# Lagrange interpolation over a finite field

Sorry if this is obvious I am not a mathematician and am only trying to do this to learn about Samir's Secret Sharing scheme which uses a finite field for security.

I've read the Sage doc here on univariate polynomial rings which works fine. but now I am curious as to how this would be done over a finite field instead in sage?

Is it simply a matter of every point being taken mod some prime? Or would this not work.