{"paper":{"title":"Computing necessary integrability conditions for planar parametrized homogeneous potentials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.SC","authors_text":"Alin Bostan (INRIA Saclay - Ile de France), Safey El Din Mohab (UPMC), Thierry Combot (IMB)","submitted_at":"2014-05-21T09:07:15Z","abstract_excerpt":"Let $V\\in\\mathbb{Q}(i)(\\a_1,\\dots,\\a_n)(\\q_1,\\q_2)$ be a rationally parametrized planar homogeneous potential of homogeneity degree $k\\neq -2, 0, 2$. We design an algorithm that computes polynomial \\emph{necessary} conditions on the parameters $(\\a_1,\\dots,\\a_n)$ such that the dynamical system associated to the potential $V$ is integrable. These conditions originate from those of the Morales-Ramis-Sim\\'o integrability criterion near all Darboux points. The implementation of the algorithm allows to treat applications that were out of reach before, for instance concerning the non-integrability o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.5342","kind":"arxiv","version":1},"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"}