{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T02:01:00Z","timestamp":1760061660331,"version":"3.41.0"},"reference-count":14,"publisher":"Association for Computing Machinery (ACM)","issue":"3","license":[{"start":{"date-parts":[[1974,8,1]],"date-time":"1974-08-01T00:00:00Z","timestamp":144547200000},"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":[[1974,8]]},"abstract":"<jats:p>Two Hensel-type univariate polynomial Greatest Common Divisor (GCD) algorithms are presented and compared. The regular linear Hensel construction is shown to be generally more efficient than the Zassenhaus quadratic construction. The UNIGCD algorithm for UNIvariate polynomial GCD computations, based on the regular Hensel construction is then presented and compared with the Modular algorithm based on the Chinese Remainder Algorithm. From both an analytical and an experimental point of view, the UNIGCD algorithm is shown to be preferable for many common univariate GCD computations. This is true even for dense polynomials, which was considered to be the most suitable case for the application of the Modular algorithm.<\/jats:p>","DOI":"10.1145\/1086837.1086844","type":"journal-article","created":{"date-parts":[[2007,1,17]],"date-time":"2007-01-17T18:32:02Z","timestamp":1169058722000},"page":"46-54","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":13,"title":["Computational aspects of Hensel-type univariate polynomial greatest common divisor algorithms"],"prefix":"10.1145","volume":"8","author":[{"given":"Alfonso","family":"Miola","sequence":"first","affiliation":[{"name":"Instituto per le Applicazioni del Calcolo (IAC), Roma, Italy"}]},{"given":"David Y. Y.","family":"Yun","sequence":"additional","affiliation":[{"name":"IBM Thomas J. Watson Research Center, Yorktown Heights, N.Y."}]}],"member":"320","published-online":{"date-parts":[[1974,8]]},"reference":[{"key":"e_1_2_1_1_1","doi-asserted-by":"publisher","DOI":"10.1002\/j.1538-7305.1967.tb03174.x"},{"key":"e_1_2_1_2_1","doi-asserted-by":"publisher","DOI":"10.1145\/321662.321664"},{"key":"e_1_2_1_3_1","doi-asserted-by":"publisher","DOI":"10.1080\/00029890.1966.11970820"},{"key":"e_1_2_1_4_1","doi-asserted-by":"publisher","DOI":"10.1145\/321371.321381"},{"key":"e_1_2_1_5_1","unstructured":"{COL73} Collins G. E. \"The Computing Time of Euclindean Algorithm\" Stanford Artificial Intelligence Laboratory Memo AIM - 187 Stanford Computer Science Department Report CS - 331 January 1973.   {COL73} Collins G. E. \"The Computing Time of Euclindean Algorithm\" Stanford Artificial Intelligence Laboratory Memo AIM - 187 Stanford Computer Science Department Report CS - 331 January 1973."},{"key":"e_1_2_1_6_1","doi-asserted-by":"crossref","unstructured":"{HOR71} Horowitz E. \"Modular Arithmetic and Finite Field Theory\" {PET71} March 1971 pp. 188--194.  {HOR71} Horowitz E. \"Modular Arithmetic and Finite Field Theory\" {PET71} March 1971 pp. 188--194.","DOI":"10.1145\/800204.806287"},{"volume-title":"Mass.","year":"1969","author":"Knuth D. E.","key":"e_1_2_1_7_1"},{"key":"e_1_2_1_8_1","unstructured":"{MUS71} Musser D. R. \"Algorithms for Polynomial Factorization\" Ph.D. Thesis Computer Science Department University of Wisconsin August 1971.   {MUS71} Musser D. R. \"Algorithms for Polynomial Factorization\" Ph.D. Thesis Computer Science Department University of Wisconsin August 1971."},{"key":"e_1_2_1_9_1","doi-asserted-by":"publisher","DOI":"10.1145\/800192.805698"},{"volume-title":"ACM","year":"1971","author":"Proc","key":"e_1_2_1_10_1"},{"key":"e_1_2_1_11_1","unstructured":"{VDW49} Van Der Waerden B. L. \"Modern Algebra\" Vol. 1 Frederic Ungar Publishing Co. N.Y. 1949.  {VDW49} Van Der Waerden B. L. \"Modern Algebra\" Vol. 1 Frederic Ungar Publishing Co. N.Y. 1949."},{"key":"e_1_2_1_12_1","doi-asserted-by":"publisher","DOI":"10.1145\/1086814.1086819"},{"key":"e_1_2_1_13_1","unstructured":"{YUN73} Yun D. Y. Y. \"The Hensel Lemma in Algebraic Manipulation\" Ph.D. Thesis Department of Mathematics MIT November 1973.  {YUN73} Yun D. Y. Y. \"The Hensel Lemma in Algebraic Manipulation\" Ph.D. Thesis Department of Mathematics MIT November 1973."},{"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\/1086837.1086844","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/dl.acm.org\/doi\/pdf\/10.1145\/1086837.1086844","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,6,18]],"date-time":"2025-06-18T16:08:13Z","timestamp":1750262893000},"score":1,"resource":{"primary":{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/1086837.1086844"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1974,8]]},"references-count":14,"journal-issue":{"issue":"3","published-print":{"date-parts":[[1974,8]]}},"alternative-id":["10.1145\/1086837.1086844"],"URL":"https:\/\/doi.org\/10.1145\/1086837.1086844","relation":{},"ISSN":["0163-5824"],"issn-type":[{"type":"print","value":"0163-5824"}],"subject":[],"published":{"date-parts":[[1974,8]]},"assertion":[{"value":"1974-08-01","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}