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:Z:j;<Z:>:1:" }{TEXT -1 0 "" }}{PARA 260 "" 0 "" {TEXT -1 30 "CHAPITRE
 4: S\311QUENCES, LISTES," }{TEXT 375 1 "\n" }{TEXT -1 29 "ENSEMBLES, \+
TABLES ET TABLEAUX" }}{PARA 19 "" 0 "" {TEXT -1 39 "\251 Apprendre Map
le. Alain Le Stang. 2006" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "
" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }{TEXT 256 5 "LES
 S" }{TEXT 374 1 "\311" }{TEXT 373 8 "QUENCES:" }}{PARA 0 "" 0 "" 
{TEXT -1 0 "" }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 4 "Une " }{TEXT 257 8 
"s\351quence" }{TEXT -1 11 " , de type " }{TEXT 258 7 "exprseq" }
{TEXT -1 65 " , est une suite d'\351l\351ments s\351par\351s par une v
irgule . On acc\350de \340" }}{PARA 0 "" 0 "" {TEXT -1 64 "chaque \351
l\351ment par son rang , mais l'affectation est interdite :" }}{PARA 
0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "restart:
\ns:=a,b,-1,2*p-q,r;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"sG6'%\"aG%
\"bG!\"\",&%\"pG\"\"#%\"qGF(%\"rG" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 21 "s[4];s[2..5];s[3]:=0;" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6#,&%\"pG\"\"#%\"qG!\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6&%\"bG!
\"\",&%\"pG\"\"#%\"qGF$%\"rG" }}{PARA 8 "" 1 "" {TEXT -1 47 "Error, ca
nnot assign to an expression sequence\n" }}}{EXCHG {PARA 0 "" 0 "" 
{TEXT 343 4 "NULL" }{TEXT -1 26 " d\351signe la s\351quence vide:" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "v:=NULL;" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%\"vG6\"" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG 
{PARA 0 "" 0 "" {TEXT -1 54 "Pour r\351p\351ter un \351l\351ment , uti
liser l'op\351rateur dollar " }{TEXT 259 1 "$" }{TEXT -1 2 " :" }}
{PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "t:=a$2,y$5;" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%\"tG6)%\"aGF&%\"yGF'F'F'F'" }}}{EXCHG {PARA 0 "" 0 "
" {TEXT -1 58 "Pour concat\351ner 2 s\351quences ,utiliser l'op\351rat
eur virgule " }{TEXT 260 1 "," }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "u:=
s,t;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"uG6.%\"aG%\"bG!\"\",&%\"pG
\"\"#%\"qGF(%\"rGF&F&%\"yGF.F.F.F." }}}{EXCHG {PARA 0 "" 0 "" {TEXT 
-1 0 "" }}{PARA 0 "" 0 "" {TEXT 261 8 "op(expr)" }{TEXT -1 59 " retour
ne la s\351quence form\351e des op\351randes de l'expression " }{TEXT 
262 4 "expr" }{TEXT -1 2 " :" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 
0 "> " 0 "" {MPLTEXT 1 0 22 "op(a-y*(a+y+z)+3*z);  " }}{PARA 11 "" 1 "
" {XPPMATH 20 "6%%\"aG,$*&%\"yG\"\"\",(F#F'F&F'%\"zGF'F'!\"\",$F)\"\"$
" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 12 "La fonction " }{TEXT 263 3 "s
eq" }{TEXT -1 29 " permet de cr\351er une s\351quence" }}{PARA 0 "" 0 
"" {TEXT -1 15 "pour un indice " }{TEXT 264 2 "i " }{TEXT -1 11 "varia
nt de " }{TEXT 265 1 "a" }{TEXT -1 3 " \340 " }{TEXT 266 1 "b" }{TEXT 
-1 28 " avec un pas de 1 : syntaxe " }{TEXT 267 16 "seq(expr,i=a..b)" 
}{TEXT -1 6 " , ou " }}{PARA 0 "" 0 "" {TEXT -1 56 "pour un indice d
\351crivant les op\351randes d'une expression " }{TEXT 268 1 "e" }
{TEXT -1 11 " : syntaxe " }{TEXT 269 14 "seq(expr,i=e) " }{TEXT -1 1 "
:" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 
19 "seq(i^3,i=-1/2..2);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%#!\"\"\"\")
#\"\"\"F%#\"#FF%" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 40 "e:=a-y*
(a+y+z)+3*z:op(e);\nseq(mu+i,i=e);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%
%\"aG,$*&%\"yG\"\"\",(F#F'F&F'%\"zGF'F'!\"\",$F)\"\"$" }}{PARA 11 "" 
1 "" {XPPMATH 20 "6%,&%#muG\"\"\"%\"aGF%,&F$F%*&%\"yGF%,(F&F%F)F%%\"zG
F%F%!\"\",&F$F%*&\"\"$F%F+F%F%" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 32 "seq(seq(a||i||j,j=1..3),i=1..3);" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6+%$a11G%$a12G%$a13G%$a21G%$a22G%$a23G%$a31G%$a32G%$a33G" }}}
{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 270 11 "LES LIST
ES:" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "" 0 "" {TEXT 
-1 4 "Une " }{TEXT 271 5 "liste" }{TEXT -1 11 " , de type " }{TEXT 
272 4 "list" }{TEXT -1 66 " , est obtenue en pla\347ant une s\351quenc
e entre les crochets [ et ] ." }}{PARA 0 "" 0 "" {TEXT -1 26 "La liste
 vide se note [] ." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "> " 0 "
" {MPLTEXT 1 0 29 "s:=a$2,b$3,alpha,beta;L:=[s];" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%\"sG6)%\"aGF&%\"bGF'F'%&alphaG%%betaG" }}{PARA 11 "" 
1 "" {XPPMATH 20 "6#>%\"LG7)%\"aGF&%\"bGF'F'%&alphaG%%betaG" }}}
{EXCHG {PARA 0 "" 0 "" {TEXT -1 82 "On acc\350de \340 chaque \351l\351
ment d'une liste par son rang , l'affectation est autoris\351e:" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "L[6];L[2..5];L[3]:=delta;" }
}{PARA 11 "" 1 "" {XPPMATH 20 "6#%&alphaG" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#7&%\"aG%\"bGF%F%" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%
\"LG6#\"\"$%&deltaG" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 273 2 "op" }
{TEXT -1 36 " transforme une liste en s\351quence , " }{TEXT 274 4 "no
ps" }{TEXT -1 41 " donne le nombre d'\351l\351ments d'une liste ." }}
{PARA 0 "" 0 "" {TEXT -1 14 "Les fonctions " }{TEXT 275 2 "op" }{TEXT 
-1 4 " et " }{TEXT 276 4 "nops" }{TEXT -1 34 " ne peuvent agir sur une
 s\351quence " }{TEXT 277 1 "s" }{TEXT -1 8 ": faire " }{TEXT 278 9 "o
ps([s]) " }{TEXT -1 3 "et " }{TEXT 279 9 "nops([s])" }}{PARA 0 "" 0 "
" {TEXT -1 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "op(L);" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6)%\"aGF#%&deltaG%\"bGF%%&alphaG%%betaG" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "nops(L);" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#\"\"(" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 48 "Pour modi
fier une liste, on peut aussi utiliser " }{TEXT 280 5 "subs " }{TEXT 
-1 3 "ou " }{TEXT 281 6 "subsop" }{TEXT -1 2 " :" }}}{EXCHG {PARA 0 ">
 " 0 "" {MPLTEXT 1 0 16 "L:=subs(b=b1,L);" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%\"LG7)%\"aGF&%&deltaG%#b1GF(%&alphaG%%betaG" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "L:=subsop(3=gamma,L);" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"LG7)%\"aGF&%&gammaG%#b1GF(%&alphaG
%%betaG" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "" 0 "" 
{TEXT -1 21 "La fonction bool\351enne" }{TEXT 377 7 " member" }{TEXT 
-1 59 " permet de savoir si une expression est membre d'une liste:" }}
}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 35 "member(gamma,L), member(eps
ilon,L);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$%%trueG%&falseG" }}}{PARA 
0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 282 15 "LES ENSEMBLES \+
:" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 
3 "Un " }{TEXT 283 8 "ensemble" }{TEXT -1 10 ", de type " }{TEXT 284 
3 "set" }{TEXT -1 59 " , est obtenu en pla\347ant une s\351quence entr
e les accolades \{" }{TEXT 345 1 " " }{TEXT -1 5 "et \}." }}{PARA 0 "
" 0 "" {TEXT -1 112 "Les \351l\351ments sont rang\351s par adresse , d
onc l'ordre initial n'est pas n\351cessairement conserv\351 et les \+
\351l\351ments en" }}{PARA 0 "" 0 "" {TEXT -1 51 "double sont supprim
\351s. L'ensemble vide se note \{\} ." }}{PARA 0 "" 0 "" {TEXT -1 0 "
" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "s:=a$2,b$3,alpha,beta;e:=\{s\};
" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"sG6)%\"aGF&%\"bGF'F'%&alphaG%%
betaG" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"eG<&%\"aG%\"bG%&alphaG%%b
etaG" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 90 "On acc\350de \340 chaque \+
\351l\351ment d'un ensemble par son rang , mais l'affectation est inte
rdite :" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 
1 0 25 "e[2];e[2..3];e[3]:=delta;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%
\"bG" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#<$%\"bG%&alphaG" }}{PARA 8 "" 
1 "" {TEXT -1 30 "Error, cannot assign to a set\n" }}}{EXCHG {PARA 0 "
" 0 "" {TEXT 285 2 "op" }{TEXT -1 38 " transforme un ensemble en s\351
quence , " }{TEXT 286 4 "nops" }{TEXT -1 43 " donne le nombre d'\351l
\351ments d'un ensemble ." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "
> " 0 "" {MPLTEXT 1 0 14 "op(e);nops(e);" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6&%\"aG%\"bG%&alphaG%%betaG" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"
\"%" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 69 "Pour modifier un ensemble \+
, l'affectation \351tant interdite , utiliser " }{TEXT 287 3 "sub" }
{TEXT -1 5 "s ou " }{TEXT 288 6 "subsop" }{TEXT -1 2 " :" }}{PARA 0 "
" 0 "" {TEXT -1 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "e:=subs(b=b1
,e);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"eG<&%\"aG%&alphaG%%betaG%#
b1G" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "e:=subsop(3=delta,e)
;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"eG<&%\"aG%&alphaG%&deltaG%#b1
G" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 
21 "La fonction bool\351enne" }{TEXT 376 7 " member" }{TEXT -1 61 " pe
rmet de savoir si une expression est membre d'un ensemble:" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 35 "member(delta,e), member(epsilon,e);
" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$%%trueG%&falseG" }}}{PARA 0 "" 0 "
" {TEXT -1 0 "" }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 79 "Convertir un ens
emble en somme, en produit, en liste, ou convertir une liste en" }}
{PARA 0 "" 0 "" {TEXT -1 14 "ensemble avec " }{TEXT 289 7 "convert" }
{TEXT -1 2 " :" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 69 "convert(e
,`+`);convert(e,`*`);\ne:=convert(e,list);e:=convert(e,set); " }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#,*%\"aG\"\"\"%&alphaGF%%&deltaGF%%#b1G
F%" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#**%\"aG\"\"\"%&alphaGF%%&deltaGF
%%#b1GF%" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"eG7&%\"aG%&alphaG%&del
taG%#b1G" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"eG<&%\"aG%&alphaG%&del
taG%#b1G" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 290 29 "Op\351rations sur le
s ensembles:" }}{PARA 0 "" 0 "" {TEXT 291 5 "union" }{TEXT -1 11 " (un
ion) , " }{TEXT 292 9 "intersect" }{TEXT -1 18 " (intersection) , " }
{TEXT 293 6 "minus " }{TEXT -1 37 "(diff\351rence) .\nla fonction bool
\351enne " }{TEXT 344 2 "a " }{TEXT 349 6 "subset" }{TEXT -1 2 "  " }
{TEXT 346 1 "b" }{TEXT -1 12 " indique si " }{TEXT 347 1 "a" }{TEXT 
-1 25 " est un sous-ensemble de " }{TEXT 348 1 "b" }{TEXT -1 2 ". " }}
}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 107 "e:=\{alpha,beta,gamma,delta\}:f:=\{beta,delta,epsilon,phi,lambd
a\}:\nu:=e union f;i:=e intersect f;m:=f minus e;" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%\"uG<)%&alphaG%%betaG%&deltaG%(epsilonG%'lambdaG%&gam
maG%$phiG" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"iG<$%%betaG%&deltaG" 
}}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"mG<%%(epsilonG%'lambdaG%$phiG" }
}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "i subset e, i subset m;" }
}{PARA 11 "" 1 "" {XPPMATH 20 "6$%%trueG%&falseG" }}}{PARA 0 "" 0 "" 
{TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 294 36 "QUELQUES OUTILS DU PACKA
GE COMBINAT:" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 
"" {MPLTEXT 1 0 22 "with(combinat,choose):" }}{PARA 0 "" 0 "" {TEXT 
-1 18 "(appel de l'outil " }{TEXT 295 6 "choose" }{TEXT -1 58 ", qui g
\351n\350re les sous-listes ordonn\351es d'une liste donn\351e)" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "choose([a,b,c]); " }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#7*7\"7#%\"aG7#%\"bG7$F&F(7#%\"cG7$F&F+7$F(F+
7%F&F(F+" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 87 "G\351n\351ration de t
outes les sous-listes de longueur 2 ordonn\351es d'une liste de longue
ur 3:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "choose([a,b,c],2);
 " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7%7$%\"aG%\"bG7$F%%\"cG7$F&F(" }}
}{EXCHG {PARA 0 "" 0 "" {TEXT 350 6 "choose" }{TEXT -1 1 "(" }{TEXT 
351 1 "n" }{TEXT -1 1 "," }{TEXT 355 1 "p" }{TEXT -1 6 ") avec" }
{TEXT 356 2 " n" }{TEXT -1 1 "," }{TEXT 364 1 "p" }{TEXT -1 54 " entie
rs , g\351n\350re toutes les sous-listes de longueur  " }{TEXT 353 1 "
p" }{TEXT -1 22 " ordonn\351es de [1,2,..," }{TEXT 354 1 "n" }{TEXT 
-1 1 "]" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "choose(4,3); " }
}{PARA 11 "" 1 "" {XPPMATH 20 "6#7&7%\"\"\"\"\"#\"\"$7%F%F&\"\"%7%F%F'
F)7%F&F'F)" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 23 "with(combinat,permute):" }}{PARA 0 "" 0 "" {TEXT 
-1 18 "(appel de l'outil " }{TEXT 296 7 "permute" }{TEXT -1 58 ", qui \+
g\351n\350re les listes de permutation d'une liste donn\351e)" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "permute([a,b,c]);" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#7(7%%\"aG%\"bG%\"cG7%F%F'F&7%F&F%F'7%F&F'F%7
%F'F%F&7%F'F&F%" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 79 "G\351n\351rati
on de toutes les sous-listes de permutation de longueur 2 de [a,b,c] :
 " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "permute([a,b,c],2);   \+
   " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7(7$%\"aG%\"bG7$F%%\"cG7$F&F%7$
F&F(7$F(F%7$F(F&" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 352 7 "permute" }
{TEXT -1 1 "(" }{TEXT 357 1 "n" }{TEXT -1 8 ") , avec" }{TEXT 360 2 " \+
n" }{TEXT -1 54 " entier , donne les listes de permutation de [1,2,...
," }{TEXT 359 1 "n" }{TEXT -1 1 "]" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 12 "permute(3); " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7(7%
\"\"\"\"\"#\"\"$7%F%F'F&7%F&F%F'7%F&F'F%7%F'F%F&7%F'F&F%" }}}{EXCHG 
{PARA 0 "" 0 "" {TEXT 358 7 "permute" }{TEXT -1 1 "(" }{TEXT 361 1 "n
" }{TEXT -1 1 "," }{TEXT 362 1 "p" }{TEXT -1 9 ") , avec " }{TEXT 363 
1 "n" }{TEXT -1 1 "," }{TEXT 365 1 "p" }{TEXT -1 63 " entiers , donne \+
les sous-listes de permutation de de longueur " }{TEXT 367 1 "p" }
{TEXT -1 13 " de [1,2,...," }{TEXT 366 1 "n" }{TEXT -1 2 "] " }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "permute(3,2); " }}{PARA 11 "
" 1 "" {XPPMATH 20 "6#7(7$\"\"\"\"\"#7$F%\"\"$7$F&F%7$F&F(7$F(F%7$F(F&
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart;" }}}{PARA 0 "" 
0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 297 11 "LES TABLES:" }}
{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 4 "Une
 " }{TEXT 298 5 "table" }{TEXT -1 36 " est une structure index\351e do
nt les " }{TEXT 341 7 "indices" }{TEXT -1 5 " (ou " }{TEXT 342 5 "inde
x" }{TEXT -1 38 ") peuvent \352tre de n'importe quel type." }}{PARA 0 
"" 0 "" {TEXT -1 12 "La fonction " }{TEXT 299 5 "table" }{TEXT -1 28 "
 permet de cr\351er une table :" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}
{PARA 0 "" 0 "" {TEXT -1 26 "Cr\351ation d'une table vide:" }}{PARA 0 
"> " 0 "" {MPLTEXT 1 0 13 "v:=table();  " }}{PARA 11 "" 1 "" {XPPMATH 
20 "6#>%\"vG-%&TABLEG6#7\"" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 49 "Cr
\351ation d'une table T avec une liste de valeurs:" }}}{EXCHG {PARA 0 
"> " 0 "" {MPLTEXT 1 0 28 "T:=table([valeur1,valeur2]);" }}{PARA 11 "
" 1 "" {XPPMATH 20 "6#>%\"TG-%&TABLEG6#7$/\"\"\"%(valeur1G/\"\"#%(vale
ur2G" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 68 "Cr\351ation d'une table U
 avec liste d'index (ici \260 . *) et de valeurs:" }}}{EXCHG {PARA 0 "
> " 0 "" {MPLTEXT 1 0 48 "U:=table([`\260`=valeur1,`.`=valeur2,`*`=val
eur3]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"UG-%&TABLEG6#7%/%\".G%(
valeur2G/%\"|[vG%(valeur1G/%\"*G%(valeur3G" }}}{EXCHG {PARA 0 "" 0 "" 
{TEXT -1 48 "Pour afficher le contenu d'une table , utiliser " }{TEXT 
368 6 "print " }{TEXT -1 3 "ou " }{TEXT 369 4 "eval" }}}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 19 "print(T),eval(U);  " }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#-%&TABLEG6#7$/\"\"\"%(valeur1G/\"\"#%(valeur2G" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#-%&TABLEG6#7%/%\".G%(valeur2G/%\"|[vG%
(valeur1G/%\"*G%(valeur3G" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 86 "On p
eut modifier , cr\351er un nouvel \351l\351ment , ou supprimer un \351
l\351ment par affectation :" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
46 "T[a]:=valeur3:U[~]:=valeur4:print(T),eval(U); " }}{PARA 11 "" 1 "
" {XPPMATH 20 "6#-%&TABLEG6#7%/\"\"\"%(valeur1G/\"\"#%(valeur2G/%\"aG%
(valeur3G" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%&TABLEG6#7&/%\".G%(vale
ur2G/%\"|[vG%(valeur1G/%\"|irG%(valeur4G/%\"*G%(valeur3G" }}}{EXCHG 
{PARA 0 "" 0 "" {TEXT -1 55 "Une table peut \352tre directement cr\351
\351e par assignation :" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 32 "V[a]:=1:
V[b]:=2:V[c]:=3:eval(V);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%&TABLEG6
#7%/%\"cG\"\"$/%\"bG\"\"#/%\"aG\"\"\"" }}}{EXCHG {PARA 0 "" 0 "" 
{TEXT 300 34 "Fonctions agissant sur des tables:" }}{PARA 0 "> " 0 "" 
{MPLTEXT 1 0 12 "op(op(V));  " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7%/%
\"cG\"\"$/%\"bG\"\"#/%\"aG\"\"\"" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 11 "indices(V);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%7#%\"c
G7#%\"bG7#%\"aG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "entries(
V);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%7#\"\"$7#\"\"#7#\"\"\"" }}}
{EXCHG {PARA 0 "" 0 "" {TEXT -1 12 "La fonction " }{TEXT 301 3 "map" }
{TEXT -1 61 " permet d'appliquer une fonction sur les valeurs d'une ta
ble:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "V:=map(sqrt,V);" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#>%\"VG-%&TABLEG6#7%/%\"cG*$-%%sqrtG6#\"\"$\"
\"\"/%\"bG*$-F-6#\"\"#F0/%\"aGF0" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 
12 "La fonction " }{TEXT 370 5 "copy " }{TEXT -1 41 "permet d'effectue
r une copie d'une table:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 
"W:=copy(V); " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"WG-%&TABLEG6#7%/%
\"cG*$-%%sqrtG6#\"\"$\"\"\"/%\"bG*$-F-6#\"\"#F0/%\"aGF0" }}}{PARA 0 "
" 0 "" {TEXT -1 0 "" }}{PARA 256 "" 0 "" {TEXT 371 13 "LES TABLEAUX:" 
}{TEXT -1 0 "" }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 3 "Un " }{TEXT 302 7 
"tableau" }{TEXT -1 36 " est une structure index\351e, de type " }
{TEXT 303 5 "array" }{TEXT -1 43 ", de plusieurs dimensions, dont les \+
indices" }}{PARA 0 "" 0 "" {TEXT -1 45 "sont des entiers appartenant \+
\340 un intervalle " }{TEXT 304 4 "a..b" }{TEXT -1 10 " (de type " }
{TEXT 305 5 "range" }{TEXT -1 3 ") ." }}{PARA 0 "" 0 "" {TEXT -1 0 "" 
}}{PARA 0 "" 0 "" {TEXT -1 12 "La fonction " }{TEXT 306 5 "array" }
{TEXT -1 29 " permet de cr\351er un tableau :" }}{PARA 0 "" 0 "" 
{TEXT -1 70 "Des fonctions analogues \340 celles utilis\351es pour les
 tables existent : " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "
" {TEXT -1 38 "Cr\351ation d'un tableau \340 une dimension:" }}{PARA 
0 "> " 0 "" {MPLTEXT 1 0 15 "T:=array(1..3);" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%\"TG-%&arrayG6$;\"\"\"\"\"$7\"" }}}{EXCHG {PARA 0 "" 
0 "" {TEXT -1 68 "Cr\351ation d'un tableau \340 une dimension avec ini
tialisation partielle:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "U
:=array(1..5,[a,b,c]);  " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"UG-%'v
ectorG6#7'%\"aG%\"bG%\"cG&F$6#\"\"%&F$6#\"\"&" }}}{EXCHG {PARA 0 "" 0 
"" {TEXT -1 66 "Cr\351ation d'un tableau \340 2 dimensions avec initia
lisation compl\350te:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 31 "V:
=array([[a,b,c],[d,e,f]]);   " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"V
G-%'matrixG6#7$7%%\"aG%\"bG%\"cG7%%\"dG%\"eG%\"fG" }}}{PARA 0 "" 0 "" 
{TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 259 "" 0 
"" {TEXT 372 93 "Cr\351ation d'un tableau rectangulaire d'entiers par \+
affectation \340 l'aide de boucles imbriqu\351es:" }{TEXT -1 0 "" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 104 "T:=array(1..2,1..3):\nfor i
 to 2 do\n  for j to 3 do \n     T[i,j]:=(i-1)*3+j; \n  end do;\nend d
o:\nprint(T);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'matrixG6#7$7%\"\"
\"\"\"#\"\"$7%\"\"%\"\"&\"\"'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 10 "op(op(T));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%;\"\"\"\"\"#;F$\"
\"$7(/6$F%F%\"\"&/6$F$F%F%/6$F$F$F$/6$F%F$\"\"%/6$F$F'F'/6$F%F'\"\"'" 
}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "indices(T);" }}{PARA 11 "
" 1 "" {XPPMATH 20 "6(7$\"\"#F$7$\"\"\"F$7$F&F&7$F$F&7$F&\"\"$7$F$F*" 
}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "entries(T);" }}{PARA 11 "
" 1 "" {XPPMATH 20 "6(7#\"\"&7#\"\"#7#\"\"\"7#\"\"%7#\"\"$7#\"\"'" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "map(x->x^2,T);" }}{PARA 11 "
" 1 "" {XPPMATH 20 "6#-%'matrixG6#7$7%\"\"\"\"\"%\"\"*7%\"#;\"#D\"#O" 
}}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 104 "Conversion d'un tableau en lis
te (si la dimension est 1) ou en liste de listes (si la dimension est \+
>1):" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 36 "convert(U,list);convert(T,l
istlist);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7'%\"aG%\"bG%\"cG&%\"UG6#
\"\"%&F(6#\"\"&" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7$7%\"\"\"\"\"#\"\"
$7%\"\"%\"\"&\"\"'" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 60 "Conversion \+
d'un tableau de dimension quelconque en ensemble:" }}{PARA 0 "> " 0 "
" {MPLTEXT 1 0 15 "convert(T,set);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#
<(\"\"\"\"\"#\"\"$\"\"%\"\"&\"\"'" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 28 "T:=convert([a,b,c,d],array);" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%\"TG-%'vectorG6#7&%\"aG%\"bG%\"cG%\"dG" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "U:=copy(T);" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%\"UG-%'vectorG6#7&%\"aG%\"bG%\"cG%\"dG" }}}{PARA 0 "
" 0 "" {TEXT -1 0 "" }}{PARA 256 "" 0 "" {TEXT -1 21 "Exercices corrig
\351s 4:" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "" 0 "" 
{TEXT 307 8 "Ex 4.1: " }{TEXT -1 59 "Ecrire une proc\351dure qui inver
se les \351l\351ments d'une liste ." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }
}{PARA 0 "> " 0 "" {MPLTEXT 1 0 89 "restart;\nlisteinverse:= proc(L::l
ist)\n  local i;\n  [seq(op(nops(L)-i,L),i=0..nops(L)-1)];" }}{PARA 0 
"" 0 "" {TEXT -1 6 "      " }{MPLTEXT 1 0 9 "end proc:" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "listeinverse([a,b,c,d,e,f]);" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#7(%\"fG%\"eG%\"dG%\"cG%\"bG%\"aG" }}}
{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "" 0 "" {TEXT 308 7 "Ex
 4.2:" }{TEXT -1 42 " Cr\351er une matrice de Vandermonde d'ordre " }
{TEXT 309 1 "n" }{TEXT -1 18 " . Exemple , pour " }{XPPEDIT 18 0 "n=4
" "6#/%\"nG\"\"%" }{TEXT -1 3 " :\n" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 
161 "VDM:=proc(n::posint)\n  local i,j,a,V;\n  a:=array(1..n):V:=array
(1..n,1..n):\n  for i to n do for j to n do V[i,j]:=a[i]^(j-1) end do \+
end do;\n  print(V);\nend proc:" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "VDM(4);" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#-%'matrixG6#7&7&\"\"\"&%\"aG6#F(*$)F)\"\"#F(*$)F)\"\"$F
(7&F(&F*6#F.*$)F3F.F(*$)F3F1F(7&F(&F*6#F1*$)F:F.F(*$)F:F1F(7&F(&F*6#\"
\"%*$)FAF.F(*$)FAF1F(" }}}{PARA 256 "" 0 "" {TEXT -1 17 "Travail dirig
\351 4:" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "" 0 "" 
{TEXT 378 7 "TD 4.1:" }{TEXT -1 15 "\n1\260 Un tableau " }{TEXT 311 1 
"T" }{TEXT -1 3 " \340 " }{TEXT 312 1 "n" }{TEXT -1 11 " lignes et " }
{TEXT 313 1 "p" }{TEXT -1 44 " colonnes \351tant donn\351 , \351crire \+
une proc\351dure" }}{PARA 0 "" 0 "" {TEXT -1 5 "     " }{TEXT 314 18 "
ligne( T , p , i )" }{TEXT -1 38 " qui calcule la somme des \351l\351m
ents de " }{TEXT 315 1 "T" }{TEXT -1 17 " situ\351s en ligne " }{TEXT 
316 1 "i" }{TEXT -1 2 " ." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "
" 0 "" {TEXT -1 14 "2\260 Un tableau " }{TEXT 317 1 "T" }{TEXT -1 3 " \+
\340 " }{TEXT 318 1 "n" }{TEXT -1 11 " lignes et " }{TEXT 319 1 "p" }
{TEXT -1 44 " colonnes \351tant donn\351 , \351crire une proc\351dure
" }}{PARA 0 "" 0 "" {TEXT -1 5 "     " }{TEXT 320 21 "colonne( T , n ,
 j ) " }{TEXT -1 37 "qui calcule la somme des \351l\351ments de " }
{TEXT 321 1 "T" }{TEXT -1 18 " situ\351s en colonne" }{TEXT 322 2 " j
" }{TEXT -1 2 " ." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" 
{TEXT -1 20 "3\260 Un tableau carr\351 " }{TEXT 323 1 "T" }{TEXT -1 3 
" \340 " }{TEXT 324 1 "n" }{TEXT -1 11 " lignes et " }{TEXT 325 1 "n" 
}{TEXT -1 44 " colonnes \351tant donn\351 , \351crire une proc\351dure
" }}{PARA 0 "" 0 "" {TEXT -1 4 "    " }{TEXT 326 20 " diagonale1( T , \+
n )" }{TEXT -1 38 " qui calcule la somme des \351l\351ments de " }
{TEXT 327 1 "T" }{TEXT -1 34 " situ\351s sur la premi\350re diagonale.
" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 20 "4\260
 Un tableau carr\351 " }{TEXT 328 1 "T" }{TEXT -1 3 " \340 " }{TEXT 
329 1 "n" }{TEXT -1 11 " lignes et " }{TEXT 330 1 "n" }{TEXT -1 44 " c
olonnes \351tant donn\351 , \351crire une proc\351dure" }}{PARA 0 "" 
0 "" {TEXT -1 5 "     " }{TEXT 331 19 "diagonale2( T , n )" }{TEXT -1 
38 " qui calcule la somme des \351l\351ments de " }{TEXT 332 1 "T" }
{TEXT -1 33 " situ\351s sur la seconde diagonale." }}{PARA 0 "" 0 "" 
{TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 14 "5\260 Un tableau " }
{TEXT 333 1 "T" }{TEXT -1 9 " carr\351 \340 " }{TEXT 334 1 "n" }{TEXT 
-1 11 " lignes et " }{TEXT 335 1 "n" }{TEXT -1 53 " colonnes est dit m
agique si la somme des \351l\351ments de" }}{PARA 0 "" 0 "" {TEXT -1 
96 "     n'importe quelle ligne , de n'importe quelle colonne , et de \+
n'importe quelle diagonale est" }}{PARA 0 "" 0 "" {TEXT -1 16 "     la
 m\352me .  " }}{PARA 0 "" 0 "" {TEXT -1 66 "     Utiliser les proc
\351dures pr\351c\351dentes pour \351crire une fonction " }{TEXT 337 
9 "bool\351enne" }{TEXT -1 1 " " }{TEXT 336 16 "magique( T , n )" }}
{PARA 0 "" 0 "" {TEXT -1 23 "     rendant la valeur " }{TEXT 338 4 "tr
ue" }{TEXT -1 4 " si " }{TEXT 339 1 "T" }{TEXT -1 17 " est magique, et
 " }{TEXT 340 5 "false" }{TEXT -1 8 " sinon ." }}{PARA 0 "" 0 "" 
{TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 310 9 "Exemples:" }}}{PARA 11 "
" 1 "" {XPPMATH 20 "6#>%\"TG-%'MATRIXG6#7%7%\"\")\"\"\"\"\"'7%\"\"$\"
\"&\"\"(7%\"\"%\"\"*\"\"#" }}{PARA 257 "" 0 "" {TEXT -1 0 "" }}{PARA 
0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "ma
gique(T,3);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%%trueG" }}}{PARA 0 "" 
0 "" {TEXT -1 0 "" }}{PARA 11 "" 1 "" {TEXT -1 0 "" }{XPPMATH 20 "6#>%
\"UG-%'matrixG6#7%7%\"\"&\"\"'\"\"$7%\"\"!\"\")\"\"\"7%\"\"%\"\"(\"\"#
" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "magique(U,3);" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#%&falseG" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }
}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "" 0 "" {TEXT 389 6 "T
D 4.2" }{TEXT -1 32 ":\nEcrire la proc\351dure intitul\351e " }{TEXT 
379 17 "coder(st::string)" }{TEXT -1 39 " qui convertit la cha\356ne d
e caract\350res " }{TEXT 380 2 "st" }{TEXT -1 1 " " }}{PARA 0 "" 0 "" 
{TEXT -1 44 "(\351crite en lettres minuscules) en un nombre." }}{PARA 
0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 11 "On code :  " }
{XPPEDIT 18 0 "a -> 1" "6#f*6#%\"aG7\"6$%)operatorG%&arrowG6\"\"\"\"F*
F*F*" }{TEXT -1 3 " , " }{XPPEDIT 19 1 "b -> 2" "6#f*6#%\"bG7\"6$%)ope
ratorG%&arrowG6\"\"\"#F*F*F*" }{TEXT -1 13 " , etc ... , " }{XPPEDIT 
19 1 "z -> 26" "6#f*6#%\"zG7\"6$%)operatorG%&arrowG6\"\"#EF*F*F*" }
{TEXT -1 2 " ." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" 
{TEXT 388 8 "Exemple:" }{TEXT -1 5 " si  " }{XPPEDIT 18 0 "st=maple" "
6#/%#stG%&mapleG" }{TEXT -1 7 " alors " }{XPPEDIT 18 0 "m -> 13" "6#f*
6#%\"mG7\"6$%)operatorG%&arrowG6\"\"#8F*F*F*" }{TEXT -1 3 " , " }
{XPPEDIT 18 0 "a -> 1" "6#f*6#%\"aG7\"6$%)operatorG%&arrowG6\"\"\"\"F*
F*F*" }{TEXT -1 3 " , " }{XPPEDIT 18 0 "p -> 1" "6#f*6#%\"pG7\"6$%)ope
ratorG%&arrowG6\"\"\"\"F*F*F*" }{TEXT -1 4 "6 , " }{XPPEDIT 18 0 "l ->
 12" "6#f*6#%\"lG7\"6$%)operatorG%&arrowG6\"\"#7F*F*F*" }{TEXT -1 3 " \+
, " }{XPPEDIT 18 0 "e -> 5" "6#f*6#%\"eG7\"6$%)operatorG%&arrowG6\"\"
\"&F*F*F*" }{TEXT -1 4 " .  " }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "coder(\"maple\");" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#\"+07;,8" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }
}{EXCHG {PARA 0 "" 0 "" {TEXT 381 5 "Aide:" }{TEXT -1 88 " pour \351cr
ire cette proc\351dure , on construira un alphabet puis une table T de
 conversion " }}{PARA 0 "" 0 "" {XPPEDIT 18 0 "lettres -> nombres" "6#
f*6#%(lettresG7\"6$%)operatorG%&arrowG6\"%(nombresGF*F*F*" }{TEXT -1 
60 " et on utilisera au besoin les fonctions de Maple suivantes:" }}
{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 9 "         \+
" }{TEXT 382 10 "length(st)" }{TEXT -1 50 " qui donne la longueur de l
a cha\356ne de caract\350res " }{TEXT 385 2 "st" }{TEXT -1 2 " ." }}
{PARA 0 "" 0 "" {TEXT -1 9 "         " }{TEXT 383 19 "substring(st,m..
n) " }{TEXT -1 15 "qui extrait de " }{TEXT 384 2 "st" }{TEXT -1 47 " l
a sous-cha\356ne des caract\350res situ\351s entre les" }}{PARA 0 "" 
0 "" {TEXT -1 19 "         positions " }{TEXT 386 1 "m" }{TEXT -1 4 " \+
et " }{TEXT 387 1 "n" }{TEXT -1 3 ".  " }}}}{MARK "0 0" 0 }{VIEWOPTS 
1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }