{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,18]],"date-time":"2026-08-18T16:52:55Z","timestamp":1787071975282,"version":"build-2736575974"},"reference-count":14,"publisher":"Association for Computing Machinery (ACM)","issue":"4","license":[{"start":{"date-parts":[[2025,12,1]],"date-time":"2025-12-01T00:00:00Z","timestamp":1764547200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.acm.org\/publications\/policies\/publication-rights-and-licensing-policy"}],"content-domain":{"domain":["dl.acm.org"],"crossmark-restriction":true},"short-container-title":["ACM Commun. Comput. Algebra"],"published-print":{"date-parts":[[2025,12,1]]},"abstract":"<jats:p>\n                    A complete reduction\n                    <jats:italic toggle=\"yes\">\u03d5<\/jats:italic>\n                    for derivatives in a differential field\n                    <jats:italic toggle=\"yes\">F<\/jats:italic>\n                    is a linear idempotent on\n                    <jats:italic toggle=\"yes\">F<\/jats:italic>\n                    over its constant subfield whose kernel is equal to the subspace consisting of derivatives in\n                    <jats:italic toggle=\"yes\">F.<\/jats:italic>\n                    It enables us to decompose an element\n                    <jats:italic toggle=\"yes\">f<\/jats:italic>\n                    as the sum of a derivative and\n                    <jats:italic toggle=\"yes\">\u03d5<\/jats:italic>\n                    (\n                    <jats:italic toggle=\"yes\">f)<\/jats:italic>\n                    such that\n                    <jats:italic toggle=\"yes\">f<\/jats:italic>\n                    is a derivative in\n                    <jats:italic toggle=\"yes\">F<\/jats:italic>\n                    if and only if\n                    <jats:italic toggle=\"yes\">\u03d5<\/jats:italic>\n                    (\n                    <jats:italic toggle=\"yes\">f)<\/jats:italic>\n                    = 0.\n                  <\/jats:p>\n                  <jats:p>We outline a complete reduction algorithmically for derivatives in a transcendental Liouvillian extension of the field of rational functions. Typical examples for transcendental Liouvillian extensions are differential fields generated by (poly-)logarithmic functions, hyperexponential functions, as well as the logarithmic integral, the exponential integral and the error function. Such extensions may contain non-elementary and non-D-finite functions.<\/jats:p>","DOI":"10.1145\/3832046.3832051","type":"journal-article","created":{"date-parts":[[2026,8,18]],"date-time":"2026-08-18T16:12:06Z","timestamp":1787069526000},"page":"85-88","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":0,"title":["Complete Reduction for Derivatives in Transcendental Liouvillian Extensions"],"prefix":"10.1145","volume":"59","author":[{"given":"Shaoshi","family":"Chen","sequence":"first","affiliation":[{"name":"Key Lab of Mathematics Mechanization, AMSS, University of Chinese Academy of Sciences, Beijing, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Hao","family":"Du","sequence":"additional","affiliation":[{"name":"School of Mathematical Sciences, Beijing University of Posts and Telecommunications, Beijing, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yiman","family":"Gao","sequence":"additional","affiliation":[{"name":"Johannes Kepler University Linz, Research Institute for Symbolic Computation (RISC), Altenberger Stra\u00dfe, Linz, Austria"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Hui","family":"Huang","sequence":"additional","affiliation":[{"name":"School of Mathematics and Statistics, Fuzhou University, Fuzhou, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Wenqiao","family":"Li","sequence":"additional","affiliation":[{"name":"Key Lab of Mathematics Mechanization, AMSS, University of Chinese Academy of Sciences, Beijing, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Ziming","family":"Li","sequence":"additional","affiliation":[{"name":"Key Lab of Mathematics Mechanization, AMSS, University of Chinese Academy of Sciences, Beijing, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"320","published-online":{"date-parts":[[2026,8,18]]},"reference":[{"key":"e_1_2_1_1_1","doi-asserted-by":"publisher","DOI":"10.1145\/2465506.2465946"},{"key":"e_1_2_1_2_1","first-page":"102","volume-title":"Proceedings of ISSAC'18","author":"Bostan A.","year":"2018","unstructured":"A. Bostan, F. Chyzak, P. Lairez, and B. Salvy. Generalized Hermite reduction, creative telecoping and definite integration of D-finite functions. In Proceedings of ISSAC'18, pages 95\u2013102, ACM, 2018."},{"key":"e_1_2_1_3_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jsc.2016.01.002"},{"key":"e_1_2_1_4_1","volume-title":"Symbolic Integration I: Transcendental Functions","author":"Bronstein M.","year":"2005","unstructured":"M. Bronstein. Symbolic Integration I: Transcendental Functions. Springer-Verlag, Berlin, 2nd edition, 2005.","edition":"2"},{"key":"e_1_2_1_5_1","doi-asserted-by":"publisher","DOI":"10.1007\/s11424-024-3325-7"},{"key":"e_1_2_1_6_1","doi-asserted-by":"publisher","DOI":"10.1145\/3597066.3597092"},{"key":"e_1_2_1_7_1","doi-asserted-by":"publisher","DOI":"10.1145\/2930889.2930901"},{"key":"e_1_2_1_8_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jsc.2017.07.005"},{"key":"e_1_2_1_9_1","volume-title":"ACM","author":"Du H.","year":"2025","unstructured":"H. Du, Y. Gao, W. Li, and Z. Li. Complete reduction for derivatives in a primitive tower. To appear in Proceedings of ISSAC'25, ACM, 2025."},{"key":"e_1_2_1_10_1","unstructured":"Y. Gao. Additive Decomposition and Elementary Integration over Exponential Extensions. PhD. Thesis KLMM AMSS Chinese Academy of Sciences Beijing China 2024 (in Chinese)."},{"key":"e_1_2_1_11_1","volume-title":"Algorithms and Computation in Mathematics 30","author":"Kauers M.","year":"2023","unstructured":"M. Kauers. D-Finite Functions. Algorithms and Computation in Mathematics 30, Springer, 2023."},{"key":"e_1_2_1_12_1","unstructured":"C. Raab. Definite Integration in Differential Fields. PhD. Thesis RISC-Linz Johannes Kepler University Linz Austria."},{"key":"e_1_2_1_13_1","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9947-1969-0237477-8"},{"key":"e_1_2_1_14_1","first-page":"575","article-title":"Constructing reductions for creative telescoping. Applicable Algebra in Engineering","volume":"32","author":"van der Hoeven J.","year":"2021","unstructured":"J. van der Hoeven. Constructing reductions for creative telescoping. Applicable Algebra in Engineering, Communication and Computing, 32:575-602, 2021.","journal-title":"Communication and Computing"}],"container-title":["ACM Communications in Computer Algebra"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/dl.acm.org\/doi\/pdf\/10.1145\/3832046.3832051","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,18]],"date-time":"2026-08-18T16:12:35Z","timestamp":1787069555000},"score":1,"resource":{"primary":{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/3832046.3832051"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,12,1]]},"references-count":14,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2025,12,1]]}},"alternative-id":["10.1145\/3832046.3832051"],"URL":"https:\/\/doi.org\/10.1145\/3832046.3832051","relation":{},"ISSN":["1932-2232","1932-2240"],"issn-type":[{"value":"1932-2232","type":"print"},{"value":"1932-2240","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,12,1]]},"assertion":[{"value":"2026-08-18","order":3,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}