{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,31]],"date-time":"2025-10-31T20:11:55Z","timestamp":1761941515882,"version":"build-2065373602"},"publisher-location":"Cham","reference-count":29,"publisher":"Springer Nature Switzerland","isbn-type":[{"value":"9783032096449","type":"print"},{"value":"9783032096456","type":"electronic"}],"license":[{"start":{"date-parts":[[2025,11,1]],"date-time":"2025-11-01T00:00:00Z","timestamp":1761955200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2025,11,1]],"date-time":"2025-11-01T00:00:00Z","timestamp":1761955200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2026]]},"DOI":"10.1007\/978-3-032-09645-6_20","type":"book-chapter","created":{"date-parts":[[2025,10,31]],"date-time":"2025-10-31T20:06:52Z","timestamp":1761941212000},"page":"380-400","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Parallel Computation of\u00a0the\u00a0Power Series Solutions to\u00a0Linear Ordinary Differential Equations"],"prefix":"10.1007","author":[{"ORCID":"https:\/\/orcid.org\/0009-0004-6437-4412","authenticated-orcid":false,"given":"Greg Alejandro","family":"Solis-Reyes","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3011-0756","authenticated-orcid":false,"given":"Marc","family":"Moreno Maza","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1294-9710","authenticated-orcid":false,"given":"Alexander","family":"Brandt","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2025,11,1]]},"reference":[{"key":"20_CR1","unstructured":"Asadi, M., et al.: Basic Polynomial Algebra Subprograms (BPAS) (2021). http:\/\/www.bpaslib.org\/"},{"key":"20_CR2","series-title":"Communications in Computer and Information Science","doi-asserted-by":"publisher","first-page":"48","DOI":"10.1007\/978-3-030-81698-8_4","volume-title":"Maple in Mathematics Education and Research","author":"M Asadi","year":"2021","unstructured":"Asadi, M., Brandt, A., Kazemi, M., Moreno\u00a0Maza, M., Postma, E.J.: Multivariate power series in maple. In: Corless, R.M., Gerhard, J., Kotsireas, I.S. (eds.) MC 2020. CCIS, vol. 1414, pp. 48\u201366. Springer, Cham (2021). https:\/\/doi.org\/10.1007\/978-3-030-81698-8_4"},{"issue":"5","key":"20_CR3","doi-asserted-by":"publisher","first-page":"441","DOI":"10.3390\/math7050441","volume":"7","author":"M Asadi","year":"2019","unstructured":"Asadi, M., Brandt, A., Moir, R.H.C., Maza, M.M.: Algorithms and data structures for sparse polynomial arithmetic. Mathematics 7(5), 441 (2019)","journal-title":"Mathematics"},{"key":"20_CR4","unstructured":"Bostan, A., Chyzak, F., Ollivier, F., Salvy, B., Schost, \u00c9., Sedoglavic, A.: Fast computation of power series solutions of systems of differential equations. In: Bansal, N., Pruhs, K., Stein, C. (eds.) Proceedings of the Eighteenth Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2007, New Orleans, Louisiana, USA, 7\u20139 January 2007, pp. 1012\u20131021. SIAM (2007)"},{"key":"20_CR5","unstructured":"Brandt, A.: The Design and Implementation of a High-Performance Polynomial System Solver. Ph.D. thesis, Western University, London, Canada (2022)"},{"key":"20_CR6","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"108","DOI":"10.1007\/978-3-030-60026-6_7","volume-title":"Computer Algebra in Scientific Computing","author":"A Brandt","year":"2020","unstructured":"Brandt, A., Kazemi, M., Moreno-Maza, M.: Power series arithmetic with the BPAS library. In: Boulier, F., England, M., Sadykov, T.M., Vorozhtsov, E.V. (eds.) CASC 2020. LNCS, vol. 12291, pp. 108\u2013128. Springer, Cham (2020). https:\/\/doi.org\/10.1007\/978-3-030-60026-6_7"},{"key":"20_CR7","volume-title":"Introduction to Algorithms","author":"TH Cormen","year":"2022","unstructured":"Cormen, T.H., Leiserson, C.E., Rivest, R.L., Stein, C.: Introduction to Algorithms, 4th edn. MIT Press, Cambridge (2022)","edition":"4"},{"key":"20_CR8","doi-asserted-by":"crossref","unstructured":"Fischer, G.: Plane Algebraic Curves. AMS (2001)","DOI":"10.1090\/stml\/015"},{"key":"20_CR9","doi-asserted-by":"crossref","unstructured":"Frigo, M., Leiserson, C.E., Randall, K.H.: The implementation of the Cilk-5 multithreaded language. In: Proceedings of PLDI, pp. 212\u2013223 (1998)","DOI":"10.1145\/277650.277725"},{"key":"20_CR10","doi-asserted-by":"crossref","unstructured":"Frigo, M., Leiserson, C.E., Prokop, H., Ramachandran, S.: Cache-oblivious algorithms. ACM Trans. Algor. 8(1) (2012)","DOI":"10.1145\/2071379.2071383"},{"key":"20_CR11","unstructured":"Granlund, T., the GMP development team: GNU MP: The GNU Multiple Precision Arithmetic Library (version 6.2.0) (2025). http:\/\/gmplib.org"},{"issue":"6","key":"20_CR12","doi-asserted-by":"publisher","first-page":"415","DOI":"10.1007\/s00200-003-0144-2","volume":"14","author":"G Hanrot","year":"2004","unstructured":"Hanrot, G., Quercia, M., Zimmermann, P.: The middle product algorithm I. Appl. Algebra Eng. Commun. Comput. 14(6), 415\u2013438 (2004)","journal-title":"Appl. Algebra Eng. Commun. Comput."},{"issue":"9","key":"20_CR13","doi-asserted-by":"publisher","first-page":"824","DOI":"10.1080\/00029890.1989.11972289","volume":"96","author":"IH Herron","year":"1989","unstructured":"Herron, I.H.: The radius of convergence of power series solutions to linear differential equations. Am. Math. Mon. 96(9), 824\u2013827 (1989)","journal-title":"Am. Math. Mon."},{"issue":"6","key":"20_CR14","doi-asserted-by":"publisher","first-page":"479","DOI":"10.1006\/jsco.2002.0562","volume":"34","author":"J van der Hoeven","year":"2002","unstructured":"van der Hoeven, J.: Relax, but don\u2019t be too lazy. J. Symb. Comput. 34(6), 479\u2013542 (2002)","journal-title":"J. Symb. Comput."},{"key":"20_CR15","unstructured":"van\u00a0der Hoeven, J., Lecerf, G.: Mathemagix User Guide, p. 101 (2013). https:\/\/hal.science\/hal-00785549"},{"issue":"6","key":"20_CR16","doi-asserted-by":"publisher","first-page":"581","DOI":"10.1016\/S0747-7171(10)80012-4","volume":"13","author":"W Koepf","year":"1992","unstructured":"Koepf, W.: Power series in computer algebra. J. Symb. Comput. 13(6), 581\u2013604 (1992). https:\/\/doi.org\/10.1016\/S0747-7171(10)80012-4","journal-title":"J. Symb. Comput."},{"key":"20_CR17","doi-asserted-by":"publisher","unstructured":"Leiserson, C.E.: Cilk. In: Encyclopedia of Parallel Computing, pp. 273\u2013288. Springer, Heidelberg (2011). https:\/\/doi.org\/10.1007\/978-0-387-09766-4_289","DOI":"10.1007\/978-0-387-09766-4_289"},{"key":"20_CR18","volume-title":"Advanced Engineering Mathematics","author":"RJ Lopez","year":"2001","unstructured":"Lopez, R.J.: Advanced Engineering Mathematics. Addison-Wesley Longman, Boston (2001)"},{"key":"20_CR19","unstructured":"Maplesoft, a division of Waterloo Maple Inc.: Maple (2025). www.maplesoft.com\/"},{"key":"20_CR20","unstructured":"Maplesoft, a division of Waterloo Maple Inc.: Maple help: series (2024). https:\/\/www.maplesoft.com\/support\/help\/Maple\/view.aspx?path=series"},{"key":"20_CR21","unstructured":"Maplesoft, a division of Waterloo Maple Inc.: Maple help: Multivariatepowerseries (2025). https:\/\/www.maplesoft.com\/support\/help\/Maple\/view.aspx?path=MultivariatePowerSeries"},{"key":"20_CR22","volume-title":"Structured Parallel Programming: Patterns for Efficient Computation","author":"M McCool","year":"2012","unstructured":"McCool, M., Reinders, J., Robison, A.: Structured Parallel Programming: Patterns for Efficient Computation. Elsevier, Amsterdam (2012)"},{"key":"20_CR23","doi-asserted-by":"crossref","unstructured":"Moreno Maza, M.: Multithreaded programming on the GPU: pointers and hints for the computer algebraist. In: Proceedings of the International Workshop on Parallel Symbolic Computation, PASCO@ISSAC 2017, p.\u00a03:1. ACM (2017)","DOI":"10.1145\/3115936.3115939"},{"key":"20_CR24","doi-asserted-by":"crossref","unstructured":"Moreno Maza, M.: Design and implementation of multi-threaded algorithms in polynomial algebra. In: Proceedings of ISSAC \u201921, pp. 15\u201320. ACM (2021)","DOI":"10.1145\/3452143.3465511"},{"key":"20_CR25","doi-asserted-by":"crossref","unstructured":"Niven, I.: Formal power series. Am. Math. Monthly 76(8), 871\u2013889 (1969). http:\/\/www.jstor.org\/stable\/2317940","DOI":"10.1080\/00029890.1969.12000359"},{"issue":"5","key":"20_CR26","doi-asserted-by":"publisher","first-page":"1071","DOI":"10.1007\/s10208-018-09411-x","volume":"19","author":"B Salvy","year":"2019","unstructured":"Salvy, B.: Linear differential equations as a data structure. Found. Comput. Math. 19(5), 1071\u20131112 (2019)","journal-title":"Found. Comput. Math."},{"key":"20_CR27","doi-asserted-by":"crossref","unstructured":"Sideris, T.C.: Ordinary Differential Equations and Dynamical Systems, vol.\u00a02. Springer, Heidelberg (2013)","DOI":"10.2991\/978-94-6239-021-8"},{"key":"20_CR28","unstructured":"The Sage Developers: SageMath, the Sage Mathematics Software System (Version 9.1) (2020). https:\/\/www.sagemath.org"},{"key":"20_CR29","unstructured":"Wolfram Research Inc.: Mathematica (2025). www.wolfram.com\/mathematica"}],"container-title":["Lecture Notes in Computer Science","Computer Algebra in Scientific Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-032-09645-6_20","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,31]],"date-time":"2025-10-31T20:06:55Z","timestamp":1761941215000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/978-3-032-09645-6_20"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,11,1]]},"ISBN":["9783032096449","9783032096456"],"references-count":29,"URL":"https:\/\/doi.org\/10.1007\/978-3-032-09645-6_20","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"value":"0302-9743","type":"print"},{"value":"1611-3349","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,11,1]]},"assertion":[{"value":"1 November 2025","order":1,"name":"first_online","label":"First Online","group":{"name":"ChapterHistory","label":"Chapter History"}},{"value":"CASC","order":1,"name":"conference_acronym","label":"Conference Acronym","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"International Workshop on Computer Algebra in Scientific Computing","order":2,"name":"conference_name","label":"Conference Name","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Dubai","order":3,"name":"conference_city","label":"Conference City","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"United Arab Emirates","order":4,"name":"conference_country","label":"Conference Country","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"2025","order":5,"name":"conference_year","label":"Conference Year","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"24 November 2025","order":7,"name":"conference_start_date","label":"Conference Start Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"28 November 2025","order":8,"name":"conference_end_date","label":"Conference End Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"27","order":9,"name":"conference_number","label":"Conference Number","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"casc2025","order":10,"name":"conference_id","label":"Conference ID","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"http:\/\/casc-conference.org\/","order":11,"name":"conference_url","label":"Conference URL","group":{"name":"ConferenceInfo","label":"Conference Information"}}]}}