Functional Decomposition Using Principal Subfields

Luiz E. Allem, Juliane G. Capaverde, Mark van Hoeij, Jonas Szutkoski
2017 Proceedings of the 2017 ACM on International Symposium on Symbolic and Algebraic Computation - ISSAC '17  
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 type algorithm with improved complexity and better run times for finding all non-equivalent complete decompositions of f.
doi:10.1145/3087604.3087608 dblp:conf/issac/AllemCHS17 fatcat:b5y2uycufnhabog4dtz45aeaem