{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,13]],"date-time":"2026-02-13T10:20:37Z","timestamp":1770978037853,"version":"3.50.1"},"reference-count":0,"publisher":"Centre pour la Communication Scientifique Directe (CCSD)","license":[{"start":{"date-parts":[[2019,2,15]],"date-time":"2019-02-15T00:00:00Z","timestamp":1550188800000},"content-version":"am","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2019,2,15]],"date-time":"2019-02-15T00:00:00Z","timestamp":1550188800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2019,2,15]],"date-time":"2019-02-15T00:00:00Z","timestamp":1550188800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"accepted":{"date-parts":[[2025,3,31]]},"abstract":"<jats:p>We consider reasoning and minimization in systems of polynomial ordinary differential equations (ode's). The ring of multivariate polynomials is employed as a syntax for denoting system behaviours. We endow this set with a transition system structure based on the concept of Lie-derivative, thus inducing a notion of L-bisimulation. We prove that two states (variables) are L-bisimilar if and only if they correspond to the same solution in the ode's system. We then characterize L-bisimilarity algebraically, in terms of certain ideals in the polynomial ring that are invariant under Lie-derivation. This characterization allows us to develop a complete algorithm, based on building an ascending chain of ideals, for computing the largest L-bisimulation containing all valid identities that are instances of a user-specified template. A specific largest L-bisimulation can be used to build a reduced system of ode's, equivalent to the original one, but minimal among all those obtainable by linear aggregation of the original equations. A computationally less demanding approximate reduction and linearization technique is also proposed.<\/jats:p><jats:p>Comment: 27 pages, extended and revised version of FOSSACS 2017 paper<\/jats:p>","DOI":"10.23638\/lmcs-15(1:14)2019","type":"journal-article","created":{"date-parts":[[2025,4,3]],"date-time":"2025-04-03T17:34:23Z","timestamp":1743701663000},"source":"Crossref","is-referenced-by-count":3,"title":["Algebra, coalgebra, and minimization in polynomial differential equations"],"prefix":"10.23638","volume":"Volume 15, Issue 1","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-1972-7491","authenticated-orcid":false,"given":"Michele","family":"Boreale","sequence":"first","affiliation":[]}],"member":"25203","published-online":{"date-parts":[[2019,2,15]]},"container-title":["Logical Methods in Computer Science"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/arxiv.org\/pdf\/1710.08350v4","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/arxiv.org\/pdf\/1710.08350v4","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,4,3]],"date-time":"2025-04-03T17:34:23Z","timestamp":1743701663000},"score":1,"resource":{"primary":{"URL":"http:\/\/lmcs.episciences.org\/4009"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,2,15]]},"references-count":0,"URL":"https:\/\/doi.org\/10.23638\/lmcs-15(1:14)2019","relation":{"has-preprint":[{"id-type":"arxiv","id":"1710.08350v3","asserted-by":"subject"},{"id-type":"arxiv","id":"1710.08350v2","asserted-by":"subject"},{"id-type":"arxiv","id":"1710.08350v1","asserted-by":"subject"}],"is-same-as":[{"id-type":"arxiv","id":"1710.08350","asserted-by":"subject"},{"id-type":"doi","id":"10.48550\/arXiv.1710.08350","asserted-by":"subject"}]},"ISSN":["1860-5974"],"issn-type":[{"value":"1860-5974","type":"electronic"}],"subject":[],"published":{"date-parts":[[2019,2,15]]},"article-number":"4009"}}