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{SECT 0 {EXCHG {PARA 0 "" 0 "" {MPLTEXT 0 21 17 "limitthirteen.mws" }}
}{EXCHG {PARA 0 "" 0 "" {MPLTEXT 0 21 0 "" }}}{EXCHG {PARA 0 "" 0 "" 
{MPLTEXT 0 21 48 "The special case v(theta)=-1 , with constraints," }}
}{EXCHG {PARA 0 "" 0 "" {MPLTEXT 0 21 36 "Notation diff(v(thtea),theta
$n)=v[n]" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart:" }}}
{EXCHG {PARA 0 "" 0 "" {MPLTEXT 0 21 35 "the following substitution is
 made." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 435 "P(t,theta) = P[i
nfinity](theta)-v(theta)*ln(t)+1/4*exp(P[infinity](theta))^2*diff(Q[in
finity](theta),`$`(theta,2))^2*t^2*ln(t)^2+V[1](theta)*t^2+(exp(2*P[in
finity](theta))*psi[Q](theta)*diff(Q[infinity](theta),`$`(theta,2))-1/
4*diff(Q[infinity](theta),`$`(theta,2))^2-1/4*diff(v(theta),`$`(theta,
2)))*t^2*ln(t),Q(t,theta) = Q[infinity](theta)+psi[Q](theta)*t^(2*v(th
eta))+1/2*diff(Q[infinity](theta),`$`(theta,2))*t^(2*v(theta))*ln(t);
" }}}{EXCHG {PARA 0 "" 0 "" {MPLTEXT 0 21 0 "" }}}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 7 "grtw();" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 13 "qload(gowdy);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "grca
lc(WeylSq);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "gralter(_,13
,6,7);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 453 "grmap(_,subs,P(t
,theta) = P[infinity](theta)-v(theta)*ln(t)+1/4*exp(P[infinity](theta)
)^2*diff(Q[infinity](theta),`$`(theta,2))^2*t^2*ln(t)^2+V[1](theta)*t^
2+(exp(2*P[infinity](theta))*psi[Q](theta)*diff(Q[infinity](theta),`$`
(theta,2))-1/4*diff(Q[infinity](theta),`$`(theta,2))^2-1/4*diff(v(thet
a),`$`(theta,2)))*t^2*ln(t),Q(t,theta) = Q[infinity](theta)+psi[Q](the
ta)*t^(2*v(theta))+1/2*diff(Q[infinity](theta),`$`(theta,2))*t^(2*v(th
eta))*ln(t),`x`);" }}}{EXCHG {PARA 0 "" 0 "" {MPLTEXT 0 21 42 "Keep al
l derivatives of Q[infinity](theta)" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 56 "grmap(_,subs,diff(Q[infinity](theta),theta$5)=Q[5],`x
`);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 53 "grmap(_,subs,diff(Q[
infinity](theta),theta$4)=0,`x`);" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 53 "grmap(_,subs,diff(Q[infinity](theta),theta$3)=0,`x`);
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 54 "grmap(_,subs,diff(Q[inf
inity](theta),theta)=Q[1],`x`);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 53 "grmap(_,subs,diff(Q[infinity](theta),theta$2)=0,`x`);" }
{MPLTEXT 0 21 0 "" }}}{EXCHG }{EXCHG {PARA 0 "" 0 "" {MPLTEXT 0 21 32 
"Keep all derivatives of v(theta)" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 46 "grmap(_,subs,diff(v(theta),theta$4)=v[4],`x`);" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 46 "grmap(_,subs,diff(v(theta),t
heta$3)=v[3],`x`);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 46 "grmap
(_,subs,diff(v(theta),theta$2)=v[2],`x`);" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 43 "grmap(_,subs,diff(v(theta),theta$1)=0,`x`):" }}}
{EXCHG {PARA 0 "" 0 "" {MPLTEXT 0 21 37 "Keep all derivatives of psi[Q
](theta)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 59 "grmap(_,subs,di
ff(psi[Q](theta),`$`(theta,3))=psi[Q3],`x`);" }}}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 53 "grmap(_,subs,diff(psi[Q](theta),`$`(theta,2))=0,
`x`);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 53 "grmap(_,subs,diff(psi[Q](theta),`$`(theta
,4))=0,`x`);" }}}{EXCHG {PARA 0 "" 0 "" {MPLTEXT 0 21 0 "" }}}{EXCHG 
{PARA 0 "" 0 "" {MPLTEXT 0 21 17 "Apply constraints" }}}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 46 "grmap(_,subs,diff(psi[Q](theta),theta)=0,
`x`):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "grmap(_,subs,psi[Q
](theta)=0,`x`):" }}}{EXCHG {PARA 0 "" 0 "" {MPLTEXT 0 21 0 "" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "grmap(_,subs,v(theta)=-1,`x`
):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "gralter(_,6,7);" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "denom(grcomponent(WeylSq,[])
);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 48 "factor(subs(t=0,numer
(grcomponent(WeylSq,[]))));" }}}{EXCHG {PARA 0 "" 0 "" {MPLTEXT 0 21 
0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 91 "core:=simplify(limit
(factor(grcomponent(WeylSq,[])/(t*log(t)^2*exp(gamma(t,theta)))),t=0))
;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 40 "Ww:=t*log(t)^2*exp(gam
ma(t,theta))*core;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#WwG,$*,\"\"$
\"\"\"%\"tGF()-%#lnG6#F)\"\"#F(-%$expG6#-%&gammaG6$F)%&thetaGF()&%\"vG
6#F.F.F(F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 37 "subs(v[2]=dif
f(v(theta),theta$2),Ww);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$*,\"\"$
\"\"\"%\"tGF&)-%#lnG6#F'\"\"#F&-%$expG6#-%&gammaG6$F'%&thetaGF&)-%%dif
fG6$-%\"vG6#F3-%\"$G6$F3F,F,F&F&" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 9 "latex(%);" }}{PARA 6 "" 1 "" {TEXT -1 67 "3\\,t \\left
( \\ln  \\left( t \\right)  \\right) ^\{2\}\{e^\{\\gamma \\left( t," }
}{PARA 6 "" 1 "" {TEXT -1 70 "\\theta \\right) \}\} \\left( \{\\frac \+
\{d^\{2\}\}\{d\{\\theta\}^\{2\}\}\}v \\left( \\theta" }}{PARA 6 "" 1 "
" {TEXT -1 22 " \\right)  \\right) ^\{2\}" }}}{EXCHG {PARA 0 "> " 0 "
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