{"paper":{"title":"Approximate Parametrization of Plane Algebraic Curves by Linear Systems of Curves","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"J. Rafael Sendra, Juana Sendra, Sonia L. Rueda, Sonia Perez-Diaz","submitted_at":"2009-01-03T13:02:41Z","abstract_excerpt":"It is well known that an irreducible algebraic curve is rational (i.e. parametric) if and only if its genus is zero. In this paper, given a tolerance $\\epsilon>0$ and an $\\epsilon$-irreducible algebraic affine plane curve $\\mathcal C$ of proper degree $d$, we introduce the notion of $\\epsilon$-rationality, and we provide an algorithm to parametrize approximately affine $\\epsilon$-rational plane curves, without exact singularities at infinity, by means of linear systems of $(d-2)$-degree curves. The algorithm outputs a rational parametrization of a rational curve $\\bar{\\mathcal C}$ of degree at"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0901.0320","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"}