{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 }{PSTYLE "Maple Plot" -1 13 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 
1 2 2 2 2 2 2 1 1 1 1 }3 1 0 0 0 0 1 0 1 0 2 2 0 1 }}
{SECT 0 {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "
> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}
{PARA 0 "" 0 "" {TEXT -1 19 "Construct some data" }}{PARA 0 "" 0 "" 
{TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 90 "f := 2*sin(
t)+3*t^2;  # the function we are trying \n                      # to a
pproximate" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"fG,&*&\"\"#\"\"\"-%$
sinG6#%\"tGF(F(*&\"\"$F()F,F'F(F(" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 16 "f1 := diff(f,t);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>
%#f1G,&*&\"\"#\"\"\"-%$cosG6#%\"tGF(F(*&\"\"'F(F,F(F(" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "f2 := diff(f,t$2);" }}{PARA 11 "" 
1 "" {XPPMATH 20 "6#>%#f2G,&*&\"\"#\"\"\"-%$sinG6#%\"tGF(!\"\"\"\"'F(
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 36 "x := Vector[row]([0.5,1.0,1.5,2.0]);" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#>%\"xG-%'RTABLEG6%\"*;&*zX\"-%'VECTORG6#7&$
\"\"&!\"\"$\"#5F/$\"#:F/$\"#?F/&%'VectorG6#%$rowG" }}}{EXCHG {PARA 0 "
> " 0 "" {MPLTEXT 1 0 117 "for k from 1 to 4 do\n   print(evalf(subs(t
=x[k],f)),evalf(subs(t=x[k],f1)),\n         evalf(subs(t=x[k],f2)));\n
end do;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%$\"+x5&)3<!\"*$\"+C^;bZF%$
\"+B*[6/&F%" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%$\"+q>%Ho%!\"*$\"+7Yg!3
(F%$\"+I!eqJ%F%" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%$\"+t**)\\u)!\"*$\"
+.WZT\"*F%$\"+F+,0SF%" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%$\"+&[f=Q\"!
\")$\"+L1x;6F%$\"+Y^S\"=%!\"*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 50 "y := Vector[row]([1.7,4.7,8.7,13.8,7.1,9.1,4.18]);" }}{PARA 11 "
" 1 "" {XPPMATH 20 "6#>%\"yG-%'RTABLEG6%\"*Oq'f9-%'VECTORG6#7)$\"#<!\"
\"$\"#ZF/$\"#()F/$\"$Q\"F/$\"#rF/$\"#\"*F/$\"$=%!\"#&%'VectorG6#%$rowG
" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 
32 "Solve the interpolation problem:" }}{PARA 0 "" 0 "" {TEXT -1 0 "" 
}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 103 "g := c[1] + c[2]*t + c[3
]*t^2 + c[4]*t^3 + c[5]*t^4 + c[6]*t^5+c[7]*t^6;   # define the target
 function" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"gG,0&%\"cG6#\"\"\"F)*
&&F'6#\"\"#F)%\"tGF)F)*&&F'6#\"\"$F))F.F-F)F)*&&F'6#\"\"%F))F.F2F)F)*&
&F'6#\"\"&F))F.F7F)F)*&&F'6#\"\"'F))F.F<F)F)*&&F'6#\"\"(F))F.FAF)F)" }
}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 84 "for k from 1 to 4 do   # d
efine equations\n   eq[k] := subs(t=x[k],g) = y[k]\nend do; " }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#>&%#eqG6#\"\"\"/,0&%\"cGF&F'*&$\"\"&!\"\"F'&
F+6#\"\"#F'F'*&$\"#D!\"#F'&F+6#\"\"$F'F'*&$\"$D\"!\"$F'&F+6#\"\"%F'F'*
&$\"$D'!\"%F'&F+6#F.F'F'*&$\"%DJ!\"&F'&F+6#\"\"'F'F'*&$\"&Dc\"!\"'F'&F
+6#\"\"(F'F'$\"#<F/" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%#eqG6#\"\"#/
,0&%\"cG6#\"\"\"F-*&$\"#5!\"\"F-&F+F&F-F-*&$\"$+\"!\"#F-&F+6#\"\"$F-F-
*&$\"%+5!\"$F-&F+6#\"\"%F-F-*&$\"&++\"!\"%F-&F+6#\"\"&F-F-*&$\"'++5!\"
&F-&F+6#\"\"'F-F-*&$\"(+++\"!\"'F-&F+6#\"\"(F-F-$\"#ZF1" }}{PARA 11 "
" 1 "" {XPPMATH 20 "6#>&%#eqG6#\"\"$/,0&%\"cG6#\"\"\"F-*&$\"#:!\"\"F-&
F+6#\"\"#F-F-*&$\"$D#!\"#F-&F+F&F-F-*&$\"%vL!\"$F-&F+6#\"\"%F-F-*&$\"&
D1&!\"%F-&F+6#\"\"&F-F-*&$\"'v$f(!\"&F-&F+6#\"\"'F-F-*&$\")D1R6!\"'F-&
F+6#\"\"(F-F-$\"#()F1" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%#eqG6#\"\"
%/,0&%\"cG6#\"\"\"F-*&$\"#?!\"\"F-&F+6#\"\"#F-F-*&$\"$+%!\"#F-&F+6#\"
\"$F-F-*&$\"%+!)!\"$F-&F+F&F-F-*&$\"'++;!\"%F-&F+6#\"\"&F-F-*&$\"(++?$
!\"&F-&F+6#\"\"'F-F-*&$\")+++k!\"'F-&F+6#\"\"(F-F-$\"$Q\"F1" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 37 "eq[5] := subs(t=x[2],diff(g,
t))=y[5];" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%#eqG6#\"\"&/,.&%\"cG6#
\"\"#\"\"\"*&$\"#?!\"\"F.&F+6#\"\"$F.F.*&$\"$+$!\"#F.&F+6#\"\"%F.F.*&$
\"%+S!\"$F.&F+F&F.F.*&$\"&++&!\"%F.&F+6#\"\"'F.F.*&$\"'++g!\"&F.&F+6#
\"\"(F.F.$\"#rF2" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 37 "eq[6] :
= subs(t=x[3],diff(g,t))=y[6];" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%#
eqG6#\"\"'/,.&%\"cG6#\"\"#\"\"\"*&$\"#I!\"\"F.&F+6#\"\"$F.F.*&$\"$v'!
\"#F.&F+6#\"\"%F.F.*&$\"&+N\"!\"$F.&F+6#\"\"&F.F.*&$\"'DJD!\"%F.&F+F&F
.F.*&$\"(]ib%!\"&F.&F+6#\"\"(F.F.$\"#\"*F2" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 41 "eq[7] := subs(t=x[4],diff(g,t$2)) = y[7];" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#>&%#eqG6#\"\"(/,,*&\"\"#\"\"\"&%\"cG6#\"\"$F
,F,*&$\"$?\"!\"\"F,&F.6#\"\"%F,F,*&$\"%+[!\"#F,&F.6#\"\"&F,F,*&$\"'++;
!\"$F,&F.6#\"\"'F,F,*&$\"(++![!\"%F,&F.F&F,F,$\"$=%F;" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 49 "solve( \{seq(eq[k],k=1..7)\}, \{seq
(c[k],k=1..7)\} );" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#<)/&%\"cG6#\"\"(
$\"++++c6!\"*/&F&6#\"\"'$!+LLL+5!\")/&F&6#\"\"&$\"+LLB$[$F2/&F&6#\"\"%
$!+nm\"\\?'F2/&F&6#\"\"$$\"+nmcBhF2/&F&6#\"\"#$!+++DZDF2/&F&6#\"\"\"$
\"++++,]F+" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "assign(%);" }
}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 2 "g;" }}{PARA 12 "" 1 "" 
{XPPMATH 20 "6#,0$\"++++,]!\"*\"\"\"*&$\"+++DZD!\")F'%\"tGF'!\"\"*&$\"
+nmcBhF+F')F,\"\"#F'F'*&$\"+nm\"\\?'F+F')F,\"\"$F'F-*&$\"+LLB$[$F+F')F
,\"\"%F'F'*&$\"+LLL+5F+F')F,\"\"&F'F-*&$\"++++c6F&F')F,\"\"'F'F'" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "plot1 := plot(f,t=0..2.5):" 
}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "plot2 := plot(g,t=0..2.5)
:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "plots[display](\{plot1
,plot2\});" }}{PARA 13 "" 1 "" {GLPLOT2D 446 252 252 {PLOTDATA 2 "6&-%
'CURVESG6$7S7$$\"\"!F)F(7$$\"3WmmmT&)G\\a!#>$\"3a@(>6k-%y6!#=7$$\"3PL$
ek`o!>5F0$\"3-v6\"4VhhM#F07$$\"3omm\"z>)G_:F0$\"3DWCiJI+:QF07$$\"3-nmT
&QU!*3#F0$\"3yH'RI:\"*pX&F07$$\"3HL$eRZXKi#F0$\"31$R?r`]4D(F07$$\"3xm;
z>,_=JF0$\"3eN&3-B()R0*F07$$\"3v**\\7G$[8j$F0$\"3b@0jvM,16!#<7$$\"35n;
z%*frhTF0$\"3!y0#42+7G8FO7$$\"3A+]ilFQ!p%F0$\"3adpa#)z/k:FO7$$\"3@ML$3
_\"=M_F0$\"3t1`P?oe@=FO7$$\"3HnmTg(fJr&F0$\"37-WwQ[og?FO7$$\"3k++]7eP_
iF0$\"3\"[*o8^fMVBFO7$$\"3Q++]Pf!Qz'F0$\"3m))=a8lHTEFO7$$\"3@++](=ubJ(
F0$\"3)*)f)\\>veTHFO7$$\"37n;zW(*Q*y(F0$\"3cZN-IsGDKFO7$$\"3#QLL3F-GN)
F0$\"3k0h$GI[gd$FO7$$\"3=MLL$e'3I))F0$\"3A[ba(e<W)QFO7$$\"3?+]7.<G&Q*F
0$\"39G&*R'p$)eD%FO7$$\"3)HLL$eMsw)*F0$\"3)\\0Mw4$)ff%FO7$$\"3;+DJ&H\"
fT5FO$\"3CqkETY:\")\\FO7$$\"35+v$f)[$H4\"FO$\"3S1RHm3[f`FO7$$\"3cL$ek`
1l9\"FO$\"3_i_;*Q%4mdFO7$$\"3OLe*[.-d>\"FO$\"3mZ!\\7Bc+:'FO7$$\"3km;/E
gw[7FO$\"3%\\:=\"e$Rad'FO7$$\"3zm\"z%*f%)QI\"FO$\"3')p8KB__HqFO7$$\"3/
+voza'=N\"FO$\"3kAN@]7)[V(FO7$$\"3(om\"zWho.9FO$\"3sbDV$\\VJ)yFO7$$\"3
-++]i>Ad9FO$\"3EcXVnAgd$)FO7$$\"32+]i:jf4:FO$\"36u,'f$))*G$))FO7$$\"39
+DJ&>r-c\"FO$\"3EAcRJyA.$*FO7$$\"3++]P4q`;;FO$\"3oXuuiQ[P)*FO7$$\"3;LL
$eM%4n;FO$\"3[SI#HXMG.\"!#;7$$\"37++v$4v5s\"FO$\"3G9)=(>dP'3\"Fgu7$$\"
3cm\"zWn*)*p<FO$\"3tLq`PV!f8\"Fgu7$$\"3H++DJiYB=FO$\"3#*pqy8%e6>\"Fgu7
$$\"3CLek.Nyt=FO$\"32Vl&pF4UC\"Fgu7$$\"3=+Dc^&zj#>FO$\"3miM@u,x+8Fgu7$
$\"3CLL3-=!y(>FO$\"3akBSh?<d8Fgu7$$\"3))*\\7G8O;.#FO$\"3')fS5$[*R<9Fgu
7$$\"3!pmm;*\\[$3#FO$\"3'f)H4v'elZ\"Fgu7$$\"3*pmT&Qz]O@FO$\"3fE07F8CQ:
Fgu7$$\"3iLekG=4*=#FO$\"3)HtB(R/h+;Fgu7$$\"3F++]i4TPAFO$\"3/uANJi)*e;F
gu7$$\"3qL$3F9!z#H#FO$\"3g`nN+R;F<Fgu7$$\"3'pmm;%>KUBFO$\"3#[A!e$=6$*y
\"Fgu7$$\"3/+DJqJ8&R#FO$\"3gL.Oew!o&=Fgu7$$\"3G+voa-oXCFO$\"3R')yHhFiA
>Fgu7$$\"3++++++++DFO$\"3G\"z?)GWp%*>Fgu-%'COLOURG6&%$RGBG$\"#5!\"\"F(
F(-F$6$7S7$F($\"3L++++++,]FO7$F+$\"3?PhW(fH]y$FO7$F2$\"35;Fx2;4zHFO7$F
7$\"3v=4gC$=(4BFO7$F<$\"3W'GQ<)y$)[=FO7$FA$\"3Y#Hp)3]il:FO7$FF$\"3>e')
)=#[yJ9FO7$FK$\"3u/RX([K**R\"FO7$FQ$\"3_XM)o5*\\f9FO7$FV$\"3;*))>\"\\k
Z$f\"FO7$Fen$\"3//$Gf-s@z\"FO7$Fjn$\"3z`M%[H^q+#FO7$F_o$\"3Q\"fYrdMLG#
FO7$Fdo$\"3=!o,o#oq)e#FO7$Fio$\"3u0)4nDXH!HFO7$F^p$\"3(yi`OXv7?$FO7$Fc
p$\"35%3Dnz9&oNFO7$Fhp$\"3W@`EAqD))QFO7$F]q$\"3aO)4xVY(oUFO7$Fbq$\"34(
*yI\"3%o7YFO7$Fgq$\"3K#Gdt6Lx*\\FO7$F\\r$\"33%o@]inAP&FO7$Far$\"3#fxO&
\\w&>x&FO7$Ffr$\"3UJfd9<xZhFO7$F[s$\"37z/y\"oSMc'FO7$F`s$\"3s#=SeSsu+(
FO7$Fes$\"3)Rh4=lp[S(FO7$Fjs$\"3%o`-Ic)*f%yFO7$F_t$\"3nW/#*yh::$)FO7$F
dt$\"37nTBM%\\vy)FO7$Fit$\"3![$*G1fHsD*FO7$F^u$\"3/s>'Hq<Iz*FO7$Fcu$\"
3UErLpyoG5Fgu7$Fiu$\"3eOoW*fhE3\"Fgu7$F^v$\"37f%[d?EE8\"Fgu7$Fcv$\"33A
TEMNM)=\"Fgu7$Fhv$\"3(eT!ps(p<C\"Fgu7$F]w$\"3kW/!4uI')H\"Fgu7$Fbw$\"3=
(z$*o;R_N\"Fgu7$Fgw$\"3oR`L`rk:9Fgu7$F\\x$\"3a9&[7km]Z\"Fgu7$Fax$\"3vr
Mo$f9t`\"Fgu7$Ffx$\"3+H$eg[g3g\"Fgu7$F[y$\"3%>H/Y')R7m\"Fgu7$F`y$\"32#
Gy6-8Mt\"Fgu7$Fey$\"3xt\\p!yu8!=Fgu7$Fjy$\"3iI(*p=:Ny=Fgu7$F_z$\"338@O
xX^d>Fgu7$Fdz$\"3_ZiS;+5]?FguFhz-%+AXESLABELSG6%Q\"t6\"Q!Fidl-%%FONTG6
#%(DEFAULTG-%%VIEWG6$;F($\"#DF^[lF^el" 1 2 0 1 10 0 2 9 1 4 2 
1.000000 45.000000 45.000000 0 0 "Curve 1" "Curve 2" }}}}{EXCHG {PARA 
0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 
0 "" {TEXT -1 28 "Spline approximation example" }}{PARA 0 "" 0 "" 
{TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "x := Vector
[row]([1,1.2,1.5,1.8]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"xG-%'RT
ABLEG6%\"*!3Zp9-%'VECTORG6#7&\"\"\"$\"#7!\"\"$\"#:F0$\"#=F0&%'VectorG6
#%$rowG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 36 "y := Vector[row]
([2.3,2.6,2.4,2.1]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"yG-%'RTABL
EG6%\"*?r%p9-%'VECTORG6#7&$\"#B!\"\"$\"#EF/$\"#CF/$\"#@F/&%'VectorG6#%
$rowG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "c := 'c';  # clear
 variable c" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"cGF$" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 63 "p[1] := a[1]+a[2]*(t-x[1]) + a[3]*(
t-x[1])^2 + a[4]*(t-x[1])^3;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%\"p
G6#\"\"\",*&%\"aGF&F'*&&F*6#\"\"#F',&%\"tGF'F'!\"\"F'F'*&&F*6#\"\"$F')
F/F.F'F'*&&F*6#\"\"%F')F/F5F'F'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 63 "p[2] := b[1]+b[2]*(t-x[2]) + b[3]*(t-x[2])^2 + b[4]*(t-x[2])^3
;" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6#>&%\"pG6#\"\"#,*&%\"bG6#\"\"\"F,*&&F*F&F,,&%\"tGF,$\"#7!\"\"F3F,
F,*&&F*6#\"\"$F,)F/F'F,F,*&&F*6#\"\"%F,)F/F7F,F," }}}{EXCHG {PARA 0 ">
 " 0 "" {MPLTEXT 1 0 63 "p[3] := c[1]+c[2]*(t-x[3]) + c[3]*(t-x[3])^2 \+
+ c[4]*(t-x[3])^3;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%\"pG6#\"\"$,*
&%\"cG6#\"\"\"F,*&&F*6#\"\"#F,,&%\"tGF,$\"#:!\"\"F5F,F,*&&F*F&F,)F1F0F
,F,*&&F*6#\"\"%F,)F1F'F,F," }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
34 "eq[1] := subs(t=x[1],p[1]) = y[1];" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6#>&%#eqG6#\"\"\"/&%\"aGF&$\"#B!\"\"" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 34 "eq[2] := subs(t=x[2],p[1]) = y[2];" }}{PARA 11 "" 1 "
" {XPPMATH 20 "6#>&%#eqG6#\"\"#/,*&%\"aG6#\"\"\"F-*&$F'!\"\"F-&F+F&F-F
-*&$\"\"%!\"#F-&F+6#\"\"$F-F-*&$\"\")!\"$F-&F+6#F4F-F-$\"#EF0" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "eq[3] := subs(t=x[2],p[2]) =
 y[2];" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%#eqG6#\"\"$/&%\"bG6#\"\"
\"$\"#E!\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "eq[4] := su
bs(t=x[3],p[2]) = y[3];" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%#eqG6#\"
\"%/,*&%\"bG6#\"\"\"F-*&$\"\"$!\"\"F-&F+6#\"\"#F-F-*&$\"\"*!\"#F-&F+6#
F0F-F-*&$\"#F!\"$F-&F+F&F-F-$\"#CF1" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 34 "eq[5] := subs(t=x[3],p[3]) = y[3];" }}{PARA 11 "" 1 "
" {XPPMATH 20 "6#>&%#eqG6#\"\"&/&%\"cG6#\"\"\"$\"#C!\"\"" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "eq[6] := subs(t=x[4],p[3]) = y[4];
" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%#eqG6#\"\"'/,*&%\"cG6#\"\"\"F-*
&$\"\"$!\"\"F-&F+6#\"\"#F-F-*&$\"\"*!\"#F-&F+6#F0F-F-*&$\"#F!\"$F-&F+6
#\"\"%F-F-$\"#@F1" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 63 "eq[7] \+
:= subs(t=x[2],diff(p[1],t)) = subs(t=x[2],diff(p[2],t));" }}{PARA 11 
"" 1 "" {XPPMATH 20 "6#>&%#eqG6#\"\"(/,(&%\"aG6#\"\"#\"\"\"*&$\"\"%!\"
\"F.&F+6#\"\"$F.F.*&$\"#7!\"#F.&F+6#F1F.F.&%\"bGF," }}}{EXCHG {PARA 0 
"> " 0 "" {MPLTEXT 1 0 63 "eq[8] := subs(t=x[3],diff(p[2],t)) = subs(t
=x[3],diff(p[3],t));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%#eqG6#\"\")
/,(&%\"bG6#\"\"#\"\"\"*&$\"\"'!\"\"F.&F+6#\"\"$F.F.*&$\"#F!\"#F.&F+6#
\"\"%F.F.&%\"cGF," }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 67 "eq[9] \+
:= subs(t=x[2],diff(p[1],t$2)) = subs(t=x[2],diff(p[2],t$2));" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%#eqG6#\"\"*/,&*&\"\"#\"\"\"&%\"aG6#
\"\"$F,F,*&$\"#7!\"\"F,&F.6#\"\"%F,F,,$*&F+F,&%\"bGF/F,F," }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 68 "eq[10] := subs(t=x[3],diff(p[2],t$2
)) = subs(t=x[3],diff(p[3],t$2));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>
&%#eqG6#\"#5/,&*&\"\"#\"\"\"&%\"bG6#\"\"$F,F,*&$\"#=!\"\"F,&F.6#\"\"%F
,F,,$*&F+F,&%\"cGF/F,F," }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 42 "
eq[11] := subs(t=x[1],diff(p[1],t$2)) = 0;" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>&%#eqG6#\"#6/,$*&\"\"#\"\"\"&%\"aG6#\"\"$F,F,\"\"!" }}
}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 42 "eq[12] := subs(t=x[4],diff(
p[3],t$2)) = 0;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%#eqG6#\"#7/,&*&
\"\"#\"\"\"&%\"cG6#\"\"$F,F,*&$\"#=!\"\"F,&F.6#\"\"%F,F,\"\"!" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 81 "solve(\{seq(eq[k],k=1..12)\}
,\{seq(a[k],k=1..4),seq(b[k],k=1..4),seq(c[k],k=1..4)\});" }}{PARA 12 
"" 1 "" {XPPMATH 20 "6#<./&%\"aG6#\"\"$$\"\"!F*/&F&6#\"\"\"$\"+++++B!
\"*/&%\"bGF-$\"+++++EF1/&%\"cGF-$\"+++++CF1/&F96#\"\"#$!+r6<r6F1/&F46#
\"\"%$\"+e%e%e%)F1/&F4F'$!+dnvcnF1/&F4F>$\"+\"*4*4*f!#5/&F&FD$!+Eh7E6!
\")/&F&F>$\"+]/X]>F1/&F9FD$!+5&4&4&*FP/&F9F'$\"+f&e&e&)FP" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "assign(%);" }}}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 0 "" }}}}{MARK "43 0 0" 0 }{VIEWOPTS 1 1 0 3 2 1804 
1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }{RTABLE_HANDLES 145799516 
145967036 146947080 146947120 }{RTABLE 
M7R0
I6RTABLE_SAVE/145799516X*%)anythingG6"6"[gl!$%!!!"%"%$""&!""$"#5F)$"#:F)$"#?F)F
&
}
{RTABLE 
M7R0
I6RTABLE_SAVE/145967036X*%)anythingG6"6"[gl!$%!!!"("($"#<!""$"#ZF)$"#()F)$"$Q"F
)$"#rF)$"#"*F)$"$=%!"#F&
}
{RTABLE 
M7R0
I6RTABLE_SAVE/146947080X*%)anythingG6"6"[gl!$%!!!"%"%"""$"#7!""$"#:F*$"#=F*F&
}
{RTABLE 
M7R0
I6RTABLE_SAVE/146947120X*%)anythingG6"6"[gl!$%!!!"%"%$"#B!""$"#EF)$"#CF)$"#@F)F
&
}