{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,6,19]],"date-time":"2025-06-19T04:55:26Z","timestamp":1750308926710,"version":"3.41.0"},"reference-count":5,"publisher":"Association for Computing Machinery (ACM)","issue":"2","license":[{"start":{"date-parts":[[1985,5,1]],"date-time":"1985-05-01T00:00:00Z","timestamp":483753600000},"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":[[1985,5]]},"abstract":"<jats:p>We are concerned with factoring polynomials over algebraic extensions of the rationals, and have implemented a variant of Trager's [1976] algorithm, which reduces this problem to that of factoring polynomials over the integers, for which we use Wang's [1978] algorithm (as implemented in REDUCE [Hearn 82] by Moore and Norman [1981]). However, Trager's method often produces a norm polynomial which factors profusely modulo every prime, leading to a combinatorial explosion of trial divisions in Wang's algorithm. We present some simple divisibility tests for polynomials to help combat the cost of this explosion.<\/jats:p>","DOI":"10.1145\/1089402.1089408","type":"journal-article","created":{"date-parts":[[2007,1,17]],"date-time":"2007-01-17T18:32:02Z","timestamp":1169058722000},"page":"31-33","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":8,"title":["A remark on factorisation"],"prefix":"10.1145","volume":"19","author":[{"given":"J. A.","family":"Abbott","sequence":"first","affiliation":[{"name":"University of Bath, England"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"R. J.","family":"Bradford","sequence":"additional","affiliation":[{"name":"University of Bath, England"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"J. H.","family":"Davenport","sequence":"additional","affiliation":[{"name":"University of Bath, England"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"320","published-online":{"date-parts":[[1985,5]]},"reference":[{"volume-title":"Hearn REDUCE - A Case Study in Algebra System Development. Proc. Eurocam '82","author":"Hearn A. C.","key":"e_1_2_1_1_1"},{"unstructured":"{Swinnerton-Dyer 69} H. P. F. Swinnerton-Dyer Private communication to E. Berlekamp.  {Swinnerton-Dyer 69} H. P. F. Swinnerton-Dyer Private communication to E. Berlekamp.","key":"e_1_2_1_2_1"},{"doi-asserted-by":"publisher","key":"e_1_2_1_3_1","DOI":"10.1145\/800206.806379"},{"doi-asserted-by":"publisher","key":"e_1_2_1_4_1","DOI":"10.1145\/800205.806338"},{"doi-asserted-by":"publisher","key":"e_1_2_1_5_1","DOI":"10.1090\/S0025-5718-1978-0568284-3"}],"container-title":["ACM SIGSAM Bulletin"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/1089402.1089408","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/dl.acm.org\/doi\/pdf\/10.1145\/1089402.1089408","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,6,18]],"date-time":"2025-06-18T21:36:45Z","timestamp":1750282605000},"score":1,"resource":{"primary":{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/1089402.1089408"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1985,5]]},"references-count":5,"journal-issue":{"issue":"2","published-print":{"date-parts":[[1985,5]]}},"alternative-id":["10.1145\/1089402.1089408"],"URL":"https:\/\/doi.org\/10.1145\/1089402.1089408","relation":{},"ISSN":["0163-5824"],"issn-type":[{"type":"print","value":"0163-5824"}],"subject":[],"published":{"date-parts":[[1985,5]]},"assertion":[{"value":"1985-05-01","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}