{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,22]],"date-time":"2026-04-22T13:26:43Z","timestamp":1776864403495,"version":"3.51.2"},"reference-count":17,"publisher":"Wiley","issue":"A","license":[{"start":{"date-parts":[[2014,8,1]],"date-time":"2014-08-01T00:00:00Z","timestamp":1406851200000},"content-version":"unspecified","delay-in-days":212,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["LMS J. Comput. Math."],"published-print":{"date-parts":[[2014]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>We develop algorithms to turn quotients of rings of integers into effective Euclidean rings by giving polynomial algorithms for all fundamental ring operations. In addition, we study normal forms for modules over such rings and their behavior under certain quotients. We illustrate the power of our ideas in a new modular normal form algorithm for modules over rings of integers, vastly outperforming classical algorithms.<\/jats:p>","DOI":"10.1112\/s1461157014000291","type":"journal-article","created":{"date-parts":[[2014,8,5]],"date-time":"2014-08-05T10:34:15Z","timestamp":1407234855000},"page":"349-365","source":"Crossref","is-referenced-by-count":3,"title":["Computing in quotients of rings of integers"],"prefix":"10.1112","volume":"17","author":[{"given":"Claus","family":"Fieker","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Tommy","family":"Hofmann","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2014,8,1]]},"reference":[{"key":"S1461157014000291_r15","doi-asserted-by":"publisher","DOI":"10.1007\/BF01456721"},{"key":"S1461157014000291_r14","doi-asserted-by":"publisher","DOI":"10.1007\/BF01456849"},{"key":"S1461157014000291_r4","article-title":"On the computation of the HNF of a module over the ring of integers of a number field","author":"Biasse","journal-title":"J. Symbolic Comput."},{"key":"S1461157014000291_r11","doi-asserted-by":"publisher","DOI":"10.1137\/0220067"},{"key":"S1461157014000291_r1","first-page":"291","article-title":"Euclidean rings","volume":"19","author":"A\u011farg\u00fcn","year":"1995","journal-title":"Turkish J. Math."},{"key":"S1461157014000291_r7","doi-asserted-by":"publisher","DOI":"10.1090\/S0025-5718-96-00766-1"},{"key":"S1461157014000291_r17","doi-asserted-by":"crossref","first-page":"139","DOI":"10.1007\/3-540-68530-8_12","volume-title":"Algorithms \u2014 ESA \u201998 (Venice)","author":"Storjohann","year":"1998"},{"key":"S1461157014000291_r3","doi-asserted-by":"crossref","first-page":"75","DOI":"10.1145\/2442829.2442844","volume-title":"Proceedings of the 37th International Symposium on Symbolic and Algebraic Computation (ISSAC \u201912)","author":"Biasse","year":"2012"},{"key":"S1461157014000291_r12","doi-asserted-by":"publisher","DOI":"10.1080\/03081088608817705"},{"key":"S1461157014000291_r10","doi-asserted-by":"publisher","DOI":"10.1112\/jlms\/s2-4.1.79"},{"key":"S1461157014000291_r8","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4419-8489-0"},{"key":"S1461157014000291_r2","doi-asserted-by":"publisher","DOI":"10.5802\/jtnb.433"},{"key":"S1461157014000291_r5","doi-asserted-by":"publisher","DOI":"10.1006\/jsco.1996.0125"},{"key":"S1461157014000291_r6","doi-asserted-by":"publisher","DOI":"10.1145\/120694.120714"},{"key":"S1461157014000291_r13","doi-asserted-by":"publisher","DOI":"10.1137\/0218045"},{"key":"S1461157014000291_r16","unstructured":"16. A. Storjohann , \u2018Algorithms for matrix canonical forms\u2019, PhD Thesis, Department of Computer Science, Swiss Federal Institute of Technology \u2013 ETH, 2000."},{"key":"S1461157014000291_r9","doi-asserted-by":"publisher","DOI":"10.1287\/moor.12.1.50"}],"container-title":["LMS Journal of Computation and Mathematics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S1461157014000291","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,4,13]],"date-time":"2022-04-13T17:00:40Z","timestamp":1649869240000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S1461157014000291\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014]]},"references-count":17,"journal-issue":{"issue":"A","published-print":{"date-parts":[[2014]]}},"alternative-id":["S1461157014000291"],"URL":"https:\/\/doi.org\/10.1112\/s1461157014000291","relation":{},"ISSN":["1461-1570"],"issn-type":[{"value":"1461-1570","type":"electronic"}],"subject":[],"published":{"date-parts":[[2014]]}}}