{"paper":{"title":"Deterministic Factorization of Sparse Polynomials with Bounded Individual Degree","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CC"],"primary_cat":"math.AC","authors_text":"Ilya Volkovich, Shubhangi Saraf, Vishwas Bhargava","submitted_at":"2018-08-20T19:10:39Z","abstract_excerpt":"In this paper we study the problem of deterministic factorization of sparse polynomials. We show that if $f \\in \\mathbb{F}[x_{1},x_{2},\\ldots ,x_{n}]$ is a polynomial with $s$ monomials, with individual degrees of its variables bounded by $d$, then $f$ can be deterministically factored in time $s^{\\mathrm{poly}(d) \\log n}$. Prior to our work, the only efficient factoring algorithms known for this class of polynomials were randomized, and other than for the cases of $d=1$ and $d=2$, only exponential time deterministic factoring algorithms were known.\n  A crucial ingredient in our proof is a qua"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.06655","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"}