{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,6,18]],"date-time":"2025-06-18T04:14:09Z","timestamp":1750220049373,"version":"3.41.0"},"reference-count":15,"publisher":"Association for Computing Machinery (ACM)","issue":"2","license":[{"start":{"date-parts":[[2022,6,1]],"date-time":"2022-06-01T00:00:00Z","timestamp":1654041600000},"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":[[2022,6]]},"abstract":"<jats:p>\n            Linear recurrence equations with constant coefficients define the power series coefficients of rational functions. However, one usually prefers to have an explicit formula for the sequence of coefficients, provided that such a formula is \"simple\" enough. Simplicity is related to the compactness of the formula due to the presence of algebraic numbers: \"the smaller, the simpler\". This poster showcases the capacity of recent updates on the Formal Power Series (FPS) algorithm, implemented in Maxima and Maple (convert\/FormalPowerSeries), to find simple formulas for sequences like those from https:\/\/oeis.org\/A307717, https:\/\/oeis.org\/A226782, or https:\/\/oeis.org\/A226784 by computing power series representations of their correctly guessed generating functions. We designed the algorithm for the more general context of univariate\n            <jats:italic>P<\/jats:italic>\n            -recursive sequences. Our implementations are available at http:\/\/www.mathematik.uni-kassel.de\/~bteguia\/FPS_webpage\/FPS.htm\n          <\/jats:p>","DOI":"10.1145\/3572867.3572873","type":"journal-article","created":{"date-parts":[[2022,11,24]],"date-time":"2022-11-24T00:37:32Z","timestamp":1669250252000},"page":"46-50","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":1,"title":["FPS in action"],"prefix":"10.1145","volume":"56","author":[{"given":"Bertrand Teguia","family":"Tabuguia","sequence":"first","affiliation":[{"name":"Nonlinear Algebra Group, Leipzig, Germany"}]},{"given":"Wolfram","family":"Koepf","sequence":"additional","affiliation":[{"name":"University of Kassel, Kassel, Germany"}]}],"member":"320","published-online":{"date-parts":[[2022,11,23]]},"reference":[{"key":"e_1_2_1_1_1","doi-asserted-by":"publisher","DOI":"10.1007\/s00200-005-0192-x"},{"key":"e_1_2_1_2_1","doi-asserted-by":"publisher","DOI":"10.1145\/355826.355835"},{"key":"e_1_2_1_3_1","doi-asserted-by":"publisher","DOI":"10.1007\/s11786-012-0107-8"},{"key":"e_1_2_1_4_1","volume-title":"Guessing with Little Data. arXiv preprint arXiv:2202.07966","author":"Kauers Manuel","year":"2022","unstructured":"Manuel Kauers and Christoph Koutschan . 2022. Guessing with Little Data. arXiv preprint arXiv:2202.07966 ( 2022 ). Manuel Kauers and Christoph Koutschan. 2022. Guessing with Little Data. arXiv preprint arXiv:2202.07966 (2022)."},{"key":"e_1_2_1_5_1","doi-asserted-by":"publisher","DOI":"10.1145\/3377006.3377017"},{"key":"e_1_2_1_6_1","doi-asserted-by":"publisher","DOI":"10.1016\/S0747-7171(10)80012-4"},{"key":"e_1_2_1_7_1","doi-asserted-by":"publisher","DOI":"10.1016\/0747-7171(92)90038-6"},{"key":"e_1_2_1_8_1","doi-asserted-by":"publisher","DOI":"10.1145\/164081.164087"},{"key":"e_1_2_1_9_1","doi-asserted-by":"publisher","DOI":"10.1023\/A:1014880918779"},{"key":"e_1_2_1_10_1","doi-asserted-by":"publisher","DOI":"10.1145\/178365.178368"},{"volume-title":"Power Series Representations of Hypergeometric Types and Non-Holonomic Functions in Computer Algebra. Ph. D. Dissertation","author":"Tabuguia Bertrand Teguia","key":"e_1_2_1_11_1","unstructured":"Bertrand Teguia Tabuguia . 2020. Power Series Representations of Hypergeometric Types and Non-Holonomic Functions in Computer Algebra. Ph. D. Dissertation . University of Kassel , https:\/\/kobra.uni-kassel.de\/handle\/123456789\/11598. Bertrand Teguia Tabuguia. 2020. Power Series Representations of Hypergeometric Types and Non-Holonomic Functions in Computer Algebra. Ph. D. Dissertation. University of Kassel, https:\/\/kobra.uni-kassel.de\/handle\/123456789\/11598."},{"volume-title":"4th International Conference \"Computer Algebra\"","author":"Tabuguia Bertrand Teguia","key":"e_1_2_1_12_1","unstructured":"Bertrand Teguia Tabuguia and W Koepf . 2021a. Hypergeometric type power series . In 4th International Conference \"Computer Algebra\" . Dorodnicyn Computing Center, Federal Research Center \"Computer Science and Control\" of Russian Academy of Sciences (CCAS) and Peoples Friendship University of Russia , 105--108. Bertrand Teguia Tabuguia and W Koepf. 2021a. Hypergeometric type power series. In 4th International Conference \"Computer Algebra\". Dorodnicyn Computing Center, Federal Research Center \"Computer Science and Control\" of Russian Academy of Sciences (CCAS) and Peoples Friendship University of Russia, 105--108."},{"key":"e_1_2_1_13_1","volume-title":"Maple in Mathematics Education and Research. MC","author":"Tabuguia Bertrand Teguia","year":"2020","unstructured":"Bertrand Teguia Tabuguia and Wolfram Koepf . 2021b. Power series representations of hypergeometric type functions . In Maple in Mathematics Education and Research. MC 2020 . Editors : Corless R., Gerhard J., Kotsireas I., Communications in Computer and Information Science, Springer , 376--393. Bertrand Teguia Tabuguia and Wolfram Koepf. 2021b. Power series representations of hypergeometric type functions. In Maple in Mathematics Education and Research. MC 2020. Editors: Corless R., Gerhard J., Kotsireas I., Communications in Computer and Information Science, Springer, 376--393."},{"key":"e_1_2_1_14_1","doi-asserted-by":"publisher","DOI":"10.1134\/S0361768822020104"},{"key":"e_1_2_1_15_1","first-page":"1","article-title":"Finite singularities and hypergeometric solutions of linear recurrence equations","volume":"139","author":"Hoeij Mark Van","year":"1999","unstructured":"Mark Van Hoeij . 1999 . Finite singularities and hypergeometric solutions of linear recurrence equations . J. Pure Appl. Algebra 139 , 1 -- 3 (1999), 109--131. Mark Van Hoeij. 1999. Finite singularities and hypergeometric solutions of linear recurrence equations. J. Pure Appl. Algebra 139, 1--3 (1999), 109--131.","journal-title":"J. Pure Appl. Algebra"}],"container-title":["ACM Communications in Computer Algebra"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/3572867.3572873","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/dl.acm.org\/doi\/pdf\/10.1145\/3572867.3572873","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,6,17]],"date-time":"2025-06-17T18:08:10Z","timestamp":1750183690000},"score":1,"resource":{"primary":{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/3572867.3572873"}},"subtitle":["an easy way to find explicit formulas for interlaced hypergeometric sequences"],"short-title":[],"issued":{"date-parts":[[2022,6]]},"references-count":15,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2022,6]]}},"alternative-id":["10.1145\/3572867.3572873"],"URL":"https:\/\/doi.org\/10.1145\/3572867.3572873","relation":{},"ISSN":["1932-2240"],"issn-type":[{"type":"print","value":"1932-2240"}],"subject":[],"published":{"date-parts":[[2022,6]]},"assertion":[{"value":"2022-11-23","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}