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 sage-support+unsubscr...@googlegroups.com. To view this discussion on the web visit https://groups.google.com/d/msgid/sage-support/b01ced68-390f-4a1f-ae64-0b5b4617f806n%40googlegroups.com.
