{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,6,19]],"date-time":"2025-06-19T05:05:25Z","timestamp":1750309525313,"version":"3.41.0"},"reference-count":5,"publisher":"Association for Computing Machinery (ACM)","issue":"2","license":[{"start":{"date-parts":[[2024,6,1]],"date-time":"2024-06-01T00:00:00Z","timestamp":1717200000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.acm.org\/publications\/policies\/copyright_policy#Background"}],"content-domain":{"domain":["dl.acm.org"],"crossmark-restriction":true},"short-container-title":["ACM Commun. Comput. Algebra"],"published-print":{"date-parts":[[2024,6]]},"abstract":"<jats:p>\n            We present a Mathematica package to help investigate the existence of Darboux polynomials for (polynomial) ordinary differential equations (ODE). If we denote the derivation encoded by a given ODE by\n            <jats:italic>D<\/jats:italic>\n            , the package infers and propagates necessary conditions for a\n            <jats:italic>generic<\/jats:italic>\n            ansatz\n            <jats:italic>p<\/jats:italic>\n            to be a Darboux polynomial for\n            <jats:italic>D.<\/jats:italic>\n            By generic, we mean that not only the coefficients of\n            <jats:italic>p<\/jats:italic>\n            are unknown, but also the exponent\n            <jats:italic>d<\/jats:italic>\n            of its leading monomial. We present some examples for which the package produces a formal certificate proving the nonexistence of nontrivial Darboux polynomials. The package complements well standard algorithms that search for Darboux polynomials up to a fixed bound on the total degree.\n          <\/jats:p>","DOI":"10.1145\/3712023.3712027","type":"journal-article","created":{"date-parts":[[2025,1,10]],"date-time":"2025-01-10T16:56:37Z","timestamp":1736528197000},"page":"31-34","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":0,"title":["A Mathematica Package for Certifying the Nonexistence of Darboux Polynomials"],"prefix":"10.1145","volume":"58","author":[{"given":"Maxime","family":"Bridoux","sequence":"first","affiliation":[{"name":"Inria, France"}]},{"given":"Khalil","family":"Ghorbal","sequence":"additional","affiliation":[{"name":"Inria, France"}]}],"member":"320","published-online":{"date-parts":[[2025,1,10]]},"reference":[{"key":"e_1_2_1_1_1","volume-title":"On bounding the degree of irreducible darboux polynomials. Submitted to ISSAC","author":"Ghorbal Khalil","year":"2024","unstructured":"[GB24] Khalil Ghorbal and Maxime Bridoux. On bounding the degree of irreducible darboux polynomials. Submitted to ISSAC 2024., 2024."},{"key":"e_1_2_1_2_1","doi-asserted-by":"publisher","DOI":"10.1142\/3846"},{"key":"e_1_2_1_3_1","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127402004474"},{"key":"e_1_2_1_4_1","doi-asserted-by":"publisher","DOI":"10.1006\/jsco.1993.1057"},{"key":"e_1_2_1_5_1","doi-asserted-by":"publisher","DOI":"10.1007\/3-540-15984-3_321"}],"container-title":["ACM Communications in Computer Algebra"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/3712023.3712027","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/dl.acm.org\/doi\/pdf\/10.1145\/3712023.3712027","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,6,19]],"date-time":"2025-06-19T01:18:10Z","timestamp":1750295890000},"score":1,"resource":{"primary":{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/3712023.3712027"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,6]]},"references-count":5,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2024,6]]}},"alternative-id":["10.1145\/3712023.3712027"],"URL":"https:\/\/doi.org\/10.1145\/3712023.3712027","relation":{},"ISSN":["1932-2232","1932-2240"],"issn-type":[{"type":"print","value":"1932-2232"},{"type":"electronic","value":"1932-2240"}],"subject":[],"published":{"date-parts":[[2024,6]]},"assertion":[{"value":"2025-01-10","order":3,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}