Is there a computer algebra method to compute the curvature of a Riemannian metric on the plane when the metric tensor has long entries $E,F,G$

The computation by hand is very complicated and long.

I would like to apply this possible software to calculate the Gaussian curvature described in the following posts:

A curvature description for center condition for quadratic vector field

Limit cycles as closed geodesics(2)

Finding a 1-form adapted to a smooth flow

I computed by hand, for two particular vector fields

$V=y\partial_x-x\partial_y$ and $V=y\partial_x -(x+x^2)\partial_y$

Now I need try other vector fields so I need computer help.

Thank you for your help, comments or answers.