{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,6,19]],"date-time":"2025-06-19T04:59:04Z","timestamp":1750309144704,"version":"3.41.0"},"reference-count":14,"publisher":"Association for Computing Machinery (ACM)","issue":"2","license":[{"start":{"date-parts":[[2023,6,1]],"date-time":"2023-06-01T00:00:00Z","timestamp":1685577600000},"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":[[2023,6]]},"abstract":"<jats:p>A function is differentially algebraic (or simply D-algebraic) if there is a polynomial relationship between some of its derivatives and the indeterminate variable. Many functions in the sciences, such as Mathieu functions, the Weierstrass elliptic functions, and holonomic or D-finite functions are D-algebraic. These functions form a field, and are closed under composition, taking functional inverse, and derivation. We present implementation for each underlying operation. We also give a systematic way for computing an algebraic differential equation from a linear differential equation with D-finite function coefficients.<\/jats:p>\n          <jats:p>Each command is a feature of our Maple package NLDE available at https:\/\/mathrepo.mis.mpg.de\/DAlgebraicFunctions\/NLDEpackage.<\/jats:p>","DOI":"10.1145\/3614408.3614415","type":"journal-article","created":{"date-parts":[[2023,8,7]],"date-time":"2023-08-07T16:06:15Z","timestamp":1691424375000},"page":"51-56","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":3,"title":["Operations for D-Algebraic Functions"],"prefix":"10.1145","volume":"57","author":[{"given":"Bertrand Teguia","family":"Tabuguia","sequence":"first","affiliation":[{"name":"Nonlinear Algebra Group, Max Planck Institute for Mathematics in the Sciences\/ MPI for Software Systems, Leipzig\/ Saarbr\u00fccken, Germany"}]}],"member":"320","published-online":{"date-parts":[[2023,8,7]]},"reference":[{"key":"e_1_2_1_1_1","doi-asserted-by":"publisher","DOI":"10.1137\/141000671"},{"key":"e_1_2_1_2_1","unstructured":"Boulier F.: DifferentialAlgebra project: A C library for differential elimination. Available at https:\/\/codeberg.org\/francois.boulier\/DifferentialAlgebra  Boulier F.: DifferentialAlgebra project: A C library for differential elimination. Available at https:\/\/codeberg.org\/francois.boulier\/DifferentialAlgebra"},{"key":"e_1_2_1_3_1","first-page":"16","volume":"70","author":"Fevola C.","year":"2022","unstructured":"Fevola , C. , G\u00f6rgen , C. : The mathematical research-data repository MathRepo. Computeralgebra Rundbrief 70 , 16 -- 20 ( 2022 ) Fevola, C., G\u00f6rgen, C.: The mathematical research-data repository MathRepo. Computeralgebra Rundbrief 70, 16--20 (2022)","journal-title":"MathRepo. Computeralgebra Rundbrief"},{"issue":"2","key":"e_1_2_1_4_1","doi-asserted-by":"crossref","first-page":"119","DOI":"10.1016\/0001-8708(85)90113-6","volume":"58","author":"Harris W.A.","year":"1985","unstructured":"Harris Jr , W.A. , Sibuya , Y. : The reciprocals of solutions of linear ordinary differential equations. Advances in Mathematics 58 ( 2 ), 119 -- 132 ( 1985 ) Harris Jr, W.A., Sibuya, Y.: The reciprocals of solutions of linear ordinary differential equations. Advances in Mathematics 58(2), 119--132 (1985)","journal-title":"Advances in Mathematics"},{"key":"e_1_2_1_5_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jsc.2011.01.004"},{"key":"e_1_2_1_6_1","first-page":"1","volume-title":"Symbolic and Numerical Scientific Computation: Second International Conference, SNSC 2001","author":"Hubert E.","year":"2001","unstructured":"Hubert , E. : Notes on triangular sets and triangulation-decomposition algorithms i: Polynomial systems . In: Symbolic and Numerical Scientific Computation: Second International Conference, SNSC 2001 , Hagenberg, Austria, September 12--14 , 2001 . Revised Papers. pp. 1 -- 39 . Springer (2003) Hubert, E.: Notes on triangular sets and triangulation-decomposition algorithms i: Polynomial systems. In: Symbolic and Numerical Scientific Computation: Second International Conference, SNSC 2001, Hagenberg, Austria, September 12--14, 2001. Revised Papers. pp. 1--39. Springer (2003)"},{"key":"e_1_2_1_7_1","doi-asserted-by":"publisher","DOI":"10.1145\/3208976.3209009"},{"key":"e_1_2_1_8_1","volume-title":"Singer","author":"Jim\u00e9nez-Pastor A.","year":"2027","unstructured":"Jim\u00e9nez-Pastor , A. , Pillwein , V. , Singer , M.F. : Some structural results on dn-finite functions. Advances in Applied Mathematics 117, 10 2027 (2020) Jim\u00e9nez-Pastor, A., Pillwein, V., Singer, M.F.: Some structural results on dn-finite functions. Advances in Applied Mathematics 117, 102027 (2020)"},{"key":"e_1_2_1_9_1","unstructured":"Manssour Ait El R. Sattelberger A.L. Teguia Tabuguia B.: D-algebraic functions. arXiv preprint arXiv:2301.02512 (2023)  Manssour Ait El R. Sattelberger A.L. Teguia Tabuguia B.: D-algebraic functions. arXiv preprint arXiv:2301.02512 (2023)"},{"key":"e_1_2_1_10_1","volume-title":"Scanlon","author":"Ovchinnikov A.","year":"2004","unstructured":"Ovchinnikov , A. , Pillay , A. , Pogudin , G. , Scanlon , T. : Computing all identifiable functions for ODE models. arXiv preprint arXiv: 2004 .07774 (2020) Ovchinnikov, A., Pillay, A., Pogudin, G., Scanlon, T.: Computing all identifiable functions for ODE models. arXiv preprint arXiv:2004.07774 (2020)"},{"key":"e_1_2_1_11_1","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-319-11445-3"},{"key":"e_1_2_1_12_1","volume-title":"Guessing with quadratic differential equations","author":"Teguia Tabuguia B.","year":"2022","unstructured":"Teguia Tabuguia , B. : Guessing with quadratic differential equations ( 2022 ), Software Demo at ISSAC '22. Teguia Tabuguia, B.: Guessing with quadratic differential equations (2022), Software Demo at ISSAC'22."},{"key":"e_1_2_1_13_1","unstructured":"Teguia Tabuguia B.: Arithmetic of D-algebraic functions. arXiv preprint arXiv:2305.00702 (2023)  Teguia Tabuguia B.: Arithmetic of D-algebraic functions. arXiv preprint arXiv:2305.00702 (2023)"},{"issue":"1","key":"e_1_2_1_14_1","doi-asserted-by":"crossref","DOI":"10.5206\/mt.v2i1.14315","volume":"2","author":"Teguia Tabuguia B.","year":"2022","unstructured":"Teguia Tabuguia , B. , Koepf , W. : On the representation of non-holonomic univariate power series. Maple Trans. 2 ( 1 ) ( 2022 ), article 14315 Teguia Tabuguia, B., Koepf, W.: On the representation of non-holonomic univariate power series. Maple Trans. 2(1) (2022), article 14315","journal-title":"Maple Trans."}],"container-title":["ACM Communications in Computer Algebra"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/3614408.3614415","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/dl.acm.org\/doi\/pdf\/10.1145\/3614408.3614415","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,6,18]],"date-time":"2025-06-18T22:50:29Z","timestamp":1750287029000},"score":1,"resource":{"primary":{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/3614408.3614415"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,6]]},"references-count":14,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2023,6]]}},"alternative-id":["10.1145\/3614408.3614415"],"URL":"https:\/\/doi.org\/10.1145\/3614408.3614415","relation":{},"ISSN":["1932-2240"],"issn-type":[{"type":"print","value":"1932-2240"}],"subject":[],"published":{"date-parts":[[2023,6]]},"assertion":[{"value":"2023-08-07","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}