{"paper":{"title":"Effective Differential Nullstellensatz for Ordinary DAE Systems with Constant Coefficients","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.SC"],"primary_cat":"math.AC","authors_text":"Gabriela Jeronimo, Lisi D'Alfonso, Pablo Solern\\'o","submitted_at":"2013-05-27T19:14:14Z","abstract_excerpt":"We give upper bounds for the differential Nullstellensatz in the case of ordinary systems of differential algebraic equations over any field of constants $K$ of characteristic $0$. Let $\\vec{x}$ be a set of $n$ differential variables, $\\vec{f}$ a finite family of differential polynomials in the ring $K\\{\\vec{x}\\}$ and $f\\in K\\{\\vec{x}\\}$ another polynomial which vanishes at every solution of the differential equation system $\\vec{f}=0$ in any differentially closed field containing $K$. Let $d:=\\max\\{\\deg(\\vec{f}), \\deg(f)\\}$ and $\\epsilon:=\\max\\{2,{\\rm{ord}}(\\vec{f}), {\\rm{ord}}(f)\\}$. We show"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.6298","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"}