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{SECT 0 {EXCHG {PARA 200 "" 0 "" {TEXT 202 10 "EXERCICE 3" }{TEXT 203 
0 "" }}}{EXCHG {PARA 201 "> " 0 "" {MPLTEXT 1 204 8 "restart:" }
{MPLTEXT 1 204 0 "" }}}{EXCHG {PARA 201 "> " 0 "" {MPLTEXT 1 204 0 "" 
}}}{EXCHG {PARA 202 "" 0 "" {TEXT 205 11 "Question a)" }{TEXT 203 0 ""
 }}}{EXCHG {PARA 201 "> " 0 "" {MPLTEXT 1 204 15 "imageL:=proc(u)" }
{MPLTEXT 1 204 0 "" }{MPLTEXT 1 204 13 "\nlocal i,s,l;" }{MPLTEXT 1 
204 0 "" }{MPLTEXT 1 204 9 "\ns:=NULL;" }{MPLTEXT 1 204 0 "" }
{MPLTEXT 1 204 21 "\nfor i from 1 to 5 do" }{MPLTEXT 1 204 0 "" }
{MPLTEXT 1 204 19 "\n s:=s,evalf(u(i));" }{MPLTEXT 1 204 0 "" }
{MPLTEXT 1 204 4 "\nod;" }{MPLTEXT 1 204 0 "" }{MPLTEXT 1 204 8 "\nl:=
[s];" }{MPLTEXT 1 204 0 "" }{MPLTEXT 1 204 5 "\nend:" }{MPLTEXT 1 204 
0 "" }{MPLTEXT 1 204 1 "\n" }}{PARA 203 "" 0 "" {TEXT 200 49 "Cette pr
oc\351dure renvoie la liste des cinq valeurs" }{TEXT 206 27 " [u(1),u(
2),u(3),u(4),u(5)]" }{TEXT 200 7 " d'une " }{TEXT 206 13 "permutation \+
u" }{TEXT 200 0 "" }}}{EXCHG {PARA 201 "> " 0 "" {TEXT 207 0 "" }}
{PARA 201 "> " 0 "" {TEXT 207 11 "Question b)" }{MPLTEXT 1 204 0 "" }}
}{EXCHG {PARA 201 "> " 0 "" {MPLTEXT 1 204 61 "r:=array(0..5);R:=array
(0..5);s:=array(1..5);S:=array(1..5); " }{TEXT 208 33 "On alloue l'esp
ace destin\351 aux 4 " }{TEXT 209 16 "tableaux s,S,r,R" }{MPLTEXT 1 
204 0 "" }}{PARA 204 "" 1 "" {XPPMATH 20 "6#>I\"rG6\"-I&arrayGI*protec
tedGF(6$;\"\"!\"\"&7\"" }{TEXT 210 0 "" }}{PARA 204 "" 1 "" {XPPMATH 
20 "6#>I\"RG6\"-I&arrayGI*protectedGF(6$;\"\"!\"\"&7\"" }{TEXT 210 0 "
" }}{PARA 204 "" 1 "" {XPPMATH 20 "6#>I\"sG6\"-I&arrayGI*protectedGF(6
$;\"\"\"\"\"&7\"" }{TEXT 210 0 "" }}{PARA 204 "" 1 "" {XPPMATH 20 "6#>
I\"SG6\"-I&arrayGI*protectedGF(6$;\"\"\"\"\"&7\"" }{TEXT 210 0 "" }}}
{EXCHG {PARA 201 "> " 0 "" {TEXT 207 11 "Question c)" }{MPLTEXT 1 204 
0 "" }}}{EXCHG {PARA 202 "" 0 "" {TEXT 203 11 "On cr\351e les" }{TEXT 
206 17 " permutations r1 " }{TEXT 203 3 "et " }{TEXT 206 2 "s1" }
{TEXT 203 0 "" }}}{EXCHG {PARA 202 "" 0 "" {TEXT 203 0 "" }}}{EXCHG 
{PARA 201 "> " 0 "" {MPLTEXT 1 204 50 "r[1]:=x->piecewise(x=1,2,x=2,3,
x=3,4,x=4,5,x=5,1);" }{MPLTEXT 1 204 0 "" }}{PARA 204 "" 1 "" 
{XPPMATH 20 "6#>&I\"rG6\"6#\"\"\"f*6#I\"xGF&F&6$I)operatorGF&I&arrowGF
&F&-I*piecewiseGI*protectedGF16,/9$F(\"\"#/F4F5\"\"$/F4F7\"\"%/F4F9\"
\"&/F4F;F(F&F&F&" }{TEXT 210 0 "" }}}{EXCHG {PARA 201 "> " 0 "" 
{MPLTEXT 1 204 50 "s[1]:=x->piecewise(x=1,1,x=2,5,x=3,4,x=4,3,x=5,2);"
 }{MPLTEXT 1 204 0 "" }}{PARA 204 "" 1 "" {XPPMATH 20 "6#>&I\"sG6\"6#
\"\"\"f*6#I\"xGF&F&6$I)operatorGF&I&arrowGF&F&-I*piecewiseGI*protected
GF16,/9$F(F(/F4\"\"#\"\"&/F4\"\"$\"\"%/F4F:F9/F4F7F6F&F&F&" }{TEXT 
210 0 "" }}}{EXCHG {PARA 201 "> " 0 "" {TEXT 207 11 "Question d)" }
{MPLTEXT 1 204 0 "" }}}{EXCHG {PARA 201 "> " 0 "" {TEXT 208 25 "On cr
\351e les permutations " }{TEXT 209 2 "rk" }{TEXT 208 14 ", obtenue pa
r " }{TEXT 209 30 "compositions successives de r1" }{TEXT 208 15 " ave
c elle-m\352me" }{MPLTEXT 1 204 1 " " }{MPLTEXT 1 204 0 "" }}}{EXCHG 
{PARA 201 "> " 0 "" {MPLTEXT 1 204 0 "" }}}{EXCHG {PARA 201 "> " 0 "" 
{MPLTEXT 1 204 47 "for k from 2 to 5 do r[k]:=(r[1])@(r[k-1]) od; " }
{MPLTEXT 1 204 0 "" }}{PARA 204 "" 1 "" {XPPMATH 20 "6#>&I\"rG6\"6#\"
\"#-I#@@G6$I*protectedGF,I(_syslibGF&6$&F%6#\"\"\"F(" }{TEXT 210 0 "" 
}}{PARA 204 "" 1 "" {XPPMATH 20 "6#>&I\"rG6\"6#\"\"$-I#@@G6$I*protecte
dGF,I(_syslibGF&6$&F%6#\"\"\"F(" }{TEXT 210 0 "" }}{PARA 204 "" 1 "" 
{XPPMATH 20 "6#>&I\"rG6\"6#\"\"%-I#@@G6$I*protectedGF,I(_syslibGF&6$&F
%6#\"\"\"F(" }{TEXT 210 0 "" }}{PARA 204 "" 1 "" {XPPMATH 20 "6#>&I\"r
G6\"6#\"\"&-I#@@G6$I*protectedGF,I(_syslibGF&6$&F%6#\"\"\"F(" }{TEXT 
210 0 "" }}}{EXCHG {PARA 201 "> " 0 "" {MPLTEXT 1 204 11 "r[0]:=r[5]:"
 }{TEXT 208 12 " On affecte " }{TEXT 209 2 "r5" }{TEXT 208 3 " \340 " 
}{TEXT 209 2 "r0" }{MPLTEXT 1 204 0 "" }}}{EXCHG {PARA 201 "> " 0 "" 
{MPLTEXT 1 204 0 "" }}}{EXCHG {PARA 201 "> " 0 "" {TEXT 207 0 "" }}
{PARA 201 "> " 0 "" {TEXT 207 11 "Question e)" }{MPLTEXT 1 204 0 "" }}
}{EXCHG {PARA 202 "" 0 "" {TEXT 203 27 "On d\351fnit les permutations \+
" }{TEXT 206 2 "sk" }{TEXT 203 16 " composition de " }{TEXT 206 2 "s1"
 }{TEXT 203 6 " avec " }{TEXT 206 6 "r(k-1)" }{TEXT 203 0 "" }}}
{EXCHG {PARA 201 "> " 0 "" {MPLTEXT 1 204 43 "for k from 2 to 5 do s[k
]:=s[1]@r[k-1] od; " }{MPLTEXT 1 204 0 "" }}{PARA 204 "" 1 "" 
{XPPMATH 20 "6#>&I\"sG6\"6#\"\"#-I\"@G6$I*protectedGF,I(_syslibGF&6$&F
%6#\"\"\"&I\"rGF&F0" }{TEXT 210 0 "" }}{PARA 204 "" 1 "" {XPPMATH 20 "
6#>&I\"sG6\"6#\"\"$-I\"@G6$I*protectedGF,I(_syslibGF&6$&F%6#\"\"\"-I#@
@GF+6$&I\"rGF&F0\"\"#" }{TEXT 210 0 "" }}{PARA 204 "" 1 "" {XPPMATH 
20 "6#>&I\"sG6\"6#\"\"%-I\"@G6$I*protectedGF,I(_syslibGF&6$&F%6#\"\"\"
-I#@@GF+6$&I\"rGF&F0\"\"$" }{TEXT 210 0 "" }}{PARA 204 "" 1 "" 
{XPPMATH 20 "6#>&I\"sG6\"6#\"\"&-I\"@G6$I*protectedGF,I(_syslibGF&6$&F
%6#\"\"\"-I#@@GF+6$&I\"rGF&F0\"\"%" }{TEXT 210 0 "" }}}{EXCHG {PARA 
201 "> " 0 "" {TEXT 207 11 "Question f)" }{MPLTEXT 1 204 0 "" }}}
{EXCHG {PARA 202 "" 0 "" {TEXT 203 16 "On defiunit les " }{TEXT 206 
16 "listes images Rk" }{TEXT 203 5 " et  " }{TEXT 206 2 "Sk" }{TEXT 
203 28 " associ\351es aux permutations " }{TEXT 206 8 "rk et sk" }
{TEXT 203 15 " respectivement" }}}{EXCHG {PARA 201 "> " 0 "" {MPLTEXT 
1 204 21 "for i from 1 to 5 do " }{MPLTEXT 1 204 0 "" }{MPLTEXT 1 204 
44 "\n R[i-1]:=imageL(r[i-1]);S[i]:=imageL(s[i]);" }{MPLTEXT 1 204 0 "
" }{MPLTEXT 1 204 4 "\nod;" }{MPLTEXT 1 204 0 "" }{MPLTEXT 1 204 2 "\n
 " }{MPLTEXT 1 204 0 "" }}{PARA 204 "" 1 "" {XPPMATH 20 "6#>&I\"RG6\"6
#\"\"!7'$\"\"\"F($\"\"#F($\"\"$F($\"\"%F($\"\"&F(" }{TEXT 210 0 "" }}
{PARA 204 "" 1 "" {XPPMATH 20 "6#>&I\"SG6\"6#\"\"\"7'$F(\"\"!$\"\"&F+$
\"\"%F+$\"\"$F+$\"\"#F+" }{TEXT 210 0 "" }}{PARA 204 "" 1 "" {XPPMATH 
20 "6#>&I\"RG6\"6#\"\"\"7'$\"\"#\"\"!$\"\"$F,$\"\"%F,$\"\"&F,$F(F," }
{TEXT 210 0 "" }}{PARA 204 "" 1 "" {XPPMATH 20 "6#>&I\"SG6\"6#\"\"#7'$
\"\"&\"\"!$\"\"%F,$\"\"$F,$F(F,$\"\"\"F," }{TEXT 210 0 "" }}{PARA 204 
"" 1 "" {XPPMATH 20 "6#>&I\"RG6\"6#\"\"#7'$\"\"$\"\"!$\"\"%F,$\"\"&F,$
\"\"\"F,$F(F," }{TEXT 210 0 "" }}{PARA 204 "" 1 "" {XPPMATH 20 "6#>&I
\"SG6\"6#\"\"$7'$\"\"%\"\"!$F(F,$\"\"#F,$\"\"\"F,$\"\"&F," }{TEXT 210 
0 "" }}{PARA 204 "" 1 "" {XPPMATH 20 "6#>&I\"RG6\"6#\"\"$7'$\"\"%\"\"!
$\"\"&F,$\"\"\"F,$\"\"#F,$F(F," }{TEXT 210 0 "" }}{PARA 204 "" 1 "" 
{XPPMATH 20 "6#>&I\"SG6\"6#\"\"%7'$\"\"$\"\"!$\"\"#F,$\"\"\"F,$\"\"&F,
$F(F," }{TEXT 210 0 "" }}{PARA 204 "" 1 "" {XPPMATH 20 "6#>&I\"RG6\"6#
\"\"%7'$\"\"&\"\"!$\"\"\"F,$\"\"#F,$\"\"$F,$F(F," }{TEXT 210 0 "" }}
{PARA 204 "" 1 "" {XPPMATH 20 "6#>&I\"SG6\"6#\"\"&7'$\"\"#\"\"!$\"\"\"
F,$F(F,$\"\"%F,$\"\"$F," }{TEXT 210 0 "" }}}{EXCHG {PARA 201 "> " 0 ""
 {MPLTEXT 1 204 0 "" }}}{EXCHG {PARA 202 "" 0 "" {TEXT 203 35 "On d\35
1fnit la liste des \351l\351ments de " }{TEXT 206 25 "G: [r0,r1,..,r4,
s1,..,s5]" }{TEXT 203 0 "" }}}{EXCHG {PARA 201 "> " 0 "" {MPLTEXT 1 
204 39 "G:=[seq(r[k],k=0..4),seq(s[k],k=1..5)];" }{MPLTEXT 1 204 0 "" 
}}{PARA 204 "" 1 "" {XPPMATH 20 "6#>I\"GG6\"7,-I#@@G6$I*protectedGF*I(
_syslibGF%6$&I\"rGF%6#\"\"\"\"\"&F--F(6$F-\"\"#-F(6$F-\"\"$-F(6$F-\"\"
%&I\"sGF%F/-I\"@GF)6$F;F--F>6$F;F2-F>6$F;F5-F>6$F;F8" }{TEXT 210 0 "" 
}}}{EXCHG {PARA 204 "" 1 "" {TEXT 210 0 "" }}}{EXCHG {PARA 201 "> " 0 
"" {TEXT 207 11 "Question g)" }{MPLTEXT 1 204 0 "" }}}{EXCHG {PARA 
201 "> " 0 "" {MPLTEXT 1 204 12 "Nom:=proc(u)" }{MPLTEXT 1 204 0 "" }
{MPLTEXT 1 204 15 "\nlocal i,sol,N;" }{MPLTEXT 1 204 0 "" }{MPLTEXT 1 
204 22 "\nsol:=XX;N:=imageL(u);" }{MPLTEXT 1 204 0 "" }{MPLTEXT 1 204 
22 "\nfor i from 1 to 5 do " }{MPLTEXT 1 204 0 "" }{MPLTEXT 1 204 49 "
\n if evalb(R[i-1]=N) then sol:=evaln(r[i-1]); fi;" }{MPLTEXT 1 204 0 
"" }{MPLTEXT 1 204 45 "\n if evalb(S[i]=N) then sol:=evaln(s[i]); fi;"
 }{MPLTEXT 1 204 0 "" }{MPLTEXT 1 204 4 "\nod;" }{MPLTEXT 1 204 0 "" }
{MPLTEXT 1 204 5 "\nsol;" }{MPLTEXT 1 204 0 "" }{MPLTEXT 1 204 5 "\nen
d:" }{MPLTEXT 1 204 0 "" }}{PARA 203 "" 0 "" {TEXT 200 15 "Cette proc
\351dure" }{TEXT 206 15 " renvoie le nom" }{TEXT 200 27 " (r0,r,1...,s
1,..s4 ou s5) " }{TEXT 206 17 "de la permutation" }{TEXT 200 19 " donn
\351e en argument" }}}{EXCHG {PARA 201 "> " 0 "" {MPLTEXT 1 204 0 "" }
}}{EXCHG {PARA 204 "" 1 "" {TEXT 210 0 "" }}}{EXCHG {PARA 201 "> " 0 "
" {TEXT 207 11 "Question h)" }{MPLTEXT 1 204 0 "" }}}{EXCHG {PARA 201 
"> " 0 "" {MPLTEXT 1 204 0 "" }}}{EXCHG {PARA 201 "> " 0 "" {MPLTEXT 
1 204 23 "GC:=array(1..10,1..10);" }{TEXT 208 36 " On alloue l'espace \+
pour le tableau " }{TEXT 209 2 "GC" }{TEXT 208 18 " qui contiendra la"
 }{TEXT 209 26 " table de composition de G" }{MPLTEXT 1 204 0 "" }}
{PARA 204 "" 1 "" {XPPMATH 20 "6#>I#GCG6\"-I&arrayGI*protectedGF(6%;\"
\"\"\"#5F*7\"" }{TEXT 210 0 "" }}}{EXCHG {PARA 201 "> " 0 "" {MPLTEXT 
1 204 21 "for i from 1 to 10 do" }{MPLTEXT 1 204 0 "" }{MPLTEXT 1 204 
23 "\n for j from 1 to 10 do" }{MPLTEXT 1 204 0 "" }{MPLTEXT 1 204 23 
"\n   GC[i,j]:=G[i]@G[j];" }{MPLTEXT 1 204 0 "" }{MPLTEXT 1 204 7 "\no
d;od;" }{MPLTEXT 1 204 0 "" }}{PARA 205 "> " 0 "" {MPLTEXT 1 0 9 "eval
(GC);" }{MPLTEXT 1 0 0 "" }}{PARA 205 "> " 0 "" {MPLTEXT 1 0 0 "" }}
{PARA 204 "" 1 "" {XPPMATH 20 "6#-I'matrixG6\"6#7,7,-I#@@G6$I*protecte
dGF,I(_syslibGF%6$&I\"rGF%6#\"\"\"\"#5-F*6$F/\"\"'-F*6$F/\"\"(-F*6$F/
\"\")-F*6$F/\"\"*-I\"@GF+6$-F*6$F/\"\"&&I\"sGF%F1-FA6%FCFFF/-FA6%FCFF-
F*6$F/\"\"#-FA6%FCFF-F*6$F/\"\"$-FA6%FCFF-F*6$F/\"\"%7,F4FLFQFVFC-FA6$
F/FF-FA6%F/FFF/-FA6%F/FFFL-FA6%F/FFFQ-FA6%F/FFFV7,F7FQFVFCF4-FA6$FLFF-
FA6%FLFFF/-FA6%FLFFFL-FA6%FLFFFQ-FA6%FLFFFV7,F:FVFCF4F7-FA6$FQFF-FA6%F
QFFF/-FA6%FQFFFL-FA6%FQFFFQ-FA6%FQFFFV7,F=FCF4F7F:-FA6$FVFF-FA6%FVFFF/
-FA6%FVFFFL-FA6%FVFFFQ-FA6%FVFFFV7,-FA6$FFFC-FA6$FFF/-FA6$FFFL-FA6$FFF
Q-FA6$FFFV-F*6$FFFN-FA6%FFFFF/-FA6%FFFFFL-FA6%FFFFFQ-FA6%FFFFFV7,-FA6$
FFF4-FA6%FFF/F/FfqFhqF`q-FA6%FFF/FF-FA6&FFF/FFF/-FA6&FFF/FFFL-FA6&FFF/
FFFQ-FA6&FFF/FFFV7,-FA6$FFF7FfqFhqF`qFer-FA6%FFFLFF-FA6&FFFLFFF/-FA6&F
FFLFFFL-FA6&FFFLFFFQ-FA6&FFFLFFFV7,-FA6$FFF:FhqF`qFerFds-FA6%FFFQFF-FA
6&FFFQFFF/-FA6&FFFQFFFL-FA6&FFFQFFFQ-FA6&FFFQFFFV7,-FA6$FFF=F`qFerFdsF
at-FA6%FFFVFF-FA6&FFFVFFF/-FA6&FFFVFFFL-FA6&FFFVFFFQ-FA6&FFFVFFFV" }
{TEXT 210 0 "" }}}{EXCHG {PARA 201 "> " 0 "" {MPLTEXT 1 204 18 "Tab:=m
ap(Nom,GC); " }{TEXT 208 16 "Tab contient le " }{TEXT 209 48 "nom de c
haque \351l\351ment de la table de composition" }{MPLTEXT 1 204 0 "" }
}{PARA 204 "" 1 "" {XPPMATH 20 "6#>I$TabG6\"-I'matrixGF%6#7,7,&I\"rGF%
6#\"\"!&F,6#\"\"\"&F,6#\"\"#&F,6#\"\"$&F,6#\"\"%&I\"sGF%F0&F<F3&F<F6&F
<F9&F<6#\"\"&7,F/F2F5F8F+F@F;F=F>F?7,F2F5F8F+F/F?F@F;F=F>7,F5F8F+F/F2F
>F?F@F;F=7,F8F+F/F2F5F=F>F?F@F;7,F;F=F>F?F@F+F/F2F5F87,F=F>F?F@F;F8F+F
/F2F57,F>F?F@F;F=F5F8F+F/F27,F?F@F;F=F>F2F5F8F+F/7,F@F;F=F>F?F/F2F5F8F
+" }{TEXT 210 0 "" }}}{EXCHG {PARA 201 "> " 0 "" {TEXT 208 48 "Tous le
s \351l\350ments de la table sont dans G, donc " }{TEXT 209 28 "G est \+
stable par composition" }{MPLTEXT 1 204 0 "" }}}{EXCHG {PARA 202 "" 0 
"" {TEXT 203 92 "la colonne r0 laisse invariant les \351l\351ments par
courus, c'est donc un \351l\351ment neutre \340 droite" }{TEXT 203 91 
"\nla ligne r0 laisse invariant les \351l\351ments parcourus, c'est do
nc un \351l\351ment neutre \340 droite" }{TEXT 211 11 "\nConclusion" }
{TEXT 203 2 ": " }{TEXT 206 28 "r0 est l'\351l\351ment neutre de G" }
{TEXT 203 28 " (en fait r0 est l'identit\351)" }{TEXT 203 124 "\ntoute
 ligne contient l'\351l\351ment neutre r0, donc tout \351l\351ment de \+
G admet un sym\351trique \340 droite (voir colonne correspondante)" }
{TEXT 203 122 "\ntoute ligne contient l'\351l\351ment neutre r0, donc \+
tout \351l\351ment de G admet un sym\351trique \340 gauche (voir ligne
 correspondante)" }{TEXT 211 11 "\nConclusion" }{TEXT 203 1 " " }
{TEXT 206 38 "G est stable par passage au sym\351trique" }{TEXT 203 0 
"" }{TEXT 203 1 "\n" }}}{EXCHG {PARA 200 "" 0 "" {TEXT 206 52 "G est d
onc un sous-groupe du groupe des permutations" }{TEXT 203 0 "" }}}
{EXCHG {PARA 201 "> " 0 "" {MPLTEXT 1 204 0 "" }}}{EXCHG {PARA 202 "" 
0 "" {TEXT 203 13 "V\351rifions la " }{TEXT 206 13 "commutativit\351" 
}{TEXT 203 46 ", c'est \340 dire si la table de composition est " }
{TEXT 206 37 "sym\351trique par rapport \340 sa diagonale" }{TEXT 203 
0 "" }}}{EXCHG {PARA 201 "> " 0 "" {MPLTEXT 1 204 26 "rep:=true: #Comm
utativit\351?" }{MPLTEXT 1 204 0 "" }{MPLTEXT 1 204 22 "\nfor i from 1
 to 10 do" }{MPLTEXT 1 204 0 "" }{MPLTEXT 1 204 23 "\n for j from i to
 10 do" }{MPLTEXT 1 204 0 "" }{MPLTEXT 1 204 57 "\n  if evalb(Tab[i,j]
<>Tab[j,i]) then rep:=false,i,j; fi; " }{MPLTEXT 1 204 0 "" }{MPLTEXT 
1 204 13 "\nod: od: rep;" }{MPLTEXT 1 204 0 "" }}{PARA 204 "" 1 "" 
{XPPMATH 20 "6%I&falseGI*protectedGF$\"\"*\"#5" }{TEXT 210 0 "" }}}
{EXCHG {PARA 202 "" 0 "" {TEXT 206 19 "G n'est pas ab\351lien" }{TEXT 
203 50 ", en effet l'element (10,9) est distinct de (9,10)" }}}{EXCHG 
{PARA 201 "> " 0 "" {MPLTEXT 1 204 0 "" }}}{EXCHG {PARA 201 "> " 0 "" 
{TEXT 207 11 "Question i)" }{MPLTEXT 1 204 0 "" }}}{EXCHG {PARA 201 ">
 " 0 "" {MPLTEXT 1 204 0 "" }}}{EXCHG {PARA 201 "> " 0 "" {TEXT 208 
15 "cette proc\351dure" }{TEXT 209 26 " toute les compos\351es de u " 
}{TEXT 208 41 "avec les \351l\351ments de G jusqu'\340 trouver l'" }
{TEXT 209 17 "\351l\351ment neutre r0" }{MPLTEXT 1 204 0 "" }}}{EXCHG 
{PARA 201 "> " 0 "" {MPLTEXT 1 204 16 "inverse:=proc(u)" }{MPLTEXT 1 
204 11 "\nlocal i,F;" }{MPLTEXT 1 204 16 "\ni:=1:F:=G[i]@u;" }
{MPLTEXT 1 204 58 "\nwhile evalb(evaln(r[0])<>Nom(F)) do i:=i+1;F:=G[i
]@u; od;" }{MPLTEXT 1 204 11 "\nNom(G[i]);" }{MPLTEXT 1 204 5 "\nend:"
 }{MPLTEXT 1 204 0 "" }}}{EXCHG {PARA 201 "> " 0 "" {MPLTEXT 1 204 0 "
" }}}{EXCHG {PARA 201 "> " 0 "" {MPLTEXT 1 204 14 "inverse(r[1]);" }
{MPLTEXT 1 204 0 "" }}{PARA 204 "" 1 "" {XPPMATH 20 "6#&I\"rG6\"6#\"\"
%" }{TEXT 210 0 "" }}}{EXCHG {PARA 201 "> " 0 "" {MPLTEXT 1 204 0 "" }
}}{EXCHG {PARA 201 "> " 0 "" {TEXT 207 11 "Question j)" }{MPLTEXT 1 
204 0 "" }}}{EXCHG {PARA 202 "" 0 "" {TEXT 203 14 "pour r\351soudre " 
}{TEXT 206 4 "ux=v" }{TEXT 203 22 " il suffit de prendre " }{TEXT 206 
17 "x=symetrique(u)ov" }{TEXT 203 0 "" }}}{EXCHG {PARA 201 "> " 0 "" 
{MPLTEXT 1 204 19 "resoudre:=proc(u,v)" }{MPLTEXT 1 204 0 "" }
{MPLTEXT 1 204 11 "\nlocal sol;" }{MPLTEXT 1 204 0 "" }{MPLTEXT 1 204 
19 "\nsol:=inverse(u)@v;" }{MPLTEXT 1 204 0 "" }{MPLTEXT 1 204 10 "\nN
om(sol);" }{MPLTEXT 1 204 0 "" }{MPLTEXT 1 204 5 "\nend:" }{MPLTEXT 1 
204 0 "" }}}{EXCHG {PARA 201 "> " 0 "" {MPLTEXT 1 204 20 "resoudre(r[1
],s[2]);" }{MPLTEXT 1 204 0 "" }}{PARA 204 "" 1 "" {XPPMATH 20 "6#&I\"
sG6\"6#\"\"$" }{TEXT 210 0 "" }}}{EXCHG {PARA 201 "> " 0 "" {MPLTEXT 
1 204 0 "" }}}{PARA 206 "" 0 "" {TEXT 212 0 "" }}{PARA 206 "" 0 "" 
{TEXT 212 0 "" }}{PARA 206 "" 0 "" {TEXT 212 0 "" }}{PARA 206 "" 0 "" 
{TEXT 212 0 "" }}{PARA 206 "" 0 "" {TEXT 212 0 "" }}{PARA 206 "" 0 "" 
{TEXT -1 0 "" }}}{MARK "0 0 0" 0 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }
{PAGENUMBERS 0 1 2 33 1 1 }