{"paper":{"title":"A fast algorithm for computing the characteristic polynomial of the p-curvature","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), \\'Eric Schost, Xavier Caruso (IRMAR)","submitted_at":"2014-05-21T09:05:33Z","abstract_excerpt":"We discuss theoretical and algorithmic questions related to the $p$-curvature of differential operators in characteristic $p$. Given such an operator $L$, and denoting by $\\Chi(L)$ the characteristic polynomial of its $p$-curvature, we first prove a new, alternative, description of $\\Chi(L)$. This description turns out to be particularly well suited to the fast computation of $\\Chi(L)$ when $p$ is large: based on it, we design a new algorithm for computing $\\Chi(L)$, whose cost with respect to $p$ is $\\softO(p^{0.5})$ operations in the ground field. This is remarkable since, prior to this work"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.5341","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"}