{"paper":{"title":"Divide and Conquer Roadmap for Algebraic Sets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Marie-Francoise Roy, Saugata Basu","submitted_at":"2013-05-14T17:10:02Z","abstract_excerpt":"Let $\\mathrm{R}$ be a real closed field, and $\\mathrm{D} \\subset \\mathrm{R}$ an ordered domain. We describe an algorithm that given as input a polynomial $P \\in \\mathrm{D} [ X_{1},\\ldots,X_{k} ]$, and a finite set, $\\mathcal{A}= \\{ p_{1}, \\ldots,p_{m} \\}$, of points contained in $V= \\mathrm{Zer}( P, \\mathrm{R}^{k})$ described by real univariate representations, computes a roadmap of $V$ containing $\\mathcal{A}$. The complexity of the algorithm, measured by the number of arithmetic operations in $\\mathrm{D} $ is bounded by $\\left( \\sum_{i=1}^{m} D^{O ( \\log^{2} ( k ) )}_{i} +1 \\right) ( k^{\\log"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.3211","kind":"arxiv","version":6},"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"}