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{PARA 0 "> " 0 "" {MPLTEXT 1 0 172 "x[1]:=(u,v)->cos(u)*cos(v)*(1.5+si
n(5*u+3*v)*cos(2*u+7*v));\nx[2]:=(u,v)->sin(u)*cos(v)*(1.5+sin(5*u+3*v
)*cos(2*u+7*v));\nx[3]:=(u,v)->sin(v)*(1.5+sin(5*u+3*v)*cos(2*u+7*v));
" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%\"xG6#\"\"\"R6$%\"uG%\"vG6\"6$%
)operatorG%&arrowGF,*(-%$cosG6#9$F'-F26#9%F',&$\"#:!\"\"F'*&-%$sinG6#,
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{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%\"xG6#\"\"#R6$%\"uG%\"vG6\"6$%)oper
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F4\"\"&*&\"\"$F5F9F5F5F5-F76#,&F4F'*&\"\"(F5F9F5F5F5F5F5F,F,F," }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%\"xG6#\"\"$R6$%\"uG%\"vG6\"6$%)oper
atorG%&arrowGF,*&-%$sinG6#9%\"\"\",&$\"#:!\"\"F5*&-F26#,&9$\"\"&*&F'F5
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{PARA 11 "" 1 "" {XPPMATH 20 "6#>%&deltaGR6$%\"xG%\"yG6\"6$%)operatorG
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{MPLTEXT 1 0 13 "with(linalg):" }}{PARA 7 "" 1 "" {TEXT -1 32 "Warning
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:=(k,l)->simplify(sum('sum('delta(i,j)*diff(x[i](u[1],u[2]),u[k])*diff
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{XPPMATH 20 "6#>%\"GGR6$%\"kG%\"lG6\"6$%)operatorG%&arrowGF)-%)simplif
yG6#-%$sumG6$.-F16$.*(-%&deltaG6$%\"iG%\"jG\"\"\"-%%diffG6$-&%\"xG6#F;
6$&%\"uG6#F=&FG6#\"\"#&FG6#9$F=-F?6$-&FC6#F<FE&FG6#9%F=/.F;;F=\"\"$/.F
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\"\"!\"\"\"*$)-%$cosG6#&%\"uG6#\"\"#F7F.$\"++++]A!\"**(F0F.)-F26#,&&F5
6#F.$\"\"&F-F4$\"\"$F-F7F.)-F26#,&F@$F7F-F4$\"\"(F-F7F.$!\"\"F-*&F0F.F
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{PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "ginv:=inverse(g);" }}{PARA 12 "" 1 
"" {XPPMATH 20 "6#>%%ginvG-%'matrixG6#7$7$,$*&,.*$)-%$cosG6#,&&%\"uG6#
\"\"\"$\"\"&\"\"!&F46#\"\"#$\"\"$F9F<F6$!#\\F9*$)-F06#,&F3$F<F9F:$\"\"
(F9F<F6$!#[F9$\"++++D^!\")F6*&-%$sinGF1F6FCF6F=*&F.F6FBF6$\"#dF9**F/F6
FCF6FOF6-FPFDF6$!#UF9F6,`o*$)-F06#F:F<F6$!++]7`6!\"(*(FZF6F.F6FBF6$!#G
F9*&FZF6FBF6$\"++++vcFMF-$\"\"*F9FAF7*(FZF6FOF6FCF6$!++++0;Fin*(FZF6)F
OF<F6FBF6$!\"*F9FgoF6FN$!#7F9FQ$!+++]#)*)Fin*&FZF6F.F6$\"+++]-6Fin*,FZ
F6F/F6FCF6FOF6FUF6$\"++++]%*FM*&)FCF>F6FOF6$\"#7F9*&)FC\"\"%F6F.F6$\"$
3)F9*(F.F6FOF6FCF6Fep*,FZF6FfoF6FBF6F/F6FUF6$\"$E\"F9*,FZF6FdpF6F/F6FO
F6FUF6$\"#UF9*,FZF6)F/F>F6FdpF6FOF6FUF6FV**FdpF6F/F6FOF6FUF6$\"#?F9**F
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FUF6$!#?F9**F/F6FBF6FfoF6FUF6$\"#gF9**FZF6F.F6FdpF6FOF6$!$o\"F9*&)F/Fi
pF6FhpF6$!$7)F9*&FZF6FhpF6$\"#[F9*&FirF6FBF6$\"$P)F9*(F.F6FdpF6FOF6$!#
()F9*(FZF6FirF6FBF6F?*(FZF6F.F6FhpF6$!$0\"F9*(FZF6FirF6FhpF6FR*(FZF6Fd
pF6FOF6$\"$T\"F9*$FhpF6$FipF9FT$\"#XF9!\"\"Fat*&,,$\"#9F9F6F-$!#9F9FAF
ftFQ$\"#HF9FT$!#TF9F6FXFat7$Fbt*&,4$!\"%F9F6FY$!++++]AFhoFjnF6F]o$FatF
9F-F^tFAF^tFbo$!\"$F9FQ$!#HF9FTFfqF6FXFat" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 108 "GammaTerm:=(k,i,j)->1/2*(sum('ginv[k,l]*(diff(g[l,
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11 "" 1 "" {XPPMATH 20 "6#>%*GammaTermGR6%%\"kG%\"iG%\"jG6\"6$%)operat
orG%&arrowGF*,$-%$sumG6$.*&&%%ginvG6$9$%\"lG\"\"\",(-%%diffG6$&%\"gG6$
F89&&%\"uG6#9%F9-F<6$&F?6$FEF8&FC6#FAF9-F<6$&F?6$FEFA&FC6#F8!\"\"F9/.F
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ma:=(k,i,j)->unapply(simplify(GammaTerm(k,i,j)),u[1],u[2]);" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#>%&GammaGR6%%\"kG%\"iG%\"jG6\"6$%)operatorG%
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%$u_1G%$u_2G6\"6$%)operatorG%&arrowGF',&*&*&,,$\"#9\"\"!\"\"\"*$)-%$co
sG6#,&9$$\"\"&F19%$\"\"$F1\"\"#F2$!#9F1*$)-F66#,&F9$F?F1F<$\"\"(F1F?F2
F@*&F4F2FCF2$\"#HF1**F5F2FDF2-%$sinGF7F2-FOFEF2$!#TF1F2,@*&-F66#F<F2-F
OFVF2$!+++++X!\"***FUF2F4F2FCF2FWF2FG**)FUF?F2F5F2FCF2FNF2$\"\"'F1**Fg
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$%)operatorG%&arrowGF',$*&,bq*&-%$cosG6#,&9$$\"\"&\"\"!9%$\"\"$F6\"\"
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F06#F7F:-F<FLF:$!$_#F6*&F/F:F@F:$\"$g*F6*&F@F:)F/F9F:$!$g*F6*,FTF:)F@F
DF:FGF:FKF:FMF:$!$%)*F6*,F/F:FXF:FGF:FKF:FMF:$\"$%)*F6**)F@\"\"%F:)FKF
DF:F/F:F;F:$!%C_F6*&)F@F9F:FTF:$\"%SWF6*,)F/FDF:F_oF:FKF:F;F:FMF:$!$'p
F6*(FTF:FinF:F;F:$\"%![\"F6*&F_oF:F/F:$!%SWF6*,F;F:FXF:F[oF:FcoF:FGF:$
!%_xF6*.FTF:F_oF:F;F:FGF:FKF:FMF:$!$G$F6*.F/F:F@F:F;F:FGF:FKF:FMF:$\"$
Q(F6*.F/F:F_oF:F;F:FGF:FKF:FMF:$\"$G$F6*(FinF:FKF:FMF:$\"$7\"F6*(F_oF:
F[oF:FGF:$\"%_:F6*&F_oF:FGF:$\"$k%F6*,FcoF:FKF:F;F:F@F:FMF:$\"$O$F6**F
KF:F;F:F@F:FMF:$!$O$F6**F[oF:FcoF:F@F:FGF:$\"%WKF6**F[oF:F/F:FXF:F;F:$
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XF:FcoF:FGF:$!%#z$F6**FarF:F[oF:F@F:FGF:$!%o:F6**FarF:F_oF:F[oF:FGF:$
\"%+_F6**FTF:FinF:F[oF:F;F:$\"%WfF6**F_oF:FKF:F;F:FMF:Fbq**FarF:FinF:F
KF:FMF:$\"$K#F6**FXF:F[oF:F;F:FGF:$\"%!G#F6**FinF:FKF:FcoF:FMF:$!$W$F6
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:FGF:$!%_nF6*(FcoF:F@F:FGF:$!%WGF6*(F/F:FXF:F;F:$!%5IF6*(F[oF:F;F:FGF:
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$S\"F6*(F_oF:FcoF:FGF:$!%G<F6*(F;F:FXF:FGF:$\"%#R\"F6*(FarF:F_oF:FGF:$
\"%k7F6*(F_oF:F[oF:F/F:$!%;xF6*(FcoF:FKF:FMF:$\"$_#F6*(FTF:F[oF:F@F:$!
%'*yF6*(FTF:FXF:F;F:$!$?$F6*(FinF:F/F:F;F:$!%![\"F6*(FTF:F_oF:F[oF:$\"
%'z)F6F:,`o*&FcoF:FXF:$!$;*F6*$FcoF:$\"$W\"F6*$FXF:$\"#!)F6*$FinF:$\"#
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s'F6*,F[oF:FTF:F_oF:F;F:FGF:$!$s'F6*&F;F:F@F:$!$#>F6*&FarF:FXF:$!#kF6*
&FarF:FinF:F_q*&F[oF:FinF:$\"$o(F6*&F[oF:FXF:$\"$k(F6$!$W\"F6F:*(F[oF:
F_oF:F;F:$\"%cAF6*(F[oF:FarF:FXF:$!$%yF6*(FcoF:F;F:F@F:Fgx*(F[oF:F;F:F
@F:$!%oDF6**F[oF:F;F:F@F:FcoF:F^t**F_oF:F/F:F;F:FGF:$\"$?$F6**F[oF:Fco
F:F_oF:F;F:$!%)o#F6**FTF:F_oF:F;F:FGF:Fhv**F/F:F@F:F;F:FGF:F=**F[oF:FX
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TF:FXF:FGF:FU*(F/F:FXF:FGF:FQ!\"\"$!\"#F6F'F'F'" }}{PARA 12 "" 1 "" 
{XPPMATH 20 "6#R6$%$u_1G%$u_2G6\"6$%)operatorG%&arrowGF',$*&,dq*&-%$co
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#F6F7$\"\"(F6F:-F<FAF:$\"%ODF6*&-F06#F7F:-F<FLF:$!%X=F6*&F;F:FGF:$\"$s
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FKF:FMF:$\"$o(F6*(FboF:F^oF:FGF:$\"%w`F6*&FboF:FGF:$\"$![F6*,FfoF:FKF:
F;F:F@F:FMF:$\"%_BF6**FKF:F;F:F@F:FMF:$!%oDF6**F^oF:FfoF:F@F:FGF:$\"&K
<\"F6**F^oF:F/F:FenF:F;F:$\"%!Q(F6**FKF:FfoF:FenF:FMF:$!$/$F6*(FfoF:F;
F:FGF:F`p*()F/F]oF:F@F:FGF:$\"$[%F6**F`rF:FKF:FenF:FMF:$!$%yF6**F;F:Fe
nF:FfoF:FGF:$!%7jF6**F`rF:F^oF:F@F:FGF:$!%)[&F6**F`rF:FboF:F^oF:FGF:$
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F:$!%!o\"F6**FWF:F^oF:FenF:F;F:$!%cqF6**FfoF:F^oF:F;F:FGF:$\"%K#)F6**F
boF:F^oF:FfoF:FGF:$!&wP\"F6*(FfoF:F@F:FGF:$!&k.\"F6*(F/F:FenF:F;F:$!%#
H*F6*(F^oF:F;F:FGF:$!%5')F6*(F^oF:F/F:F@F:$\"&Y2\"F6*(F^oF:F@F:FGF:$!%
WiF6*(FKF:FenF:FMF:$\"$k(F6*(FboF:FfoF:FGF:$!$![F6*(F;F:FenF:FGF:$\"%7
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\"#kF6*&F^oF:FfoF:Fcv*,F^oF:F/F:F@F:F;F:FGF:Fcp*(F^oF:FfoF:F\\oF:F\\t*
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F6*(F^oF:F`rF:F\\oF:Ffs*,F^oF:FboF:F/F:F;F:FGF:FQ*,F^oF:FWF:FboF:F;F:F
GF:F`p*&F;F:F@F:$!$#>F6*&F`rF:FenF:$!#kF6*&F`rF:F\\oF:$\"$k%F6*&F^oF:F
\\oF:Fgp*&F^oF:FenF:Fgu$!$W\"F6F:*(F^oF:FboF:F;F:Fcs*(F^oF:F`rF:FenF:F
dr*(FfoF:F;F:F@F:Fbx*(F^oF:F;F:F@F:Fcq**F^oF:F;F:F@F:FfoF:F`q**FboF:F/
F:F;F:FGF:$\"$?$F6**F^oF:FfoF:FboF:F;F:Fgo**FWF:FboF:F;F:FGF:$!$?$F6**
F/F:F@F:F;F:FGF:$\"$?(F6**F^oF:FenF:FWF:FGF:Ffn**F^oF:FenF:F/F:FGF:Fin
*(F^oF:FfoF:FenF:F\\r*(FWF:FenF:FGF:$!$g*F6*(F/F:FenF:FGF:$\"$g*F6!\"
\"$Fc[lF6F'F'F'" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#R6$%$u_1G%$u_2G6\"6
$%)operatorG%&arrowGF',$*&,dq*&-%$cosG6#,&9$$\"\"&\"\"!9%$\"\"$F6\"\"
\"-%$sinGF1F:$\"%_HF6*&-F06#,&F3$\"\"#F6F7$\"\"(F6F:-F<FAF:$\"%ODF6*&-
F06#F7F:-F<FLF:$!%X=F6*&F;F:FGF:$\"$s'F6*&F/F:F@F:$\"$)GF6*&F@F:)F/F9F
:$!$)GF6*,FWF:)F@FDF:FGF:FKF:FMF:$!%;?F6*,F/F:FenF:FGF:FKF:FMF:$\"%;?F
6**)F@\"\"%F:)FKFDF:F/F:F;F:$!%3qF6*&)F@F9F:FWF:$\"%[aF6*,)F/FDF:FboF:
FKF:F;F:FMF:$!%)o#F6*&FboF:F/F:$!%[sF6*,F;F:FenF:F^oF:FfoF:FGF:$!&kA\"
F6*.FWF:FboF:F;F:FGF:FKF:FMF:$!$s'F6*.F/F:F@F:F;F:FGF:FKF:FMF:$\"%7:F6
*.F/F:FboF:F;F:FGF:FKF:FMF:FQ*(F\\oF:FKF:FMF:$\"$o(F6*(FboF:F^oF:FGF:$
\"%w`F6*&FboF:FGF:$\"$![F6*,FfoF:FKF:F;F:F@F:FMF:$\"%_BF6**FKF:F;F:F@F
:FMF:$!%oDF6**F^oF:FfoF:F@F:FGF:$\"&K<\"F6**F^oF:F/F:FenF:F;F:$\"%!Q(F
6**FKF:FfoF:FenF:FMF:$!$/$F6*(FfoF:F;F:FGF:F`p*()F/F]oF:F@F:FGF:$\"$[%
F6**F`rF:FKF:FenF:FMF:$!$%yF6**F;F:FenF:FfoF:FGF:$!%7jF6**F`rF:F^oF:F@
F:FGF:$!%)[&F6**F`rF:FboF:F^oF:FGF:$\"%+%)F6**FWF:F\\oF:F^oF:F;F:$\"%S
uF6**FboF:FKF:F;F:FMF:$\"%cAF6**F`rF:F\\oF:FKF:FMF:$\"$7*F6**FenF:F^oF
:F;F:FGF:$\"%GxF6**F\\oF:FKF:FfoF:FMF:$!%!o\"F6**FWF:F^oF:FenF:F;F:$!%
cqF6**FfoF:F^oF:F;F:FGF:$\"%K#)F6**FboF:F^oF:FfoF:FGF:$!&wP\"F6*(FfoF:
F@F:FGF:$!&k.\"F6*(F/F:FenF:F;F:$!%#H*F6*(F^oF:F;F:FGF:$!%5')F6*(F^oF:
F/F:F@F:$\"&Y2\"F6*(F^oF:F@F:FGF:$!%WiF6*(FKF:FenF:FMF:$\"$k(F6*(FboF:
FfoF:FGF:$!$![F6*(F;F:FenF:FGF:$\"%7@F6*(FboF:F^oF:F/F:$!&o.\"F6*(FfoF
:FKF:FMF:$\"%k<F6*(FWF:F^oF:F@F:$!&%e5F6*(FWF:FenF:F;F:$\"%?6F6*(F\\oF
:F/F:F;F:$!%+7F6*(FWF:FboF:F^oF:$\"&;5\"F6F:,`o*&FfoF:FenF:$!$;*F6*$Ff
oF:$\"$W\"F6*$FenF:$\"#!)F6*$F\\oF:$\"#kF6*&F^oF:FfoF:Fcv*,F^oF:F/F:F@
F:F;F:FGF:Fcp*(F^oF:FfoF:F\\oF:F\\t*&FboF:F;F:$\"$#>F6*&F\\oF:FfoF:$!$
G&F6*$F^oF:FN*(FfoF:FboF:F;F:$!%#R\"F6*(F^oF:F`rF:F\\oF:Ffs*,F^oF:FboF
:F/F:F;F:FGF:FQ*,F^oF:FWF:FboF:F;F:FGF:F`p*&F;F:F@F:$!$#>F6*&F`rF:FenF
:$!#kF6*&F`rF:F\\oF:$\"$k%F6*&F^oF:F\\oF:Fgp*&F^oF:FenF:Fgu$!$W\"F6F:*
(F^oF:FboF:F;F:Fcs*(F^oF:F`rF:FenF:Fdr*(FfoF:F;F:F@F:Fbx*(F^oF:F;F:F@F
:Fcq**F^oF:F;F:F@F:FfoF:F`q**FboF:F/F:F;F:FGF:$\"$?$F6**F^oF:FfoF:FboF
:F;F:Fgo**FWF:FboF:F;F:FGF:$!$?$F6**F/F:F@F:F;F:FGF:$\"$?(F6**F^oF:Fen
F:FWF:FGF:Ffn**F^oF:FenF:F/F:FGF:Fin*(F^oF:FfoF:FenF:F\\r*(FWF:FenF:FG
F:$!$g*F6*(F/F:FenF:FGF:$\"$g*F6!\"\"$Fc[lF6F'F'F'" }}{PARA 12 "" 1 "
" {XPPMATH 20 "6#R6$%$u_1G%$u_2G6\"6$%)operatorG%&arrowGF',$*&,H*(-%$s
inG6#,&9$$\"\"&\"\"!9%$\"\"$F6\"\"\")-%$cosG6#,&F3$\"\"#F6F7$\"\"(F6FA
F:-F0F>F:$!$/&F6**F/F:F;F:)-F=F1FAF:FDF:$\"#sF6*()F<\"\"%F:FIF:F/F:$!%
KAF6*()F<F9F:FHF:FDF:$!%;KF6*()FIF9F:F;F:F/F:$!%#f%F6*&FRF:FDF:$\"$C'F
6*&FRF:FIF:$\"%g7F6*&FRF:FVF:$!$!=F6*&F<F:FVF:$!%!)eF6*()FIFNF:F<F:FDF
:$!%o:F6*(FHF:F/F:FDF:$\"%_BF6*&F/F:FDF:$!%1CF6*&FIF:F/F:$!%7:F6*(FHF:
F<F:FDF:$\"%7\"*F6*(FIF:F;F:F/F:$\"&%f6F6*&F<F:FDF:$!%kPF6*(F`oF:FRF:F
DF:$\"%#f#F6*(FVF:FMF:F/F:$\"%_HF6*&FIF:F<F:$\"%:gF6F:,`o*&FHF:F;F:$\"
$;*F6*$FHF:$!$W\"F6*$F;F:$!#!)F6*$FMF:$!#kF6*&)-F=6#F7FAF:FHF:$!%k<F6*
,F\\rF:FIF:F<F:F/F:FDF:Fjo*(F\\rF:FHF:FMF:$\"%!o\"F6*&FRF:F/F:$!$#>F6*
&FMF:FHF:$\"$G&F6*$F\\rF:$\"%X=F6*(FHF:FRF:F/F:$\"%#R\"F6*(F\\rF:F`oF:
FMF:$!$7*F6*,F\\rF:FRF:FIF:F/F:FDF:$!$s'F6*,F\\rF:FVF:FRF:F/F:FDF:$\"$
s'F6*&F/F:F<F:$\"$#>F6*&F`oF:F;F:$\"#kF6*&F`oF:FMF:$!$k%F6*&F\\rF:FMF:
$!$o(F6*&F\\rF:F;F:$!$k(F6$\"$W\"F6F:*(F\\rF:FRF:F/F:$!%cAF6*(F\\rF:F`
oF:F;F:$\"$%yF6*(FHF:F/F:F<F:Ffr*(F\\rF:F/F:F<F:$\"%oDF6**F\\rF:F/F:F<
F:FHF:$!%_BF6**FRF:FIF:F/F:FDF:$!$?$F6**F\\rF:FHF:FRF:F/F:$\"%)o#F6**F
VF:FRF:F/F:FDF:$\"$?$F6**FIF:F<F:F/F:FDF:$!$?(F6**F\\rF:F;F:FVF:FDF:$
\"%;?F6**F\\rF:F;F:FIF:FDF:$!%;?F6*(F\\rF:FHF:F;F:$\"$/$F6*(FVF:F;F:FD
F:$\"$g*F6*(FIF:F;F:FDF:$!$g*F6!\"\"$!\"#F6F'F'F'" }}{PARA 12 "" 1 "" 
{XPPMATH 20 "6#R6$%$u_1G%$u_2G6\"6$%)operatorG%&arrowGF'*&*&-%$cosG6#9
%\"\"\",^r*,)-F.6#,&9$$\"\"&\"\"!F0$\"\"$F;F=F1)-F.6#,&F8$\"\"#F;F0$\"
\"(F;F=F1-%$sinGF6F1-FGF@F1-FGF/F1$\"$?$F;*,)F-F=F1)F5FCF1)F?FCF1FFF1F
HF1$!$/&F;*,)F-FCF1FNF1F>F1FFF1FIF1$!#'*F;*,F5F1F>F1FFF1FHF1FIF1$!$?$F
;*,F5F1F?F1FFF1FHF1FIF1$!$?(F;*(FSF1)F?\"\"%F1FIF1$\"#;F;*(F-F1F?F1FHF
1$\"%/#)F;*(F-F1F5F1F?F1$!$w&F;*(F>F1FFF1FIF1$!$#>F;*(FFF1F?F1FIF1$\"$
#>F;*&FSF1FIF1$\"#\")F;*(FSF1FOF1FIF1$\"$;#F;*&FgnF1FIF1$!#kF;*&FNF1FI
F1$!$W\"F;*&FOF1FIF1$!#!)F;**FSF1FNF1FgnF1FIF1$!#KF;**F-F1F5F1FOF1FFF1
$!&'z5F;**FMF1FNF1F?F1FHF1$!$c(F;**FSF1FFF1F?F1FIF1F[p**F5F1FOF1FHF1FI
F1$!$g*F;**F4F1FOF1FHF1FIF1$\"$g*F;**F4F1F-F1FOF1FFF1$\"%CEF;*(FMF1F>F
1F5F1$!$;#F;*(F4F1F-F1F?F1$\"$w&F;**FNF1F-F1FFF1FHF1$!%W8F;**)F5FhnF1F
>F1F-F1FHF1$!%3UF;**F4F1FgnF1F-F1FFF1$!%KOF;*(FMF1F?F1FHF1$\"$c(F;**Fc
rF1F-F1F?F1FHF1$\"$'*)F;**F>F1F-F1FNF1FHF1$\"%c=F;**FNF1FFF1F?F1FIF1Fb
o**FNF1F>F1FFF1FIF1$\"%#R\"F;**FMF1FOF1FFF1FHF1$\"$/&F;**FMF1F4F1FgnF1
FFF1$\"#[F;*(F>F1F-F1F5F1$!%+OF;**FMF1FgnF1F5F1FFF1$!#[F;**FSF1F>F1FFF
1FIF1$\"#'*F;*(FMF1FFF1FHF1$\"$y$F;**F-F1FOF1FHF1FFF1$\"%+%)F;**FMF1Fc
rF1F>F1FHF1$\"$7\"F;**FSF1FNF1FOF1FIF1Fjq**FMF1F5F1FOF1FFF1$!$C$F;**Fg
nF1F-F1F5F1FFF1$\"%K7F;**FSF1FcrF1FgnF1FIF1Fin**F-F1FNF1F?F1FHF1$!&g7
\"F;**FMF1FNF1F>F1FHF1$!$C#F;*(F-F1F5F1FFF1$\"%S]F;*(FMF1F5F1F?F1$!$i
\"F;*(F>F1F-F1FHF1$\"%_BF;*(FMF1F>F1FHF1F\\u*(FcrF1FgnF1FIF1$!$k%F;*(F
gnF1FNF1FIF1$\"$G&F;*(FMF1F4F1F>F1F[p*(FNF1FOF1FIF1$\"$;*F;*(F-F1FFF1F
HF1$\"%W8F;*(FcrF1FOF1FIF1$\"#kF;FI$\"$W\"F;F1F1,`o*&FNF1FOF1F^w*$FNF1
Fap*$FOF1Fdp*$FgnF1F^p*&FSF1FNF1$!%k<F;*,FSF1F5F1F?F1FFF1FHF1$!%7:F;*(
FSF1FNF1FgnF1$\"%!o\"F;*&F>F1FFF1Fbo*&FgnF1FNF1Fjv*$FSF1$\"%X=F;*(FNF1
F>F1FFF1Fds*(FSF1FcrF1FgnF1$!$7*F;*,FSF1F>F1F5F1FFF1FHF1$!$s'F;*,FSF1F
4F1F>F1FFF1FHF1$\"$s'F;*&FFF1F?F1Feo*&FcrF1FOF1Fdw*&FcrF1FgnF1Fgv*&FSF
1FgnF1$!$o(F;*&FSF1FOF1$!$k(F;FfwF1*(FSF1F>F1FFF1$!%cAF;*(FSF1FcrF1FOF
1$\"$%yF;*(FNF1FFF1F?F1Fbo*(FSF1FFF1F?F1$\"%oDF;**FSF1FFF1F?F1FNF1$!%_
BF;**F>F1F5F1FFF1FHF1FW**FSF1FNF1F>F1FFF1$\"%)o#F;**F4F1F>F1FFF1FHF1FJ
**F5F1F?F1FFF1FHF1FZ**FSF1FOF1F4F1FHF1$\"%;?F;**FSF1FOF1F5F1FHF1$!%;?F
;*(FSF1FNF1FOF1$\"$/$F;*(F4F1FOF1FHF1Fdq*(F5F1FOF1FHF1Faq!\"\"F'F'F'" 
}}{PARA 12 "" 1 "" {XPPMATH 20 "6#R6$%$u_1G%$u_2G6\"6$%)operatorG%&arr
owGF',$*&,hq**)-%$cosG6#,&9$$\"\"&\"\"!9%$\"\"$F7\"\"#\"\"\")-F16#F8F;
F<-%$sinGF2F<-FA6#,&F4$F;F7F8$\"\"(F7F<$\"%w6F7**)F0F:F<)-F1FC\"\"%F<F
=F<F@F<$\"#SF7**)FMF:F<F=F<F/F<FBF<$\"$3)F7**)F0FNF<F=F<FMF<FBF<$!$%yF
7*,F/F<F>F<F@F<FMF<-FAF?F<$\"$O$F7*.F0F<FRF<F@F<FBF<F>F<FZF<$\"$G$F7*,
F0F<)FMF;F<FBF<F>F<FZF<$\"$%)*F7*,FKF<F[oF<FBF<F>F<FZF<$!$%)*F7*&FRF<F
0F<$\"$?(F7**FVF<F>F<F[oF<FZF<$!$7\"F7*(FRF<F=F<FBF<$!$C)F7*(F/F<FRF<F
BF<$\"%G8F7*(FVF<FRF<FBF<$!%k7F7*.FKF<FRF<F@F<FBF<F>F<FZF<$!$G$F7*&FMF
<FBF<$\"#kF7*&F>F<FZF<$!$_#F7*&FKF<FRF<$!%?AF7*&FKF<FMF<Fbo*&FRF<FBF<$
!#kF7*(FRF<F=F<F0F<$\"%[[F7*(FLF<F0F<F@F<$\"$![F7*(FKF<FLF<F@F<$!%![\"
F7*(F/F<F@F<FBF<$!#'*F7*(FKF<FRF<F=F<$!%3VF7*(F=F<F0F<F@F<$!%m^F7*&F@F
<FBF<$\"#'*F7*&F0F<FMF<$!$?(F7*,F/F<FRF<F>F<F@F<FZF<$!$'pF7*,F/F<F[oF<
F=F<F@F<FBF<$\"%SQF7*(F[oF<F@F<FBF<Fjq*(FKF<F=F<FMF<$\"%SHF7*(FVF<FMF<
FBF<Fdp*(FKF<F[oF<F@F<Fdq**F/F<F[oF<F@F<FBF<$\"%'*=F7**F>F<F@F<FMF<FZF
<$!$O$F7**F=F<F/F<FMF<FBF<$\"%GtF7**F=F<F0F<F[oF<F@F<$\"%)z'F7**F>F<F/
F<F[oF<FZF<$!$)HF7**FVF<FLF<F>F<FZF<$\"$K#F7**F[oF<F=F<F@F<FBF<$!%COF7
**FLF<F>F<F/F<FZF<$!$W$F7**FKF<F=F<F[oF<F@F<Fhs**FVF<FRF<F=F<FBF<$\"#;
F7*(F/F<FMF<FBF<$!$G\"F7*(F0F<F[oF<F@F<$!$![F7*(F=F<F@F<FBF<$!%A6F7*(F
=F<F0F<FMF<$!%vIF7*(F=F<FMF<FBF<$!%IVF7*(F>F<F[oF<FZF<$\"$S\"F7**FRF<F
>F<F@F<FZF<Fen**FLF<F=F<F0F<F@F<$\"$?$F7*(FLF<F>F<FZF<$\"$7\"F7*(F/F<F
>F<FZF<$\"$_#F7*.F0F<FMF<F@F<FBF<F>F<FZF<$\"$Q(F7F<,`o*&F/F<F[oF<$!$;*
F7*$F/F<$\"$W\"F7*$F[oF<$\"#!)F7*$FLF<Fdp*&F=F<F/F<$\"%k<F7*,F=F<F0F<F
MF<F@F<FBF<$\"%7:F7*(F=F<F/F<FLF<$!%!o\"F7*&FRF<F@F<$\"$#>F7*&FLF<F/F<
$!$G&F7*$F=F<$!%X=F7*(F/F<FRF<F@F<$!%#R\"F7*(F=F<FVF<FLF<$\"$7*F7*,F=F
<FRF<F0F<F@F<FBF<$\"$s'F7*,F=F<FKF<FRF<F@F<FBF<$!$s'F7*&F@F<FMF<$!$#>F
7*&FVF<F[oF<F^q*&FVF<FLF<$\"$k%F7*&F=F<FLF<$\"$o(F7*&F=F<F[oF<$\"$k(F7
$!$W\"F7F<*(F=F<FRF<F@F<$\"%cAF7*(F=F<FVF<F[oF<FW*(F/F<F@F<FMF<Fdx*(F=
F<F@F<FMF<$!%oDF7**F=F<F@F<FMF<F/F<$\"%_BF7**FRF<F0F<F@F<FBF<Fdv**F=F<
F/F<FRF<F@F<$!%)o#F7**FKF<FRF<F@F<FBF<$!$?$F7**F0F<FMF<F@F<FBF<Fbo**F=
F<F[oF<FKF<FBF<$!%;?F7**F=F<F[oF<F0F<FBF<$\"%;?F7*(F=F<F/F<F[oF<$!$/$F
7*(FKF<F[oF<FBF<$!$g*F7*(F0F<F[oF<FBF<$\"$g*F7!\"\"FEF'F'F'" }}{PARA 
12 "" 1 "" {XPPMATH 20 "6#R6$%$u_1G%$u_2G6\"6$%)operatorG%&arrowGF',$*
&,hq**)-%$cosG6#,&9$$\"\"&\"\"!9%$\"\"$F7\"\"#\"\"\")-F16#F8F;F<-%$sin
GF2F<-FA6#,&F4$F;F7F8$\"\"(F7F<$\"%w6F7**)F0F:F<)-F1FC\"\"%F<F=F<F@F<$
\"#SF7**)FMF:F<F=F<F/F<FBF<$\"$3)F7**)F0FNF<F=F<FMF<FBF<$!$%yF7*,F/F<F
>F<F@F<FMF<-FAF?F<$\"$O$F7*.F0F<FRF<F@F<FBF<F>F<FZF<$\"$G$F7*,F0F<)FMF
;F<FBF<F>F<FZF<$\"$%)*F7*,FKF<F[oF<FBF<F>F<FZF<$!$%)*F7*&FRF<F0F<$\"$?
(F7**FVF<F>F<F[oF<FZF<$!$7\"F7*(FRF<F=F<FBF<$!$C)F7*(F/F<FRF<FBF<$\"%G
8F7*(FVF<FRF<FBF<$!%k7F7*.FKF<FRF<F@F<FBF<F>F<FZF<$!$G$F7*&FMF<FBF<$\"
#kF7*&F>F<FZF<$!$_#F7*&FKF<FRF<$!%?AF7*&FKF<FMF<Fbo*&FRF<FBF<$!#kF7*(F
RF<F=F<F0F<$\"%[[F7*(FLF<F0F<F@F<$\"$![F7*(FKF<FLF<F@F<$!%![\"F7*(F/F<
F@F<FBF<$!#'*F7*(FKF<FRF<F=F<$!%3VF7*(F=F<F0F<F@F<$!%m^F7*&F@F<FBF<$\"
#'*F7*&F0F<FMF<$!$?(F7*,F/F<FRF<F>F<F@F<FZF<$!$'pF7*,F/F<F[oF<F=F<F@F<
FBF<$\"%SQF7*(F[oF<F@F<FBF<Fjq*(FKF<F=F<FMF<$\"%SHF7*(FVF<FMF<FBF<Fdp*
(FKF<F[oF<F@F<Fdq**F/F<F[oF<F@F<FBF<$\"%'*=F7**F>F<F@F<FMF<FZF<$!$O$F7
**F=F<F/F<FMF<FBF<$\"%GtF7**F=F<F0F<F[oF<F@F<$\"%)z'F7**F>F<F/F<F[oF<F
ZF<$!$)HF7**FVF<FLF<F>F<FZF<$\"$K#F7**F[oF<F=F<F@F<FBF<$!%COF7**FLF<F>
F<F/F<FZF<$!$W$F7**FKF<F=F<F[oF<F@F<Fhs**FVF<FRF<F=F<FBF<$\"#;F7*(F/F<
FMF<FBF<$!$G\"F7*(F0F<F[oF<F@F<$!$![F7*(F=F<F@F<FBF<$!%A6F7*(F=F<F0F<F
MF<$!%vIF7*(F=F<FMF<FBF<$!%IVF7*(F>F<F[oF<FZF<$\"$S\"F7**FRF<F>F<F@F<F
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eric);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#eqGR6#%(rkf45_xG6'%\"iG%(
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0 "" {MPLTEXT 1 0 152 "X:=proc(t) if type(t[1],float) and type(t[2],fl
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#>%\"XGR6#%\"tG6\"F(F(@%3-%%typeG6$&9$6#\"\"\"%&floatG-F,6$&F/6#\"\"#F
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{PARA 11 "" 1 "" {XPPMATH 20 "6#>%)GeodesicG7\"" }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 98 "Geodesic:=[op(Geodesic),PLOT3D(CURVES(map(X,op
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0 "> " 0 "" {MPLTEXT 1 0 44 "with(plots):display3d(Surface,op(Geodesic
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