{"paper":{"title":"Low Dimensional Test Sets for Nonnegativity of Even Symmetric Forms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Sadik Iliman, Timo de Wolff","submitted_at":"2013-03-18T13:12:13Z","abstract_excerpt":"An important theorem by Timofte states that nonnegativity of real $n$-variate symmetric polynomials of degree $d$ can be decided at test sets given by all points with at most $\\lfloor\\frac{d}{2}\\rfloor$ distinct components. However, if the degree is sufficiently larger than the number of variables, then the theorem obviously does not provide nontrivial information. Our approach is to look at $(m + 1)$-dimensional subspaces of even symmetric forms of degree 4d, at which nonnegativity can be checked at $(m - 1)$-points, i.e., points with at most $m - 1 \\in \\N$ distinct components, where $m$ is i"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.4241","kind":"arxiv","version":1},"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"}