{"paper":{"title":"Test Sets for Nonnegativity of Polynomials Invariant under a Finite Reflection Group","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG","math.OC"],"primary_cat":"math.CO","authors_text":"Jose Acevedo, Mauricio Velasco","submitted_at":"2015-02-01T13:33:32Z","abstract_excerpt":"A set $S\\subset \\mathbb{R}^n$ is a nonnegativity witness for a set $U$ of real homogeneous polynomials if $F$ in $U$ is nonnegative on $\\mathbb{R}^n$ if and only if it is nonnegative at all points of $S$. We prove that the union of the hyperplanes perpendicular to the elements of a root system $\\Phi\\subseteq \\mathbb{R}^n$ is a witness set for nonnegativity of forms of low degree which are invariant under the reflection group defined by $\\Phi$. We prove that our bound for the degree is sharp for all reflection groups which contain multiplication by $-1$. We then characterize subspaces of forms "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.00252","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"}