code: def main():
      print("Initial metric:")
      pprint(gdd)
      print("-" * 40)
      print("Christoffel symbols:")
      pprint_Gamma_udd(0, 1, 0)
      pprint_Gamma_udd(0, 0, 1)
      print()
      pprint_Gamma_udd(1, 0, 0)
      pprint_Gamma_udd(1, 1, 1)
      pprint_Gamma_udd(1, 2, 2)
      pprint_Gamma_udd(1, 3, 3)
      print()
      pprint_Gamma_udd(2, 2, 1)
      pprint_Gamma_udd(2, 1, 2)
      pprint_Gamma_udd(2, 3, 3)
      print()
      pprint_Gamma_udd(3, 2, 3)
      pprint_Gamma_udd(3, 3, 2)
      pprint_Gamma_udd(3, 1, 3)
      pprint_Gamma_udd(3, 3, 1)
      print("-" * 40)
      print("Ricci tensor:")
      pprint_Rmn_dd(0, 0)
      e = Rmn.dd(1, 1)
      pprint_Rmn_dd(1, 1)
      pprint_Rmn_dd(2, 2)
      pprint_Rmn_dd(3, 3)
      print("-" * 40)
      print("Solve Einstein's equations:")
      e = e.subs(nu(r), -lam(r)).doit()
      l = dsolve(e, lam(r))
      pprint(l)
      lamsol = solve(l, lam(r))[0]
      metric = gdd.subs(lam(r), lamsol).subs(
          nu(r), -lamsol
      )  # .combine()
      print("metric:")
      pprint(metric)
  
imports: from sympy import exp, Symbol, sin, dsolve, Function, Matrix, Eq, pprint, solve
label_desc: Use image node_id 10 for calling a global function with example usage: main() without return types