Thank you again, Eric! Em segunda-feira, 20 de novembro de 2023 às 10:55:45 UTC-3, Eric Gourgoulhon escreveu:
> Hi, > > The complicated result that you get is due to a lack of simplification in > Sage. More precisely, the default simplification chain automatically > applied in tensor calculus on manifolds, namely > > https://doc.sagemath.org/html/en/reference/manifolds/sage/manifolds/utilities.html#sage.manifolds.utilities.simplify_chain_real > yields overcomplicated expressions in your case. > To get a much simpler result, which looks much closer to Eq. (37) of the > paper, you have to replace the default simplification chain by a customized > one. In your case, it suffices to use the function factor(). > For this, use the manifold's method set_simplify_function() just after the > declaration of the chart X > > https://doc.sagemath.org/html/en/reference/manifolds/sage/manifolds/manifold.html#sage.manifolds.manifold.TopologicalManifold.set_simplify_function > i.e. start you notebook with > > N = Manifold(2,'N') > X.<M,J> = N.chart(r' M:(0,oo) J:(-oo,oo)') > N.set_simplify_function(factor) > > Best wishes, > > Eric. > > Le lundi 20 novembre 2023 à 04:44:49 UTC+1, Rogerio a écrit : > > Recently I encountered an odd result while using Sagemanifolds to > calculate the Ricci scalar for a specific 2D metric. I was trying to > reproduce Eq. (37) of this paper <https://arxiv.org/pdf/gr-qc/0304015.pdf>, > but the result was quite different. Here is the code > N = Manifold(2,'N') > X.<M,J> = N.chart(r' M:(0,oo) J:(-oo,oo)') > > dM = X.coframe()[0] > dJ = X.coframe()[1] > g0 = 2/(1-J^2/M^4)^(3/2)*(-2*((1-J^2/M^4)^(3/2) +1-3*J^2/M^4)*dM*dM - 2*J > /M^3*dM*dJ - 2*J/M^3*dJ*dM + dJ*dJ/M^2) > > g = N.metric('g') > g[:] = g0[:] > ric = g.ricci_scalar() > > The result is a high order rational function not resembling the paper > result. However, taking > R = > N.scalar_field(1/(4*M^2)*(sqrt(1-J^2/M^4)-2)/sqrt(1-J^2/M^4),name='R') > delta_R = ric-R > > delta_R == 0 > > Results True. > > How to express the Ricci scalar as shown in the paper? > > Thanks in advance! > > -- You received this message because you are subscribed to the Google Groups "sage-support" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To view this discussion on the web visit https://groups.google.com/d/msgid/sage-support/5f748bc5-742a-41a7-86d3-ddd1adc6bbe9n%40googlegroups.com.
