{"paper":{"title":"On the Complexity of Noncommutative Polynomial Factorization","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CC","authors_text":"Gaurav Rattan, Pushkar S Joglekar, V. Arvind","submitted_at":"2015-01-04T12:56:47Z","abstract_excerpt":"In this paper we study the complexity of factorization of polynomials in the free noncommutative ring $\\mathbb{F}\\langle x_1,x_2,\\dots,x_n\\rangle$ of polynomials over the field $\\mathbb{F}$ and noncommuting variables $x_1,x_2,\\ldots,x_n$. Our main results are the following.\n  Although $\\mathbb{F}\\langle x_1,x_2,\\dots,x_n \\rangle$ is not a unique factorization ring, we note that variable-disjoint factorization in $\\mathbb{F}\\langle x_1,x_2,\\dots,x_n \\rangle$ has the uniqueness property. Furthermore, we prove that computing the variable-disjoint factorization is polynomial-time equivalent to Pol"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.00671","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"}