-v(theta)*ln(t)+V(theta)*t^2*ln(t)^2+V[1](theta)*t^2+V[2](theta)*t^2*ln(t), Q(t,theta) = Q[infinity](theta)+q(theta)*t^(2*v(theta))+qq(theta)*t^(2*v(theta))*ln(t)](limittwo1.gif){kind=small}
limittwo.mws
The special case v(theta)=1 , diff(Q[infinify](theta),theta)=0 for consistency and diff(v(theta),theta) not 0
Notation diff(v(thtea),theta$n)=v[n], diff(Q[infinify](theta),theta$n)=Q[n]
| > | restart: |
| > |
The following substitutions for P(t,theta) and Q(t,theta) are made:
| > | P(t,theta)=P[infinity](theta)-v(theta)*log(t)+V(theta)*t^2*(log(t))^2+V[1](theta)*t^2+V[2](theta)*t^2*(log(t)),Q(t,theta)=Q[infinity](theta)+q(theta)*t^(2*(v(theta)))+qq(theta)*t^(2*(v(theta)))*log(t); |
| > | restart: |
| > | grtw(); |
Scalar invariant library.
Last modified 25 March 1997.
`Differential Invariants`
`Last modified Jan. 20, 1995`
`Basis/tetrad related object definitions`
`Last modified 23 January 2001`
`Last built 27 May, 1999`
`Last built 27 May, 1999`
| > | qload(gowdy); |
![`x `^a = vector([t, theta, x1, x2])](limittwo12.gif){kind=small}
| > | grcalc(WeylSq); |
| > | gralter(_,13,6,7); |
Component simplification of a GRTensorII object:
Applying routine `Apply constraints repeatedly` to object WeylSq
Applying routine expand to object WeylSq
Applying routine factor to object WeylSq
| > | grmap(_,subs,P(t,theta)=P[infinity](theta)-v(theta)*log(t)+V(theta)*t^2*(log(t))^2+V[1](theta)*t^2+V[2](theta)*t^2*(log(t)),Q(t,theta)=Q[infinity](theta)+q(theta)*t^(2*(v(theta)))+qq(theta)*t^(2*(v(theta)))*log(t),`x`); |
Applying routine subs to WeylSq
| > |
Apply consistency relation but keep all derivatives of Q(theta)
| > | grmap(_,subs,diff(Q[infinity](theta),theta$4)=Q[4],`x`); |
Applying routine subs to WeylSq
| > | grmap(_,subs,diff(Q[infinity](theta),theta$3)=Q[3],`x`); |
Applying routine subs to WeylSq
| > | grmap(_,subs,diff(Q[infinity](theta),theta$2)=Q[2],`x`); |
Applying routine subs to WeylSq
| > | grmap(_,subs,diff(Q[infinity](theta),theta)=0,`x`); |
Applying routine subs to WeylSq
Make sure you keep all derivatives of v(theta)
| > | grmap(_,subs,diff(v(theta),theta$4)=v[4],`x`); |
Applying routine subs to WeylSq
| > | grmap(_,subs,diff(v(theta),theta$3)=v[3],`x`); |
Applying routine subs to WeylSq
| > | grmap(_,subs,diff(v(theta),theta$2)=v[2],`x`); |
Applying routine subs to WeylSq
| > | grmap(_,subs,diff(v(theta),theta$1)=v[1],`x`); |
Applying routine subs to WeylSq
| > | grmap(_,subs,v(theta)=1,`x`); |
Applying routine subs to WeylSq
| > | gralter(_,6,7); |
Component simplification of a GRTensorII object:
Applying routine expand to object WeylSq
Applying routine factor to object WeylSq
| > | core:=simplify(limit(factor(t^1*grcomponent(WeylSq,[])/(exp(gamma(t,theta)))),t=0)); |
![core := -4*v[1]^2+4*exp(2*P[infinity](theta))*Q[2]^2](limittwo20.gif){kind=small}
| > |
| > | factor(subs(v[1]=diff(v(theta),theta$1),Q[2]=diff(Q[infinity](theta),theta$2),core)*exp(gamma(t,theta))/t); |
)*diff(Q[infinity](theta),`$`(theta,2))^2)*exp(gamma(t,theta))/t](limittwo21.gif)
| > | kernelopts(cputime); |
| > | latex(-4*(diff(v(theta),theta)^2-exp(2*P[infinity](theta))*diff(Q[infinity](theta),`$`(theta,2))^2)*exp(gamma(t,theta))/t); |
-4\,{\frac { \left( \left( {\frac {d}{d\theta}}v \left( \theta
\right) \right) ^{2}-{e^{2\,P_{{\infty }} \left( \theta \right) }}
\left( {\frac {d^{2}}{d{\theta}^{2}}}Q_{{\infty }} \left( \theta
\right) \right) ^{2} \right) {e^{\gamma \left( t,\theta \right) }}}{
t}}
| > |