{"paper":{"title":"On the Complexity of the F5 Gr\\\"obner basis Algorithm","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.SC","authors_text":"Bruno Salvy, Jean-Charles Faug\\`ere, Magali Bardet","submitted_at":"2013-12-05T19:47:02Z","abstract_excerpt":"We study the complexity of Gr\\\"obner bases computation, in particular in the generic situation where the variables are in simultaneous Noether position with respect to the system.\n  We give a bound on the number of polynomials of degree $d$ in a Gr\\\"obner basis computed by Faug\\`ere's $F_5$ algorithm~(Fau02) in this generic case for the grevlex ordering (which is also a bound on the number of polynomials for a reduced Gr\\\"obner basis, independently of the algorithm used). Next, we analyse more precisely the structure of the polynomials in the Gr\\\"obner bases with signatures that $F_5$ computes"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.1655","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"}