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RFE$\"3BF2CU&Hx\"fF*7$$\"3\")*o_Y]v,s\"F*$\"3H%[-CxV*)>'F*7$$\"35\"4$f /k.4HF*$\"3L')4rlsi^kF*7$$\"3rMwbs\"*RyTF*$\"3>X&H!H3U@nF*7$$\"3M7lt/0 jG`F*$\"3VySg'*Q*e'pF*7$$\"3W(*ermr8'e'F*$\"3n`@ELv;LsF*7$$\"38HF&e$HN pxF*$\"3INeB'>^Y[(F*7$$\"3*ooFFMah+*F*$\"3'o1nd3Cvu(F*7$$\"3:7jYy``@5F -$\"3[+N2%QIX+)F*7$$\"3fv(fPNF\"[6F-$\"3aiiHg@ft#)F*7$$\"3aQ0yr/0q7F-$ \"3&4W\\&H1tK&)F*7$$\"31!*GqpWt%R\"F-$\"3*)R#fD9Pxz)F*7$$\"3k_3<@gQ=:F -$\"35 " 0 "" {MPLTEXT 1 0 57 "read \"/export/web/dumas/GoSaZi95/Answers /IV.1/EC_V5.mpl\";" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 40 "ec1:= EC(f1,[x,y],N,radnormal,radnormal):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "Lpt:=[N,P,Q,R,S]: " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 57 "for i to nops(Lpt) do\n pt.i:=[Lpt[i][1],Lpt[i][2],1 ]\nod;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$pt1G7%,&#\"\"'\"\"&\"\"\" *&-%%sqrtG6#\"\"$\"\"\"-F-6#\"\")F0#F*\"#5,&#\"\"#F)F*F+#!\"$F5F*" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%$pt2G7%,&#!\"\"\"\"&\"\"\"*$-%%sqrtG 6#\"\"'\"\"\"F',&#\"\"$F)F*F+#F(\"#:F*" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$pt3G7%,&#!\"\"\"\"&\"\"\"*$-%%sqrtG6#\"#C\"\"\"#F*\"#5,&#\"\" #F)F*F+#F*\"#?F*" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$pt4G7%,$*&*$-%% sqrtG6#\"\"'\"\"\"F-,&*$F)F-\"#N!#7\"\"\"!\"\"F0,$*&,&F/\"#5!\"(F2F-F. 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else \n\011 if state=1 then\n\011 \+ y:=y/z;\n\011 z:=z^2;\n\011 state:=11\n\011 fi;\n\011 \+ z:=z^2\n\011 fi\n fi;\n od;\n y*z\n fi\n end: \n " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "expodiv(31,x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*$)%\"xG\"#J\"\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 613 "expodiv:=proc(n::integer,x)\n local L ,y,z,i,state;\n if n=0 then 1\n elif n<0 then expodiv(-n,1/x)\n \+ else\n L:=convert(n,base,2);\n y:=1; \n z:=x;\n \+ state:=0;\n for i to nops(L) do\n if L[i]=0 then \n\011 \+ if state=0 then\n\011 z:=``(z)^2\n\011 elif state=1 then\n\011 \+ y:=``(y)*``(z);\n\011 z:=``(``(z)^2)^2; \n\011 state:=0 \n \+ else\n\011 state:=1\n\011 fi;\n else\n\011 if state=0 \+ then \n\011 state:=1\n else \n\011 if state=1 then\n \011 y:=``(y)/``(z);\n\011 z:=``(z)^2;\n\011 state:=11 \n\011 fi;\n\011 z:=``(z)^2\n\011 fi\n fi;\n od;\n \+ ``(y)*``(z)\n fi\n end:\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "expodiv(31,x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*&- 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7$F^[yFV7$Fa[yFY7$Fd[yFV7$Fg[yFY7$Fj[yFY7$F]\\yFfn7$F`\\yFS-Fc\\y6&Fe \\y$\"*++++\"!\")F*F*Ff\\y-%+AXESLABELSG6$%!GF`\\]l-%%VIEWG6$%(DEFAULT GFd\\]l" 2 249 249 249 2 0 1 0 2 9 0 4 2 1.000000 45.000000 45.000000 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "f2:=y^2-(x^3-4*x+4);" }}{PARA 11 " " 1 "" {XPPMATH 20 "6#>%#f2G,**$)%\"yG\"\"#\"\"\"\"\"\"*$)%\"xG\"\"$F* !\"\"F.\"\"%!\"%F+" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 180 "redp roc:=proc(pt) \n local g,i,pt1; \n g:=igcd(op(pt)); \n if g=0 then \+ ERROR() \n else pt1:=[seq(pt[i]/g,i=1..3)] \n fi;\n if pt1[3]<0 the n [seq(-pt1[i],i=1..3)] else pt1 fi;\nend:\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 39 "ec2:=EC(f2,[x,y],[0,1,0],x->x,redproc):" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "pt:=[2,2,1];" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#ptG7%\"\"#F&\"\"\"" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 19 "readlib(exprofile):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 152 "kernelopts(profile=true):\nwriteto(\"output_add.txt \");\npt1:=pt:\nfor i to 100 do\n pt1:=ec2[Add](pt1,pt)\nod:\nkernelo pts(profile=false):\nwriteto(terminal);\n" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 64 "# le fichier a pour taille 163642 bytes, donc entre 150 et 200K." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "excallgrap h(\"output_add.txt\");" }}{PARA 6 "" 1 "" {TEXT -1 74 " \+ used by Callee" }}{PARA 6 "" 1 "" {TEXT -1 79 " Caller Callee \+ #calls time words" }}{PARA 6 "" 1 "" {TEXT -1 79 " = ===== ====== ====== ==== = ====" }}{PARA 6 "" 1 "" {TEXT -1 79 "#++ calls \+ Main_Routine 1, 105.223, 9608673" }}{PARA 6 "" 1 "" {TEXT -1 79 "#++ Main_Routine calls ec2[Add] \+ 100, 20.110, 718473" }}{PARA 6 "" 1 "" {TEXT -1 79 "#++ ec2[Add] \+ calls thirdpoint1 199, 14.563, 584687" }} {PARA 6 "" 1 "" {TEXT -1 79 "#++ thirdpoint1 calls collect \+ 199, 11.720, 410775" }}{PARA 6 "" 1 "" {TEXT -1 79 "#++ collect calls collect/recursive 200, 6.95 0, 344085" }}{PARA 6 "" 1 "" {TEXT -1 79 "#++ collect/recursive \+ calls collect/series 200, 2.377, 256092" }}{PARA 6 "" 1 " " {TEXT -1 79 "#++ ec2[Add] calls reductionproc \+ 100, 1.497, 77230" }}{PARA 6 "" 1 "" {TEXT -1 79 "#++ ec2[Add] \+ calls isequal 200, 1.990, 31997" }} {PARA 6 "" 1 "" {TEXT -1 79 "#++ collect/recursive calls collect/ recursive 400, 1.460, 31874" }}{PARA 6 "" 1 "" {TEXT -1 79 "#++ collect calls unknown 400, 1.38 0, 14048" }}{PARA 6 "" 1 "" {TEXT -1 79 "#++ isequal \+ calls normalizationproc 203, .670, 6365" }}{PARA 6 "" 1 " " {TEXT -1 79 "#++ ec2[Add] calls thirdpoint2 \+ 1, .070, 3595" }}{PARA 6 "" 1 "" {TEXT -1 79 "#++ thirdpoin t2 calls collect 1, .060, 2299" }} {PARA 6 "" 1 "" {TEXT -1 79 "#++ collect/series calls gc \+ 1, .573, 65" }}{PARA 6 "" 1 "" {TEXT -1 79 "#++ thirdpoint1 calls gc 1, .55 0, 65" }}{PARA 6 "" 1 "" {TEXT -1 79 "#++ collect \+ calls gc 1, .527, 65" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 154 "kernelopts(profile=true):\nwriteto(\"out put_subt.txt\");\npt1:=pt:\nfor i to 100 do\n pt1:=ec2[Subt](pt1,pt) \nod:\nkernelopts(profile=false):\nwriteto(terminal);\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 31 "excallgraph(\"output_subt.txt\");" }}{PARA 6 "" 1 "" {TEXT -1 74 " \+ used by Callee" }}{PARA 6 "" 1 "" {TEXT -1 79 " \+ Caller Callee #calls time \+ words" }}{PARA 6 "" 1 "" {TEXT -1 79 " ====== \+ ====== ====== ==== =====" }}{PARA 6 "" 1 "" {TEXT -1 79 "#++ calls Main_Routine \+ 1, 149.723,11638195" }}{PARA 6 "" 1 "" {TEXT -1 79 "#++ Main_Routin e calls ec2[Subt] 100, 20.130, 729145" }} {PARA 6 "" 1 "" {TEXT -1 79 "#++ ec2[Subt] calls thirdpoi nt1 198, 14.633, 606596" }}{PARA 6 "" 1 "" {TEXT -1 79 "#++ thirdpoint1 calls collect 198, 12.46 0, 460572" }}{PARA 6 "" 1 "" {TEXT -1 79 "#++ collect \+ calls collect/recursive 199, 8.293, 398347" }}{PARA 6 "" 1 " " {TEXT -1 79 "#++ collect/recursive calls collect/series \+ 199, 3.837, 316717" }}{PARA 6 "" 1 "" {TEXT -1 79 "#++ ec2[Subt] calls reductionproc 100, 1.427, 69345" }} {PARA 6 "" 1 "" {TEXT -1 79 "#++ ec2[Subt] calls isequal \+ 200, 2.047, 31087" }}{PARA 6 "" 1 "" {TEXT -1 79 "#++ collect/recursive calls collect/recursive 398, 1.39 0, 30141" }}{PARA 6 "" 1 "" {TEXT -1 79 "#++ collect \+ calls unknown 398, 1.257, 12733" }}{PARA 6 "" 1 " " {TEXT -1 79 "#++ isequal calls normalizationproc \+ 205, .597, 6240" }}{PARA 6 "" 1 "" {TEXT -1 79 "#++ ec2[Subt] calls thirdpoint2 1, .063, 3048" }} {PARA 6 "" 1 "" {TEXT -1 79 "#++ thirdpoint2 calls collect \+ 1, .050, 1939" }}{PARA 6 "" 1 "" {TEXT -1 79 "#++ collect/series calls gc 3, 1.68 0, 198" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 117 "normalNproc: =proc(N::posint)\n local _N;\n subs(_N=N,\n proc(pt) \n map(proc (expr) expr mod _N end,pt) \n end)\nend:" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 233 "modNredproc:=proc(N::posint)\n local _N;\n subs( _N=N,\n proc(pt)\n local g,i,pt1; \n pt1:=map(proc(expr) expr m od N end,pt);\n g:=igcd(op(pt1)); \n if g=0 then ERROR() \n e lse pt1:=[seq(pt1[i]/g,i=1..3)] \n fi\n end)\nend:" }}}{EXCHG {PARA 0 "> " 0 "" 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