{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,6,19]],"date-time":"2025-06-19T04:22:10Z","timestamp":1750306930874,"version":"3.41.0"},"reference-count":13,"publisher":"Association for Computing Machinery (ACM)","issue":"3\/4","license":[{"start":{"date-parts":[[2013,1,15]],"date-time":"2013-01-15T00:00:00Z","timestamp":1358208000000},"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":[[2013,1,15]]},"abstract":"Puiseux series are power series in which the exponents can be fractional and\/or negative rational numbers. Several computer algebra systems have one or more built-in or loadable functions for computing truncated Puiseux series -- perhaps generalized to allow coefficients containing functions of the series variable that are dominated by any power of that variable, such as logarithms and nested logarithms of the series variable. Some computer-algebra systems also offer functions that can compute more-general truncated recursive hierarchical series. However, for all of these kinds of truncated series there are important implementation details that haven't been addressed before in the published literature and in current implementations.<\/jats:p>\n \n For implementers this article contains ideas for designing more convenient, correct, and efficient implementations or improving existing ones. For users, this article is a warning about some of these limitations. More specifically, this article discusses issues such as\n \n \n avoiding unnecessary restrictions such as prohibiting negative or fractional requested orders,<\/jats:p>\n <\/jats:list-item>\n \n \n the pros and cons of displaying results with explicit infectious error terms of the form\n o<\/jats:italic>\n (...),\n O<\/jats:italic>\n (...), and\/or \u03b8(...),\n <\/jats:p>\n <\/jats:list-item>\n \n efficient data structures, and<\/jats:p>\n <\/jats:list-item>\n \n algorithms that efficiently give users exactly the order or number of nonzero terms they request.<\/jats:p>\n <\/jats:list-item>\n <\/jats:list>\n .\n <\/jats:p>\n Most of the ideas in this article have been implemented in the computer-algebra within the TI-Nspire calculator, Windows and Macintosh products.<\/jats:p>","DOI":"10.1145\/2429135.2429168","type":"journal-article","created":{"date-parts":[[2013,1,22]],"date-time":"2013-01-22T15:28:56Z","timestamp":1358868536000},"page":"134-153","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":1,"title":["Series misdemeanors"],"prefix":"10.1145","volume":"46","author":[{"given":"David R.","family":"Stoutemyer","sequence":"first","affiliation":[{"name":"dstout at hawaii dot edu"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"320","published-online":{"date-parts":[[2013,1,15]]},"reference":[{"key":"e_1_2_1_1_1","doi-asserted-by":"publisher","DOI":"10.1145\/322092.322099"},{"key":"e_1_2_1_2_1","first-page":"490","volume-title":"Proceedings of ISSAC","author":"Geddes K.O.","year":"1998"},{"key":"e_1_2_1_3_1","doi-asserted-by":"publisher","DOI":"10.1145\/164081.164136"},{"key":"e_1_2_1_4_1","unstructured":"Knuth D.E. The Art of Computer Programming Volume 2 Addison-Wesley 3rd edition 1998 Section 4.7. Knuth D.E. The Art of Computer Programming Volume 2 Addison-Wesley 3rd edition 1998 Section 4.7."},{"key":"e_1_2_1_5_1","doi-asserted-by":"publisher","DOI":"10.1145\/1008328.1008329"},{"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":"10.1145\/355656.355660"},{"key":"e_1_2_1_8_1","doi-asserted-by":"publisher","DOI":"10.1145\/236869.237089"},{"key":"e_1_2_1_9_1","unstructured":"Silver A. and Sullivan E. The numerical solution of ordinary differential equations by the Taylor series method NASA-TM-X-70438 1973. Silver A. and Sullivan E. The numerical solution of ordinary differential equations by the Taylor series method NASA-TM-X-70438 1973."},{"first-page":"221","volume-title":"Proceedings of the 1984 Macsyma User's Conference, Schenectady N.Y.","author":"Stoutemyer D.R.","key":"e_1_2_1_10_1"},{"key":"e_1_2_1_11_1","unstructured":"Stoutemyer D.R. Series Crimes submitted for publication. Stoutemyer D.R. Series Crimes submitted for publication."},{"key":"e_1_2_1_12_1","doi-asserted-by":"publisher","DOI":"10.1145\/800205.806335"},{"key":"e_1_2_1_13_1","doi-asserted-by":"crossref","unstructured":"Zippel R.E. Effective Polynomial Computation Kluwer Academic Publishers 1993 Chapter 10 pp. 157--171. Zippel R.E. Effective Polynomial Computation Kluwer Academic Publishers 1993 Chapter 10 pp. 157--171.","DOI":"10.1007\/978-1-4615-3188-3_10"}],"container-title":["ACM Communications in Computer Algebra"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/2429135.2429168","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/dl.acm.org\/doi\/pdf\/10.1145\/2429135.2429168","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,6,18]],"date-time":"2025-06-18T08:35:36Z","timestamp":1750235736000},"score":1,"resource":{"primary":{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/2429135.2429168"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013,1,15]]},"references-count":13,"journal-issue":{"issue":"3\/4","published-print":{"date-parts":[[2013,1,15]]}},"alternative-id":["10.1145\/2429135.2429168"],"URL":"https:\/\/doi.org\/10.1145\/2429135.2429168","relation":{},"ISSN":["1932-2240"],"issn-type":[{"type":"print","value":"1932-2240"}],"subject":[],"published":{"date-parts":[[2013,1,15]]},"assertion":[{"value":"2013-01-15","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}