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{PSTYLE "" 0 283 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }
3 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 0 284 1 {CSTYLE "" -1 -1 "
" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }3 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }
{PSTYLE "" 0 285 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }
3 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 0 286 1 {CSTYLE "" -1 -1 "
" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }3 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }
{PSTYLE "" 0 287 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }
3 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 0 288 1 {CSTYLE "" -1 -1 "
" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }3 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }
{PSTYLE "" 0 289 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }
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{SECT 0 {EXCHG {PARA 277 "" 0 "" {TEXT 256 55 "TP 4 Initiation a un lo
giciel de calcul formel :  Maple" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 276 "" 0 "" {TEXT -1 62 "Tapez les l
ignes suivantes (ne pas oublier le point virgule !)" }}}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 4 "3*5;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"
#:" }}}{EXCHG {PARA 275 "" 0 "" {TEXT -1 39 "\" rappelle le resultat c
alcul precedent" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 2 "\";" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#\"#:" }}}{EXCHG {PARA 278 "" 0 "" 
{TEXT -1 48 "On peut stocker les resultats dans des variables" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "a:=3;\nb:=5;\na*b;" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#>%\"aG\"\"$" }}{PARA 11 "" 1 "" {XPPMATH 20 
"6#>%\"bG\"\"&" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"#:" }}}{EXCHG 
{PARA 279 "" 0 "" {TEXT -1 75 "On peut utiliser des fractions, des nom
bres complexes, des nombres reels..." }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 46 "1/2;\n2/4;\n2+I;abs(2+I);\nI^2;\nln(2);\nPi;\n3.45; \+
" }}{PARA 11 "" 1 "" {XPPMATH 20 "6##\"\"\"\"\"#" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6##\"\"\"\"\"#" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,&\"\"#
\"\"\"%\"IGF%" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*$\"\"&#\"\"\"\"\"#" 
}}{PARA 11 "" 1 "" {XPPMATH 20 "6#!\"\"" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6#-%#lnG6#\"\"#" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%#PiG" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#$\"$X$!\"#" }}}{EXCHG {PARA 280 "" 0 "" 
{TEXT -1 55 "On peut demander les decimales (evaluation en flottant)" 
}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "evalf(Pi);" }}{PARA 11 "
" 1 "" {XPPMATH 20 "6#$\"+aEfTJ!\"*" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 
-1 41 "On peut demander encore plus de decimales" }}}{EXCHG {PARA 0 ">
 " 0 "" {MPLTEXT 1 0 13 "evalf(Pi,20);" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6#$\"5&QKz*e`EfTJ!#>" }}}{EXCHG {PARA 289 "" 0 "" {TEXT -1 32 "On \+
peut factoriser et developper" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 31 "expand((x-1)*(x-2));\nfactor(\");" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6#,(*$%\"xG\"\"#\"\"\"F%!\"$F&F'" }}{PARA 11 "" 1 "" {XPPMATH 20 "
6#*&,&%\"xG\"\"\"!\"\"F&F&,&F%F&!\"#F&F&" }}}{EXCHG {PARA 281 "" 0 "" 
{TEXT -1 28 "On peut manipuler des listes" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 17 "L:=[1,1,2];\nL[3];" }}{PARA 11 "" 1 "" {XPPMATH 20 
"6#>%\"LG7%\"\"\"F&\"\"#" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"#" }}}
{EXCHG {PARA 0 "" 0 "" {TEXT -1 31 "On peut manipuler des ensembles" }
}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "E:=\{1,1,2\};\nE[3];" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"EG<$\"\"\"\"\"#" }}{PARA 8 "" 1 "
" {TEXT -1 33 "Error, invalid subscript selector" }}}{EXCHG {PARA 282 
"" 0 "" {TEXT -1 71 "Justifiez le message d'erreur que provoque la deu
xieme ligne ci-dessus." }}}{EXCHG {PARA 283 "" 0 "" {TEXT -1 48 "Faiso
ns maintenant quelques calculs d'integrales" }}}{EXCHG {PARA 0 "> " 0 
"" {MPLTEXT 1 0 16 "int(1/x,x=u..v);" }}{PARA 11 "" 1 "" {XPPMATH 20 "
6#,&-%#lnG6#%\"vG\"\"\"-F%6#%\"uG!\"\"" }}}{EXCHG {PARA 0 "" 0 "" 
{TEXT -1 203 "Voici maintenant pourquoi on parle de trois-demi et de c
inq-demi en classe prepa : \nComparez : \"J'integre X entre la premier
e et deuxieme annee\"\npuis    \"j'integre X entre la deuxieme et troi
sieme annee\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "int(x,x=1.
.2);\nint(x,x=2..3);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6##\"\"$\"\"#" }
}{PARA 11 "" 1 "" {XPPMATH 20 "6##\"\"&\"\"#" }}}{EXCHG {PARA 284 "" 
0 "" {TEXT -1 51 "Les integrales indefinies sont calculees egalement \+
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "int(sin(x)/x,x=0..infin
ity);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$%#PiG#\"\"\"\"\"#" }}}
{EXCHG {PARA 285 "" 0 "" {TEXT -1 59 "On peut donc faire des calculs d
e primitives et de derivees" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
26 "int(1/x,x);\ndiff(ln(x),x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%#
lnG6#%\"xG" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*$%\"xG!\"\"" }}}{EXCHG 
{PARA 286 "" 0 "" {TEXT -1 55 "On peut aussi faire des developpement e
n serie deTaylor" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "series(
exp(x),x=0);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#+1%\"xG\"\"\"\"\"!F%\"
\"\"#F%\"\"#\"\"##F%\"\"'\"\"$#F%\"#C\"\"%#F%\"$?\"\"\"&-%\"OG6#F%\"\"
'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "series(sin(x),x=0,8);
" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#+-%\"xG\"\"\"\"\"\"#!\"\"\"\"'\"\"
$#F%\"$?\"\"\"&#F(\"%S]\"\"(-%\"OG6#F%\"\")" }}}{EXCHG {PARA 287 "" 0 
"" {TEXT -1 27 "On peut calculer des sommes" }}}{EXCHG {PARA 0 "> " 0 
"" {MPLTEXT 1 0 25 "sum(k,k=1..n);\nfactor(\");" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#,(*$,&%\"nG\"\"\"F'F'\"\"##F'F(F&#!\"\"F(F*F'" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#,$*&%\"nG\"\"\",&F%F&F&F&F&#F&\"\"#" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "sum(1/n!,n=0..infinity);" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#-%$expG6#\"\"\"" }}}{EXCHG {PARA 274 "
" 0 "" {TEXT -1 137 "On peut demander de l'aide sur une commande en ut
ilisant le ?\nPar exemple demandons de l'aide sur la commande pour res
oudre les equations" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "?solv
e" }}}{EXCHG {PARA 11 "" 1 "" {TEXT -1 50 "Resolvons maintenant une eq
uation du second degre " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "
solve(x^2-x-6);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$!\"#\"\"$" }}}
{EXCHG {PARA 256 "" 0 "" {TEXT -1 131 "Bien sur Maple peut utiliser la
 puissance du calcul formel pour donner la formule du discriminant (co
nnu depuis les Babylonniens) :" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 23 "solve(a*x^2+b*x+c=0,x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$,&#
!\"&\"\"'\"\"\"*$,&\"#DF'%\"cG!#7#F'\"\"##F'F&,&F$F'F(#!\"\"F&" }}}
{EXCHG {PARA 257 "" 0 "" {TEXT -1 47 "De meme avec une equation du tro
isieme de degre" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "solve(x^
3+x^2-x-1);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"\"\"!\"\"F$" }}}
{EXCHG {PARA 258 "" 0 "" {TEXT -1 72 "La formule generale est connu so
us le nom de formule de Cardan-Tartaglia" }}{PARA 0 "" 0 "" {TEXT -1 
207 "(en fait Tartaglia [1500-1557] avait communique a Cardan  [1501-1
576] la formule en question en faisant promettre a Cardan de garder le
 secret,\nCardan s'est parjure et s'est empresse de publier la formule
 !)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "solve(a+b*x+c*x^2+c*
x^3,x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%,(*&%\"cG!\"\"*&,(!#=\"\"\"
F%F&*&\"\"$#F*\"\"#*&,(\"$D\"F*F%!#8*$F%F.F,F*F%F&F-F,F*F%F.#F*F,F4*&,
&!#:F*F%F*F*F'#F&F,F4F8F*,*F$#F&\"\"'F5F:F8F**(%\"IGF*F,F-,&F$F4F5F8F*
F-,*F$F:F5F:F8F*F<#F&F." }}}{EXCHG {PARA 259 "" 0 "" {TEXT -1 26 "Voic
i la premiere racine :" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "\"
[1];" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,(*&%\"cG!\"\"*&,(!#=\"\"\"F%F
&*&\"\"$#F*\"\"#*&,(\"$D\"F*F%!#8*$F%F.F,F*F%F&F-F,F*F%F.#F*F,F4*&,&!#
:F*F%F*F*F'#F&F,F4F8F*" }}}{EXCHG {PARA 260 "" 0 "" {TEXT -1 66 "Et qu
'est ce que cela donne pour une equation du quatrieme degre ?" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 33 "solve(a+b*x+c*x^2+c*x^3+d*x^
4,x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'RootOfG6#,,\"\"$\"\"\"%#_Z
G\"\"&*&%\"cGF(F)\"\"#F(*&F,F(F)F'F(*&%\"dGF(F)\"\"%F(" }}}{EXCHG 
{PARA 261 "" 0 "" {TEXT -1 67 "La formule est tellement horrible que M
aple ne veut pas la donner !" }}{PARA 262 "" 0 "" {TEXT -1 37 "On va q
uand meme lui forcer la main :" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 19 "_EnvExplicit:=true:" }}}{EXCHG {PARA 263 "" 0 "" {TEXT -1 66 "
Et on obtient la formule de Ferrari [1522-1565], l'eleve de Cardan" }}
}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 33 "solve(a+b*x+c*x^2+c*x^3+d*x
^4,x);" }}{PARA 12 "" 1 "" {XPPMATH 257 "6&,(*&%\"cG\"\"\"%\"dG!\"\"#F
(\"\"%*(\"\"$#F&\"\"#F'F(*&,.*&F%F.,,*$F%F.\"$W\"*&F%F&F'F&!$k)F'\"%+F
*$F%F,\"\")*$,6F8\"%+:*&F%F.F'F&!%+a*$F%F*!$c\"*&F%F&F'F.!%!['*&F%F,F'
F&\"#7*$F%\"\"&\"#O*$F'F,!&O2#*&F%F.F'F.\"%cM*&F'F&F%F*!$W\"*$F'F.\"&D
1&F-FD#F&F,F,*(F%F&F'F&F2FP!\")*&F2#F.F,F'F&F.F5!$?\"FN\"$)GF=F9F&F2#F
(F,F-#F&FD*&F'F(,$*(,4*(F%F.F2FPF/F-!#=**F%F&F'F&F2FPF/F-\"#[*(F/F-F2F
TF'F&\"\"'*(F/F-F%F&F'F&!$g$*&F/F-F'F.\"$k)*(F/F-F%F.F'F&\"#C*(F,F-F2F
PF'F.\"$?(*(F,F-F2FPF%F,\"#=**F,F-F2FPF%F.F'F&!#sF&F2FWF/#F(F.F(F-FX,(
F$F)F+FXFY#F(FD,(F$F)F+F[p*&F'F(,$*(,4FgnFhnFinFjnF[oF\\oF]oF^oF_oF`oF
aoFboFco!$?(FeoFhnFgo\"#sF&F2FWF/FioF(F-FX,(F$F)F+F[pF]pF[p" }}}
{EXCHG {PARA 0 "" 0 "" {TEXT -1 48 "Meme la premiere racine a une form
e compliquee :" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "\"[1];" }}
{PARA 11 "" 1 "" {XPPMATH 258 "6#,(*&%\"cG\"\"\"%\"dG!\"\"#F(\"\"%*(\"
\"$#F&\"\"#F'F(*&,.*&F%F.,,*$F%F.\"$W\"*&F%F&F'F&!$k)F'\"%+F*$F%F,\"\"
)*$,6F8\"%+:*&F%F.F'F&!%+a*$F%F*!$c\"*&F%F&F'F.!%!['*&F%F,F'F&\"#7*$F%
\"\"&\"#O*$F'F,!&O2#*&F%F.F'F.\"%cM*&F'F&F%F*!$W\"*$F'F.\"&D1&F-FD#F&F
,F,*(F%F&F'F&F2FP!\")*&F2#F.F,F'F&F.F5!$?\"FN\"$)GF=F9F&F2#F(F,F-#F&FD
*&F'F(,$*(,4*(F%F.F2FPF/F-!#=**F%F&F'F&F2FPF/F-\"#[*(F/F-F2FTF'F&\"\"'
*(F/F-F%F&F'F&!$g$*&F/F-F'F.\"$k)*(F/F-F%F.F'F&\"#C*(F,F-F2FPF'F.\"$?(
*(F,F-F2FPF%F,\"#=**F,F-F2FPF%F.F'F&!#sF&F2FWF/#F(F.F(F-FX" }}}{EXCHG 
{PARA 264 "" 0 "" {TEXT -1 101 "On s'est longtemps demande a quoi pouv
ait ressembler la formule pour une equation du cinquieme degre." }}
{PARA 265 "" 0 "" {TEXT -1 168 "La reponse, trouvee par le mathematici
en norvegien Niels Henrik Abel (1802-1829) \net par le mathematicien E
variste Galois (1811-1832 mort en duel a 20 ans)  c'est que :" }}
{PARA 266 "" 0 "" {TEXT -1 118 "IL N'Y PAS DE FORMULE POUR LES EQUATIO
NS DE DEGRE >4\n(cela se prouve par la theorie des groupes, inventee p
ar Galois)." }}}{EXCHG {PARA 267 "" 0 "" {TEXT -1 215 "De nos jours, c
'est toujours un challenge de calculer numeriquement (rapidement) les \+
racines d'un polynome de degre eleve.\nMaple sait le faire, on peut ai
nsi lui demander toutes les racines complexes d'un polynome :" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "fsolve(x^5+x^4+x-3,x,complex
);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6',&$!+<k#oI\"!\"*\"\"\"%\"IG$!+Sl
Q)o(!#5,&F$F'F($\"+SlQ)o(F+,&$\"+vTEoIF+F'F($!+s[P+6F&,&F0F'F($\"+s[P+
6F&$F'\"\"!" }}}{EXCHG {PARA 268 "" 0 "" {TEXT -1 25 "Maple sait aussi
 integrer" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "int(1/x,x=a..b
);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,&-%#lnG6#%\"bG\"\"\"-F%6#%\"aG!
\"\"" }}}{EXCHG {PARA 269 "" 0 "" {TEXT -1 67 "Les integrales indefini
es ne lui posent pas non plus de problemes :" }}}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 23 "int(1/x,x=1..infinity);" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#%)infinityG" }}}{EXCHG {PARA 270 "" 0 "" {TEXT -1 76 "C
ette integrale represente l'aire sous la courbe y=1/x, tracons cette c
ourbe" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 31 "plot(\{1/x,1/floor
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