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C'est un bon moyen, mais il faut y faire attention, car si vous v ous \352tes tromp\351s \340 l'avant-derni\350re ligne (par exemple, vo us aviez \351crit [seq(%[i]*24, i=1..100)];), que vous la corrigez et \+ validez, vous serez surpris du r\351sultat, car % contiendra 23, la de rni\350re instruction en m\351moire !!" }{MPLTEXT 1 0 0 "" }}}}}{SECT 1 {PARA 3 "" 0 "" {TEXT 273 11 "Exercice 22" }}{SECT 1 {PARA 3 "" 0 " " {TEXT -1 9 "Question " }{TEXT 264 1 "a" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 45 "L2 := [seq(i^2, i=floor(sqrt(1000)+1)..100)];" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%#L2G7ao\"%C5\"%*3\"\"%c6\"%D7\"%'H\"\"%p8\"%W9\"%@:\" %+;\"%\"o\"\"%k<\"%\\=\"%O>\"%D?\"%;@\"%4A\"%/B\"%,C\"%+D\"%,E\"%/F\"% 4G\"%;H\"%DI\"%OJ\"%\\K\"%kL\"%\"[$\"%+O\"%@P\"%WQ\"%pR\"%'4%\"%DU\"%c V\"%*[%\"%CY\"%hZ\"%+\\\"%T]\"%%=&\"%H`\"%wa\"%Dc\"%wd\"%Hf\"%%3'\"%Ti \"%+k\"%hl\"%Cn\"%*)o\"%cq\"%Ds\"%'R(\"%pv\"%Wx\"%@z\"%+\")\"%\"G)\"%k %)\"%\\')\"%O))\"%D!*\"%;#*\"%4%*\"%/'*\"%,)*\"&++\"" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 22 "Puisque les carr\351s de " }{TEXT 265 1 "i" } {TEXT -1 47 " doivent \352tre entre 1000 et 10000, on sait que " } {TEXT 266 1 "i" }{TEXT -1 50 " doit \352tre entre sqrt(1000) et sqrt(1 0000) = 100. " }{TEXT 267 1 "i" }{TEXT -1 230 " devant \352tre un enti er, on doit appliquer la fonction floor. Or floor(sqrt(1000)) va donne r un nombre entier strictement inf\351rieur \340 sqrt(1000) (qui n'est pas entier... d'o\371 l'inf\351riorit\351 stricte), donc on rajoute 1 \340 floor(1000)." }}}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 9 "Question \+ " }{TEXT 268 1 "b" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 45 "L3 := [ seq(i^3, i=10..floor((10000)^(1/3)))];" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#L3G7.\"%+5\"%J8\"%G<\"%(>#\"%WF\"%vL\"%'4%\"%8\\\"%Ke\"%fo\"% +!)\"%h#*" }}}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 9 "Question " }{TEXT 270 1 "c" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "\{op(L2), op(L3) \};" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#<\\p\"%+5\"%C5\"%*3\"\"%c6\"%D7 \"%'H\"\"%J8\"%p8\"%W9\"%@:\"%+;\"%\"o\"\"%G<\"%k<\"%\\=\"%O>\"%D?\"%; @\"%(>#\"%4A\"%/B\"%,C\"%+D\"%,E\"%/F\"%WF\"%4G\"%;H\"%DI\"%OJ\"%\\K\" %kL\"%vL\"%\"[$\"%+O\"%@P\"%WQ\"%pR\"%'4%\"%DU\"%cV\"%*[%\"%CY\"%hZ\"% +\\\"%8\\\"%T]\"%%=&\"%H`\"%wa\"%Dc\"%wd\"%Ke\"%Hf\"%%3'\"%Ti\"%+k\"%h l\"%Cn\"%fo\"%*)o\"%cq\"%Ds\"%'R(\"%pv\"%Wx\"%@z\"%+!)\"%+\")\"%\"G)\" %k%)\"%\\')\"%O))\"%D!*\"%;#*\"%h#*\"%4%*\"%/'*\"%,)*\"&++\"" }}} {EXCHG {PARA 0 "" 0 "" {TEXT 269 9 "intersect" }{TEXT -1 103 " ne s'ut ilise qu'avec des ensembles, il faut donc convertir les listes en ense mbles, puis intersecter :" }{MPLTEXT 1 0 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 37 "\{op(L2)\} intersect \{op(L3)\};\nnops(%);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#<#\"%'4%" }}{PARA 11 "" 1 "" {XPPMATH 20 "6# \"\"\"" }}}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 9 "Question " }{TEXT 271 1 "d" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 137 "L4 := [seq(i^4, i=f loor(sqrt(sqrt(1000))+1)..floor(sqrt(sqrt(10000))))];\nL6 := [seq(i^6, i=floor((1000)^(1/6)+1)..floor((10000)^(1/6)))];" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#L4G7'\"%'H\"\"%,C\"%'4%\"%hl\"&++\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#L6G7#\"%'4%" }}}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 9 "Question " }{TEXT 272 1 "e" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 66 "\{op(L2)\} intersect \{op(L3)\} intersect \{op(L4)\} intersect \{op(L6)\};" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#<#\"%'4%" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 83 "Il y a effectivement un \351l\351ment com mun aux quatre listes, il s'agit du nombre 4096." }{MPLTEXT 1 0 0 "" } }}}}{SECT 1 {PARA 3 "" 0 "" {TEXT 280 11 "Exercice 23" }}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 9 "Question " }{TEXT 274 1 "a" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart;" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 157 "M := array([[ 1,-1, 0, 0], # 1\350re ligne\n \+ [ 0, 1,-1, 0], # 2\350me ligne\n [ 0, 0, 1,-1], # 3\350me ligne\n [ 0, 0, 0, 1]]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"MG-%'matrixG6#7&7&\"\"\"!\"\"\"\"!F,7&F,F*F+F,7&F,F ,F*F+7&F,F,F,F*" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 197 "Une autre sol ution, qui \351vite de tout d\351clarer, est de cr\351er une matrice d iagonale 4 x 4 gr\342ce \340 une fonction du package \"linalg\", puis \+ on d\351finit la deuxi\350me diagonale comme sugg\351r\351 par l'\351n onc\351 :" }{MPLTEXT 1 0 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 79 "M : = linalg[diag](1,1,1,1):\nfor i to 3 do\n M[i,i+1] := -1;\nod:\n'M' = evalm(M);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/%\"MG-%'matrixG6#7&7&\" \"\"!\"\"\"\"!F,7&F,F*F+F,7&F,F,F*F+7&F,F,F,F*" }}}}{SECT 1 {PARA 3 " " 0 "" {TEXT -1 9 "Question " }{TEXT 278 1 "b" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "T := array(1..3, 1..3);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"TG-%&arrayG6%;\"\"\"\"\"$F(7\"" }}}{EXCHG {PARA 0 " > " 0 "" {MPLTEXT 1 0 28 "LdL := convert(T, listlist);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$LdLG7%7%&%\"TG6$\"\"\"F*&F(6$F*\"\"#&F(6$F*\"\" $7%&F(6$F-F*&F(6$F-F-&F(6$F-F07%&F(6$F0F*&F(6$F0F-&F(6$F0F0" }}} {EXCHG {PARA 0 "" 0 "" {TEXT -1 4 "LdL[" }{TEXT 277 1 "i" }{TEXT -1 18 "] va retourner le " }{TEXT 275 1 "i" }{TEXT -1 100 "-i\350me \351l \351ment de la liste LdL. Mais comme chaque \351l\351ment de LdL est u ne liste, cela extrait donc la " }{TEXT 276 1 "i" }{TEXT -1 64 "-i\350 me liste. On convertit comme on en a maintenant l'habitude !!" } {MPLTEXT 1 0 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 42 "L := [op(LdL[1] ), op(LdL[2]), op(LdL[3])];" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"LG7 +&%\"TG6$\"\"\"F)&F'6$F)\"\"#&F'6$F)\"\"$&F'6$F,F)&F'6$F,F,&F'6$F,F/&F '6$F/F)&F'6$F/F,&F'6$F/F/" }}}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 9 "Que stion " }{TEXT 279 1 "c" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 40 "s elect(isprime, \{seq(i, i=1235..1270)\});" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#<%\"%P7\"%\\7\"%f7" }}}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{MARK "4 0 0" 0 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }