FACTORIZATION PATTERNS OF POLYNOMIALS

Let R be a UFD. Let f is an element of R[T] be of content 1. Then f can be written as f = g(1)(a1)...g(r)(ar), where 1 <= a(1) < a(2) < ... < a(r), and the g(i) are square-free, relatively prime polynomials. The set of powers {a(1),...a(r)} is called the factorization pattern of f. We introduce an algorithm that will efficiently produce the factorization pattern of the polynomial. We also show that for some UFDs, like the rational integers, the factorization pattern can be obtained from the polynomial values.