{"paper":{"title":"Efficient algorithms for computing the Euler-Poincar\\'e characteristic of symmetric semi-algebraic sets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.SC"],"primary_cat":"math.AG","authors_text":"Cordian Riener, Saugata Basu","submitted_at":"2016-08-24T14:14:38Z","abstract_excerpt":"Let $\\mathrm{R}$ be a real closed field and $\\mathrm{D} \\subset \\mathrm{R}$ an ordered domain. We consider the algorithmic problem of computing the generalized Euler-Poincar\\'e characteristic of real algebraic as well as semi-algebraic subsets of $\\mathrm{R}^k$, which are defined by symmetric polynomials with coefficients in $\\mathrm{D}$. We give algorithms for computing the generalized Euler-Poincar\\'e characteristic of such sets, whose complexities measured by the number the number of arithmetic operations in $\\mathrm{D}$, are polynomially bounded in terms of $k$ and the number of polynomial"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.06828","kind":"arxiv","version":3},"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"}