{"paper":{"title":"Univariate real root isolation in an extension field","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.MS","cs.NA","math.AG","math.NA"],"primary_cat":"cs.SC","authors_text":"Adam Strzebonski, Elias Tsigaridas","submitted_at":"2011-01-23T13:38:46Z","abstract_excerpt":"We present algorithmic, complexity and implementation results for the problem of isolating the real roots of a univariate polynomial in $B_{\\alpha} \\in L[y]$, where $L=\\QQ(\\alpha)$ is a simple algebraic extension of the rational numbers. We consider two approaches for tackling the problem. In the first approach using resultant computations we perform a reduction to a polynomial with integer coefficients. We compute separation bounds for the roots, and using them we deduce that we can isolate the real roots of $B_{\\alpha}$ in $\\sOB(N^{10})$, where $N$ is an upper bound on all the quantities (de"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1101.4369","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"}