Hello, I'm doing a 3-dimensional curl calculation (the electric field from the magnetic field, for example) which I'd like to use to define a vector field (the Faraday tensor). To do this I define two manifolds, one with 4 dim and one with 3 dim (the same without the time dimension). Unfortunately, I can't extract the components of my 3-dim calculation to inject it into 4-dim. Here's my simplified code where I just define a vector field in 3D (F) that I'd like to inject into another in 4D (G):
M = Manifold(4, 'M') N = Manifold(3, 'N',ambient=M CM.<t,x,y,z> = M.chart() CN.<x,y,z> = N.chart()
t = var('t') phi = N.continuous_map(M, {(CN,CM): [t,x, y, z]}) phi_inv = M.continuous_map(N, {(CM, CN): [x, y, z]}) phi_inv_t = M.scalar_field({CM: t}) N.set_embedding(phi, inverse=phi_inv, var=t, t_inverse={t: phi_inv_t})
F = N.vector_field('F') Fx, Fy, Fz = function('F_x')(x,y,z), function('F_y')(x,y,z), function('F_z')(x,y,z) F[0] = Fx F[1] = Fy F[2] = Fz
G = M.vector_field('G') G[0] = t G[1] = F[0] G[2] = F[1] G[3] = F[2]
