Hi! I want to compute geodesic trajectory for following metric:
import time
comput_time0 = time.perf_counter()
M0 = M.open_subset('M_0', r'\mathcal{M}_0' )
X.<ta,r,x,y> = M0.chart(r'ta:\tau r:(0,+oo):r y:(0,+oo):y z:(0,+oo):z')
print(X); X
R3 = Manifold(3, 'R^3', latex_name=r'\mathbb{R}^3')
X3.<r,y,z> = R3.chart()
to_R3 = M.diff_map(R3, {(X, X3): [1,
1, 1]})
to_R3.display()
g = M.metric()
g[0,0], g[1,1] = -(r**6-1)*r**2, (r**13)*(r**6-1)**(-1)
g[2,2], g[3,3] = r**2, r**2
g.display()
But when I'm trying to compute geodesics with this code:
p0 = M.point((0, 1, pi/2, 1e-12), name='p_0')
v0 = M.tangent_space(p0)((1.297513, 0,1, 0.0640625), name='v_0')
v0.display()
s = var('s')
geod = M0.integrated_geodesic(g, (s, 0, 100), v0, across_charts=True)
sol = geod.solve() # numerical integration
I only obtain error unable to convert Chart (M_0, (ta, r, y, z)) to a symbolic expression. How could I solve this issue? I could not find any information about this error in the Internet. I'm working with SageManifolds/SageMath.
