Is there any (possibly free) software suitable for computing geometric quantities of parametric surfaces?
Any suggestion will be very appreciated.
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Sage is a free piece of software similar to Mathematica. Check it out here.
For example, to compute the Gaussian and mean curvatures of the sphere,
sage: sphere = surfaces.Sphere(); sphere
sage: K = sphere.gauss_curvature();
sage: H = sphere.mean_curvature();
See here for more functions.
This MO answer also contains many other software links.
This link is particularly useful to find software oriented to a particular field.
