{"paper":{"title":"The expansion of real forms on the simplex and applications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.SC"],"primary_cat":"math.AG","authors_text":"Jia Xu, Jingzhong Zhang, Yong Yao","submitted_at":"2012-09-14T02:49:19Z","abstract_excerpt":"If n points B_1,---,B_n$ in the standard simplex \\Delta_n are affinely independent, then they can span an (n-1)-simplex denoted by \\Lambda=Con(B_1,---,B_n). Here \\Lambda corresponds to an n*n matrix [\\Lambda] whose columns are B_1,---,B_n. In this paper, we firstly proved that if \\Lambda of diameter sufficiently small contains a point $P$, and f(P)>0 (<0) for a form f in R[X], then the coefficients of f([\\Lambda] X) are all positive (negative). Next, as an application of this result, a necessary and sufficient condition for determining the real zeros on \\Delta_n of a system of homogeneous alge"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.3080","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"}