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I see many methods to calculate the Gaussian curvature of parametric surfaces in SE.But how to calculate the Gaussian curvature of any point of the following explicit function:

f[x_, y_] := x^2 + y^2
J. M.'s missing motivation
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A little mouse on the pampas
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    You can easily use a Gaussian curvature routine intended for parametric surfaces on a Monge patch. Using e.g. GaussianCurvature[] from here, try this: GaussianCurvature[{x, y, x^2 + y^2}, {x, y}] – J. M.'s missing motivation Jan 29 '20 at 08:44
  • @J. M. But how to eliminate the singularity of the curvature of this function:gccolor[{x, y, (x^4 - 6 x^2 y^2 + y^4)/(x^2 + y^2)^2 BesselJ[4, 17 Sqrt[x^2 + y^2]]} /. {x -> u, y -> v}, {u, -1, 1 }, {v, -1, 1}] – A little mouse on the pampas Jan 29 '20 at 09:23

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