{"paper":{"title":"A baby step-giant step roadmap algorithm for general algebraic sets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.SC"],"primary_cat":"math.AG","authors_text":"\\'Eric Schost, Marie-Fran\\c{c}oise Roy, Mohab Safey El Din, Saugata Basu","submitted_at":"2012-01-31T04:37:58Z","abstract_excerpt":"Let $\\mathrm{R}$ be a real closed field and $\\mathrm{D} \\subset \\mathrm{R}$ an ordered domain. We give an algorithm that takes as input a polynomial $Q \\in \\mathrm{D}[X_1,\\ldots,X_k]$, and computes a description of a roadmap of the set of zeros, $\\mathrm{Zer}(Q,\\mathrm{R}^k)$, of $Q$ in $\\mathrm{R}^k$. The complexity of the algorithm, measured by the number of arithmetic operations in the ordered domain $\\mathrm{D}$, is bounded by $d^{O(k \\sqrt{k})}$, where $d = \\mathrm{deg}(Q)\\ge 2$. As a consequence, there exist algorithms for computing the number of semi-algebraically connected components o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1201.6439","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"}