{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,6,19]],"date-time":"2025-06-19T04:32:58Z","timestamp":1750307578223,"version":"3.41.0"},"reference-count":0,"publisher":"Association for Computing Machinery (ACM)","issue":"1\/2","license":[{"start":{"date-parts":[[2010,7,29]],"date-time":"2010-07-29T00:00:00Z","timestamp":1280361600000},"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":[[2010,7,29]]},"abstract":"<jats:p>For second order linear ordinary differential equations with coefficients in C(x), we present an algorithm to reduce, whenever possible, the equation to an equation defined over a subfield of C(x). At the moment, we have implemented 2-descent, which means that if there exists a reduction to a subfield of index 2, then we can find it. If n is the number of true singularities, then 2-descent, if it exists, reduces the number of true singularities to at most n\/2 + 2. In 12 out of the 17 examples sent to us by Bostan and Kauers, we found that repeated use of 2-descent reduced their regular singular equation down to 3 singularities, which means that 2-descent allows us to find 2F1-hypergeometric type solutions for about two third's of their equations.<\/jats:p>","DOI":"10.1145\/1838599.1838618","type":"journal-article","created":{"date-parts":[[2010,8,2]],"date-time":"2010-08-02T13:15:22Z","timestamp":1280754922000},"page":"26-26","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":0,"title":["Abstract only"],"prefix":"10.1145","volume":"44","author":[{"given":"Tingting","family":"Fang","sequence":"first","affiliation":[{"name":"Florida State University"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Mark","family":"van Hoeij","sequence":"additional","affiliation":[{"name":"Florida State University"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"320","published-online":{"date-parts":[[2010,7,29]]},"container-title":["ACM Communications in Computer Algebra"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/1838599.1838618","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2025,6,18]],"date-time":"2025-06-18T12:41:11Z","timestamp":1750250471000},"score":1,"resource":{"primary":{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/1838599.1838618"}},"subtitle":["Solving linear differential equations by using descent"],"short-title":[],"issued":{"date-parts":[[2010,7,29]]},"references-count":0,"journal-issue":{"issue":"1\/2","published-print":{"date-parts":[[2010,7,29]]}},"alternative-id":["10.1145\/1838599.1838618"],"URL":"https:\/\/doi.org\/10.1145\/1838599.1838618","relation":{},"ISSN":["1932-2240"],"issn-type":[{"type":"print","value":"1932-2240"}],"subject":[],"published":{"date-parts":[[2010,7,29]]},"assertion":[{"value":"2010-07-29","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}