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{XPPMATH 20 "6#%=GRTensorII~Version~1.70~(R5)G" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#%,31~May~1998G" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%ZDev
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" 1 "" {XPPMATH 20 "6#%DCopyright~1994-1998~by~the~authors.G" }}{PARA 
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11 "" 1 "" {XPPMATH 20 "6#/)%#x~G%\"aG-%'vectorG6#7&%\"rG%&thetaG%$phi
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"" 1 "" {XPPMATH 20 "6#/*$)%$~dsG\"\"#\"\"\",,*&*(,&\"\"\"F-*(%(epsilo
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{PARA 6 "" 1 "" {TEXT -1 43 "Applying routine linpert to object g(up,u
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{PARA 11 "" 1 "" {XPPMATH 20 "6#-%\"gG6$%#upGF&" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#/*&)%#g~G%\"aG\"\"\")%!G%\"bGF(-%'matrixG6#7&7&*&*&,&%
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26 "grcalcalter(R(dn,dn),13); " }}{PARA 6 "" 1 "" {TEXT -1 50 "Simplif
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-1 1 " " }}{PARA 6 "" 1 "" {TEXT -1 70 "Applying routine `Apply constr
aints repeatedly` to object g(dn,dn,pdn)" }}{PARA 6 "" 1 "" {TEXT -1 
71 "Applying routine `Apply constraints repeatedly` to object Chr(dn,d
n,dn)" }}{PARA 6 "" 1 "" {TEXT -1 71 "Applying routine `Apply constrai
nts repeatedly` to object Chr(dn,dn,up)" }}{PARA 6 "" 1 "" {TEXT -1 
66 "Applying routine `Apply constraints repeatedly` to object R(dn,dn)
" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/%*CPU~Time~G$\"$e&!\"$" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 105 "grmap(R(dn,dn),subs,diff(u(
theta),theta$2)=\n-cos(theta)/sin(theta)*diff(u(theta),theta)-j*u(thet
a),`x`); " }}{PARA 6 "" 1 "" {TEXT -1 33 "Applying routine subs to R(d
n,dn)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 103 "b1:=hcollect(expa
nd(coeff(collect(grcomponent(R(dn,dn),[r,theta]),epsilon),epsilon,1)),
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\"rG!\"\"%\"mG\"\"$\"\"\"-&%\"HG6#\"\"!6$F*%\"tGF.\"\"\"*&F*\"\"\",&F*
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\"\"F<FAF.-F?6$-%\"uG6#%&thetaGFenF." }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 95 "c1:=hcollect(coeff(collect(grcomponent(R(dn,dn),[t,th
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{XPPMATH 20 "6#>%#c1G*&,**&*&,&%\"rG!\"\"%\"mG\"\"#\"\"\"-%%diffG6$-&%
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{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 99 "d1:=hcollect(expand(coeff(co
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" 1 "" {XPPMATH 20 "6#>%#e1G*&,4*&*&-%%diffG6$-&%\"HG6#\"\"!6$%\"rG%\"
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F6-F*6$-%\"KGF1F2F4F6*&F2\"\"\"F9\"\"\"F=F:*&*&F5F6-F*6$-&F.6#F4F1F3F4
F6*$)F9\"\"#F6F=F:*&*&FGF4%\"jGF4F6*&F2\"\"\"F9\"\"\"F=#F:F;-F*6$F,-%
\"$G6$F2F;FM-F*6$FRFdoF:*&*&)F2F;F6-F*6$FG-Feo6$F3F;F4F6*$)F9\"\"#F6F=
FM*&*&-F*6%FenF2F3F4F2F4F6F9F=F4F4-%\"uG6#%&thetaGF4" }}}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 99 "f1:=hcollect(expand(coeff(collect(grcompo
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12 "" 1 "" {XPPMATH 20 "6#>%#f1G*&,4*&*(,&%\"rG!\"\"%\"mG\"\"#\"\"\"-&
%\"HG6#\"\"!6$F*%\"tGF.%\"jGF.\"\"\"*$)F*\"\"$F7!\"\"#F+F-*&*(F)F7,&F,
F.F*!\"#F.-%%diffG6$F/F*F.F7*$)F*\"\"$F7F;F<*&*(F,F.F)F7-FB6$-&F16#F-F
4F*F.F7*$)F*\"\"$F7F;#F.F-*&*(F)F7F,F7-FB6$-%\"KGF4F*F.F7*$)F*\"\"$F7F
;F+*&*&,&F,\"\"$F*F@F.-FB6$-&F16#F.F4F5F.F7*$)F*\"\"#F7F;F+*&*&)F)F-F7
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"> " 0 "" {MPLTEXT 1 0 99 "a1:=hcollect(coeff(collect(grcomponent(R(dn
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"" 1 "" {XPPMATH 20 "6#>%#a1G,&*&,4*&-&%\"HG6#\"\"!6$%\"rG%\"tG\"\"\"%
\"jGF1#!\"\"\"\"#*&-%%diffG6$F)F/F1,&F/F4%\"mGF5F1F3*&-F86$-&F+6#F5F.F
/F1F:\"\"\"F3*&,&F;\"\"$F/!\"#F1-F86$-%\"KGF.F/F1F1*&-F86$-&F+6#F1F.F0
F1F/F1F4*&,&F2F1F5F1F1F?F1#F1F5*&,&FFF1F2F1F1FIF1FS*(-F86$FI-%\"$G6$F/
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F1-F86$F^oFaoF1F1" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 134 "g1:=k
factor(hcollect(coeff(collect(grcomponent(R(dn,dn),[phi,phi]),epsilon)
,epsilon,1)\n,ufuncs,lperts),(cos(theta)-1)*(cos(theta)+1));" }}{PARA 
12 "" 1 "" {XPPMATH 20 "6#>%#g1G*(,&-%$cosG6#%&thetaG\"\"\"F+F+F+,&F'F
+!\"\"F+F+,&*&*&,L*&)%\"rG\"\"#\"\"\"-%%diffG6$-&%\"HG6#\"\"!6$F4%\"tG
F4F+F-*(F7F6%\"mGF+F4F+\"\"%*&F7F6)FBF5F6!\"%*&-F86$-&F<6#F5F?F4F+F3F6
F-*(FHF6F4F6FBF6FC*&FHF6FEF6FF*(-F86$-%\"KGF?F4F+F4F6FBF6!#9*&FPF6FEF6
\"#7*&FPF6F3F6FC*&F3F6-F86$-&F<6#F+F?F@F+F5*(FYF6F4F6FBF6FF*&FJF+F4F6!
\"#*&FJF6FBF6FC*&FRF+F4F6F5*&FRF6FBF6FF*(FRF6%\"jGF+F4F6F-*(FRF6F_oF6F
BF6F5*&-F86$FR-%\"$G6$F4F5F+)F4\"\"$F6F+*(FboF6F3F6FBF6FF*(FboF6F4F6FE
F6FC*&FgoF6-F86$FR-Feo6$F@F5F+F-F+-%\"uGF)F+F6,&F4F-FBF5!\"\"#F-F5*&**
F'F+-%$sinGF)F+,&F:F-FJF+F+-F86$F`pF*F+F6*&F&\"\"\"F,\"\"\"FcpFdpF+" }
}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 43 "hcollect(a1+g1/sin(theta)^
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\"!6$%\"rG%\"tG\"\"\"%\"jGF.#!\"\"\"\"#*&-%%diffG6$F&F,F.,&F,F1%\"mGF2
F.F1*&-F56$-&F(6#F2F+F,F.F7\"\"\"F1*&,&F8\"\"$F,!\"#F.-F56$-%\"KGF+F,F
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FFF.F.*(-F56$FF-%\"$G6$F,F2F.F,F?F7F?F.*&*&)F,FBF?-F56$FF-FX6$F-F2F.F?
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"" 1 "" {XPPMATH 20 "6#,$*&*&,&-&%\"HG6#\"\"!6$%\"rG%\"tG!\"\"-&F)6#\"
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{MPLTEXT 1 0 8 "restart:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "
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1 "" {XPPMATH 20 "6#%ZDeveloped~by~Peter~Musgrave,~Denis~Pollney~and~K
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"" {XPPMATH 20 "6#%3/home/lake/MetricsG" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 55 "read `/usr/local/MapleVR5/Grtii(5)/Lib/pertutils.mpl`
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{PARA 11 "" 1 "" {XPPMATH 20 "6#/%2Default~spacetimeG%&qschwG" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#%9For~the~qschw~spacetime:G" }}{PARA 
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20 "6#-%\"xG6#%#upG" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/)%#x~G%\"aG-%'
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\"\",,*&*(,&\"\"\"F-*&,&*&%(epsilonGF--&%\"hG6#F'6$%\"rG%\"tGF-F-*&)F1
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" {XPPMATH 20 "6#/%,ConstraintsG7*/*$)%(epsilonG\"\"$\"\"\"\"\"!/*$)F)
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-1 1 " " }}{PARA 6 "" 1 "" {TEXT -1 44 "Applying routine quadpert to o
bject g(up,up)" }}{PARA 6 "" 1 "" {TEXT -1 44 "Applying routine simpli
fy to object g(up,up)" }}{PARA 6 "" 1 "" {TEXT -1 42 "Applying routine
 factor to object g(up,up)" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/%*CPU~T
ime~G$\"$?$!\"$" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "grdispla
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1 "" {XPPMATH 20 "6#/*&)%#g~G%\"rG\"\"\")%!GF'F(,$*&*&,&F'!\"\"%\"mG\"
\"#F(,8\"\"%F(*(-&%\"hG6#F16$F'%\"tGF(%(epsilonGF()-%$cosG6#%&thetaGF1
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FAF<FAFB*(FEFA)-&F76#F(F9F1FAFHFA!\"**(FEFA-&%\"HGF8F9F(F<FAFB*(FEFAFL
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" {XPPMATH 20 "6#/*&)%#g~G%\"rG\"\"\")%!G%\"tGF(,$*(%(epsilonG\"\"\",&
*$)-%$cosG6#%&thetaG\"\"#F/\"\"$!\"\"F(F(,.**F2F/F.F(-&%\"hG6#F76$F'F+
F(-&F>6#F(F@F(!\"$**F2F/F.F/-&F>6#\"\"!F@F(FAF/F8*&F.F/-&%\"HGFCF@F(F7
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{XPPMATH 20 "6#/*&)%#g~G%&thetaG\"\"\")%!GF'F(,$*&,2\"\"%F(*(%(epsilon
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6#/*&)%#g~G%$phiG\"\"\")%!GF'F(,$*&,2\"\"%F(*(%(epsilonGF(-%\"kG6$%\"r
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F1F;F<\"\"**(F@F<FBF<F6F<F=*(F@F<-%\"KGF3F(F6F<F=*&F@F<FBF<F(*&F@F<FFF
<F;F<*()F4\"\"#F<,&!\"\"F(F7F(\"\"\",&F7F(F(F(\"\"\"!\"\"#FNF." }}
{PARA 12 "" 1 "" {XPPMATH 20 "6#/*&)%#g~G%\"tG\"\"\")%!GF'F(,$*&*&%\"r
GF(,8\"\"%F(*(%(epsilonGF(-&%\"hG6#\"\"!6$F.F'F()-%$cosG6#%&thetaG\"\"
#\"\"\"\"\"'*&F2F?F3F?!\"#*()F2F>F?)F:F0F?)F3F>F?\"\"**(FDF?FFF?F9F?!
\"'*&FDF?FFF?F(*&FDF?-&%\"HGF6F8F(FB*(FDF?)-&F56#F(F8F>F?FEF?!\"**(FDF
?FPF?F9F?F@*&FDF?FPF?!\"\"*(FDF?FLF?F9F?F@F(F?,&F.FW%\"mGF>!\"\"#F(F0
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "grcalcalter(R(dn,dn),13
); " }}{PARA 6 "" 1 "" {TEXT -1 50 "Simplification will be applied dur
ing calculation." }}{PARA 6 "" 1 "" {TEXT -1 1 " " }}{PARA 6 "" 1 "" 
{TEXT -1 70 "Applying routine `Apply constraints repeatedly` to object
 g(dn,dn,pdn)" }}{PARA 6 "" 1 "" {TEXT -1 71 "Applying routine `Apply \+
constraints repeatedly` to object Chr(dn,dn,dn)" }}{PARA 6 "" 1 "" 
{TEXT -1 71 "Applying routine `Apply constraints repeatedly` to object
 Chr(dn,dn,up)" }}{PARA 6 "" 1 "" {TEXT -1 66 "Applying routine `Apply
 constraints repeatedly` to object R(dn,dn)" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#/%*CPU~Time~G$\"%0j!\"$" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 25 "gralter(R(dn,dn),expand);" }}{PARA 6 "" 1 "" {TEXT 
-1 48 "Component simplification of a GRTensorII object:" }}{PARA 6 "" 
1 "" {TEXT -1 1 " " }}{PARA 6 "" 1 "" {TEXT -1 42 "Applying routine ex
pand to object R(dn,dn)" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/%*CPU~Time
~G$\"$G#!\"$" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "grdisplay(R
(dn,dn)); " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%9For~the~qschw~spacetim
e:G" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%0Covariant~RicciG" }}{PARA 11 
"" 1 "" {XPPMATH 20 "6#-%\"RG6$%#dnGF&" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6#/*&&%#R~G6#%\"rG\"\"\"&%!GF'F)%K~86717~words.~Exceeds~grOptionDi
splayLimitG" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/*&&%#R~G6#%\"rG\"\"\"&
%!G6#%&thetaGF)%K~28579~words.~Exceeds~grOptionDisplayLimitG" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#/*&&%#R~G6#%\"rG\"\"\"&%!G6#%\"tGF)%K~53004~
words.~Exceeds~grOptionDisplayLimitG" }}{PARA 11 "" 1 "" {XPPMATH 20 "
6#/*&&%#R~G6#%&thetaG\"\"\"&%!GF'F)%K~87057~words.~Exceeds~grOptionDis
playLimitG" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/*&&%#R~G6#%&thetaG\"\"
\"&%!G6#%\"tGF)%K~20438~words.~Exceeds~grOptionDisplayLimitG" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#/*&&%#R~G6#%$phiG\"\"\"&%!GF'F)%K~72053~word
s.~Exceeds~grOptionDisplayLimitG" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/*
&&%#R~G6#%\"tG\"\"\"&%!GF'F)%K~82672~words.~Exceeds~grOptionDisplayLim
itG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 31 "p2 := 5/2*(3*cos(the
ta)^2-1)/2;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#p2G,&*$)-%$cosG6#%&t
hetaG\"\"#\"\"\"#\"#:\"\"%#!\"&F0\"\"\"" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 82 "newH(r,t) := (2*r^2-6*m*r-3*m^2)/(r-2*m)/(2*r+3*m)*ch
i(r,t)+r^2/(r-2*m)*eta(r,t); " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>-%%n
ewHG6$%\"rG%\"tG,&*&*&,(*$)F'\"\"#\"\"\"F/*&%\"mG\"\"\"F'F3!\"'*$)F2F/
F0!\"$F3-%$chiGF&F3F0*&,&F'F3F2!\"#\"\"\",&F'F/F2\"\"$\"\"\"!\"\"F3*&*
&F.F0-%$etaGF&F3F0F;FAF3" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 61 
"Kdot(r,t) := 6*(r^2+m*r+m^2)/r^2/(2*r+3*m)*chi(r,t)+eta(r,t);" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#>-%%KdotG6$%\"rG%\"tG,&*&*&,(*$)F'\"\"
#\"\"\"\"\"\"*&%\"mGF1F'F1F1*$)F3F/F0F1F1-%$chiGF&F1F0*&)F'\"\"#F0,&F'
F/F3\"\"$\"\"\"!\"\"\"\"'-%$etaGF&F1" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 74 "a1:=coeff(collect(grcomponent(R(dn,dn),[theta,theta])
,epsilon),epsilon,1):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 70 "g1
:=coeff(collect(grcomponent(R(dn,dn),[phi,phi]),epsilon),epsilon,1):" 
}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 102 "ag1:=int(expand(a1-g1/si
n(theta)^2)*(2*cot(theta)*diff(p2,theta)+2*(2+1)*p2)*sin(theta),\nthet
a=0..Pi);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$ag1G,&-&%\"hG6#\"\"!6$
%\"rG%\"tG!#7-&F(6#\"\"#F+\"#7" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 45 "leqn[1]:= \{h[2](r,t) = solve(ag1,h[2](r,t))\};" }}{PARA 11 "
" 1 "" {XPPMATH 20 "6#>&%%leqnG6#\"\"\"<#/-&%\"hG6#\"\"#6$%\"rG%\"tG-&
F,6#\"\"!F/" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "a2:=subs(leq
n[1],a1):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "g2:=subs(leqn[
1],g1):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 33 "grmap(R(dn,dn),s
ubs,leqn[1],'x');" }}{PARA 6 "" 1 "" {TEXT -1 33 "Applying routine sub
s to R(dn,dn)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "gralter(R(
dn,dn),simplify,expand);" }}{PARA 6 "" 1 "" {TEXT -1 48 "Component sim
plification of a GRTensorII object:" }}{PARA 6 "" 1 "" {TEXT -1 1 " " 
}}{PARA 6 "" 1 "" {TEXT -1 44 "Applying routine simplify to object R(d
n,dn)" }}{PARA 6 "" 1 "" {TEXT -1 42 "Applying routine expand to objec
t R(dn,dn)" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/%*CPU~Time~G$\"&wZ\"!\"
$" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 70 "b1:=coeff(collect(grco
mponent(R(dn,dn),[theta,r]),epsilon),epsilon,1):" }}}{EXCHG {PARA 0 ">
 " 0 "" {MPLTEXT 1 0 85 "leqn[2]:=termsimp(collect(1/3*int(b1*diff(p2,
theta)*sin(theta),theta=0..Pi),lperts));" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6#>&%%leqnG6#\"\"#,*-%%diffG6$-%\"kG6$%\"rG%\"tGF/!\"\"-F*6$-&%\"h
G6#\"\"!F.F/\"\"\"*&*&%\"mGF9F4F9\"\"\"*&,&F/F1F<F'\"\"\"F/\"\"\"!\"\"
!\"#*&*&F/F9-F*6$-&F66#F9F.F0F9F=F?FBF9" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 70 "c1:=coeff(collect(grcomponent(R(dn,dn),[theta,t]),eps
ilon),epsilon,1):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 85 "leqn[3
]:=termsimp(collect(1/3*int(c1*diff(p2,theta)*sin(theta),theta=0..Pi),
lperts));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%%leqnG6#\"\"$,**&*&-&%
\"hG6#\"\"\"6$%\"rG%\"tGF/%\"mGF/\"\"\"*$)F1\"\"#F4!\"\"\"\"#*&*&,&F1!
\"\"F3F9F/-%%diffG6$F+F1F/F4F1F8F=-F?6$-&F-6#\"\"!F0F2F=-F?6$-%\"kGF0F
2F=" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 66 "d1:=coeff(collect(gr
component(R(dn,dn),[t,r]),epsilon),epsilon,1):" }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 69 "leqn[4]:=termsimp(collect(int(d1*p2*sin(theta)
,theta=0..Pi),lperts));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%%leqnG6#
\"\"%,**&-&%\"hG6#\"\"\"6$%\"rG%\"tG\"\"\"*$)F0\"\"#F2!\"\"\"\"$*&-%%d
iffG6$-&F,6#\"\"!F/F1F2F0F6F.*&*&,&F0!\"\"%\"mGF7F.-F:6$-%\"kGF/F1F.F2
*&F0\"\"\",&F0FCFD\"\"#\"\"\"F6FC-F:6%FGF0F1FC" }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 66 "e1:=coeff(collect(grcomponent(R(dn,dn),[r,r]),
epsilon),epsilon,1):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 69 "leq
n[5]:=termsimp(collect(int(e1*p2*sin(theta),theta=0..Pi),lperts));" }}
{PARA 12 "" 1 "" {XPPMATH 20 "6#>&%%leqnG6#\"\"&,2*&*&-%%diffG6$-%\"kG
6$%\"rG%\"tGF1\"\"\",&%\"mG\"\"$F1!\"#F3\"\"\"*&,&F1!\"\"F5\"\"#\"\"\"
F1\"\"\"!\"\"F;*&-F,6$-&%\"hG6#\"\"!F0F1F8F:F?F;*&FCF8*&F:\"\"\"F1\"\"
\"F?!\"$*&*&)F1F<F8-F,6$FC-%\"$G6$F2F<F3F8*$)F:\"\"#F8F?#F3F<-F,6$F.-F
S6$F1F<F;*&*&F5F3-F,6$-&FE6#F3F0F2F3F8*$)F:\"\"#F8F?F;-F,6$FCFenFX*&*&
F1F3-F,6%F[oF1F2F3F8F:F?F3" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
66 "f1:=coeff(collect(grcomponent(R(dn,dn),[t,t]),epsilon),epsilon,1):
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 69 "leqn[6]:=termsimp(colle
ct(int(f1*p2*sin(theta),theta=0..Pi),lperts));" }}{PARA 12 "" 1 "" 
{XPPMATH 20 "6#>&%%leqnG6#\"\"',2*&*(%\"mG\"\"\",&%\"rG!\"\"F+\"\"#F,-
%%diffG6$-%\"kG6$F.%\"tGF.F,\"\"\"*$)F.\"\"$F8!\"\"F/*&*&F-F8-F26$-&%
\"hG6#\"\"!F6F.F,F8*$)F.\"\"#F8F<F,*&*&F-F8FAF,F8*$)F.\"\"$F8F<!\"$-F2
6$FA-%\"$G6$F7F0#F/F0*&*&,&F+\"\"$F.!\"#F,-F26$-&FC6#F,F6F7F,F8*$)F.\"
\"#F8F<F/-F26$F4FQF/*&*&)F-F0F8-F26$FA-FR6$F.F0F,F8*$)F.\"\"#F8F<FT*&*
&F-F8-F26%FfnF.F7F,F8F.F<F/" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
87 "leqn[7]:=termsimp(collect(int((a2+g2/sin(theta)^2)*p2*sin(theta),t
heta=0..Pi),lperts));" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>&%%leqnG6#\"
\"(,0-%\"kG6$%\"rG%\"tG\"\"%*&-%%diffG6$F)F,\"\"\",&%\"mG\"\"$F,!\"#F3
\"\"#*&-F16$-&%\"hG6#\"\"!F+F,F3,&F,!\"\"F5F8F3F7F<F8*(-F16$F)-%\"$G6$
F,F8F3FA\"\"\"F,F3F3*&-F16$-&F>6#F3F+F-F3F,FIF7*&*&-F16$F)-FG6$F-F8F3)
F,F6FIFIFA!\"\"FB" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 135 "lsub1
:=\{diff(k(r,t),t,t) = termsimp(collect(solve(expand((r-2*m)^2*leqn[5]
+r^2*leqn[6]\n-leqn[7]/r*(r-2*m)),diff(k(r,t),t,t)),lperts))\};" }}
{PARA 12 "" 1 "" {XPPMATH 20 "6#>%&lsub1G<#/-%%diffG6$-%\"kG6$%\"rG%\"
tG-%\"$G6$F.\"\"#,,*&*&,&F-!\"\"%\"mGF2\"\"\"F*F9\"\"\"*$)F-\"\"$F:!\"
\"F2*&*(F6F:,&F8F9F-F7F9-F(6$F*F-F9F:*$)F-\"\"$F:F>F9*&*&)F6F2F:-F(6$-
&%\"hG6#\"\"!F,F-F9F:*$)F-\"\"$F:F>F7*&*&F6F:FLF9F:*$)F-\"\"$F:F>!\"#*
&*&F6F:-F(6$-&FN6#F9F,F.F9F:*$)F-\"\"#F:F>FY" }}}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 91 "aa1:=simplify(coeff(collect(grcomponent(R(dn,dn)
,[theta,theta]),epsilon),epsilon,2),\ntrig):" }}}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 112 "gg1:=simplify(expand(1/sin(theta)^2*(coeff(coll
ect(grcomponent(R(dn,dn),[phi,phi]),\nepsilon),epsilon,2))),trig):" }}
}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 31 "zz1:=simplify(expand(gg1-aa
1));" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%$zz1G,6-&%\"HG6#\"\"!6$%\"rG
%\"tG#!\"$\"\"#-&F(6#F0F+#\"\"$F0*$)-&%\"hG6#\"\"\"F+F0\"\"\"F.*$)-&F:
F)F+F0F=F4*&F7F=)-%$cosG6#%&thetaGF0F=#\"#@F0*&F1F<FCF=F.*&F&F<FCF=F4*
&F7F=)FD\"\"%F=!\"**&FMF=F?F=\"\"**&FCF=F?F=#!#@F0" }}}{EXCHG {PARA 0 
"> " 0 "" {MPLTEXT 1 0 78 "zz2:=int(zz1*(2*cot(theta)*diff(p2,theta)+2
*(2+1)*p2)*sin(theta),theta=0..Pi);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6
#>%$zz2G,*-&%\"HG6#\"\"!6$%\"rG%\"tG\"#7*$)-&%\"hGF)F+\"\"#\"\"\"#!#7
\"\"(*$)-&F36#\"\"\"F+F4F5#F.F8-&F(6#F4F+F7" }}}{EXCHG {PARA 0 "> " 0 
"" {MPLTEXT 1 0 43 "qeqn1:= \{H[2](r,t) = solve(zz2,H[2](r,t))\};" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#>%&qeqn1G<#/-&%\"HG6#\"\"#6$%\"rG%\"tG
,(-&F)6#\"\"!F,\"\"\"*$)-&%\"hGF2F,F+\"\"\"#!\"\"\"\"(*$)-&F96#F4F,F+F
:#F4F=" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "qeqn[1]:=qeqn1;" 
}}{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%%qeqnG6#\"\"\"<#/-&%\"HG6#\"\"#6$
%\"rG%\"tG,(-&F,6#\"\"!F/F'*$)-&%\"hGF5F/F.\"\"\"#!\"\"\"\"(*$)-&F;F&F
/F.F<#F'F?" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 32 "grmap(R(dn,dn
),subs,qeqn1,`x`); " }}{PARA 6 "" 1 "" {TEXT -1 33 "Applying routine s
ubs to R(dn,dn)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 92 "aa1:=sim
plify(coeff(collect(grcomponent(R(dn,dn),[theta,theta]),epsilon),epsil
on,2),\ntrig): " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 112 "gg1:=si
mplify(expand(1/sin(theta)^2*(coeff(collect(grcomponent(R(dn,dn),[phi,
phi]),\nepsilon),epsilon,2))),trig):" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 77 "qeqn[2]:=termsimp(collect(int((gg1+aa1)*p2*sin(theta)
,theta=0..Pi),qperts)): " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 86 
"bb1:=simplify(coeff(collect(grcomponent(R(dn,dn),[theta,r]),epsilon),
epsilon,2),trig):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 82 "qeqn[3
]:=termsimp(collect(int(bb1*diff(p2,theta)*sin(theta),theta=0..Pi),qpe
rts)):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 86 "cc1:=simplify(coe
ff(collect(grcomponent(R(dn,dn),[t,theta]),epsilon),epsilon,2),trig):
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 86 "qeqn[4]:=termsimp(colle
ct(1/3*int(cc1*diff(p2,theta)*sin(theta),theta=0..Pi),qperts)):" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 82 "dd1:=simplify(coeff(collect(
grcomponent(R(dn,dn),[r,t]),epsilon),epsilon,2),trig):" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 70 "qeqn[5]:=termsimp(collect(int(dd1*p
2*sin(theta),theta=0..Pi),qperts)):" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 82 "ee1:=simplify(coeff(collect(grcomponent(R(dn,dn),[r,r
]),epsilon),epsilon,2),trig):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 78 "qeqn[6]:=termsimp(collect(expand(int(ee1*p2*sin(theta),theta=0..
Pi)),qperts)):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 83 "#ff1:=sim
plify(coeff(collect(grcomponent(R(dn,dn),[t,t]),epsilon),epsilon,2),tr
ig):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 67 "#ff2:=termsimp(coll
ect(int(ff1*p2*sin(theta),theta=0..Pi),qperts)):" }}}{EXCHG {PARA 0 ">
 " 0 "" {MPLTEXT 1 0 60 "qsub1:=\{diff(H[0](r,t),t)=solve(qeqn[4],diff
(H[0](r,t),t))\};" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%&qsub1G<#/-%%di
ffG6$-&%\"HG6#\"\"!6$%\"rG%\"tGF1,$*&,0*&-&F,6#\"\"\"F/F9%\"mGF9!#9*&-
F(6$-%\"KGF/F1F9)F0\"\"#\"\"\"\"\"(*&-F(6$F6F0F9FAFC!\"(*(FFFCF:FCF0F9
\"#9*(-&%\"hGF-F/F9-F(6$FLF1F9FAFC!\"$*(-%\"kGF/F9-F(6$FSF1F9FAFC!\"#*
(-&FNF8F/F9-F(6$FYF1F9FAFC\"\"$FC*$)F0\"\"#FC!\"\"#!\"\"FD" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "qeqn[1];" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#<#/-&%\"HG6#\"\"#6$%\"rG%\"tG,(-&F'6#\"\"!F*\"\"\"*$)-&
%\"hGF0F*F)\"\"\"#!\"\"\"\"(*$)-&F76#F2F*F)F8#F2F;" }}}{EXCHG {PARA 0 
"> " 0 "" {MPLTEXT 1 0 16 "undiff(qeqn[4]);" }}{PARA 12 "" 1 "" 
{XPPMATH 20 "6#-%'undiffG6#,0*&*&-&%\"HG6#\"\"\"6$%\"rG%\"tGF-%\"mGF-
\"\"\"*$)F/\"\"#F2!\"\"\"\"#-%%diffG6$-&F+6#\"\"!F.F0!\"\"-F96$-%\"KGF
.F0F?*&*&,&F/F?F1F7F--F96$F)F/F-F2F/F6F?*&-&%\"hGF=F.F--F96$FJF0F-#\"
\"$\"\"(*&-%\"kGF.F--F96$FSF0F-#F7FQ*&-&FLF,F.F--F96$FYF0F-#!\"$FQ" }}
}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "eta1:=qeqn[5]:" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 49 "eta2:=termsimp(collect(subs(qsub1,e
ta1),qperts)):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 134 "eta3:=te
rmsimp(collect(simplify(subs(H[1](r,t)=newH(r,t),diff(K(r,t),t)=Kdot(r
,t),\ndiff(K(r,t),r,t)=diff(Kdot(r,t),r),eta2)),zfuncs)):" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 62 "eta4:=eta(r,t)-termsimp(collect(sol
ve(eta3,eta(r,t)),zfuncs)):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
101 "eta5:=termsimp(collect(subs(\{diff(h[0](r,t),r,r)=solve(leqn[5],d
iff(h[0](r,t),r,r))\},eta4),\nzfuncs)):" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 146 "eta6:=termsimp(collect(subs(\{diff(h[0](r,t),r)=solv
e(leqn[2],diff(h[0](r,t),r)),\ndiff(k(r,t),r,t)=solve(leqn[4],diff(k(r
,t),r,t))\},eta5),zfuncs)):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
214 "ug:=\{diff(k(r,t),r,r)=termsimp(collect(solve(subs(diff(h[0](r,t)
,r)=\nsolve(leqn[2],diff(h[0](r,t),r)),subs(lsub1,solve(leqn[6],diff(h
[0](r,t),r,r))-\nsolve(leqn[5],diff(h[0](r,t),r,r)))),diff(k(r,t),r,r)
),lperts))\}:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 46 "eta7:=term
simp(collect(subs(ug,eta6),zfuncs)):" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 13 "etaeqn:=eta7:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 470 "etasource:=kfactor(mcollect(mcollect(mcollect(mcollect(mcolle
ct(mcollect(mcollect(\nmcollect(mcollect(mcollect(expand(eval(subs(eta
(r,t)=0,chi(r,t)=0,etaeqn))),\n\{h[1](r,t),h[0](r,t)\}),\{h[1](r,t),di
ff(h[1](r,t),t)\}),\{h[1](r,t),diff(k(r,t),r)\}),\n\{h[0](r,t),diff(k(
r,t),t)\}),\{diff(h[1](r,t),t),diff(k(r,t),t)\}),\{k(r,t),h[1](r,t)\})
,\n\{k(r,t),diff(k(r,t),t)\}),\{diff(k(r,t),r),diff(h[0](r,t),t)\}),\{
k(r,t),diff(h[0](r,t),t)\}),\n\{h[0](r,t),diff(h[0](r,t),t)\}),(r-2*m)
/7/(2*r+3*m)):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 128 "etafinal
:=\{eta(r,t) = termsimp(collect(solve(eval(subs(h[0](r,t)=0,h[1](r,t)=
0,k(r,t)=0,\netaeqn)),eta(r,t)),zfuncs))-etasource\};" }}{PARA 12 "" 
1 "" {XPPMATH 20 "6#>%)etafinalG<#/-%$etaG6$%\"rG%\"tG,&*&*&-%%diffG6$
-%$chiGF)F*\"\"\",&F*!\"\"%\"mG\"\"#F4\"\"\"F*!\"\"F6*&*&,&F*F4F7!\"#F
4,6*&-&%\"hG6#\"\"!F)F4-F06$FAF+F4F6*&-%\"kGF)F4FFF9F8*(F*F4-F06$FIF*F
4FFF9F4*&FIF9-F06$FIF+F4F8*&*&-&FC6#F4F)F4FIF9F9F*F:\"\"%*&*(F7F4FSF9F
LF9F9F*F:F>*&FSF9-F06$FSF+F4F4*&*(F5F9FSF9FAF9F9*$)F*\"\"#F9F:F>*&*(F7
F9FOF9FAF9F9F5F:F>*&*()F*F8F9FOF9FZF9F9F5F:F4F4F9,&F*F8F7\"\"$F:#F6\"
\"(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "atmp1:=diff(qeqn[2],
t):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 87 "atmp2:=termsimp(coll
ect(expand(subs(qsub1,diff(qsub1,r),atmp1)),\{diff(K(r,t),t,t,t)\})):
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 179 "atmp3:=termsimp(collec
t(expand(eval(subs(H[1](r,t)=newH(r,t),\ndiff(K(r,t),t)=Kdot(r,t),diff
(K(r,t),t,r)=diff(Kdot(r,t),r),diff(K(r,t),t,r,r)=diff(Kdot(r,t),r,r),
atmp2))),zfuncs)):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 68 "atmp4
:=termsimp(collect(expand(eval(subs(etafinal,atmp3))),zfuncs)):" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 53 "coefa:=simplify(coeff(atmp4,
diff(chi(r,t),t,r,t),1));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%&coefaG
,$*$)%\"rG\"\"#\"\"\"!\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
118 "btmp1:=termsimp(collect(expand(subs(qsub1,diff(qsub1,r),diff(qeqn
[3],t))),\n\{diff(H[1](r,t),t,t),diff(K(r,t),t,t,t)\})):" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 140 "btmp2:=termsimp(collect(expand(eva
l(subs(H[1](r,t)=newH(r,t),diff(K(r,t),t)=Kdot(r,t),\ndiff(K(r,t),r,t)
=diff(Kdot(r,t),r),btmp1))),zfuncs)):" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 68 "btmp3:=termsimp(collect(expand(eval(subs(etafinal,btm
p2))),zfuncs)):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 53 "coefb:=s
implify(coeff(btmp3,diff(chi(r,t),r,t,t),1));" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%&coefbG,$*&*$)%\"rG\"\"#\"\"\"F+,&F)!\"\"%\"mGF*!\"\"
\"\"$" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 204 "ftmp1:=termsimp(c
ollect(expand(atmp4/coefa-btmp3/coefb),\{chi(r,t),diff(chi(r,t),r),\nd
iff(chi(r,t),t),diff(chi(r,t),t,t),diff(chi(r,t),r,r),diff(chi(r,t),r,
t),diff(chi(r,t),r,t,t),\ndiff(chi(r,t),r,r,r)\})):" }}}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 173 "ftmp2:=termsimp(collect(expand(eval(subs
(k(r,t)=0,h[1](r,t)=0,h[0](r,t)=0,ftmp1))),\n\{chi(r,t),diff(chi(r,t),
r),diff(chi(r,t),r,r),diff(chi(r,t),t,t),diff(chi(r,t),r,r,r)\})):" }}
}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 83 "chi1:=termsimp(collect(diff
(chi(r,t),t,t)-solve(ftmp1,diff(chi(r,t),t,t)),zfuncs)):" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "chieqn:=ftmp1:" }}}{EXCHG {PARA 0 "
> " 0 "" {MPLTEXT 1 0 13 "nops(chieqn);" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6#\"$@%" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 203 "termsimp(co
llect(expand(eval(subs(k(r,t)=0,h[1](r,t)=0,h[0](r,t)=0,\nchieqn/coeff
(chieqn,diff(chi(r,t),t,t),1)))),\{chi(r,t),diff(chi(r,t),r),\ndiff(ch
i(r,t),r,r),diff(chi(r,t),t,t),diff(chi(r,t),r,r,r)\}));" }}{PARA 12 "
" 1 "" {XPPMATH 20 "6#,**&*&-%%diffG6$-%$chiG6$%\"rG%\"tG-%\"$G6$F,\"
\"#\"\"\"),&F,!\"\"%\"mGF1F1\"\"\"F7*$)F,\"\"#F7!\"\"F5-F'6$F)-F/6$F-F
1F2*&*(F4F2,**$)F6\"\"$F7FE*&F,F2)F6F1F7\"\"'*&)F,F1F7F6F2\"\"%*$)F,FE
F7FKF2F)F2F7*&)F,\"\"%F7),&F,F1F6FE\"\"#F7F;!\"'*&*(-F'6$F)F,F2F4F7F6F
7F7*$)F,\"\"$F7F;F1" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 84 "zeta
sub:= \{chi(r,t) = zeta(r,t)+2/7*(r^2/(2*r+3*m)*k(r,t)*diff(k(r,t),t)+
k(r,t)^2)\};" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%(zetasubG<#/-%$chiG6
$%\"rG%\"tG,(-%%zetaGF)\"\"\"*&*()F*\"\"#\"\"\"-%\"kGF)F/-%%diffG6$F5F
+F/F4,&F*F3%\"mG\"\"$!\"\"#F3\"\"(*$)F5F3F4F>" }}}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 32 "zeta1:=eval(subs(zetasub,chi1)):" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "nops(expand(zeta1));" }}{PARA 11 "
" 1 "" {XPPMATH 20 "6#\"$h\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 62 "new2:=termsimp(collect(expand(leqn[4]-leqn[3]/2/m*3),lperts));" 
}}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%new2G,**&*&,&%\"rG!\"\"%\"mG\"\"#
\"\"\"-%%diffG6$-&%\"hG6#F-6$F)%\"tGF)F-\"\"\"*&F+\"\"\"F)\"\"\"!\"\"#
\"\"$F,*&*&,&F+F,F)F=F--F/6$-&F36#\"\"!F5F6F-F7*&F+\"\"\"F)\"\"\"F;#F-
F,*&*&,(*&F+F-F)F-!\")*$)F+F,F7\"\"'*$)F)F,F7F=F--F/6$-%\"kGF5F6F-F7*(
F(\"\"\"F)\"\"\"F+\"\"\"F;#F*F,-F/6%FWF)F6F*" }}}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 85 "leqn8:=\{diff(h[1](r,t),r) = termsimp(collect(so
lve(new2,diff(h[1](r,t),r)),lperts))\};" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6#>%&leqn8G<#/-%%diffG6$-&%\"hG6#\"\"\"6$%\"rG%\"tGF0,(*&*&,&%\"mG
\"\"#F0\"\"$F.-F(6$-&F,6#\"\"!F/F1F.\"\"\",&F0!\"\"F6F7!\"\"#FAF8*&*&,
(*&F6F.F0F.!\")*$)F6F7F?\"\"'*$)F0F7F?F8F.-F(6$-%\"kGF/F1F.F?*$)F@\"\"
#F?FB#F.F8*&*(-F(6%FPF0F1F.F0F?F6F?F?F@FB#F7F8" }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 150 "new3:=termsimp(collect(expand(solve(leqn[3],d
iff(h[1](r,t),r))-solve(diff(epxand(\nleqn[4]/coeff(leqn[4],h[1](r,t),
1)),r),diff(h[1](r,t),r))),lperts));" }}{PARA 12 "" 1 "" {XPPMATH 20 "
6#>%%new3G,2*&*&-&%\"hG6#\"\"\"6$%\"rG%\"tGF,%\"mGF,\"\"\"*&F.\"\"\",&
F.!\"\"F0\"\"#\"\"\"!\"\"F6*&*&,&F0F,F.!\"#F,-%%diffG6$-&F*6#\"\"!F-F/
F,F1F4F8#F6\"\"$*&F.F,-F>6%F@F.F/F,#F,FE*&*&,(*$)F0F6F1FE*&F0F1F.F1F,*
$)F.F6F1F5F,-F>6$-%\"kGF-F/F,F1*$)F4\"\"#F1F8#F<FE*&*(,&F0\"\"(F.!\"$F
,F.F1-F>6%FTF.F/F,F1F4F8#F5FE*&*(-F>6%FT-%\"$G6$F.F6F/F,FQF1FNF1F1*$)F
4\"\"#F1F8#!\"%FE*&*&F^oF1)F.\"\"%F1F1*$)F4\"\"#F1F8F[o*&*(F^oF1)F.FEF
1F0F1F1*$)F4\"\"#F1F8#F[pFE" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
69 "leqn9:=\{h[1](r,t) = termsimp(collect(solve(new3,h[1](r,t)),lperts
))\};" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%&leqn9G<#/-&%\"hG6#\"\"\"6$
%\"rG%\"tG,,*&*(-%%diffG6$-&F)6#\"\"!F,F.F+,&%\"mGF+F-!\"#F+F-F+\"\"\"
F:!\"\"#!\"\"\"\"$*&*(-F36%F5F-F.F+)F-\"\"#F<,&F-F?F:FFF+F<F:F=#F?\"\"
'*&*(,(*$)F:FFF<F@*&F:F+F-F<F+*$FEF<F?F+-F36$-%\"kGF,F.F+F-F<F<*&F:\"
\"\"FG\"\"\"F=#F+F@*&*(-F36%FSF-F.F+,&F:\"\"(F-!\"$F+FEF<F<F:F=#F+FI*&
*(FGF<-F36%FS-%\"$G6$F-FFF.F+)F-F@F<F<F:F=Fjn" }}}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 95 "leqn10:=\{diff(h[1](r,t),t)=termsimp(collect(exp
and(solve(leqn[2],diff(h[1](r,t),t))),lperts))\};" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%'leqn10G<#/-%%diffG6$-&%\"hG6#\"\"\"6$%\"rG%\"tGF1,(*
&*&,&F0!\"\"%\"mG\"\"#F.-F(6$-%\"kGF/F0F.\"\"\"F0!\"\"F.*&*&F5F=-F(6$-
&F,6#\"\"!F/F0F.F=F0F>F6*&*&F7F.FCF.F=*$)F0\"\"#F=F>F8" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 115 "aux1:=termsimp(collect(expand(solv
e(leqn[2],diff(h[1](r,t),t))-solve(diff(leqn[4],t),\ndiff(h[1](r,t),t)
)),lperts));" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%%aux1G,0*&*&,&%\"rG!
\"\"%\"mG\"\"#\"\"\"-%%diffG6$-%\"kG6$F)%\"tGF)F-\"\"\"F)!\"\"F-*&*&F(
F5-F/6$-&%\"hG6#\"\"!F3F)F-F5F)F6F**&*&F+F-F;F-F5*$)F)\"\"#F5F6F,*&-F/
6$F;-%\"$G6$F4F,F-F)F-#F-\"\"$*&*(F)F5,&F)F*F+FLF--F/6$F1FHF-F5F(F6#F*
FL*&*()F)F,F5-F/6%F1F)FHF-F+F5F5F(F6#!\"#FL*&*&)F)FLF5FVF5F5F(F6FK" }}
}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 76 "aux2:=termsimp(collect(expa
nd(diff((r-2*m)*r*leqn[4]/3,r))-leqn[3],lperts));" }}{PARA 12 "" 1 "" 
{XPPMATH 20 "6#>%%aux2G,.-%%diffG6$-&%\"hG6#\"\"!6$%\"rG%\"tGF0#\"\"%
\"\"$*&,&F/!\"\"%\"mG\"\"#\"\"\"-F'6%F)F/F0F9#F6F3-F'6$-%\"kGF.F0#F8F3
*&,&F7\"\"&F/!\"$F9-F'6%F?F/F0F9#F9F3*(F/F9F7F9-F'6%F?-%\"$G6$F/F8F0F9
FA*&)F/F8\"\"\"FJFQF<" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 107 "a
ux3:=termsimp(collect(expand(solve(leqn[2],diff(h[1](r,t),t))-solve(le
qn[7],\ndiff(h[1](r,t),t))),lperts));" }}{PARA 11 "" 1 "" {XPPMATH 20 
"6#>%%aux3G,,*&-%\"kG6$%\"rG%\"tG\"\"\"F*!\"\"!\"#*&*&,&%\"mG\"\"\"F*!
\"\"F3-%%diffG6$F'F*F3F,F*F-F4*&*&,&F*F4F2\"\"#F3-&%\"hG6#\"\"!F)F3F,*
$)F*\"\"#F,F-F3*&F:F,-F66$F'-%\"$G6$F*F;F3#F4F;*&*&)F*F;F,-F66$F'-FH6$
F+F;F3F,F:F-#F3F;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 113 "tmpau
x:=termsimp(collect(expand(solve(leqn[5],diff(h[1](r,t),r,t))-solve(le
qn[6],\ndiff(h[1](r,t),r,t))),lperts));" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6#>%'tmpauxG,,*&*&,&%\"rG!\"\"%\"mG\"\"#\"\"\"-%%diffG6$-%\"kG6$F)
%\"tGF)F-\"\"\"*$)F)\"\"#F5!\"\"F,*&-&%\"hG6#\"\"!F3F5*$)F)\"\"#F5F9\"
\"'*&*&F(F5-F/6$F1-%\"$G6$F)F,F-F5F)F9F-*&-F/6$-&F=6#F-F3F4F5F)F9F,*&*
&F)F--F/6$F1-FI6$F4F,F-F5F(F9F-" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 109 "tmpaux2:=termsimp(collect(expand(solve(tmpaux,diff(h[1](r,t),
t))-solve(leqn[2],\ndiff(h[1](r,t),t))),lperts));" }}{PARA 12 "" 1 "" 
{XPPMATH 20 "6#>%(tmpaux2G,,*&*&,&%\"rG!\"\"%\"mG\"\"#\"\"\"-%%diffG6$
-%\"kG6$F)%\"tGF)F-\"\"\"F)!\"\"!\"#*&*&F(F5-F/6$-&%\"hG6#\"\"!F3F)F-F
5F)F6F-*&*&,&F+F,F)\"\"$F-F<F-F5*$)F)\"\"#F5F6F**&F(F5-F/6$F1-%\"$G6$F
)F,F-#F*F,*&*&)F)F,F5-F/6$F1-FL6$F4F,F-F5F(F6FN" }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 108 "tmpaux3:=termsimp(collect(expand(solve(tmpaux
2,diff(k(r,t),t,t))-solve(leqn[7],\ndiff(k(r,t),t,t))),lperts));" }}
{PARA 12 "" 1 "" {XPPMATH 20 "6#>%(tmpaux3G,.*&*&,&%\"rG!\"\"%\"mG\"\"
#\"\"\"-%\"kG6$F)%\"tGF-\"\"\"*$)F)\"\"$F2!\"\"!\"%*&*(F(F2,&F+\"\"(F)
F7F--%%diffG6$F.F)F-F2*$)F)\"\"$F2F6!\"#*&*&)F(F,F2-F=6$-&%\"hG6#\"\"!
F0F)F-F2*$)F)\"\"$F2F6\"\"%*&*(,&F+F-F)F,F-F(F2FHF-F2*$)F)\"\"%F2F6F7*
&*&FEF2-F=6$F.-%\"$G6$F)F,F-F2*$)F)\"\"#F2F6FB*&*&F(F2-F=6$-&FJ6#F-F0F
1F-F2*$)F)\"\"#F2F6F," }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 107 "a
ux4:=termsimp(collect(expand(solve(tmpaux3,diff(h[1](r,t),t))-solve(le
qn[2],\ndiff(h[1](r,t),t))),lperts));" }}{PARA 11 "" 1 "" {XPPMATH 20 
"6#>%%aux4G,,*&-%\"kG6$%\"rG%\"tG\"\"\"F*!\"\"\"\"#*&*&,&%\"mG\"\"&F*!
\"$\"\"\"-%%diffG6$F'F*F5F,F*F-F5*&*&,&F*!\"\"F2F.F5-F76$-&%\"hG6#\"\"
!F)F*F5F,F*F-F<*&F?F,F*F-\"\"%*&F;F,-F76$F'-%\"$G6$F*F.F5F5" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 169 "aux5:=termsimp(collect(solv
e(solve(diff(leqn[3],t),diff(h[1](r,t),r,t))-solve(leqn[5],\ndiff(h[1]
(r,t),r,t)),diff(h[1](r,t),t))-solve(leqn[2],diff(h[1](r,t),t)),lperts
));" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%%aux5G,0*&*(,&%\"rG!\"\"%\"mG
\"\"#\"\"\",&F+F-F)F*F--%%diffG6$-%\"kG6$F)%\"tGF)F-\"\"\"*&F+\"\"\"F)
\"\"\"!\"\"F,*&*(F(F6,&F)F-F+F-F--F06$-&%\"hG6#\"\"!F4F)F-F6*&F)\"\"\"
F+\"\"\"F:F-*&*&,(*&F+F-F)F-!\"'*$)F)F,F6\"\"$*$)F+F,F6F,F-F@F-F6*&)F)
\"\"#F6F+\"\"\"F:F**&*&FNF6-F06$F@-%\"$G6$F5F,F-F6F+F:#F-F,*&*&)F(F,F6
-F06$F2-Fen6$F)F,F-F6F+F:F-*&*&FNF6-F06$F2FZF-F6F+F:F-*&*&FjnF6-F06$F@
F]oF-F6F+F:#F*F," }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 99 "aux6:=t
ermsimp(collect(expand(solve(aux5,diff(k(r,t),t,t))-solve(aux3,diff(k(
r,t),t,t))),\nlperts));" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%%aux6G,0*
&*&,&%\"rG!\"\"%\"mG\"\"#\"\"\"-%\"kG6$F)%\"tGF-\"\"\"*$)F)\"\"$F2!\"
\"!\"%*&*(F(F2,&F+F-F)F*F--%%diffG6$F.F)F-F2*$)F)\"\"$F2F6F7*&*(F(F2,&
F)F-F+F-F--F<6$-&%\"hG6#\"\"!F0F)F-F2*$)F)\"\"$F2F6F**&*&,(*$)F)F,F2\"
\"&*$)F+F,F2\"#5*&F+F-F)F-!#9F-FFF-F2*$)F)\"\"%F2F6F--F<6$FF-%\"$G6$F1
F,#F*F,*&*&)F(F,F2-F<6$F.-Fin6$F)F,F-F2*$)F)\"\"#F2F6!\"#*&*&F^oF2-F<6
$FFFaoF-F2*$)F)\"\"#F2F6#F-F," }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 86 "psisub:=\{h[0](r,t) = (psi(r,t) - r/3*k(r,t))*3*(2*r+3*m)/r/(r-2
*m) +r*diff(k(r,t),r)\};" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%'psisubG
<#/-&%\"hG6#\"\"!6$%\"rG%\"tG,&*&*&,&-%$psiGF,\"\"\"*&F-F5-%\"kGF,F5#!
\"\"\"\"$F5,&F-\"\"#%\"mGF;F5\"\"\"*&F-\"\"\",&F-F5F>!\"#\"\"\"!\"\"F;
*&F-F?-%%diffG6$F7F-F5F5" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 93 
"aux7:=termsimp(collect(expand(subs(psisub,aux4)),lperts union \{psi(r
,t),\ndiff(psi(r,t),r)\}));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%aux7
G,(*&*&,&%\"rG\"\"#%\"mG\"\"$\"\"\"-%%diffG6$-%$psiG6$F)%\"tGF)F-\"\"
\"*$)F)\"\"#F5!\"\"F,*&*&,(*$)F)F*F5F-*&F+F-F)F-F-*$)F+F*F5F-F-F1F-F5*
&)F)\"\"$F5,&F)!\"\"F+F*\"\"\"F9!#=*&*&F(F5-%\"kGF3F-F5*&F)\"\"\"FE\"
\"\"F9F," }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 46 "zsource1:=expan
d(simplify(subs(leqn8,zeta1))):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 15 "nops(zsource1);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"$@#" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 56 "zsource2:=expand(simplify(ev
al(subs(leqn10,zsource1)))):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 15 "nops(zsource2);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"$)>" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 49 "zsource3:=expand(simplify(su
bs(leqn9,zsource2))):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "no
ps(zsource3);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"$(G" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 101 "zsource3a:=expand(simplify(eval(su
bs(diff(k(r,t),t,t,r)=solve(aux1,diff(k(r,t),t,t,r)),\nzsource3)))):" 
}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 97 "zsource4:=expand(simplify
(eval(subs(diff(k(r,t),t,t)=solve(aux3,diff(k(r,t),t,t)),\nzsource3a))
)):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 100 "zsource5:=expand(si
mplify(eval(subs(diff(k(r,t),r,r,t)=solve(aux2,diff(k(r,t),r,r,t)),\nz
source4)))):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 102 "zsource6:=
expand(simplify(eval(subs(diff(h[0](r,t),t,t)=solve(aux6,diff(h[0](r,t
),t,t)),\nzsource5)))):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "
nops(zsource6);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"#()" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 56 "zsource7:=expand(simplify(eval(subs
(psisub,zsource6)))):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "no
ps(zsource7);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"#&*" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 75 "zsource8:=expand(simplify(eval(subs
(k(r,t)=solve(aux7,k(r,t)),zsource7)))):" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 15 "nops(zsource8);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"
$a\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "zetaeqn:=zsource8:
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "s_ren := make_s():" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "sprime:=make_s_mu():" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "psisub;" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#<#/-&%\"hG6#\"\"!6$%\"rG%\"tG,&*&*&,&-%$psiGF*\"\"\"*&F
+F3-%\"kGF*F3#!\"\"\"\"$F3,&F+\"\"#%\"mGF9F3\"\"\"*&F+\"\"\",&F+F3F<!
\"#\"\"\"!\"\"F9*&F+F=-%%diffG6$F5F+F3F3" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 14 "nops(zetaeqn);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"$
a\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 64 "final1:=mcollect(exp
and(zetaeqn),\{psi(r,t),diff(psi(r,t),r,r)\}):" }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 53 "final2:=mcollect(final1,\{psi(r,t),diff(psi(r,
t),t)\}):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 65 "final3:=mcolle
ct(final2,\{diff(psi(r,t),t),diff(psi(r,t),r,r,r)\}):" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 61 "final4:=mcollect(final3,\{diff(psi(
r,t),r),diff(psi(r,t),t)\}):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 63 "final5:=mcollect(final4,\{diff(psi(r,t),t),diff(psi(r,t),t,r)\})
:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 53 "final6:=mcollect(final
5,\{psi(r,t),diff(psi(r,t),r)\}):" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 65 "final7:=mcollect(final6,\{diff(psi(r,t),r),diff(psi(r
,t),t,r,r)\}):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 63 "final8:=m
collect(final7,\{diff(psi(r,t),t),diff(psi(r,t),r,r)\}):" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 55 "final9:=mcollect(final8,\{psi(r,t),
diff(psi(r,t),r,t)\}):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 64 "f
inal10:=mcollect(final9,\{diff(psi(r,t),r),diff(psi(r,t),r,t)\}):" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 59 "final11:=mcollect(final10,\{
psi(r,t),diff(psi(r,t),t,r,r)\}):" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 65 "final12:=mcollect(final11,\{diff(psi(r,t),r),diff(psi
(r,t),r,r)\}):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 38 "final13:=
mcollect(final12,\{psi(r,t)\}):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 46 "final14:=mcollect(final13,\{diff(psi(r,t),t)\}):" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 46 "final15:=mcollect(final14,\{diff(ps
i(r,t),r)\}):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 48 "final16:=m
collect(final15,\{diff(psi(r,t),r,r)\}):" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 48 "final17:=mcollect(final16,\{diff(psi(r,t),r,t)\}):" }
}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "nops(final17);" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#\"#U" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 126 "zetasource:=subs((r-2*m)=mu,(2*m-r)=-mu,(2*r+3*m)=lambda,\nkf
actor(eval(subs(zeta(r,t)=0,-final17)),12/7*(r-2*m)^3/(2*r+3*m)));" }}
{PARA 12 "" 1 "" {XPPMATH 20 "6#>%+zetasourceG,$*&*&)%#muG\"\"$\"\"\",
D*&*(,**$)%\"rGF*F+\"\"#*&)F2F3F+%\"mG\"\"\"\"\"%*&F2F7)F6F3F+\"\"**$)
F6F*F+\"\"'F7-%$psiG6$F2%\"tGF7-%%diffG6$F?-%\"$G6$F2F3F7F+*&)F2\"\"'F
+%'lambdaG\"\"\"!\"\"!\"%*&*(,.*$)F2\"\"&F+\"$7\"*&)F2F8F+F6F+\"$![*&F
1F+F:F+\"$#p*&F5F+F=F+\"$i(*&F2F+)F6F8F+\"$T%*$)F6FUF+\"$W\"F7-FD6$F?F
BF7F?F+F+*()F)\"\"#F+)FL\"\"$F+)F2\"\"&F+FNF7*&*&)-FD6%F?F2FBF3F+FLF7F
+*&F)\"\"\")F2\"\"#F+FN#!\"\"F**&*(,(*$F5F+\"\")*&F6F+F2F+\"#7*$F:F+\"
\"(F7F?F+FjoF7F+*(F)\"\"\")F2\"\"%F+FL\"\"\"FNF7*&*(,&F6FjpF2!\"$F7-FD
6$F?F2F7FjoF+F+*&F)\"\"\")F2\"\"$F+FNF`p*&*(,(FepF7FgpF7FipF7F7F^oF+Fj
oF+F+*&)F)\"\"#F+)F2\"\"$F+FNFO*&*&,.FS!\"#FW!\"*FZ!\"'FfnF3Fhn\"#:F[o
FhrF7)F?F3F+F+*()F)\"\"#F+)F2\"\")F+FL\"\"\"FN!#7*&*&)F\\rF3F+)F^oF3F+
F+*()F2\"\"%F+)F)\"\"$F+FL\"\"\"FNF`s*&*(,*F0!#=F4F8F9\"#LF<\"#[F7FdqF
+F^oF+F+*()F)\"\"#F+)F2\"\"%F+FL\"\"\"FNF`p*&*(,.FS\"#KFW\"#))FZ\"$'HF
fn\"$5&Fhn\"$h&F[o\"$q#F7FdqF+F?F+F+*(F)\"\"\")F2\"\"(F+)FL\"\"#F+FNFe
r*&*&F^oF+-FD6$F?-FG6$F2F*F7F+*$)F2\"\"#F+FNF`p*&*(F)F7)FCF3F+FLF+F+*$
)F2\"\"%F+FN#F7F**&*(F6F+F?F+-FD6%F?FFFBF7F+*&)F2\"\"$F+FL\"\"\"FNFap*
&*&,*F0FhpF4\"#OF9\"#fF<\"#!*F7)FdqF3F+F+*&F)\"\"\")F2\"\"'F+FNFev*&*(
,(FepF*FgpFUFipF>F7FdqF+FCF+F+*$)F2\"\"&F+FN#F8F**&*(,&FipF7FepFerF7F^
oF+FCF+F+*(F)\"\"\")F2\"\"$F+FL\"\"\"FNF7*&*&FdqF+FhvF+F+*$)F2\"\"#F+F
NFevF7F+FLFN#FhpFjp" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 64 "fina
l18:=subs((r-2*m)=mu,(-r+2*m)=-mu,(2*r+3*m)=lambda,final17):" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 123 "final19:=kfactor(collect(fi
nal18,\{zeta(r,t),diff(zeta(r,t),r),diff(zeta(r,t),r,r),\ndiff(zeta(r,
t),t,t)\}),12/7*mu^3/lambda):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 34 "simplify(expand(final19-final18));" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6#\"\"!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 89 "termsimp(sim
plify(expand(subs(zeta(r,t)=0,lambda=(2*r+3*m),mu=(r-2*m),\nfinal19)+s
_ren)));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$*&*(,(\"\"\"F'%\"mG\"\"#
%\"rG!\"\"F'),(*$)F*F)\"\"\"F'*&F(F'F*F'F'*$)F(F)F0F'F)F0)-%%diffG6$-%
$psiG6$F*%\"tGF;F)F0F0*&)F*\"\"%F0),&F*F)F(\"\"$\"\"#F0!\"\"#\"$W\"\"
\"(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 90 "termsimp(simplify(ex
pand(subs(zeta(r,t)=0,lambda=(2*r+3*m),mu=(r-2*m),final19)\n+sprime)))
;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"!" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 20 "kernelopts(cputime);" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6#$\"'ef7!\"$" }}}}{MARK "163 1" 0 }{VIEWOPTS 1 1 0 1 1 1803 }