Functional Decomposition Using Principal Subfields

Let f ∈ K(t) be a univariate rational function. It is well known that any non-trivial decomposition g ◦ h, with g, h ∈ K(t), corresponds to a non-trivial subfield K(f(t)) ( L ( K(t) and vice-versa. In this paper we use the idea of principal subfields and fast subfield-intersection techniques to compute the subfield lattice of K(t)/K(f(t)). This yields a Las Vegas algorithm with improved complexity and better run times for finding all non-equivalent complete decompositions of f . CCS Concepts •Computing methodologies → Algebraic algorithms;