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{SECT 0 {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart:" }}}{EXCHG 
{PARA 0 "" 0 "" {MPLTEXT 0 21 38 "Consistency relation for v(theta):=-
1:" }}}{EXCHG {PARA 0 "" 0 "" {MPLTEXT 0 21 93 "This is obtained from \+
the 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),`$`(theta,2))^2-1/4*diff(v(the
ta),`$`(theta,2)))*t^2*ln(t);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>-%\"
PG6$%\"tG%&thetaG,,-&F%6#%)infinityG6#F(\"\"\"*&-%\"vGF.F/-%#lnG6#F'F/
!\"\"*&#F/\"\"%F/**)-%$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$F1FGF/F6F/F
JF/F3F/F/" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 125 "Q(t,theta):= \+
Q[infinity](theta)+psi[Q](theta)*t^(2*v(theta))+1/2*diff(Q[infinity](t
heta),`$`(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(F8F/F5F/-%#lnG6#F'F/F/F/" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 175 "diff(h(t,theta),t)= factor(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*d
iff(Q(t,theta),theta)^2-t*diff(P(t,theta),theta)^2)):" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "A(t,theta):=rhs(%):" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 154 "diff(h(t,theta),theta) = factor(si
mplify(-2*t*diff(P(t,theta),theta)*diff(P(t,theta),t)-2*t*exp(P(t,thet
a))^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
(theta),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 36 "subs(diff(v(theta),theta$3)=v[3],%):" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 36 "subs(diff(v(theta),theta$4)=v[4],%)
:" }}}{EXCHG {PARA 0 "" 0 "" {MPLTEXT 0 21 26 "Here we retain derivati
ves" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 51 "subs(diff(Q[infinity
](theta),`$`(theta,1))=Q[1],%):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 51 "subs(diff(Q[infinity](theta),`$`(theta,2))=Q[2],%):" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 51 "subs(diff(Q[infinity](theta)
,`$`(theta,3))=Q[3],%):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 51 "
subs(diff(Q[infinity](theta),`$`(theta,4))=Q[4],%):" }}}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 49 "subs(diff(psi[Q](theta),`$`(theta,2))=psi
[Q2],%):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 49 "subs(diff(psi[Q
](theta),`$`(theta,3))=psi[Q3],%):" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 49 "subs(diff(psi[Q](theta),`$`(theta,4))=psi[Q4],%):" }}
}{EXCHG {PARA 0 "" 0 "" {MPLTEXT 0 21 23 "Here are the conditions" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 43 "subs(diff(psi[Q](theta),`$`(
theta,1))=0,%):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "subs(psi
[Q](theta)=0,%):" }}}{EXCHG {PARA 0 "" 0 "" {MPLTEXT 0 21 0 "" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "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#\"\"\"" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 27 "factor(subs(t=0,numer(C)));" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#\"\"!" }}}{EXCHG {PARA 0 "" 0 "" {MPLTEXT 0 21 58 "Dive
rges unless psi[Q](theta)=diff(psi[Q](theta),theta)=0 " }}}{EXCHG 
{PARA 0 "" 0 "" {MPLTEXT 0 21 37 "Try removing either of the condition
s" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 0 "" }}}}{MARK "35" 0 }{VIEWOPTS 1 1 0 1 1 1803 1 
1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }