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{SECT 0 {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart:" }}}{EXCHG 
{PARA 0 "" 0 "" {MPLTEXT 0 21 37 "Consistency relation for v(theta):=1
:" }}}{EXCHG {PARA 0 "" 0 "" {MPLTEXT 0 21 93 "This is obtained from t
he condition diff(gamma(t,theta),t,theta)=diff(gamma(t,theta),theta,t)
" }}}{EXCHG {PARA 0 "" 0 "" {MPLTEXT 0 21 44 "(see the constraints in \+
the input gowdy.mpl)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 310 "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);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>-%\"P
G6$%\"tG%&thetaG,,-&F%6#%)infinityG6#F(\"\"\"*&-%\"vGF.F/-%#lnG6#F'F/!
\"\"*&#F/\"\"%F/**)-%$expG6#F*\"\"#F/)-%%diffG6$-&%\"QGF,F.-%\"$G6$F(F
?F?F/)F'F?F/)F3F?F/F/F/*&-&%\"VG6#F/F.F/FJF/F/*(,(*(-F=6#,$*&F?F/F*F/F
/F/-&%$psiG6#FFF.F/FAF/F/*&#F/F9F/*$F@F/F/F6*&#F/F9F/-FB6$F1FGF/F6F/FJ
F/F3F/F/" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 124 "Q(t,theta):= Q
[infinity](theta)+psi[Q](theta)*t^(2*v(theta))+1/2*diff(Q[infinity](th
eta),`$`(theta,2))*t^(2*v(theta))*ln(t);" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6#>-%\"QG6$%\"tG%&thetaG,(-&F%6#%)infinityG6#F(\"\"\"*&-&%$psiG6#F
%F.F/)F',$*&\"\"#F/-%\"vGF.F/F/F/F/*&#F/F8F/*(-%%diffG6$F*-%\"$G6$F(F8
F/F5F/-%#lnG6#F'F/F/F/" }}}{EXCHG {PARA 0 "" 0 "" {MPLTEXT 0 21 0 "" }
}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 175 "diff(h(t,theta),t)= facto
r(simplify(-t*exp(P(t,theta))^2*diff(Q(t,theta),t)^2-t*diff(P(t,theta)
,t)^2-t*exp(P(t,theta))^2*diff(Q(t,theta),theta)^2-t*diff(P(t,theta),t
heta)^2)):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "A(t,theta):=r
hs(%):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 154 "diff(h(t,theta),theta) = factor(simplify
(-2*t*diff(P(t,theta),theta)*diff(P(t,theta),t)-2*t*exp(P(t,theta))^2*
diff(Q(t,theta),t)*diff(Q(t,theta),theta))):" }}}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 19 "B(t,theta):=rhs(%):" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 58 "factor(expand(diff(A(t,theta),theta)-diff(B(t,theta
),t))):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "subs(diff(v(thet
a),theta)=v[1],%):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 36 "subs(
diff(v(theta),theta$2)=v[2],%):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 19 "subs(v(theta)=1,%):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
31 "C:=factor(expand(simplify(%))):" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 9 "denom(C);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$*&\"\"%
\"\"\"%\"tGF&F&" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 53 "factor(s
ubs(t=0,v[1]=diff(v(theta),theta),numer(C)));" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#,$*,\"\")\"\"\")-%$expG6#-&%\"PG6#%)infinityG6#%&thetaG
\"\"#F&)-F)6#\"\"!\"\"$F&)-%%diffG6$-&%\"QGF.F0F1F2F&,&*&-%#lnGF5F&-F:
6$-%\"vGF0F1F&F&-F:6$F+F1!\"\"F&F&" }}}{EXCHG {PARA 0 "" 0 "" 
{MPLTEXT 0 21 66 "Diverges unless diff(Q[infinity](theta),theta)=0 eve
n if v[1] = 0." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{MARK "20 0 0" 0 }
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