Functional Decomposition Using Principal Subfields

Abstract

Let f ∈ K(t) be a univariate rational function. It is well known that any non-trivial decomposition • h, with , h ∈ K(t), corresponds to a non-trivial subfield K(f (t)) L K(t) and viceversa. In this paper we use the idea of principal subfields and fast subfield-intersection techniques to compute the subfield la ice of K(t)/K(f (t)). is yields a Las Vegas type algorithm with improved complexity and be er run times for finding all non-equivalent complete decompositions of f .