I used to have Mathematica 8 previously and whenever I ran the NSolve command on underdetermined systems, NSolve[x^2 + y^2 + z^2 == 1 && x y z == 2, {x, y, z}]

it used to give me a warning: “Inverse functions are being used by NSolve, so some solutions may not be found.”

However, I switched to Mathematica 11 recently, and I no longer get this warning. This warning is important as it used to hint me that the system is underdetermined (or, technically, at least one positive-dimensional component) in the system. In the above example, it is clear that there is one equation less than the number of variables, but in many cases the number of equations and variables are the same, yet it can be underdetermined. Any idea what changed? Has the method changed? And in the end, what do the solutions that this command give mean, if there are infinitely many solutions? Thanks, dbm