Let $x(v,u) = sech(v) sin(u)$, $y(v,u) = sech(v) cos(u)$, $z(v,u) = v - tanh(v)$ the equations of a pseudosphere. I computed its mean curvature and got $\frac{Csch(v) - Sinh(v)}{2}$, although I found that Wolfram reports the opposite value of my mean curvature, here.
I computed my mean curvature summing the two principal curvatures (which I got as eigenvalues of Weingarten matrix) and dividing by two. I got the same exact principal curvatures reported in the first answer here. What am I doing wrong?
Principal curvatures, and therefore mean curvature, change sign under change of orientation; presumably you and Wolfram have chosen opposite normal vectors. (Gaussian curvature is independent of orientation, of course.)