Functional Decomposition using Principal Subfields

01/12/2017

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by   Luiz E. Allem, et al.

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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.