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"Curve 4" "Curve 5" "Curve 6" "Curve 7" "Curve 8" "Curve 9" "Curve 10
" "Curve 11" "Curve 12" "Curve 13" }}}}{PARA 0 "" 0 "" {TEXT -1 0 "" }
{TEXT -1 58 "Note: above parameterization by s does not cover all of U
." }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "> " 0 "" 
{MPLTEXT 1 0 500 "# Alternative parametrization:\ng:=x->x^2;\nx1alt:=D
(g)(x2g)*(s-1);\nx2alt:=(g(x2g)/D(g)(x2g))*(s-1) + x2g;\nz_alt:=g(x2g)
*s^2;\npalt:=plot3d([x1alt,x2alt,z_alt],s=-10..10,x2g=-2..2,labels=[\"
x1\",\"x2\",\"u\"],axes=boxed,color=pink,grid=[100,100]):\npcalt:=plot
s[display](seq(plots[spacecurve](subs(x2g=x20min+i*dx20,[x1alt,x2alt,z
_alt]),s=-10..10,numpoints=200),i=0..ncrv),\n   thickness=2,color=gree
n):\nplots[display](pcalt,palt,view=[-2..2,-1..1,0..3]);\nplots[displa
y](pcalt,pb,pc,ps,view=[-2..2,-1..1,0..3]);" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%\"gGf*6#%\"xG6\"6$%)operatorG%&arrowGF(*$)9$\"\"#\"\"
\"F(F(F(" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%&x1altG,$*(\"\"#\"\"\"%$
x2gGF(,&%\"sGF(F(!\"\"F(F(" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%&x2alt
G,&*(\"\"#!\"\"%$x2gG\"\"\",&%\"sGF*F*F(F*F*F)F*" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%&z_altG*&)%$x2gG\"\"#\"\"\")%\"sGF(F)" }}{PARA 13 "" 
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