{"paper":{"title":"A perturbed differential resultant based implicitization algorithm for linear DPPEs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Sonia L. Rueda","submitted_at":"2010-03-23T11:03:55Z","abstract_excerpt":"Let $\\bbK$ be an ordinary differential field with derivation $\\partial$. Let $\\cP$ be a system of $n$ linear differential polynomial parametric equations in $n-1$ differential parameters with implicit ideal $\\id$. Given a nonzero linear differential polynomial $A$ in $\\id$ we give necessary and sufficient conditions on $A$ for $\\cP$ to be $n-1$ dimensional. We prove the existence of a linear perturbation $\\cP_{\\phi}$ of $\\cP$ so that the linear complete differential resultant $\\dcres_{\\phi}$ associated to $\\cP_{\\phi}$ is nonzero. A nonzero linear differential polynomial in $\\id$ is obtained fr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1003.4375","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"}