{VERSION 2 3 "DEC ALPHA UNIX" "2.3" } {USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0 1 0 0 0 0 }{CSTYLE "2D Math" -1 2 "Times" 0 1 0 0 0 0 0 0 2 0 0 0 0 0 0 }{CSTYLE "2D Output" 2 20 "" 0 1 0 0 255 1 0 0 0 0 0 0 0 0 0 } {PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "" 0 1 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 "Text Output" -1 2 1 {CSTYLE "" -1 -1 "Courier" 1 10 0 0 255 1 0 0 0 0 0 1 3 0 3 }1 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Warning" 2 7 1 {CSTYLE "" -1 -1 "" 0 1 0 0 255 1 0 0 0 0 0 0 1 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 } {PSTYLE "Maple Output" 0 11 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }3 3 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 11 12 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }1 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Maple Plot" 0 13 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }3 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }} {SECT 0 {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 43 "#Gomes Texeira page \+ 45, focales de Van Rees" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 35 " f:=x*(x^2+y^2)-a*(x^2+y^2)-b*x-c*y;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6 #>%\"fG,**&%\"xG\"\"\",&*$F'\"\"#F(*$%\"yGF+F(F(F(*&%\"aGF(F)F(!\"\"*& %\"bGF(F'F(F0*&%\"cGF(F-F(F0" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "f1:=subs(a=1,b=1,c=-1,f);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%# f1G,,*&%\"xG\"\"\",&*$F'\"\"#F(*$%\"yGF+F(F(F(F*!\"\"F,F.F'F.F-F(" }}} {EXCHG {PARA 0 "" 0 "" {TEXT -1 47 "Le package algcurves n'existe pas \+ en Maple V.4." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 110 "w1 := [u^ 3-u+v^2, (y-1)/(-1+x), x*(x-2+y)/(1-2*x+x^2), (u-1)*u/(1+u^2)-v/(1+u^2 ), -(u-1)/(1+u^2)-u*v/(1+u^2)];" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%# w1G7',(*$%\"uG\"\"$\"\"\"F(!\"\"*$%\"vG\"\"#F**&,&%\"yGF*F+F*F*,&F+F*% \"xGF*F+*(F3F*,(F3F*!\"#F*F1F*F*,(F*F*F3F6*$F3F.F*F+,&*(,&F(F*F+F*F*F( F*,&F*F**$F(F.F*F+F**&F-F*F " 0 "" {MPLTEXT 1 0 22 "V:=[solve(w1[1],\{v\})];" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"VG7$<#/%\"vG*$,&*$%\"uG\"\"$!\"\"F ,\"\"\"#F/\"\"#<#/F(,$F)F." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 50 "for i to 2 do arc[i]:=subs(V[i],[w1[4],w1[5]]) od;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%$arcG6#\"\"\"7$,&*(,&%\"uGF'!\"\"F'F'F,F',&F'F' *$F,\"\"#F'F-F'*&,&*$F,\"\"$F-F,F'#F'F0F.F-F-,&*&F+F'F.F-F-*(F,F'F2F5F .F-F-" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%$arcG6#\"\"#7$,&*(,&%\"uG \"\"\"!\"\"F-F-F,F-,&F-F-*$F,F'F-F.F-*&,&*$F,\"\"$F.F,F-#F-F'F/F.F-,&* &F+F-F/F.F.*(F,F-F2F5F/F.F-" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "p:=select(has,w1[1],u):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "lp:=-coeff(p,u,3):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "p root:=[fsolve(p,u)]:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 297 "if nops(proot)=1 then \n nb:=1;\n if lp>0 then r[1]:=proot[1]..infinit y\n else r[1]:=-infinity..proot[1]\n fi\nelse\n nb:=2;\n proot:=so rt(proot);\n if lp>0 then \n r[1]:=proot[1]..proot[2];\n r[2]:= proot[3]..infinity\n else \n r[1]:=-infinity..proot[1];\n r[2]: =proot[2]..proot[3]\n fi\nfi:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 122 "for i to nb do\n picture[i,1]:=plot([arc[1][1],arc[1][2],u=r [i]]);\n picture[i,2]:=plot([arc[2][1],arc[2][2],u=r[i]])\nod:\n" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 82 "plots[display](\{seq(op([pic ture[i,1],picture[i,2]]),i=1..nb)\},view=[-1..2,-6..6]);" }}{PARA 13 " " 1 "" {INLPLOT "6'-%'CURVESG6$7ao7$\"\"!$\"\"\"F(7$$\"3uX\"HZwM=a#!#> $\"3SW6@H:O$***!#=7$$\"3y^t\"H=3\\b$F.$\"3#4`c;2ho)**F17$$\"3cmS$4/KlJ %F.$\"3,#*3/WsW!)**F17$$\"3!yZG.NM![\\F.$\"3L>hj?<5u**F17$$\"3*)G&[W#* ed)fF.$\"3#R^,bpw:'**F17$$\"3:F;Ybe'*F17$$\" 3\"p%RImLCsz#F1$\"3&o/x2)eH(>)F17$$\"3>v7*pjn)GGF1$\"3Q=P%\\tG7 0)F17$$\"3,Sx\"zV1!eGF1$\"34$f(**\\')35zF17$$\"3'))*QH16`zGF1$\"3y0.&[ qN9y(F17$$\"3$*y<.jtd**GF1$\"39=A'p%HmFwF17$$\"3PYG%z)QA7HF1$\"37X,*)H Hd'\\(F17$$\"3zMyN9&3B#HF1$\"3#*fv(R'[&HM(F17$$\"3!>UG9bXt#HF1$\"3(**H /e\"R\"e?(F17$$\"3F5h!f<2*GHF1$\"3n[3V1X#R0(F17$$\"3Q)zdRP;n#HF1$\"3D# >(yEYu2pF17$$\"3pvzq#Q`2#HF1$\"3.g'H?**QMv'F17$$\"3:Q+jd`17HF1$\"3tEQ' *\\o(*4mF17$$\"3Q>1LYsJ**GF1$\"3Fvq?YM;`kF17$$\"3geQP#R3C)GF1$\"3`XO(p w#z(G'F17$$\"3'3ng6-cY'GF1$\"3fBWs:**eThF17$$\"3Jly0mLHUGF1$\"3x53yZ08 \")fF17$$\"3)p6ig:hc\"GF1$\"3JU(G-YHB\"eF17$$\"3Ol!Gt)>0'y#F1$\"34kSej -%Rk&F17$$\"3)p>hRqXRv#F1$\"3J0\"))33wwZ&F17$$\"3yQ@\\D!QTr#F1$\"3<7S? 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"redproc:=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 then [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 "" {TEXT -1 156 "exprofile cree un probleme. Le writeto(t erminal) ne redirige pas l'output vers la sortie standard. Detail amus ant: il cree un fichier vide de nom terminal !" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 20 "#readlib(exprofile):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 163 "#kernelopts(profile=true):\n#writeto(`output_V4 _add.txt`);\n#pt1:=pt:\n#for i to 100 do\n# pt1:=ec2[Add](pt1,pt)\n#o d:\n#kernelopts(profile=false):\n#writeto(terminal);\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 74 "#excallgraph(`/export/web/dumas/GoS aZi95/Answers/IV.1/output_V4_add.txt`);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 165 "#kernelopts(profile=true):\n#writeto(`output_V4_subt .txt`);\n#pt1:=pt:\n#for i to 100 do\n# pt1:=ec2[Subt](pt1,pt)\n#od: \n#kernelopts(profile=false):\n#writeto(terminal);\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 75 "#excallgraph(`/export/web/dumas/GoSaZi95/ Answers/IV.1/output_V4_subt.txt`);" }}}{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 mod N end,pt);\n g:=igcd(op(pt1)); \n \+ if g=0 then ERROR() \n else pt1:=[seq(pt1[i]/g,i=1..3)] \n fi \n end)\nend:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "p:=nextpr ime(10^100);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%\"pG\"`qn-++++++++++ ++++++++++++++++++++++++++++++++++++++\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "normalproc:=normalNproc(p):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "redproc:=modNredproc(p):" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 45 "ec3:=EC(f2,[x,y],[0,1,0],normalproc,redproc): " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "nmin:=1000:\nnmax:=1100 :" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 47 "Execution extremement lente, desesperante meme." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 158 "for n from nmin to nmax do \ngc():\nstart:=time():\npt2:=ec3[Ext1](n,pt): \nT1[n]:=time()-start;\ngc():\nstart:=time():\npt3:=ec3[Ext2](n,pt):\n T2[n]:=time()-start\nod:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 99 "plot([[seq([n,T1[n]],n=nmin..nmax)],\n [seq([n,T2[n]],n=nmin..nm ax)]],\n color=[red,black]);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 98 "plot([[seq([n,a1[n]+d1[n]],n=nmin..nmax)],[seq([n,a2[ n]+d2[n]],n=nmin..nmax)]],color=[red,black]);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{MARK "54 0 0" 156 }{VIEWOPTS 1 1 0 1 1 1803 }