Displaying The Christoffel Symbols in Terms of a Function "F"

edit

Try this:

Man = Manifold(4, 'Man', r'\mathcal{M}')
M = var('M')

BL.<t,r,th,ph> = Man.chart(r't r:(0,+oo) th:(0,pi):\theta ph:(0,2*pi):\phi')
g = Man.lorentzian_metric('g')

function('f')(r)
g[0,0] = f(r)
g[1,1] = -1/f(r)
g[2,2] = -r^2
g[3,3] = -(r*sin(th))^2

# Christoffel symbols
nab = g.connection()
show(nab.display())