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\n   c:= myrand(-3,3);\n   d:= myrand(-10,10);\n   if (myrand(-10,10) \+
> 0) then s:=1 else s:=-1 fi;\n   fuzz := [ random[normald[0,0.5]](poi
nts_wanted)];\n   x    := [ random[uniform[-3,3]](points_wanted)];\n  \+
 RETURN( [ [x[i], s*(a-x[i])*(b-x[i])*(c-x[i])+d+fuzz[i]] $i=1..points
_wanted]);\nend:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "cpts:=cubic_pts();" }}{PARA 12 "" 
1 "" {XPPMATH 20 "6#>%%cptsG7@7$$\"+HUES9!\"*$\"+7KrM(*!#57$$\"+&y2$>C
F)$\"+tZVlOF)7$$\"+6tC=<F)$\"+sP8')=F)7$$!+rk?/;F)$!+)Rsu8%F)7$$!+%)=a
Y6F)$\"+c72&*>F,7$$!*%*HGi$F)$\"+5<fz^F)7$$\"+^9zM@F)$\"+DJ[$\\#F)7$$
\"*GSJK$F)$\"+XkF![$F)7$$!+J;z9@F)$!+6>Qn8!\")7$$!+/`6_=F)$!+DVhJwF)7$
$\"+K\"e::\"F)$\"+!*3o()>F)7$$!+JB%*G=F)$!+G)46F(F)7$$!+Mui)>\"F)$\"+v
vB=JF,7$$\"+PTlX=F)$\"+X>Xw:F)7$$\"+ffu\"Q\"F)$\"+9@)*\\AF)7$$!)bO$G\"
F)$\"+uKk<QF)7$$\"+&))=qP#F)$\"+#H&[vLF)7$$\"+rtN8CF)$\"+vS!oN%F)7$$!)
([oC&F)$\"+&[M%eVF)7$$\"*:iV#yF)$\"+j#*oOHF)7$$!+%*>#4*>F)$!+7b^l5FU7$
$\"+xeXw7F)$\"+U0xE:F)7$$\"+Nkl&R\"F)$\"+P&[!p:F)7$$\"*91\"**)*F)$\"+I
#*)pt#F)7$$!+'>Tg:#F)$!+1\"Q;Z\"FU7$$!+:d^(f\"F)$!+R(H'oRF)7$$!)LIc'*F
)$\"+QVY;PF)7$$\"+YI0v?F)$\"+hm&e5#F)7$$\"*<2IZ)F)$\"+:mi4HF)7$$\"+`([
B#GF)$\"+9zv^hF)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 36 "cub:=(x
,a,b,c,d)->a*x^3+b*x^2+c*x+d;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$cu
bGf*6'%\"xG%\"aG%\"bG%\"cG%\"dG6\"6$%)operatorG%&arrowGF,,**&9%\"\"\")
9$\"\"$F3F3*&9&F3)F5\"\"#F3F3*&9'F3F5F3F39(F3F,F,F," }}}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 74 "E:=(a,b,c,d)->sum((cub(cpts[i][1],a,b,c,d
)-cpts[i][2])^2,i=1..nops(cpts));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>
%\"EGf*6&%\"aG%\"bG%\"cG%\"dG6\"6$%)operatorG%&arrowGF+-%$sumG6$*$),&-
%$cubG6'&&%%cptsG6#%\"iG6#\"\"\"9$9%9&9'F>&F96#\"\"#!\"\"FEF>/F<;F>-%%
nopsG6#F:F+F+F+" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "a:='a';b
:='b';c:='c';d:='d';" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"aGF$" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"bGF$" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6#>%\"cGF$" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"dGF$" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 103 "solve(\{diff(E(a,b,c,d),a)=0,diff(
E(a,b,c,d),b)=0,diff(E(a,b,c,d),c)=0,diff(E(a,b,c,d),d)=0\},\{a,b,c,d
\});" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#<&/%\"aG$\"+klGN(*!#5/%\"dG$\"
+V8b\"G%!\"*/%\"bG$!+Y4z*=#F-/%\"cG$!+ev#4#oF(" }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 10 "assign(%);" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 15 "cub(x,a,b,c,d);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,*
*&$\"+klGN(*!#5\"\"\")%\"xG\"\"$F(F(*&$\"+Y4z*=#!\"*F()F*\"\"#F(!\"\"*
&$\"+ev#4#oF'F(F*F(F2$\"+V8b\"G%F/F(" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 97 "display(plot(cub(x,a,b,c,d), x=-5..5, color=blue,axes
=boxed), plot(cpts,style=point,symbol=BOX));" }}{PARA 13 "" 1 "" 
{GLPLOT2D 567 567 567 {PLOTDATA 2 "6'-%'CURVESG6$7S7$$!\"&\"\"!$!3.++y
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F1$\"3.+++!*3o()>F17$$!3#******4LU*G=F1$!3;+++G)46F(F17$$!3/+++Mui)>\"
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17$$\"3-+++&))=qP#F1$\"3-+++#H&[vLF17$$\"3.+++rtN8CF1$\"3K+++vS!oN%F17
$$!37++++([oC&Fe`l$\"32+++&[M%eVF17$$\"3M******\\@OCyFdq$\"3))*****HE*
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******H#*)pt#F17$$!3))*****f>Tg:#F1$!3)******f5Q;Z\"FH7$$!35+++:d^(f\"
F1$!3#)******Q(H'oRF17$$!3k++++LIc'*Fe`l$\"3?+++QVY;PF17$$\"3%)*****f/
`]2#F1$\"3!)*****4mce5#F17$$\"3!)******pr+t%)Fdq$\"33+++:mi4HF17$$\"3*
******Hv[B#GF1$\"30+++9zv^hF1-F][l6&F_[l$\"#5!\"\"F`[lF`[l-%&STYLEG6#%
&POINTG-%'SYMBOLG6#%$BOXG-%*AXESSTYLEGFiel-%+AXESLABELSG6%Q\"x6\"Q!Faf
l-%%FONTG6#%(DEFAULTG-%%VIEWG6$;F(FhzFffl" 1 2 0 1 10 0 2 9 1 2 2 
1.000000 45.000000 45.000000 0 0 "Curve 1" "Curve 2" }}}}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 28 "a:='a';b:='b';c:='c';d:='d';" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#
>%\"aGF$" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"bGF$" }}{PARA 11 "" 1 
"" {XPPMATH 20 "6#>%\"cGF$" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"dGF$
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 370 "circle_pts := proc()\n
     local dat, i, rad, rads, angles, a, b;\n      rad :=  myrand(3,10
);\n      a := myrand(-10,10);\n      b:=  myrand(-10,10);\n      rads
 := [ random[normald[rad,rad/50]](points_wanted)];\n      angles := [ \+
random[uniform[0,2*Pi]](points_wanted) ];\n      RETURN ( [ [a+rads[i]
*cos(angles[i]), b+rads[i]*sin(angles[i])]  $ i=1..points_wanted  ]):
\n end:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "cpt:=circle_pts(
);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%$cptG7@7$$\"+6<^$***!\"*$\"*Qe
7j(F)7$$\"+D<B8$)F)$\"+wl8$e(F)7$$\"+#4<BY*F)$\"*T6fC&F)7$$\"+0S*>U(F)
$\"**)H$faF)7$$\"+f+DD7!\")$\"+\"p8&QRF)7$$\"+MejSgF)$\"+#=>%p6F)7$$\"
+?'f%zbF)$\"+:<KdhF)7$$\"+=Zh6^F)$\"+q%\\Lt#F)7$$\"+%>l$3')F)$\"+u]xix
F)7$$\"+H\"\\RA\"F>$\"+([4Zz$F)7$$\"+)yy:<\"F>$\"+Dc(>$>F)7$$\"+#G(>c]
F)$\"+MtozIF)7$$\"+JwXu6F>$\"+af'f6'F)7$$\"+g&30?\"F>$\"+ldc3CF)7$$\"+
'p\\%[nF)$\"*_vre)F)7$$\"+c`[]bF)$\"+TSTHjF)7$$\"+\"4Co?\"F>$\"+IZdSaF
)7$$\"+)y`\"*p(F)$\"+@3zgwF)7$$\"+Q)4O/\"F>$\"+4v9OtF)7$$\"+ATwupF)$\"
*Io'3xF)7$$\"+UfK27F>$\"+V*=x3$F)7$$\"+/F:]\"*F)$\"*N5q=$F)7$$\"+&p.U7
\"F>$\"+v2^\"\\\"F)7$$\"+0!GKX'F)$\"+L[EprF)7$$\"+KHM<lF)$\"+$GVCJ(F)7
$$\"+,\"*3@**F)$\"+PhS\"f(F)7$$\"+:MK\\()F)$\"*4K]W$F)7$$\"+fun\"*[F)$
\"+p#)y$y%F)7$$\"+$fzFB\"F>$\"+o*[eX%F)7$$\"+Ai<'*pF)$\"**H%>(fF)" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 49 "epsilon:=(pt,a,b,c)->(pt[1]-
a)^2+(pt[2]-b)^2-r^2;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%(epsilonGf*
6&%#ptG%\"aG%\"bG%\"cG6\"6$%)operatorG%&arrowGF+,(*$),&&9$6#\"\"\"F69%
!\"\"\"\"#F6F6*$),&&F46#F9F69&F8F9F6F6*$)%\"rGF9F6F8F+F+F+" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 60 "E:=(a,b,r,cpt)->sum(epsilon(cpt[i],
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&%\"aG%\"bG%\"rG%$cptG6\"6$%)operatorG%&arrowGF+-%$sumG6$*$)-%(epsilon
G6&&9'6#%\"iG9$9%9&\"\"#\"\"\"/F:;F?-%%nopsG6#F8F+F+F+" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 101 "solutions:=\{solve(\{diff(E(a,b,r,
cpt),a)=0, diff(E(a,b,r,cpt),b)=0, diff(E(a,b,r,cpt),r)=0\},\{a,b,r\})
\};" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%*solutionsG<)<%/%\"rG$\"\"!F*
/%\"aG$\"+_&)4x')!\"*/%\"bG$\"+T5$3%RF/<%F'/F,^$$\"+F8SP%)F/$!+\"*=ieb
F//F1^$$\"+..O_gF/$!+T^r=\"*!#5<%/F,^$F7$\"+\"*=iebF/F'/F1^$F=$\"+T^r=
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{MPLTEXT 1 0 73 "finalsol:=op(select(s->if(subs(s,r)>0)then true else \+
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{PARA 0 "> " 0 "" {MPLTEXT 1 0 121 "display(plot(subs(finalsol,[a+r*co
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int,symbol=BOX));" }}{PARA 13 "" 1 "" {GLPLOT2D 600 600 600 {PLOTDATA 
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F*$\"350w1sF'\\,(F-7$$\"3w+Y!ykKR/\"F*$\"3qvnz:xb\"H(F-7$$\"35)\\;F!y
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