{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 6 6 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 "cours" -1 256 1 {CSTYLE "" -1 -1 "Helvetica" 1 14 0 0 128 1 2 2 2 2 2 2 1 1 1 1 }1 1 0 0 0 0 3 -4 3 0 2 2 0 1 }{PSTYLE "re -cours" -1 257 1 {CSTYLE "" -1 -1 "Times" 1 14 0 128 0 1 2 2 2 2 2 2 1 1 1 1 }1 1 0 0 0 0 3 -4 1 0 2 2 256 1 }{PSTYLE "bullet-cours" -1 258 1 {CSTYLE "" -1 -1 "Helvetica" 1 14 0 0 128 1 2 2 2 2 2 2 1 1 1 1 }1 1 0 0 0 0 3 -4 3 0 2 2 0 2 }} {SECT 0 {EXCHG {PARA 18 "" 0 "" {TEXT -1 13 "e3a 2004 info" }}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 26 " 1 : Chercher-remplacer " }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 48 "annuleNegatifs:=liste -> map(x->max (x,0),liste);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 36 "annuleNega tifs([2,5,-4,3,11,-72,5]);" }}}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 20 " \+ 2 : Racine carr\351e " }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 159 "b abylone:=proc(a,eps)\n boulot:=proc(u)\n local v; \n \+ v:=(u+a/u)/2.; \n if abs(v-u) " 0 "" {MPLTEXT 1 0 23 "babylone(100,0.000001);" }}}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 17 " 3 : Nombre de 1" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 117 "nombreDeUn:=proc(n)\n if n=0 then 0 elif irem(n,2)=0 then nom breDeUn(iquo(n,2)) else 1+nombreDeUn(iquo(n,2)) fi end;" }{TEXT -1 0 " " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "nombreDeUn(23);" }}}} {SECT 1 {PARA 3 "" 0 "" {TEXT -1 33 " 4 : Qu'affichera ce programme ? " }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 54 "x:=1:y:=1:while x<=y do \+ print(x): x:=2*x: y:=y+10: od;" }}}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 26 " 5 : Le triangle de Pascal" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 111 "lignePascal:=proc(n)\n local l,c,k;\n l:=[1];for k from 1 to n do c:=l[1]*(n-k+1)/k;l:=[c,op(l)] od; l end;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "lignePascal(8);" }}}}{SECT 1 {PARA 3 "" 0 " " {TEXT -1 48 " 6 : Tri d'une liste \340 petit ensemble de valeurs" }} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 846 "dt:=proc(tableau)\n lo cal n,j,k,i,x;\n n:=nops(tableau);j:=0;k:=0;i:=0;\n while i< op(2,op(2,eval(tableau))); do \n x:=tableau[i+1];\n if \+ x=2 then i:=i+1 else fi; \n\n if ((x=1) and (k<>i)) then tablea u[k+1]:=1;tableau[i+1]:=2;k:=k+1; i:=i+1; else fi;\n \n if ((x= 1) and (k=i)) then k:=k+1; i:=i+1; else fi; \n\n if ((x=0) and \+ (k<>i) and (j<>k)) then tableau[j+1]:=0;tableau[k+1]:=1;tablea u[i+1]:=2;j:=j+1;k:=k+1;i:=i+1; else fi;\n\n if ((x=0) and (k<> i) and (j=k)) then tableau[j+1]:=0;tableau[k+1]:=2;j:=j+1;k:=k +1;i:=i+1; else fi;\n \n if ((x=0) and (k=i) and (j<>k)) then \+ tableau[j+1]:=0;tableau[k+1]:=1;j:=j+1;k:=k+1;i:=i+1; else fi; \n\n if ((x=0) and (k=i) and (j=k)) then \ntableau[j+1]:=0;j:=j +1;k:=k+1;i:=i+1; else fi;\n end do;\n tableau \nend: " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 83 "test:=array(1..21,[1, 0 , 1, 0, 2, 2, 0, 0, 2, 1, 1, 1, 2, 1, 1, 2, 2, 0, 2, 2, 2]);" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 82 "dt(array(1..21,[1, 0, 1, 0, \+ 2, 2, 0, 0, 2, 1, 1, 1, 2, 1, 1, 2, 2, 0, 2, 2, 2]));\011" }}}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 44 " 7 : G\351n\351ration de nombres pseudo -al\351atoires" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "puiss10 := map(k-> 10^k,[$0..12]);" }{TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 91 "sous_nombre :=proc(n,i,j) local p; p:=puiss10[12-i]; \+ iquo(n-p*iquo(n,p),puiss10[11-j]) end;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "sous_nombre (147258369, 3 ,5);" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 26 "K1:=n->sous_nombre(n,1,1);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "K2:=n->sous_nombre(n,2,2);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 70 "K3:=proc(n) local M;M:=5*puiss10[10 ]; if n<=M then n+M else n fi end; " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 81 "K4:=proc(n) local nn,m; nn:=n*n; m:=iquo(nn,puiss10[6 ]); irem(m,puiss10[11]) end;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 39 "K5:=n->irem(n*1001001001,puiss10[11]); " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 69 "K6:=n->if n<=puiss10[9] then (n+9814055677) else (puiss10[11]-n) fi;;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 60 "K7 :=n-> sous_nombre(n,1,5)+(sous_nombre(n,6,10)*puiss10[6]);" }{TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "K8:=K5;" }}}{EXCHG {PARA 256 "" 0 "" {TEXT -1 106 " Pour manipuler les chiffres j'ai eu d es ennuis de partout avec Maple (diff\351rents selon Maple 6 ou 9 ... \+ )" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 31 "chiffre_moins1:=x-> ma x(x-1,0);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 68 "chiffre:=proc( x,n) floor(x/puiss10[n])-10*floor(x/puiss10[n+1]) end;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 46 "chiffres:=n->map(k->chiffre(n,11-k) ,[$1..10]);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 35 "map(chiffre_ moins1,chiffres(5604));" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 97 " horner:=proc(liste) if nops(liste)=1 then liste[1] else horner(liste[1 ..-2]*10)+liste[-1] fi end;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 48 "K9:=n->horner(map(chiffre_moins1,chiffres(n))); " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 57 "K10:=n->if n<=puiss10[5] then n*n+99999 e lse n-99999 fi;;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 69 "K11:=pr oc(n) local m; m:=n;while m " 0 "" {MPLTEXT 1 0 81 "K12:=proc(n) local m,x; x:=n *(n-1);m:=iquo(x,puiss10[6]);irem(m,puiss10[11]) end;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 122 "K1 (2004);K2 (2004);K3 (2004);K4 ( 2004);K5 (2004);K6 (2004);K7 (2004);K8 (2004);K9(2004);K10 (2004);K11 \+ (2004);K12 (2004);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 574 "sous K:=proc(b,x) \n if b=0 then K12 (K11 (K10 (K9 (K8 (K7 (K6 (K5 \+ (K4 (K3 (x)))))))))) \n\011 elif b=1\011then K12 (K11 (K10 (K9 (K 8 (K7 (K6 (K5 (K4 (x))))))))) \n\011 elif b=2\011then K12 (K11 (K 10 (K9 (K8 (K7 (K6 (K5 (x)))))))) \n\011 elif b=3\011then K12 (K1 1 (K10 (K9 (K8 (K7 (K6 (x))))))) \n\011 elif b=4\011then K12 (K11 (K10 (K9 (K8 (K7 (x)))))) \n\011 elif b=5\011then K12 (K11 (K10 \+ (K9 (K8 (x))))) \n\011 elif b=6 then K12 (K11 (K10 (K9 (x)))) \n \011 elif b=7 then K12 (K11 (K10 (x))) \n\011 elif b=8\011th en K12 (K11 (x)) \n\011 elif b=9\011then K12 (x) \n fi end; " }{TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 93 "K:=proc( x) local a,b,z,k; a:=K1(x); z:=x; for k from 1 to (a+1) do z:= sousK(K 2(z),z) od end;" }}}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 41 " 8 : Program mation d'expressions logiques" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 96 "mod4:=proc(n) local bon,k; bon:=true; for k from 0 to n do bon:= bon and (irem(n*n,4)<=1) od end;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "test:=(x,y)->irem(x,y)<>0;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 94 "testx:=proc(x) local bon,y; bon:=true; for y from \+ 2 to x-1 do bon:=bon and test(x,y) od; end; " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 93 "testn:=proc(n) local bon,x;bon:=false; for x fro m n to (n+n) do bon:=bon or testx(x) od; end;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 109 "bertrand:=proc(max) \n local bon,k;b on:=true; for k from 3 to max do bon:=bon and testn(k) od; end;" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "bertrand(1000);" }}}}}{MARK "4 0 0" 1 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }