{"paper":{"title":"A Stabilized Normal Form Algorithm for Generic Systems of Polynomial Equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA","math.AC","math.AG"],"primary_cat":"math.NA","authors_text":"Marc Van Barel, Simon Telen","submitted_at":"2017-08-25T09:53:51Z","abstract_excerpt":"We propose a numerical linear algebra based method to find the multiplication operators of the quotient ring $\\mathbb{C}[x]/I$ associated to a zero-dimensional ideal $I$ generated by $n$ $\\mathbb{C}$-polynomials in $n$ variables. We assume that the polynomials are generic in the sense that the number of solutions in $\\mathbb{C}^n$ equals the B\\'ezout number. The main contribution of this paper is an automated choice of basis for $\\mathbb{C}[x]/I$, which is crucial for the feasibility of normal form methods in finite precision arithmetic. This choice is based on numerical linear algebra techniq"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.07670","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":""},"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"}