{VERSION 6 0 "IBM INTEL NT" "6.0" } {USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0 1 0 0 0 0 1 }{CSTYLE "2D Math" -1 2 "Times" 0 1 0 0 0 0 0 0 2 0 0 0 0 0 0 1 }{CSTYLE "2D Output" 2 20 "" 0 1 0 0 255 1 0 0 0 0 0 0 0 0 0 1 } {PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }1 1 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Maple Output" -1 11 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }3 3 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Maple Output" -1 12 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }1 3 0 0 0 0 1 0 1 0 2 2 0 1 }} {SECT 0 {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 40 "TangSurf := (t+u,t^2 +2*u*t,t^3+3*t^2*u);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%)TangSurfG6% ,&%\"tG\"\"\"%\"uGF(,&*$)F'\"\"#F(F(*(F-F(F)F(F'F(F(,&*$)F'\"\"$F(F(*( F2F(F,F(F)F(F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 126 "plot3d( \+ [TangSurf], t=-2..2, u=-2..2,\ngrid=[50,50], style=patchcontour, axes= frame, labels=[x,y,z], view=[-2..2,-2..2,-2..2]);" }}}{EXCHG {PARA 0 " > " 0 "" {MPLTEXT 1 0 89 "G := Groebner[Basis]( [x-(t+u), y-(t^2+2*u*t ), z-(t^3+3*t^2*u)],\n plex(t,u,x,y,z) );" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%\"GG7),,*$)%\"zG\"\"#\"\"\"F+**\"\"'F+%\"yGF+F)F+%\"x GF+!\"\"*&\"\"%F+)F.\"\"$F+F+*(F2F+F)F+)F/F4F+F+*(F4F+)F/F*F+)F.F*F+F0 ,.*(\"\"&F+F)F+F9F+F+**F2F+F)F+F8F+F.F+F0*(F*F+F(F+%\"uGF+F0*(F*F+F(F+ F/F+F0*(F*F+F3F+F?F+F+*&F/F+F3F+F+,,*&F)F+F.F+F0*(F*F+F)F+F8F+F+**F*F+ F)F+F?F+F/F+F+*(F*F+F9F+F?F+F0*&F/F+F9F+F0,,*&F*F+F9F+F+*&F8F+F.F+F0*& F)F+F?F+F0*&F)F+F/F+F0*(F/F+F?F+F.F+F+,,*(F4F+F/F+F.F+F+*&F*F+F6F+F0*( F*F+F?F+F.F+F0*(F*F+F8F+F?F+F+F)F0,(F.F+*$)F?F*F+F+*$F8F+F0,(F/F0%\"tG F+F?F+" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 95 "G := Groebner[Bas is]( [x-(t+u), y-(t^2+2*u*t), z-(t^3+3*t^2*u)],\n lexdeg([u,t],[x ,y,z]) );" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%\"GG7(,,*$)%\"zG\"\"#\" \"\"!\"\"**\"\"'F+%\"yGF+F)F+%\"xGF+F+*&\"\"%F+)F/\"\"$F+F,*(F2F+F)F+) F0F4F+F,*(F4F+)F0F*F+)F/F*F+F+,,*&F)F+F/F+F,*(F2F+F)F+F8F+F+**F*F+F)F+ F0F+%\"tGF+F,*(F*F+F9F+F>F+F+*(F4F+F0F+F9F+F,,**(F0F+F>F+F/F+F+*&F*F+F 9F+F,*&F)F+F>F+F,*(F*F+F)F+F0F+F+,**(F*F+F/F+F>F+F,*(F*F+F>F+F8F+F+*&F 0F+F/F+F,F)F+,(F0F,F>F+%\"uGF+,(*(F*F+F0F+F>F+F,*$)F>F*F+F+F/F+" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "T := remove(has,G,\{t,u\}); " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"TG7#,,*$)%\"zG\"\"#\"\"\"!\"\" **\"\"'F+%\"yGF+F)F+%\"xGF+F+*&\"\"%F+)F/\"\"$F+F,*(F2F+F)F+)F0F4F+F,* (F4F+)F0F*F+)F/F*F+F+" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "g \+ := unapply(T[1],x,y,z);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"gGf*6%% \"xG%\"yG%\"zG6\"6$%)operatorG%&arrowGF*,,*$)9&\"\"#\"\"\"F3**\"\"'F39 %F3F1F39$F3!\"\"*&\"\"%F3)F6\"\"$F3F3*(F:F3F1F3)F7F " 0 "" {MPLTEXT 1 0 22 "expand( g (TangSurf) );" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 106 "plots[implicitplot3d]( T[1], x=-2. .2, y=-2..2, z=-2..2,\ngrid=[20,20,20], style=patchcontour, axes=frame );" }}}{EXCHG }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{MARK " 10" 0 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }