{"paper":{"title":"Computing with Polynomial Ordinary Differential Equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CC","authors_text":"Amaury Pouly, Daniel Gra\\c{c}a, Olivier Bournez","submitted_at":"2016-01-21T15:47:59Z","abstract_excerpt":"In 1941, Claude Shannon introduced the General Purpose Analog Computer(GPAC) as a mathematical model of Differential Analysers, that is to say as a model of continuous-time analog (mechanical, and later one electronic) machines of that time.\n  Following Shannon's arguments, functions generated by GPACs must be differentially algebraic. As it is known that some computable functions like Euler's $\\Gamma(x)=\\int_{0}^{\\infty}t^{x-1}e^{-t}dt$ or Riemann's Zeta function $\\zeta(x)=\\sum_{k=0}^\\infty \\frac1{k^x}$ are not differentially algebraic, this argument has been often used to demonstrate in the "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.05683","kind":"arxiv","version":3},"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"}