How do I use Maple to calculate the Christoffel Symbols of a Metric? I have been tasked with calculating all the non-vanishing Christoffel symbols (first kind) of a metric and have done these long-hand using the Lagrangian method and shown my working.  However, for peace of mind I would like to run the metric through Maple and double-check that it returns the same answers (going back through my calculations if I have missed anything).  I have attached the code I have written at the bottom.
I have no trouble defining the metric and the manifold but I receive an error message when I try to compute the Christoffel symbols 'improper op or subscript selector'.  Could someone point out where I have made a mistake.  The metric is the FLRW metric if that helps.
with(DifferentialGeometry):with(Tensor);
g1:=evalDG(-(dt)^2 +a(t)^2*((dx)^2+(dy)^2+(dz)^2)/(1+(k/4)*(x^(2)+y^(2)+z^2))^2 );
C1:=Christoffel(g1, "FirstKind");

I don't know much about the DifferentialGeometry package, but it seems to me you want to first use

DGsetup([t,x,y,z],M);

and then in defining g1 use  dt &tensor dt etc. instead of (dt)^2 etc.
