>

restart:

Consistency relation for v(theta):=1:

This is obtained from the condition diff(gamma(t,theta),t,theta)=diff(gamma(t,theta),theta,t)

(see the constraints in the input gowdy.mpl)

>

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),`$`(theta,2))^2-1/4*diff(v(theta),`$`(theta,2)))*t^2*ln(t);

>	Q(t,theta):= Q[infinity](theta)+psi[Q](theta)*t^(2*v(theta))+1/2*diff(Q[infinity](theta),`$`(theta,2))*t^(2*v(theta))*ln(t);

>	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*diff(Q(t,theta),theta)^2-t*diff(P(t,theta),theta)^2)):

>	A(t,theta):=rhs(%):

>

>	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))):

>	B(t,theta):=rhs(%):

>	factor(expand(diff(A(t,theta),theta)-diff(B(t,theta),t))):

>	subs(diff(v(theta),theta)=v[1],%):

>	subs(diff(v(theta),theta$2)=v[2],%):

>	subs(v(theta)=1,%):

>	C:=factor(expand(simplify(%))):

>

denom(C);

>	factor(subs(t=0,v[1]=diff(v(theta),theta),numer(C)));

Diverges unless diff(Q[infinity](theta),theta)=0 even if v[1] = 0.

>

>