{VERSION 4 0 "IBM INTEL NT" "4.0" } {USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0 1 0 0 0 0 1 }{PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }1 1 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Headi ng 1" -1 3 1 {CSTYLE "" -1 -1 "Times" 1 18 0 0 0 1 2 1 2 2 2 2 1 1 1 1 }1 1 0 0 8 4 1 0 1 0 2 2 0 1 }{PSTYLE "Maple Output" -1 11 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }3 3 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Maple Plot" -1 13 1 {CSTYLE "" -1 -1 "Time s" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }3 1 0 0 0 0 1 0 1 0 2 2 0 1 } {PSTYLE "Title" -1 18 1 {CSTYLE "" -1 -1 "Times" 1 18 0 0 0 1 2 1 1 2 2 2 1 1 1 1 }3 1 0 0 12 12 1 0 1 0 2 2 19 1 }{PSTYLE "" 0 256 1 {CSTYLE "" -1 -1 "" 1 14 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 0 257 1 {CSTYLE "" -1 -1 "" 1 14 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }} {SECT 0 {EXCHG {PARA 18 "" 0 "" {TEXT -1 49 "Correction : Proc\351dure s et structures de contr\364le" }}}{SECT 0 {PARA 3 "" 0 "" {TEXT -1 13 "1. Initiation" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 136 "abs2:= x->if x>0 then x else -x fi:\nmax2:=(x,y)->if x>y then x else y fi:\nH eaviside2:=x->if x>0 then 1 elif x<0 then 0 else undefined fi:" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 149 "sum2:=proc(f, n)\nlocal s, \+ i; s:=0;\nfor i from 1 to n do s:=s+f(i) od; s; end:\nassume(k, nonneg int); sum(i^k, i=1..n):\nsum(1/i^(2*k), i=1..infinity):\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 64 "f:=x->if abs(x)<1 then exp(1/(x^2-1 )) else 0 fi:\nplot(f, -2..2);" }}{PARA 13 "" 1 "" {GLPLOT2D 796 179 179 {PLOTDATA 2 "6%-%'CURVESG6$7io7$$!\"#\"\"!$F*F*7$$!3MLLL$Q6G\">!#< F+7$$!3bmm;M!\\p$=F/F+7$$!3MLLL))Qj^'***!#=F+7$$!3k+++]miz(*FQ$\"3Y`Fef;&z3\"!#F7$$!3_++++Y0j&*FQ$\"3,- df&*3$\\I)!#B7$$!3-,++v&oZX*FQ$\"3#RKs5YC'[!)!#A7$$!3Q+++]D[Y$*FQ$\"3a (*ynQB$Hn$!#@7$$!3x*****\\_'>Q#*FQ$\"3'Q_Ka[a\")3\"!#?7$$!3E++++0\"*H \"*FQ$\"3Wa*pRDK#fCFio7$$!3=++++f\\7()FQ$\"3A)[<*yQOv:!#>7$$!35++++83& H)FQ$\"3#3Y>\\C#)=0%Fdp7$$!3!ommT&)Gg\"zFQ$\"3-tI$R'3nnoFdp7$$!3\\LLL3 k(p`(FQ$\"3]\"\\-$>YEv)*Fdp7$$!3M++](QYi3(FQ$\"3&>$=IS,sT8FQ7$$!3Anmmm j^NmFQ$\"3_)*z^)>k^n\"FQ7$$!3gnmm;*)o`iFQ$\"38m@3fXSN>FQ7$$!3)zmmmYh=( eFQ$\"3YTkT;;bt@FQ7$$!3\\ML$3P0xU&FQ$\"35v(>8CjGU#FQ7$$!3+,++v#\\N)\\F Q$\"3Gw*z9%FQ$ \"3y>K3$)GaqHFQ7$$!39*****\\FRXL$FQ$\"3w[WbiU>YKFQ7$$!3t*****\\#=/8DFQ $\"31!*o)z(p(*QMFQ7$$!3=mmm;a*el\"FQ$\"39p*yTvEld$FQ7$$!3_mm;H9Li7FQ$ \"3%)z[g3Sq>OFQ7$$!3komm;Wn(o)Fdp$\"3uhmT7M#4l$FQ7$$!3$G++]7bDW%Fdp$\" 3W\"G+YmE:n$FQ7$$!3IqLLL$eV(>Fio$\"3-=EsOFQ7$$\"3:Tm;zHz;kFdp$\"3=?IVi chjOFQ7$$\"3)Qjmm\"f`@')Fdp$\"3#pua!HxM^OFQ7$$\"3mILLL1+Y7FQ$\"3\"[\"H (\\%[B@OFQ7$$\"3%z****\\nZ)H;FQ$\"3O=Fo99wzNFQ7$$\"3ckmm;$y*eCFQ$\"3' \\N4eN&\\\\MFQ7$$\"3f)******R^bJ$FQ$\"3%zjz0yz8D$FQ7$$\"3'e*****\\5a`T FQ$\"3[*RD[!z[')HFQ7$$\"3O'***\\(3S*eXFQ$\"3hA:jk]#)HGFQ7$$\"3'o****\\ 7RV'\\FQ$\"3/\"pdJx'f_EFQ7$$\"3l'***\\PcY9aFQ$\"3DA@.8([)HCFQ7$$\"3Y'* ****\\@fkeFQ$\"3K(H!))4)py<#FQ7$$\"3[jmmT30piFQ$\"3&e.M9Dd`#>FQ7$$\"3_ ILLL&4Nn'FQ$\"3_^))pV\"*4[;FQ7$$\"3([mmm^b`5(FQ$\"3i!*4/@./F8FQ7$$\"3A *******\\,s`(FQ$\"39*>0vooM()*Fdp7$$\"3.KL$e9=&GzFQ$\"3qX%*R8uNqnFdp7$ $\"3%[mm;zM)>$)FQ$\"3/:(ftKv>)QFdp7$$\"33KL$eCZwu)FQ$\"3hg$GL-\"Q89Fdp 7$$\"3M*******pfa<*FQ$\"3m$QGz/T9z\"Fio7$$\"35m;zWU4w#*FQ$\"3K(*3CpBC@ xFco7$$\"3yJLe*yGnP*FQ$\"3^V>gTayMDFco7$$\"3Y(*\\PMLOx%*FQ$\"3F?))zhL \"fT&F]o7$$\"3Ckm;zy*zd*FQ$\"3Yq.o=\\9RbFgn7$$\"3o'**\\(opEz(*FQ$\"35z K(\\$>#*G6FW7$$\"39HLLeg`!)**FQ$\"3rMT.d5^D@!$H\"7$$\"3w****\\#G2A3\"F /F+7$$\"3;LLL$)G[k6F/F+7$$\"3#)****\\7yh]7F/F+7$$\"3xmmm')fdL8F/F+7$$ \"3bmmm,FT=9F/F+7$$\"3FLL$e#pa-:F/F+7$$\"3!*******Rv&)z:F/F+7$$\"3ILLL GUYo;F/F+7$$\"3_mmm1^rZF/F+7$$ \"\"#F*F+-%'COLOURG6&%$RGBG$\"#5!\"\"F+F+-%+AXESLABELSG6$Q!6\"Feal-%%V IEWG6$;F(Fi`l%(DEFAULTG" 1 2 0 1 10 0 2 9 1 4 2 1.000000 47.000000 41.000000 0 0 "Curve 1" }}}}}{SECT 0 {PARA 3 "" 0 "" {TEXT -1 15 "2. A rithm\351tique" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 127 "isprime2: =proc(n::nonnegint)\nlocal k;\nfor k from 2 to floor(sqrt(n)) while ir em(n, k)<>0 do od;\nevalb(k=floor(sqrt(n))+1);\nend:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 178 "expo1:=proc(x, n)\nlocal k, res;\nres:=1 ; for k from 1 to n do res:=res*x od;\nres; end:\nexpo2:=(x, n)->if n= 0 then 1 elif irem(n, 2)=0 then expo2(x, n/2)^2 else x*expo2(x, n-1) f i:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 57 "igcd2:=(a, b)-> if b< >0 then igcd2(b, a mod b) else a fi:" }}}}{SECT 0 {PARA 3 "" 0 "" {TEXT -1 18 "Suite de Fibonacci" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 35 "restart; with(plots): with(linalg):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 65 "fib1:=(n::nonnegint)->if n<2 then 1 else fib1(n-1) +fib1(n-2); fi:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 107 "fib2:=p roc(n::nonnegint)\nlocal a, b, c, k;\na:=1; b:=1;\nfor k from 2 to n d o c:=b; b:=a+b; a:=c od; \nb; end:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 200 "fib3:=proc(n::nonnegint)\nlocal a, x, k, oldD, res; \nx:=(1+sqrt(5))/2; a:=1/2+sqrt(5)/10;\nk:=ceil(log10(evalf(a*x^n))); \+ oldD:=Digits; Digits:=k+10;\nres:=round(evalf(a*x^n)); Digits:=oldD;\n res;\nend proc:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 145 "er:=(A: :matrix, n::nonnegint)->if n=0 then evalm(A&*inverse(A)) else if type( n, odd) then evalm(A&*er(A, n-1)) else er(evalm(A&*A), n/2) fi; end:" }}}{PARA 11 "" 1 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 85 "fib4:=proc(n)\nlocal A, B;\nA:=matrix(2, 2, [ 0, 1, 1, 1 ]); B :=er(A, n);\nB[2, 2];\nend:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 331 "pl:=op([]): ro:=1.2: cl:=[black, red, blue, green]:\nfc:=[fib1, f ib2, fib3, fib4]:\nfor i from 1 to 4 do\n f:=fc[i]; \n k:=8; ts:=op( []); t:=0;\n while t<1 do\n t:=time(f(round(ro^k)))+1e-2;\n ts: =ts, [log[2](ro^k), log[2](t)]; k:=k+1;\n end do; #print(round(ro^(k- 1)));\n pl:=pl, plot([ts], color=cl[i]);\n end do:\ndisplay(pl);\n" }}{PARA 13 "" 1 "" {GLPLOT2D 1103 468 468 {PLOTDATA 2 "6(-%'CURVESG6$7 -7$$\"3!******pCvU5#!#<$!3;+++!>cQk'F*7$$\"3'******Hl4tO#F*F+7$$\"3$** ****z0W.j#F*F+7$$\"3)******RYyL*GF*F+7$$\"3/+++qGTcJF*F+7$$\"34+++wsW> MF*F+7$$\"39+++#o\"[#o$F*F+7$$\"37+++(3;b%RF*F+7$$\"3t*****H\\]&3UF*$! 3u*****4Wu5N%F*7$$\"3y******)*[erWF*$!3++++n(Q:D#F*7$$\"3%)*****\\I>Yt %F*$\"35+++.T->6F*-%'COLOURG6&%$RGBG\"\"!FUFU-F$6$7QF'F-F0F3F6F9F5(F*F+7$$ \"3G+++kL'\\O(F*F+7$$\"3E+++px*zi(F*F+7$$\"3I+++v@.\"*yF*F+7$$\"3Q+++ \"emS:)F*F+7$$\"3`*****p)45<%)F*F+7$$\"3Q+++#RN,o)F*$!36+++rn&yr&F*7$$ \"3c*****zzpJ%*)F*F+7$$\"3]+++/U?1#*F*F+7$$\"3o******4'Q#p%*F*F+7$$\"3 h+++;IFK(*F*F+7$$\"3y*****>U2`***F*Fcq7$$\"3\"******H=Me-\"!#;F+7$$\"3 '******HiP@0\"FgrFE7$$\"33+++k5Wy5FgrFcq7$$\"3.+++0Xu/6Fgr$!3k*****\\4 G>K%F*7$$\"33+++Xz/J6Fgr$!3m*******G.y5&F*7$$\"3/+++'Q^t:\"Fgr$!3e**** **)o$*)eSF*7$$\"33+++E[l$=\"Fgr$!33+++rXU%=$F*7$$\"3-+++n#e*47Fgr$!3)* *****\\mFkL$F*7$$\"32+++2[#F*7$$\"3)*******)eo))G\"Fgr$!\"#FU7$$\"3,+++H?<:8Fgr$!30++ +tJd9:F*7$$\"3'*******paZT8Fgr$!3-+++*o$*)e5F*7$$\"3++++5*yxO\"Fgr$!3) )*****\\^0F>'!#=7$$\"3'******4N#3%R\"Fgr$!3'******pytp/\"Fev7$$\"33+++ #z&Q?9Fgr$\"3#******fq')4Z$Fev-FR6&FT$\"*++++\"!\")$FUFUFew-F$6$7VF'F- F0F3F67$F:$!3;+++!>cQk&F*FcQk%F*F\\oF_oFboF eoFhoF[pF^pFapFdpFgpFjpF]q7$FaqF+FeqFhqF[rF^r7$FbrFjwFdr7$FirF+7$F\\sF +7$F_sFcq7$FdsF+7$FisFas7$F^tFjw7$FctFcq7$Fht$!3e******)o$*)e]F*7$F]uF fs7$Fbu$!38+++o7]OQF*7$Fgu$!3E+++N79$3%F*7$F\\vF]y7$Fav$!31+++HqbaHF*7 $Fgv$!3#******>$HBEGF*7$F\\w$!33+++rXU%=#F*7$$\"3'******>B*oY9Fgr$!3++ ++skTV>F*7$$\"33+++tE*HZ\"Fgr$!3-+++w'GfR\"F*7$$\"3%******H6'H*\\\"Fgr $!3_******QB;K\"*Fev7$$\"32+++a&*fD:Fgr$!3/+++7kJSRFev7$$\"3%******R*H !>b\"Fgr$\"3e+++*yK*Qq!#>-FR6&FTFewFewFbw-F$6$7hn7$F(Fcq7$F.Fjw7$F1Fjw 7$F4FE7$F7Fjw7$F:Ffs7$F=F]x7$F@Fjw7$FCFfs7$FHFE7$FM$!3A+++uze6]F*7$Fgn Fjw7$FjnF`y7$F]oFix7$F`oFfs7$FcoFE7$FfoFix7$Fio$!37+++G)fs&QF*7$F\\pFi x7$F_pF`y7$FbpFfs7$FepF`y7$FhpF]x7$F[qF[t7$F^q$!3%******f1#Q!o%F*7$Faq F[t7$FfqF]y7$FiqFh]l7$F\\rF[t7$F_rF]x7$Fbr$!3;+++!>cQk$F*7$FerF]y7$Fir F_]l7$F\\sF]x7$F_sF]y7$FdsF]y7$Fis$!3%)*****f`.?m$F*7$F^tF]x7$FctF`^l7 $FhtF]y7$F]uFh^l7$Fbu$!3,+++lr.;QF*7$Fgu$!3;+++a30!\\$F*7$F\\vFh^l7$Fa vFb_l7$Fgv$!33+++&4G>K$F*7$F\\w$!3-+++7K%o%GF*7$F]zFjt7$FbzFj_l7$FgzFg y7$F\\[l$!3\")******f=a.CF*7$Fa[l$!3&)*****HN#y0?F*7$$\"31+++Nk?y:Fgr$ !3,+++V_.9@F*7$$\"3%)*****f()4Xg\"Fgr$!3!******pD@Vp\"F*7$$\"31+++;L\" 3j\"Fgr$!3!******>'y5[7F*7$$\"3-+++dn6d;Fgr$!35+++Yj9H5F*7$$\"3))***** p>?Mo\"FgrFiz7$$\"3#)*****zjB(40Li