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arXiv · 1701.03529

Functional Decomposition using Principal Subfields

Luiz E. Allem·Juliane Capaverde·Mark van Hoeij·Jonas Szutkoski
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Abstract

Let $f\in K(t)$ be a univariate rational function. It is well known that any non-trivial decomposition $g \circ h$, with $g,h\in K(t)$, corresponds to a non-trivial subfield $K(f(t))\subsetneq L \subsetneq K(t)$ 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 $f$.

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Luiz E. Allem, Juliane Capaverde, Mark van Hoeij, Jonas Szutkoski. 2017-01-12. Functional Decomposition using Principal Subfields. https://doi.org/10.1145/3087604.3087608

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