{"paper":{"title":"An improvement upon unmixed decomposition of an algebraic variety","license":"http://creativecommons.org/licenses/by/3.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.AC","authors_text":"Yongbin Li, Zhenyi Ji","submitted_at":"2010-12-06T14:52:02Z","abstract_excerpt":"Decomposing an algebraic variety into irreducible or equidimensional components is a fundamental task in classical algebraic geometry and has various applications in modern geometry engineering. Several researchers studied the problem and developed efficient algorithms using $Gr$\\\"{o}$bner$ basis method. In this paper, we try to modify the computation of unmixed decomposition of an algebraic variety based on improving the computation of $Zero(sat(\\mathbb{T}))$, where $\\mathbb{T}$ is a triangular set in $\\textbf{K[X]}$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1012.1190","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"}