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"> " 0 "" {MPLTEXT 1 0 0 "" }}{PARA 8 "" 1 "" {TEXT -1 26 "Plo tting error, empty plot" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 1028 "S1\n:= -7*x^4+4*x^3-50*z^4*x^2-10*z^2*y^2-46*z^2*x^4-18*y^2*x^2- 11*y^4+4*x^7-8*x^5+x^8+22*y^4*x^2-8*y^4*x-6*y^4*x^4+12*y^4*x^3-8*y^6*x ^2+4*y^6*x+12*y^2*x^5+6*z^2*y^6+2*x^6+4*y^2*x+14*y^2*x^4-16*y^2*x^3+24 *z^2*x*y^4+12*z^2*y^4*x^2-3*y^8+10*y^6-9*y^4*z^4-12*z^4*y^2-6*z^4*x^4- 36*z^4*x^3-20*z^6*x+6*z^2*x^4*y^2+12*z^2*x^3*y^2-52*z^2*x*y^2-46*z^2*y ^2*x^2-12*z^2*x^5+12*y^2*z^4*x^2+6*z^6*y^2-8*z^6*x^2-3*z^8-8*z^4*x+z^4 -2*z^6+4*y^2-48*z^2*x^3+4*x^2+4*z^2*x-6*z^2*x^2:\nS2\n:= -7*x^4+4*x^3- 50*z^4*x^2-10*z^2*y^2-46*z^2*x^4-18*y^2*x^2-11*y^4+4*x^7-8*x^5+x^8+22* y^4*x^2-8*y^4*x-6*y^4*x^4+12*y^4*x^3-8*y^6*x^2+4*y^6*x+12*y^2*x^5+6*z^ 2*y^6+2*x^6+4*y^2*x+14*y^2*x^4-16*y^2*x^3+24*z^2*x*y^4+12*z^2*y^4*x^2- 3*y^8+10*y^6-9*y^4*z^4-12*z^4*y^2-6*z^4*x^4-36*z^4*x^3-20*z^6*x+6*z^2* x^4*y^2+12*z^2*x^3*y^2-52*z^2*x*y^2-46*z^2*y^2*x^2-12*z^2*x^5+12*y^2*z ^4*x^2+6*z^6*y^2-8*z^6*x^2-3*z^8-8*z^4*x+z^4-2*z^6+4*y^2-48*z^2*x^3+4* x^2+4*z^2*x-6*z^2*x^2:\nwith(plots):\na:=1.5:\nimplicitplot3d(\n\{S1\} ,x=-2*a..a,y=-a..a,z=-a..a,grid=[50,50,50],style=patchnogrid); " }} {PARA 13 "" 1 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 252 "X:=(v*cos(t)+v*cos(t)^2-1+v)/(1+cos(t)):\nY:=v*sin(t):\nZ:=(1-v )*sqrt(1+2*cos(t))/(1+cos(t)):\nres:=[eliminate(\{X-x,Y-y,Z-z\},\{t,v \})]:\n# Si Maple mettait dans le m\352me ordre \340 chaque fois !!\nS :=op(res[3,2])/z ; # prudemment on copie-colle le bon morceau !!\n" }} {PARA 12 "" 1 "" {XPPMATH 20 "6#>%\"SG,\\q**\"#C\"\"\")%\"zG\"\"#F(%\" xGF()%\"y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oF(F4*&F/F()F,FIF(F(*$)F, FGF(F(*(\"#AF(F-F(F;F(F(*(F3F(F)F(FSF(F(*(FUF(F-F(F>F(F(*(FGF(FSF(F;F( F4*(F3F(F-F(F7F(F4*(FUF(F9F(F\\oF(F(*(FGF(F-F(F,F(F4" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 460 "E :=\n4*y^2+4*x^3+4*z^2*x+4*x^2-48*z^2*x ^3-6*z^2*x^2-2*z^6-8*z^4*x+z^4-7*x^4-18*y^2*x^2+2*x^6-46*z^2*x^4-50*z^ 4*x^2-10*z^2*y^2-6*z^4*x^4-9*y^4*z^4-12*z^4*y^2+12*y^2*z^4*x^2+6*z^6*y ^2-3*z^8+4*y^2*x+6*z^2*x^4*y^2+12*z^2*x^3*y^2-46*z^2*x^2*y^2-52*z^2*x* y^2-12*z^2*x^5-20*z^6*x-36*z^4*x^3+10*y^6-3*y^8-6*y^4*x^4-8*y^6*x^2+12 *y^4*x^3+12*y^2*x^5+4*y^6*x+24*z^2*x*y^4+22*y^4*x^2-8*y^4*x+6*z^2*y^6+ 12*z^2*x^2*y^4+x^8+14*y^2*x^4-16*y^2*x^3-11*y^4+4*x^7-8*x^5-8*z^6*x^2: \n" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 103 "with(plots):\na:=1.5:\nimplicitplot3d(\nS,x=-1.6*a.. a,y=-a..a,z=-a..a,grid=[80,40,40],style=patchnogrid); " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 43 "EE:=sort(expand(subs(x=x-1/2,E)),le xorder);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%#EEG,fp*$)%\"xG\"\")\"\" \"F**(\"\"'F*)F(\"\"%F*)%\"yGF.F*!\"\"**F,F*F-F*)F0\"\"#F*)%\"zGF4F*F* *(F,F*F-F*)F6F.F*F1*(F)F*)F(F4F*)F0F,F*F1**\"#7F*F:F*F/F*F5F*F***F=F*F :F*F3F*F8F*F**(F)F*F:F*)F6F,F*F1*&\"\"$F*)F0F)F*F1*(F,F*F;F*F5F*F**(\" \"*F*F/F*F8F*F1*(F,F*F3F*F@F*F**&FBF*)F6F)F*F1*(F=F*)F(\"\"&F*F3F*F**( F=F*FKF*F5F*F1*(\"#CF*)F(FBF*F/F*F**(FOF*FPF*F8F*F1*(F=F*F(F*F;F*F***F =F*F(F*F/F*F5F*F***F=F*F(F*F3F*F8F*F1*(F=F*F(F*F@F*F1*&FLF*)F(F,F*F1*( \"#;F*F-F*F3F*F1*(FYF*F-F*F5F*F1*(FLF*F:F*F/F*F1**\"#bF*F:F*F3F*F5F*F1 *(FLF*F:F*F8F*F1*&F,F*F;F*F**(FFF*F/F*F5F*F1*(FFF*F3F*F8F*F1*&F,F*F@F* F**(\"#9F*FPF*F3F*F1*(F^oF*FPF*F5F*F**(\"#=F*F(F*F/F*F1*(FaoF*F(F*F8F* F**&#\"#fF)F**$F-F*F*F**(F=F*F:F*F3F*F**(F=F*F:F*F5F*F**&#\"#FF)F**$F/ F*F*F1*&#F[pF)F**&F3F*F5F*F*F**&#F[pF)F**$F8F*F*F1*&#F[pF.F**&F(F*F3F* F*F**&#F[pF.F**&F(F*F5F*F*F1*&#\"#XFYF**$F:F*F*F1#\"#\")\"$c#F*" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "EE-subs([x=-x,y=z,z=y],EE); " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"!" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 71 "EEE:=sort(expand(subs([y=(Y+Z)/sqrt(2),z=(Y-Z)/sqrt (2)],EE)),lexorder);" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%$EEEG,^p*$)%\"xG\"\")\"\"\"F**&#\"\"$\"\"# F**&)F(\"\"%F*)%\"YGF1F*F*!\"\"**\"#@F*F0F*)F3F.F*)%\"ZGF.F*F4*&#F-F.F **&F0F*)F9F1F*F*F4*&)F(F.F*)F3\"\"'F*F***\"#LF*F?F*F2F*F8F*F4**FCF*F?F *F7F*F=F*F4*&F?F*)F9FAF*F**&#F-\"#;F**$)F3F)F*F*F4*&#F6F1F**&F@F*F8F*F *F4*&#\"$(HF)F**&F2F*F=F*F*F4*&#F6F1F**&F7F*FFF*F*F4*&#F-FIF**$)F9F)F* F*F4**\"#CF*)F(\"\"&F*F3F*F9F*F***\"#[F*)F(F-F*)F3F-F*F9F*F***FinF*Fjn F*F3F*)F9F-F*F***FenF*F(F*)F3FgnF*F9F*F***FinF*F(F*F[oF*F]oF*F***FenF* F(F*F3F*)F9FgnF*F**&FgnF*)F(FAF*F4*(FIF*F0F*F7F*F4*(FIF*F0F*F8F*F4*&# \"#lF1F**&F?F*F2F*F*F4*&#\"#DF.F**(F?F*F7F*F8F*F*F**&#FioF1F**&F?F*F=F *F*F4*&#F-F1F**$F@F*F*F4*&#\"#**F1F**&F2F*F8F*F*F**&FfpF**&F7F*F=F*F*F **&#F-F1F**$FFF*F*F4**\"#GF*FjnF*F3F*F9F*F4**\"#OF*F(F*F[oF*F9F*F4**Fa qF*F(F*F3F*F]oF*F4*&#\"#fF)F**$F0F*F*F**(\"#7F*F?F*F7F*F**(FhqF*F?F*F8 F*F**&#\"#F\"#KF**$F2F*F*F4*&#\"$*=FIF**&F7F*F8F*F*F4*&#F\\rF]rF**$F=F *F*F4*&#F\\rF.F**(F(F*F3F*F9F*F*F**&#\"#XFIF**$F?F*F*F4#\"#\")\"$c#F* " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "EEE-subs([x=-x,Y=-Y],EE E);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "with(linalg):" }}{PARA 7 "" 1 "" {TEXT -1 80 "Wa rning, the protected names norm and trace have been redefined and unpr otected\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 90 "u:=arccos(cos( t)/(1+cos(t))):\nM:=[v*cos(t )+(1-v)*(-1+cos(u)),v*sin(t),w*(1-v)*sin( u)];\n\n " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"MG7%,&*&%\"vG\"\"\"-% $cosG6#%\"tGF)F)*&,&F)F)F(!\"\"F),&F)F0*&F*F),&F)F)F*F)F0F)F)F)*&F(F)- %$sinGF,F)*(%\"wGF)F/F),&F)F)*&F*\"\"#F3!\"#F0#F)F;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 41 "j:=-simplify(det(jacobian(M,[t,v,w])));\n " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"jG,$**,(*(\"\"$\"\"\"%\"vGF*- %$cosG6#%\"tGF*F*F,!\"\"F*F*F*,&F*F0F+F*F**&,&F*F**&\"\"#F*F,F*F*F*,&F *F*F,F*!\"##F*F5F6F0F0" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 65 "j :=-(3*v*cos(t)-cos(t)+1)*(-1+v)*sqrt((1+2*cos(t)))/(1+cos(t))^2;" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"jG,$**,(*(\"\"$\"\"\"%\"vGF*-%$cos G6#%\"tGF*F*F,!\"\"F*F*F*,&F*F0F+F*F*,&F*F**&\"\"#F*F,F*F*#F*F4,&F*F*F ,F*!\"#F0" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "i1:=factor(4*i nt(j,v=0..1));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#i1G,$*(\"\"#\"\" \",&F(F(*&F'F(-%$cosG6#%\"tGF(F(#F(F',&F(F(F+F(!\"#F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}{PARA 11 "" 1 "" {XPPMATH 20 "6# ,$*(\"\"%\"\"\",&F&F&*&\"\"#F&-%$cosG6#%\"tGF&F&#F&F),(\"\"$F&*&F%F&F* F&F&-F+6#,$*&F)F&F-F&F&F&!\"\"F&" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 64 "i2:=Int(i1,t=0..2*Pi/3);\ni2:=int(i1,t=0..2*Pi/3);eva lf(i2,20);\n " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#i2G-%$IntG6$,$*(\" \"#\"\"\",&F+F+*&F*F+-%$cosG6#%\"tGF+F+#F+F*,&F+F+F.F+!\"#F+/F1;\"\"!, $*(F*F+\"\"$!\"\"%#PiGF+F+" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#i2G,& *&#\"\"#\"\"$\"\"\"-%*EllipticKG6#,$*&F(!\"\"F)#F*F(F*F*F**&#\"\"%F)F* -%*EllipticEGF-F*F*" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"5n&[PC%o%=C0 $!#>" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}{PARA 11 "" 1 " " {XPPMATH 20 "6#$\"5n&[PC%o%=C0$!#>" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 54 "Int(2*(1+2*cos(t))^(1/2)/(1+cos(t))^2,t = 0 .. 2/3*Pi )" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 90 "u:=arccos(cos(t)/(1+co s(t))):\nM:=[v*cos(t )+(1-v)*(-1+cos(u)),w*v*sin(t),(1-v)*sin(u)];\n\n " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"MG7%,&*&%\"vG\"\"\"-%$cosG6#% \"tGF)F)*&,&F)F)F(!\"\"F),&F)F0*&F*F),&F)F)F*F)F0F)F)F)*(%\"wGF)F(F)-% $sinGF,F)*&F/F),&F)F)*&F*\"\"#F3!\"#F0#F)F;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 45 "j:=abs(simplify(det(jacobian(M,[t,v,w])))):\n " }} }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "i1:=4*int(j,v=0..1):" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "i2:=int(i1,t=0..2*Pi/3):\n \+ " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "evalf(i2):" }}{PARA 7 " " 1 "" {TEXT -1 33 "Warning, computation interrupted\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 113 "evalf(sum(1/24 * (3/4)^n * (8*n^4- 36*n^3+58*n^2-3*n+27)\n *GAMMA(n+1/2)*GAMMA(n-3/2)/(GAMMA(n+1)^2),n =0..100));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+p%=C0$!\"*" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart:" }}{PARA 7 "" 1 "" {TEXT -1 50 "Warning, the name changecoords has been redefined\n" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 154 "M:=subs(v=0,[v*cos(tt)+(1-v )*(-a+cos(uu)),v*sin(tt),(1-v)*sin(uu)]);\nN:=subs(v=1,[v*cos(tt)+(1-v )*(-a+cos(uu)),v*sin(tt),(1-v)*sin(uu)]);\nOO:=[-a/2,0,0];\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"MG7%,&%\"aG!\"\"-%$cosG6#%#uuG\"\"\"\"\" !-%$sinGF+" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"NG7%*&-%$cosG6#%#uuG \"\"\",&F+F+F'!\"\"F-*$,&F+F+*&F'\"\"#F,!\"#F-#F+F1\"\"!" }}{PARA 11 " " 1 "" {XPPMATH 20 "6#>%#OOG7%,$*&\"\"#!\"\"%\"aG\"\"\"F)\"\"!F," }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 95 "ps:=proc(A,B,C,D):\n(B[1]-A[ 1])*(D[1]-C[1])+(B[2]-A[2])*(D[2]-C[2])+(B[3]-A[3])*(D[3]-C[3])\nend; " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#psGf*6&%\"AG%\"BG%\"CG%\"DG6\"F +F+,(*&,&&9%6#\"\"\"F2&9$F1!\"\"F2,&&9'F1F2&9&F1F5F2F2*&,&&F06#\"\"#F2 &F4F>F5F2,&&F8F>F2&F:F>F5F2F2*&,&&F06#\"\"$F2&F4FGF5F2,&&F8FGF2&F:FGF5 F2F2F+F+F+" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 58 "T:=[v*cos(tt) +(1-v)*(-a+cos(uu)),v*sin(tt),(1-v)*sin(uu)];" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"TG7%,&*(%\"vG\"\"\"-%$cosG6#%#uuGF),&F)F)F*!\"\"F/F )*&,&F)F)F(F/F),&%\"aGF/F*F)F)F)*&F(F),&F)F)*&F*\"\"#F.!\"#F/#F)F7*&F1 F)-%$sinGF,F)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 36 "vv:=simpli fy(solve(ps(M,N,OO,T),v));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#vvG,$ *&#\"\"\"\"\"#F(*&,0*(\"\"$F(%\"aGF()-%$cosG6#%#uuGF)F(!\"\"*(F)F(F.F( F0F(F(*&F)F(F0F(F(*&)F.F)F(F0F(F(F)F4*&F)F(F/F(F(*$F8F(F4F(,.*(F)F(F.F (F/F(F4*&F)F(F/F(F(*&F)F(F0F(F(F7F(F:F4F)F4F4F(F(" }}}{EXCHG {PARA 0 " > " 0 "" {MPLTEXT 1 0 17 "TT:=subs(v=vv,T);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%#TTG7%,&*&#\"\"\"\"\"#F)**,0*(\"\"$F)%\"aGF))-%$cosG6 #%#uuGF*F)!\"\"*(F*F)F/F)F1F)F)*&F*F)F1F)F)*&)F/F*F)F1F)F)F*F5*&F*F)F0 F)F)*$F9F)F5F),.*(F*F)F/F)F0F)F5*&F*F)F0F)F)*&F*F)F1F)F)F8F)F;F5F*F5F5 F1F),&F)F)F1F5F5F)F)*&,&F)F)*&#F)F*F)*&F,F)F " 0 "" {MPLTEXT 1 0 30 "R2:=simplify(ps(OO,TT,OO,TT));" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%#R2G,$*&#\"\"\"\"\"%F(*&,8*&)%\"aG\" \"#F()-%$cosG6#%#uuGF)F(F(*(F/F(F-F()F1\"\"$F(!\"\"*(F)F(F-F(F1F(F(*&F /F(F-F(F8*(F)F(F.F(F0F(F8*(F)F(F.F(F6F(F(*(F)F(F.F()F1F/F(F8*&F)F(F0F( F(*&F)F(F>F(F8*&\"\")F(F1F(F(F)F8F(,2*(F/F(F.F(F>F(F(*(F/F(F.F(F6F(F8* &F/F(F6F(F(*&F)F(F1F(F8*(F/F(F-F(F1F(F8*&F-F(F>F(F(*$F-F(F(F/F(F8F(F8 " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 45 "tt:=arccos(cos(uu)/(1-c os(uu))):simplify(R2);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$*&#\"\"\" \"\"%F&*&,8*&)%\"aG\"\"#F&)-%$cosG6#%#uuGF'F&F&*(F-F&F+F&)F/\"\"$F&!\" \"*(F'F&F+F&F/F&F&*&F-F&F+F&F6*(F'F&F,F&F.F&F6*(F'F&F,F&F4F&F&*(F'F&F, F&)F/F-F&F6*&F'F&F.F&F&*&F'F&F " 0 "" {MPLTEXT 1 0 21 "sol ve(diff(R2,uu),a);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#-%'RootOfG6#,4*& ,**$)-%$cosG6#%#uuG\"\"$\"\"\"F0*&\"\"#F0)F+F2F0!\"\"*&F2F0F+F0F0F0F4F 0)%#_ZG\"\"%F0F0*&,(*$)F+F8F0F4*&F8F0F*F0F4*&F8F0F3F0F0F0)F7F/F0F0*&,( *&\"\"&F0F " 0 "" {MPLTEXT 1 0 13 "subs(a= 1,R2);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$*&#\"\"\"\"\"%F&*&,,*&\"\" #F&)-%$cosG6#%#uuG\"\"$F&F&*$)F-F'F&F&*&\"\")F&)F-F+F&!\"\"*&\"#7F&F-F &F&\"\"'F7F&,(*&F1F&F6F&F&*&F:F&F-F&F7F1F&F7F&F7" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart:" }}{PARA 7 "" 1 "" {TEXT -1 50 "Warni ng, the name changecoords has been redefined\n" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 99 "x:=2*sqrt(3)/9*(-sqrt(2*(1+2*cos(t))*(1-cos(t) ))/(1+cos(t))+arccos(sqrt(2)*cos(t)/sqrt(1+cos(t))));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"xG,$*&#\"\"#\"\"*\"\"\"*&\"\"$#F*F(,&*(F(F-*&, &F*F**&F(F*-%$cosG6#%\"tGF*F*F*,&F*F*F3!\"\"F*F-,&F*F*F3F*F8F8-%'arcco sG6#*(F(F-F3F*F9#F8F(F*F*F*F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 59 "y := sqrt(3)/9*((11+7*cos(t))/(1+cos(t))+ln(2/(1+cos(t))));" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"yG,$*&#\"\"\"\"\"*F(*&\"\"$#F(\"\" #,&*&,&\"#6F(*&\"\"(F(-%$cosG6#%\"tGF(F(F(,&F(F(F4F(!\"\"F(-%#lnG6#,$* &F-F(F8F9F(F(F(F(F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 40 "plot ([x,y,t=0..Pi],scaling=constrained);" }}{PARA 13 "" 1 "" {GLPLOT2D 496 496 496 {PLOTDATA 2 "6&-%'CURVESG6$7en7$$\"\"!F)$\"+330Kr(o?rAWt\"F37 $$\"3/x$46\"z9hFY$\"3M.!RM'Hf6=F37$$\"3/EBoWt1)))*FY$\"3Id>j_F kG=F37$$\"3cb%GoI'4[:!#?$\"3WcN*y=ky%=F37$$\"33v!4%R\\9@BF]p$\"3/mNl;^ ao=F37$$\"3!G^4W4$**)G$F]p$\"3MF=\"4$oJ*)=F37$$\"3'ow\"=Jehy[F]p$\"34P 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