{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,6,19]],"date-time":"2025-06-19T05:04:29Z","timestamp":1750309469935,"version":"3.41.0"},"reference-count":17,"publisher":"Association for Computing Machinery (ACM)","issue":"3","license":[{"start":{"date-parts":[[2024,9,1]],"date-time":"2024-09-01T00:00:00Z","timestamp":1725148800000},"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":[[2024,9]]},"abstract":"<jats:p>We present in this extended abstract some ongoing work which has been presented in [13]. This extended abstract contains no new results w.r.t. [13], and is intended to present our prototype integral_elimination for performing Integral Elimination. This prototype is a first step to the generalization of the differential elimination algorithms for the integral case, where the differentiation is replaced by an integration operator.<\/jats:p>\n          <jats:p>Our approach is incomplete and still needs an important theoretical development. However it is already sufficient to handle nontrivial examples The originality of our approach consists in using new types of reductions and introducing exponential terms during the computations. Our prototype has been implemented in Python using SymPy.<\/jats:p>\n          <jats:p>We briefly motivate the context, and present some examples treated by our prototype.<\/jats:p>","DOI":"10.1145\/3717582.3717592","type":"journal-article","created":{"date-parts":[[2025,2,11]],"date-time":"2025-02-11T20:41:51Z","timestamp":1739306511000},"page":"93-96","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":0,"title":["A Prototype for Integral Elimination"],"prefix":"10.1145","volume":"58","author":[{"given":"Fran\u00e7ois","family":"Lemaire","sequence":"first","affiliation":[{"name":"Univ. Lille, CNRS, Centrale Lille, UMR, CRIStAL, Lille, France"}]},{"given":"Louis","family":"Roussel","sequence":"additional","affiliation":[{"name":"Univ. Lille, CNRS, Centrale Lille, UMR, CRIStAL, Lille, France"}]}],"member":"320","published-online":{"date-parts":[[2025,2,11]]},"reference":[{"key":"e_1_2_1_1_1","doi-asserted-by":"publisher","DOI":"10.1007\/s11202-010-0097-1"},{"key":"e_1_2_1_2_1","volume-title":"The DifferentialAlgebra project","author":"Boulier Fran\u00e7ois","year":"2023","unstructured":"Fran\u00e7ois Boulier. The DifferentialAlgebra project. 2023. url: https:\/\/codeberg.org\/francois.boulier\/DifferentialAlgebra."},{"key":"e_1_2_1_3_1","article-title":"Additive Normal Forms and Integration of Differential Fractions","author":"Fran\u00e7ois Boulier","year":"2016","unstructured":"Fran\u00e7ois Boulier et al. \"Additive Normal Forms and Integration of Differential Fractions\". In: Journal of Symbolic Computation (2016). url: https:\/\/hal.archives-ouvertes.fr\/hal-01245378.","journal-title":"Journal of Symbolic Computation ("},{"key":"e_1_2_1_4_1","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-030-38356-5_6"},{"key":"e_1_2_1_5_1","doi-asserted-by":"publisher","DOI":"10.1023\/B:NUMA.0000005366.05704.88"},{"key":"e_1_2_1_6_1","volume-title":"Differential elimination for dynamical models via projections with applications to structural identifiability","author":"Ruiwen Dong","year":"2022","unstructured":"Ruiwen Dong et al. Differential elimination for dynamical models via projections with applications to structural identifiability. 2022. arXiv: 2111.00991 [math.AG]."},{"key":"e_1_2_1_7_1","doi-asserted-by":"publisher","DOI":"10.1515\/form.1989.1.227"},{"key":"e_1_2_1_8_1","first-page":"1","article-title":"Constructions of Free Commutative Integro-Differential Algebras","volume":"8372","author":"Gao Xing","year":"2014","unstructured":"Xing Gao and Li Guo. \"Constructions of Free Commutative Integro-Differential Algebras\". In: Algebraic and Algorithmic Aspects of Differential and Integral Operators. Ed. by M. Barkatou et al. Vol. 8372. LNCS. 2014, pp. 1--22.","journal-title":"Ed. by M. Barkatou et al."},{"key":"e_1_2_1_9_1","volume-title":"Rota's program on algebraic operators, rewriting systems and Gr\u00f6bner-Shirshov bases","author":"Gao Xing","year":"2021","unstructured":"Xing Gao, Li Guo, and Huhu Zhang. Rota's program on algebraic operators, rewriting systems and Gr\u00f6bner-Shirshov bases. 2021. arXiv: 2108.11823 [math.RA]."},{"key":"e_1_2_1_10_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.cpc.2018.07.025"},{"key":"e_1_2_1_11_1","volume-title":"An Introduction to Rota-Baxter Algebra (vol. 4 in the Surveys of Modern Mathematics series). English. Paperback","author":"Guo Li","year":"2012","unstructured":"Li Guo. An Introduction to Rota-Baxter Algebra (vol. 4 in the Surveys of Modern Mathematics series). English. Paperback. International Press of Boston, Incorporated, Oct. 15, 2012, p. 238. isbn: 978-1571462534."},{"key":"e_1_2_1_12_1","first-page":"446","volume-title":"Acad. Press","author":"Kolchin Ellis Robert","year":"1973","unstructured":"Ellis Robert Kolchin. Differential algebra and algebraic groups. Acad. Press, 1973, p. 446. isbn: 9780080873695."},{"key":"e_1_2_1_13_1","unstructured":"Fran\u00e7ois Lemaire and Louis Roussel. \"Contribution to Integral Elimination\". To appear in CASC'24. url: https:\/\/hal.science\/hal-04570612."},{"key":"e_1_2_1_14_1","volume-title":"to appear in Maple Transactions","author":"Lemaire Fran\u00e7ois","year":"2024","unstructured":"Fran\u00e7ois Lemaire and Louis Roussel. \"Parameter Estimation Using Integral Equations\". to appear in Maple Transactions. 2024. url: https:\/\/hal.science\/hal-04560846."},{"key":"e_1_2_1_15_1","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-030-38356-5_3"},{"key":"e_1_2_1_16_1","doi-asserted-by":"publisher","DOI":"10.1090\/coll\/033"},{"key":"e_1_2_1_17_1","doi-asserted-by":"publisher","DOI":"10.1145\/1390768.1390805"}],"container-title":["ACM Communications in Computer Algebra"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/3717582.3717592","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/dl.acm.org\/doi\/pdf\/10.1145\/3717582.3717592","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,6,19]],"date-time":"2025-06-19T01:17:15Z","timestamp":1750295835000},"score":1,"resource":{"primary":{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/3717582.3717592"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,9]]},"references-count":17,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2024,9]]}},"alternative-id":["10.1145\/3717582.3717592"],"URL":"https:\/\/doi.org\/10.1145\/3717582.3717592","relation":{},"ISSN":["1932-2232","1932-2240"],"issn-type":[{"type":"print","value":"1932-2232"},{"type":"electronic","value":"1932-2240"}],"subject":[],"published":{"date-parts":[[2024,9]]},"assertion":[{"value":"2025-02-11","order":3,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}