{"paper":{"title":"Extended Hardness Results for Approximate Gr\\\"obner Basis Computation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.SC","authors_text":"Gwen Spencer","submitted_at":"2016-05-14T21:44:01Z","abstract_excerpt":"Two models were recently proposed to explore the robust hardness of Gr\\\"obner basis computation. Given a polynomial system, both models allow an algorithm to selectively ignore some of the polynomials: the algorithm is only responsible for returning a Gr\\\"obner basis for the ideal generated by the remaining polynomials. For the $q$-Fractional Gr\\\"obner Basis Problem the algorithm is allowed to ignore a constant $(1-q)$-fraction of the polynomials (subject to one natural structural constraint). Here we prove a new strongest-parameter result: even if the algorithm is allowed to choose a $(3/10-\\"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.04472","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"}