If f(x) is an irreducible polynomial in x, then Mod(x,f(x)) is a generic
root of f(x), and the algebra mod f(x) is isomorphic (I think) to the
algebra of the field generated by appending any root of f(x) to Q. Is
there a way of factoring f(x) mod f(x)? What I have in mind is that for
some polynomials where Mod(x,f(x)) is a root, then there may be other
rational functions of x which are also roots of f(x), e.g. if f(x) is
polcyclo(n), then Mod(x^a,f(x)) is a root whenever a is coprime to n. I
don't however see any easy way of finding such roots with polmods in
PARI. What, if anything, am I overlooking?