{"paper":{"title":"A probabilistic algorithm to compute the real dimension of a semi-algebraic set","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.SC","authors_text":"Elias Tsigaridas (LIP6, Inria Paris-Rocquencourt), Mohab Safey El Din (LIP6","submitted_at":"2013-04-06T19:23:00Z","abstract_excerpt":"Let $\\RR$ be a real closed field (e.g. the field of real numbers) and $\\mathscr{S} \\subset \\RR^n$ be a semi-algebraic set defined as the set of points in $\\RR^n$ satisfying a system of $s$ equalities and inequalities of multivariate polynomials in $n$ variables, of degree at most $D$, with coefficients in an ordered ring $\\ZZ$ contained in $\\RR$. We consider the problem of computing the {\\em real dimension}, $d$, of $\\mathscr{S}$. The real dimension is the first topological invariant of interest; it measures the number of degrees of freedom available to move in the set. Thus, computing the rea"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.1928","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"}