotG%+textplot3dG%)tubeplotG" }}}{EXCHG {PARA 0 "" 0 "" 
{TEXT -1 338 "et on obtient comme reponse la liste des nouvelles proce
dures a notre disposition. La commande suivante dessine les niveaux f(
x,y)=c d'une fonction f, pour x et y variant entre les limites indique
es. Les valeurs de c sont reparties de maniere uniforme entre les vale
urs minimales et maximales de f, pour x et y dans les limites indiquee
s." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 45 "contourplot(y^2-x^3-x
^2,x=-1.5..0.5,y=-1..1);" }}{PARA 13 "" 1 "" {GLPLOT2D 247 247 247 
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