{"paper":{"title":"Functional Decomposition using Principal Subfields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.SC","authors_text":"Jonas Szutkoski, Juliane Capaverde, Luiz E. Allem, Mark van Hoeij","submitted_at":"2017-01-12T23:14:56Z","abstract_excerpt":"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 $f$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.03529","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}