Factoring polynomials over function fields - Voloch, José Felipe (Research in number theory, 2025)
If K / k is a function field in one variable of positive characteristic, we describe a general algorithm to factor one-variable polynomials with coefficients in K . The algorithm is flexible enough to find factors subject to additional restrictions, e.g., to find all roots that belong to a given finite dimensional k -subspace of K , more efficiently. For bounded characteristic, it runs in polynomial time, relative to factorizations over the constant field k and also provides a deterministic polynomial time irreducibility test. We also discuss applications to places of reducible reduction, when k is a global field, and to list decoding of Reed-Solomon codes.