# Define multivariate even general function

I want to define a multivariate even function. This question shows how to do it for a single variable function Defining general odd function but I don't see how to generalize the syntax to multiple variables. In particular, I want a general function f[x, y, z] with the properties f[-x, y, z] = f[x, -y, z] = f[x, y, -z] = f[x, y, z]

• I am not sure if I understand the question correctly, because it seems obvious. Assume that f0 is not even. Then f= f0[Abs[x], Abs[y], Abs[z]] is even in x,y,z. Oct 22 '21 at 9:46
• I need to take gradients, curls, and Laplacians of the function, and then simplify the result using the known symmetry. Abs doesn't have a derivative at 0 so doesn't work.
– jeff
Oct 23 '21 at 17:01
• If a function is even at the origin, then the derivative must be zero. Oct 23 '21 at 19:03