{"paper":{"title":"Ideal-specific elimination orders form a star-shaped region","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Christine G\\\"artner, Hartwig Bosse, Oleg Golubitsky","submitted_at":"2012-02-13T13:44:31Z","abstract_excerpt":"This paper shows that Gr\\\"obner walks aiming for the elimination of variables from a polynomial ideal can be terminated much earlier than previously known. To this end we provide an improved stopping criterion for a known Gr\\\"obner walk algorithm for the elemination of variables. This results from two new geometric insights on Gr\\\"obner fans: We show that for any given ideal I \\subset K[x_1, ..., x_n] the collection of Gr\\\"obner cones corresponding to I-specific elimination orders may contain Gr\\\"obner cones in the relative interior of the positive orthant. Moreover we prove that the correspon"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1202.2727","kind":"arxiv","version":3},"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"}