{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,6,19]],"date-time":"2025-06-19T04:58:15Z","timestamp":1750309095624,"version":"3.41.0"},"reference-count":13,"publisher":"Association for Computing Machinery (ACM)","issue":"4","license":[{"start":{"date-parts":[[1974,11,1]],"date-time":"1974-11-01T00:00:00Z","timestamp":152496000000},"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":["SIGSAM Bull."],"published-print":{"date-parts":[[1974,11]]},"abstract":"<jats:p>A new algorithm for division with remainder of univariate and multivariate polynomials over the integers is reported. This division algorithm relies on a p-adic construction which is closely related to the Hensel-type constructions used for polynomial factorization and greatest common divisor computations. It furnishes a new and systematic way of looking at the classical problem of division (with or without remainder). Due to the sparseness-preserving property of p-adic constructions, it appears useful as an alternative division algorithm in suitable cases when the polynomials are sparse. Detailed discussion and a more complete computing time analysis will be deferred until a later time as the work progresses further. An hope, in the meantime, is to attract comments and criticism on the algorithm and its significance.<\/jats:p>","DOI":"10.1145\/1088288.1088293","type":"journal-article","created":{"date-parts":[[2007,1,17]],"date-time":"2007-01-17T18:32:02Z","timestamp":1169058722000},"page":"27-32","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":6,"title":["A p-adic division with remainder algorithm"],"prefix":"10.1145","volume":"8","author":[{"given":"David Y. Y.","family":"Yun","sequence":"first","affiliation":[{"name":"IBM Thomas J. Watson Research Center, Yorktown Height, New York"}]}],"member":"320","published-online":{"date-parts":[[1974,11]]},"reference":[{"key":"e_1_2_1_1_1","doi-asserted-by":"publisher","DOI":"10.1145\/321662.321664"},{"key":"e_1_2_1_2_1","doi-asserted-by":"publisher","DOI":"10.1080\/00029890.1966.11970820"},{"key":"e_1_2_1_3_1","doi-asserted-by":"publisher","DOI":"10.1145\/321371.321381"},{"key":"e_1_2_1_4_1","doi-asserted-by":"publisher","DOI":"10.1002\/sapm1974532145"},{"key":"e_1_2_1_5_1","doi-asserted-by":"crossref","unstructured":"{HENK13} Hensel K. Zahlentheorie Goschen Berlin and Leipzig 1913.  {HENK13} Hensel K. Zahlentheorie Goschen Berlin and Leipzig 1913.","DOI":"10.1515\/9783112360026"},{"key":"e_1_2_1_6_1","doi-asserted-by":"publisher","DOI":"10.1145\/800192.805697"},{"key":"e_1_2_1_7_1","doi-asserted-by":"publisher","DOI":"10.1145\/1086837.1086847"},{"volume-title":"Addison Wesley","year":"1969","author":"Knuth D. E.","key":"e_1_2_1_8_1"},{"key":"e_1_2_1_9_1","doi-asserted-by":"publisher","DOI":"10.1145\/1086837.1086844"},{"key":"e_1_2_1_10_1","doi-asserted-by":"publisher","DOI":"10.1145\/800192.805698"},{"key":"e_1_2_1_11_1","unstructured":"{MUSD71} Musser D. R. \"Algorithms for Polynomial Factorization\" Ph.D. Thesis Computer Science Department University of Wisconsin August 1971.   {MUSD71} Musser D. R. \"Algorithms for Polynomial Factorization\" Ph.D. Thesis Computer Science Department University of Wisconsin August 1971."},{"key":"e_1_2_1_12_1","doi-asserted-by":"publisher","DOI":"10.1145\/1086814.1086819"},{"key":"e_1_2_1_14_1","doi-asserted-by":"publisher","DOI":"10.1016\/0022-314X(69)90047-X"}],"container-title":["ACM SIGSAM Bulletin"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/1088288.1088293","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/dl.acm.org\/doi\/pdf\/10.1145\/1088288.1088293","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,6,18]],"date-time":"2025-06-18T22:43:44Z","timestamp":1750286624000},"score":1,"resource":{"primary":{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/1088288.1088293"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1974,11]]},"references-count":13,"journal-issue":{"issue":"4","published-print":{"date-parts":[[1974,11]]}},"alternative-id":["10.1145\/1088288.1088293"],"URL":"https:\/\/doi.org\/10.1145\/1088288.1088293","relation":{},"ISSN":["0163-5824"],"issn-type":[{"type":"print","value":"0163-5824"}],"subject":[],"published":{"date-parts":[[1974,11]]},"assertion":[{"value":"1974-11-01","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}