{"paper":{"title":"A certificate for semidefinite relaxations in computing positive dimensional real varieties","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Chu Wang, Lihong Zhi, Yue Ma","submitted_at":"2012-12-20T05:05:08Z","abstract_excerpt":"For an ideal I with a positive dimensional real variety, based on moment relaxations, we study how to compute a Pommaret basis which is simultaneously a Groebner basis of an ideal J generated by the kernel of a truncated moment matrix and nesting between I and its real radical ideal. We provide a certificate consisting of a condition on coranks of moment matrices for terminating the algorithm. For a generic delta-regular coordinate system, we prove that the condition is satisfiable in a large enough order of moment relaxations."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.4924","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"}