{"paper":{"title":"Numerical primary decomposition","license":"","headline":"","cross_cats":["cs.NA","math.NA"],"primary_cat":"math.AG","authors_text":"Anton Leykin","submitted_at":"2008-01-20T20:25:17Z","abstract_excerpt":"Consider an ideal $I \\subset R = \\bC[x_1,...,x_n]$ defining a complex affine variety $X \\subset \\bC^n$. We describe the components associated to $I$ by means of {\\em numerical primary decomposition} (NPD).\n  The method is based on the construction of {\\em deflation ideal} $I^{(d)}$ that defines the {\\em deflated variety} $\\dXd$ in a complex space of higher dimension. For every embedded component there exists $d$ and an isolated component $\\dYd$ of $\\dId$ projecting onto $Y$. In turn, $\\dYd$ can be discovered by existing methods for prime decomposition, in particular, the {\\em numerical irreduc"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0801.3105","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/0801.3105/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}