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"6#,X\"\"\"F$*&\"\"%F$%\"xGF$F$*&\"\"#F$)%\"yGF)F$!\"\"*(F &F$)F+F&F$)F'F)F$F$*&F&F$)F'\"\"&F$F$*(F&F$F.F$F'F$F$*(\"\")F$F*F$)F'F &F$F$*(F5F$F*F$)F'\"\"$F$F$*&F&F$)F'\"\"'F$F$*&F&F$)%\"zGF)F$F,*&F)F$F /F$F$*&F5F$F8F$F,*&\"\"(F$F6F$F,*$F.F$F$*(\"#QF$F>F$F/F$F,*(\"#?F$F'F$ F>F$F,*(FF$F 6F$F,*(\"#KF$F8F$F>F$F,*&FLF$F6F$F$*(F&F$F8F$FLF$F$*(F&F$F1F$F>F$F,**F NF$F/F$F*F$F>F$F,**F&F$F'F$F*F$F>F$F,**F&F$F*F$F8F$F>F$F," }}}{EXCHG {PARA 0 "> " 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 0 712 "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 !!\nS := \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 12 "" 1 "" {XPPMATH 20 "6#>%\"SG,\\q**\"#C\"\"\")%\"zG\"\"#F(%\"xGF()%\"yG\"\"%F(F(*(\"#?F ()F*\"\"'F(F,F(!\"\"*(\"#YF(F)F()F,F/F(F4*&F/F()F.F+F(F(*(F3F(F)F()F,F +F(F4*(\"#[F(F)F()F,\"\"$F(F4*&F/F(F;F(F(*(F/F(F)F(F,F(F(*&F/F(F>F(F(* $)F*F/F(F(*&F+F(F2F(F4*(\"\")F(FDF(F,F(F4*&\"\"(F(F7F(F4*&F+F()F,F3F(F (*(\"#5F(F)F(F9F(F4*(\"#]F(FDF(F;F(F4*(\"#=F(F9F(F;F(F4*(F/F()F.F3F(F, F(F(**\"#7F(F)F(F-F(F;F(F(*&F?F()F*FGF(F4*(FGF(F2F(F;F(F4*(F3F(F2F(F9F (F(*(\"#OF(FDF(F>F(F4*(\"\"*F(F-F(FDF(F4*(FUF(FDF(F9F(F4*(F3F(FDF(F7F( F4**FUF(F9F(FDF(F;F(F(*(FUF(F)F()F,\"\"&F(F4**FUF(F)F(F>F(F9F(F(**\"#_ F(F)F(F,F(F9F(F4**F3F(F)F(F7F(F9F(F(**F6F(F)F(F9F(F;F(F4*&FMF(FSF(F(*& F?F()F.FGF(F4*(\"#;F(F9F(F>F(F4*(\"#9F(F9F(F7F(F(*(F/F(F9F(F,F(F(*&\"# 6F(F-F(F4*&FGF(F\\oF(F4*&F/F()F,FIF(F(*$)F,FGF(F(*(\"#AF(F-F(F;F(F(*(F 3F(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 0 103 "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 0 456 "4*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^5-2 0*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=0;" }}{PARA 12 " " 1 "" {XPPMATH 20 "6#/,\\q**\"#C\"\"\")%\"zG\"\"#F'%\"xGF')%\"yG\"\"% F'F'*(\"#?F')F)\"\"'F'F+F'!\"\"*(\"#YF'F(F')F+F.F'F3*&F.F')F-F*F'F'*(F 2F'F(F')F+F*F'F3*(\"#[F'F(F')F+\"\"$F'F3*&F.F'F:F'F'*(F.F'F(F'F+F'F'*& F.F'F=F'F'*$)F)F.F'F'*&F*F'F1F'F3*(\"\")F'FCF'F+F'F3*&\"\"(F'F6F'F3*&F *F')F+F2F'F'*(\"#5F'F(F'F8F'F3*(\"#]F'FCF'F:F'F3*(\"#=F'F8F'F:F'F3*(F. F')F-F2F'F+F'F'**\"#7F'F(F'F,F'F:F'F'*&F>F')F)FFF'F3*(FFF'F1F'F:F'F3*( F2F'F1F'F8F'F'*(\"#OF'FCF'F=F'F3*(\"\"*F'F,F'FCF'F3*(FTF'FCF'F8F'F3*(F 2F'FCF'F6F'F3**FTF'F8F'FCF'F:F'F'*(FTF'F(F')F+\"\"&F'F3**FTF'F(F'F=F'F 8F'F'**\"#_F'F(F'F+F'F8F'F3**F2F'F(F'F6F'F8F'F'**F5F'F(F'F8F'F:F'F3*&F LF'FRF'F'*&F>F')F-FFF'F3*(\"#;F'F8F'F=F'F3*(\"#9F'F8F'F6F'F'*(F.F'F8F' F+F'F'*&\"#6F'F,F'F3*&FFF'F[oF'F3*&F.F')F+FHF'F'*$)F+FFF'F'*(\"#AF'F,F 'F:F'F'*(F2F'F(F'FRF'F'*(FTF'F,F'F=F'F'*(FFF'FRF'F:F'F3*(F2F'F,F'F6F'F 3*(FTF'F8F'F[oF'F'*(FFF'F,F'F+F'F3\"\"!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "evala(AFactor(S));" }}{PARA 12 "" 1 "" {XPPMATH 20 "6 #,\\q**\"#C\"\"\")%\"zG\"\"#F&%\"xGF&)%\"yG\"\"%F&F&*(\"#?F&)F(\"\"'F& F*F&!\"\"*(\"#YF&F'F&)F*F-F&F2*&F-F&)F,F)F&F&*(F1F&F'F&)F*F)F&F2*(\"#[ F&F'F&)F*\"\"$F&F2*&F-F&F9F&F&*(F-F&F'F&F*F&F&*&F-F&F " 0 "" {MPLTEXT 1 0 0 "" }}}}{MARK "17 1 0" 0 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }