# Question:How do I use Maple to calculate the Christoffel Symbols of a Metric?

## Question:How do I use Maple to calculate the Christoffel Symbols of a Metric?

Maple

FLRW_Metric.mw

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");

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