IsSquareFree

A repeated factor survives differentiation once, so it divides both the
polynomial and its derivative, and over a field the converse holds too — hence
the test on gcd(f, f'). The characteristic-p case has to be taken
separately: f' = 0 makes that gcd f itself, and it happens exactly
when f is a polynomial in x^p, which by the Frobenius map is the
p-th power of another polynomial and so is not square-free.