Factoring certain polynomials with a computer algebra system

Question

Every self-reciprocal polynomial with spectral radius one has a factorisation of the form $(x-1)^{2k} \Pi_{n \geq 2}{ \Phi_n^{e_n}}$ , where $k, e_n$ are natural numbers and $\Phi_n$ are the cyclotomic polynomials. Now given a self-reciprocal polynomial with spectral radius one, is there a program to factor $f$ quickly into this form? I prefer to use GAP, but havent found something like that.

Answer 1

If it is time-critical and the existing factorization routine is too slow:

• Do squarefree factorization using Gcd with derivative.
• Then take gcds with x^m-1 for increasing m.