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3+sqrt(3))/6*X+(3+sqrt(3))/6*Y+(sqrt(3))/3*Z/4,\nz=(-1/sqrt(3)*X-1/sqr t(3)*Y+1/sqrt(3)*Z/4),\nt=(3+sqrt(3))/6*X+(-3+sqrt(3))/6*Y+(sqrt(3))/3 *Z/4+(-3+sqrt(3))/6*X+(3+sqrt(\n3))/6*Y+(sqrt(3))/3*Z/4+(-1/sqrt(3)*X- 1/sqrt(3)*Y+1/sqrt(3)*Z/4)+1,\n(x)^3 + (y)^3 + (z)^3 + (t)^3 - (x+y+z+ t)^3);\n" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%\"GG,,*$),(*(\"\"'!\"\", &\"\"$\"\"\"*$F-#F.\"\"#F.F.%\"XGF.F.*(F*F+,&F-F+F/F.F.%\"YGF.F.*(\"#7 F+F-F0%\"ZGF.F.F-F.F.*$),(*(F*F+F4F.F2F.F.*(F*F+F,F.F5F.F.*(F7F+F-F0F8 F.F.F-F.F.*$),(*(F-F+F-F0F2F.F+*(F-F+F-F0F5F.F+*(F7F+F-F0F8F.F.F-F.F.* $),2*(F*F+F,F.F2F.F.*(F*F+F4F.F5F.F.*(\"\"%F+F-F0F8F.F.*(F*F+F4F.F2F.F .*(F*F+F,F.F5F.F.*(F-F+F-F0F2F.F+*(F-F+F-F0F5F.F+F.F.F-F.F.*$),2*(F-F+ F,F.F2F.F.*(F-F+F4F.F5F.F.*(F1F+F-F0F8F.F.*(F-F+F4F.F2F.F.*(F-F+F,F.F5 F.F.**F1F.F-F+F-F0F2F.F+**F1F.F-F+F-F0F5F.F+F.F.F-F.F+" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 48 "todesco:=subs(X=x,Y=y,Z=z,expand(G* sqrt(3))*32);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%(todescoG,4*&\"#s\" \"\"%\"zGF(!\"\"*&\"#;F()%\"xG\"\"$F(F(*&\"#JF()F)F/F(F**&F,F()%\"yGF/ F(F(*(\"#CF(F)F()F.\"\"#F(F(*(\"#[F(F8F(F5F(F**(F7F(F)F()F5F9F(F(*(F;F (F.F(F=F(F**(\"#aF(F/#F(F9)F)F9F(F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 311 "solve(\{x=(3+sqrt(3))/6*X+(-3+sqrt(3))/6*Y+(sqrt(3)) /3*Z/4,\ny=(-3+sqrt(3))/6*X+(3+sqrt(3))/6*Y+(sqrt(3))/3*Z/4,\nz=(-1/sq rt(3)*X-1/sqrt(3)*Y+1/sqrt(3)*Z/4),\nt=(3+sqrt(3))/6*X+(-3+sqrt(3))/6* Y+(sqrt(3))/3*Z/4+(-3+sqrt(3))/6*X+(3+sqrt(\n3))/6*Y+(sqrt(3))/3*Z/4+( -1/sqrt(3)*X-1/sqrt(3)*Y+1/sqrt(3)*Z/4)+T\},\{X,Y,Z,T\});" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#<&/%\"ZG,$**\"\"%\"\"\"\"\"$!\"\"F*#F)\"\"#,(% \"yGF)%\"xGF)%\"zGF)F)F)/%\"YG,$*(\"\"'F+,&F*F+*$F*F,F)F),,F1F)*&F-F)F /F)F+F0F)*&F*F,F/F)F+*&F*F,F1F)F)F)F)/%\"XG,$*(F6F+,&F*F)F8F)F),,F1F)F ;F)*&F-F)F/F)F+F0F)F " 0 "" {MPLTEXT 1 0 139 "Z = 4/3*3^(1/2)*(y+x+z), Y = 1/6*( -3+3^(1/2))*(z-2*y+x-3^(1/2)*y+3^(1/2)*z), X = 1/6*(3+3^(1/2))*(z+3^(1 /2)*y-2*y+x-3^(1/2)*z), T = t-y-x-z" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 65 "expand(2*sqrt(3)*1/6*(-3+3^(1/2))*(z-2*y+x-3^(1/2)*y+ 3^(1/2)*z));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,,*&\"\"$#\"\"\"\"\"#% \"yGF'F'*&F%F&%\"xGF'!\"\"F)F'*&F(F'%\"zGF'F,F+F'" }}}{EXCHG {PARA 0 " > " 0 "" {MPLTEXT 1 0 64 "expand(2*sqrt(3)*1/6*(3+3^(1/2))*(z+3^(1/2)* y-2*y+x-3^(1/2)*z));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,,%\"yG\"\"\"* &\"\"$#F%\"\"#F$F%!\"\"*&F'F(%\"xGF%F%*&F)F%%\"zGF%F*F,F%" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 38 "expand(2*sqrt(3)*4/3*3^(1/2)*(y+x+z ));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,(*&\"\")\"\"\"%\"yGF&F&*&F%F&% \"xGF&F&*&F%F&%\"zGF&F&" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 84 " factor(expand(subs(x=sqrt(3)*(X-Y),y=sqrt(3)*(X+Y),z=sqrt(3)*Z,todesco /sqrt(3)/3)));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,0*&\"#k\"\"\")%\"XG \"\"$F&!\"\"*(\"#[F&)F(\"\"#F&%\"ZGF&F&*(\"$#>F&F(F&)%\"YGF.F&F&*(F,F& F2F&F/F&F&*&\"#JF&)F/F)F&F**&\"#aF&)F/F.F&F**&\"#CF&F/F&F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 348 "\n rotOz := [cos(t)*X-sin(t)*Y, si n(t)*X+cos(t)*Y, Z];\n\nH3:= -72*z-31*z^3+24*x^2*z+24*y^2*z+16*y^3-48* x^2*y+16*x^3-54*sqrt(3)*z^2-48*x\n*y^2;\n H3bis:=(sort@expand)(subs(x= rotOz[1],y=rotOz[2],z=rotOz[3],H3)):\n H3ter:=map(simplify,collect(H3b is,[Z,Y,X]));\n\nH34:=sort(simplify(subs(t=Pi/4,X=X*sqrt(6),Y=Y*sqrt(6 ),Z=Z*sqrt(3),H3ter)/sqrt\n(3)/3),[X,Y,Z]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%&rotOzG7%,&*&-%$cosG6#%\"tG\"\"\"%\"XGF,F,*&-%$sinGF* F,%\"YGF,!\"\",&*&F/F,F-F,F,*&F(F,F1F,F,%\"ZG" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#H3G,4*&\"#s\"\"\"%\"zGF(!\"\"*&\"#;F()%\"xG\"\"$F(F( *&\"#JF()F)F/F(F**&F,F()%\"yGF/F(F(*(\"#CF(F)F()F.\"\"#F(F(*(\"#[F(F8F (F5F(F**(F7F(F)F()F5F9F(F(*(F;F(F.F(F=F(F**(\"#aF(F/#F(F9)F)F9F(F*" }} {PARA 12 "" 1 "" {XPPMATH 20 "6#>%&H3terG,0*&\"#J\"\"\")%\"ZG\"\"$F(! \"\"*(\"#aF(F+#F(\"\"#)F*F0F(F,*(\"#CF(,(*$)%\"XGF0F(F(*$)%\"YGF0F(F(F +F,F(F*F(F(*(\"#;F(,**&\"\"%F()-%$cosG6#%\"tGF+F(F(*(F?F()FAF0F(-%$sin GFCF(F(*&F+F(FAF(F,FGF,F()F:F+F(F(**\"#[F(,**&F?F(F@F(F(*(F?F(FFF(FGF( F,*&F+F(FAF(F,FGF(F(F7F(F9F(F,**FLF(F=F(F6F(F:F(F,*(F%$H34G,0*&\"#k\"\"\")%\"XG\"\"$F( !\"\"*(\"#[F()F*\"\"#F(%\"ZGF(F(*(\"$#>F(F*F()%\"YGF0F(F(*(F.F(F4F(F1F (F(*&\"#JF()F1F+F(F,*&\"#aF()F1F0F(F,*&\"#CF(F1F(F," }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "H3-todesco;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 298 "U:=(3+sqrt( 3))/6*X+(-3+sqrt(3))/6*Y+(sqrt(3))/3*Z/4;\nV:=(-3+sqrt(3))/6*X+(3+sqrt (3))/6*Y+(sqrt(3))/3*Z/4;\nUU:=(-1/sqrt(3)*X-1/sqrt(3)*Y+1/sqrt(3)*Z/4 );\nVV:=(3+sqrt(3))/6*X+(-3+sqrt(3))/6*Y+(sqrt(3))/3*Z/4+(-3+sqrt(3))/ 6*X+(3+sqrt(\n3))/6*Y+(sqrt(3))/3*Z/4+(-1/sqrt(3)*X-1/sqrt(3)*Y+1/sqrt (3)*Z/4)+1;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"UG,(*(\"\"'!\"\",& \"\"$\"\"\"*$F*#F+\"\"#F+F+%\"XGF+F+*(F'F(,&F*F(F,F+F+%\"YGF+F+*(\"#7F (F*F-%\"ZGF+F+" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"VG,(*(\"\"'!\"\" ,&\"\"$F(*$F*#\"\"\"\"\"#F-F-%\"XGF-F-*(F'F(,&F*F-F+F-F-%\"YGF-F-*(\"# 7F(F*F,%\"ZGF-F-" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#UUG,(*(\"\"$!\" \"F'#\"\"\"\"\"#%\"XGF*F(*(F'F(F'F)%\"YGF*F(*(\"#7F(F'F)%\"ZGF*F*" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%#VVG,2*(\"\"'!\"\",&\"\"$\"\"\"*$F*# F+\"\"#F+F+%\"XGF+F+*(F'F(,&F*F(F,F+F+%\"YGF+F+*(\"\"%F(F*F-%\"ZGF+F+* (F'F(F1F+F/F+F+*(F'F(F)F+F2F+F+*(F*F(F*F-F/F+F(*(F*F(F*F-F2F+F(F+F+" } }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 291 "U:=factor(expand(subs(X=s qrt(3)*(x-y),Y=sqrt(3)*(x+y),Z=sqrt(3)*z,U)));\nV:=factor(expand(subs( X=sqrt(3)*(x-y),Y=sqrt(3)*(x+y),Z=sqrt(3)*z,V)));\nUU:=factor(expand(s ubs(X=sqrt(3)*(x-y),Y=sqrt(3)*(x+y),Z=sqrt(3)*z,UU)));\nVV:=factor(exp and(subs(X=sqrt(3)*(x-y),Y=sqrt(3)*(x+y),Z=sqrt(3)*z,VV)));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"UG,(*&\"\"$#\"\"\"\"\"#%\"yGF)!\"\"%\"xG F)*&\"\"%F,%\"zGF)F)" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"VG,(*&\"\" $#\"\"\"\"\"#%\"yGF)F)%\"xGF)*&\"\"%!\"\"%\"zGF)F)" }}{PARA 11 "" 1 " " {XPPMATH 20 "6#>%#UUG,&*&\"\"#\"\"\"%\"xGF(!\"\"*&\"\"%F*%\"zGF(F(" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#VVG,&*(\"\"$\"\"\"\"\"%!\"\"%\"zG F(F(F(F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 88 "G:=subs(XX=U,\n YY=V,\nZZ=UU,\nTT=VV,\n(XX)^3 + (YY)^3 + (ZZ)^3 + (TT)^3 - (XX+YY+ZZ+T T)^3);\n" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "todesco:=32*expand(G)/3 ;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"GG,,*$),(*&\"\"$#\"\"\"\"\"#% \"yGF,!\"\"%\"xGF,*&\"\"%F/%\"zGF,F,F*F,F,*$),(F)F,F0F,*&F2F/F3F,F,F*F ,F,*$),&*&F-F,F0F,F/*&F2F/F3F,F,F*F,F,*$),&*(F*F,F2F/F3F,F,F,F,F*F,F,* $),&*(F*F,F-F/F3F,F,F,F,F*F,F/" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%(t odescoG,0*&\"#a\"\"\")%\"zG\"\"#F(!\"\"*(\"$#>F(%\"xGF()%\"yGF+F(F(*( \"#[F(F*F()F/F+F(F(*(F3F(F*F(F0F(F(*&\"#CF(F*F(F,*&\"#JF()F*\"\"$F(F,* &\"#kF()F/F;F(F," }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{MARK "19 1 0" 0 } {VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }