{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,6,19]],"date-time":"2025-06-19T04:39:59Z","timestamp":1750307999794,"version":"3.41.0"},"reference-count":11,"publisher":"Association for Computing Machinery (ACM)","issue":"4","license":[{"start":{"date-parts":[[2005,12,1]],"date-time":"2005-12-01T00:00:00Z","timestamp":1133395200000},"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":[[2005,12]]},"abstract":"<jats:p>The expansion base algorithm, which was devised by Abhyankar, Kuo and McCallum is very efficient for analytic factorization of bivariate polynomials. The author had extended it to more than two variables but it was only for polynomials with non-vanishing leading coefficient at the expansion point. We improve it to be able to apply to polynomials including the case of vanishing leading coefficient, that is, singular leading coefficient, which comes to a specific problem only for more than two variables.<\/jats:p>","DOI":"10.1145\/1140378.1140383","type":"journal-article","created":{"date-parts":[[2007,1,17]],"date-time":"2007-01-17T18:32:02Z","timestamp":1169058722000},"page":"122-126","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":2,"title":["Extension of expansion base algorithm for multivariate analytic factorization including the case of singular leading coefficient"],"prefix":"10.1145","volume":"39","author":[{"given":"Maki","family":"Iwami","sequence":"first","affiliation":[{"name":"University of Tsukuba, Tsukuba, Japan"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"320","published-online":{"date-parts":[[2005,12]]},"reference":[{"key":"e_1_2_1_1_1","doi-asserted-by":"publisher","DOI":"10.1007\/BF03023744"},{"key":"e_1_2_1_2_1","doi-asserted-by":"publisher","DOI":"10.1016\/0001-8708(89)90009-1"},{"key":"e_1_2_1_3_1","doi-asserted-by":"crossref","unstructured":"{Ab90} S. S. Abhyankar: Algebraic Geometry for Scientists and Engineers. Number 35 in Mathematical Surveys and Monographs. Providence RI: American Mathematical Society (1990).  {Ab90} S. S. Abhyankar: Algebraic Geometry for Scientists and Engineers. Number 35 in Mathematical Surveys and Monographs. Providence RI: American Mathematical Society (1990).","DOI":"10.1090\/surv\/035"},{"key":"e_1_2_1_4_1","doi-asserted-by":"crossref","unstructured":"{AM73} S. S. Abhyankar and T. T. Moh: Newton-Puiseux expansion and generalized Tschirnhausen transformation II.J. reine und angew. Math. 261 pp.29--pp.54 (1973).  {AM73} S. S. Abhyankar and T. T. Moh: Newton-Puiseux expansion and generalized Tschirnhausen transformation II.J. reine und angew. Math. 261 pp.29--pp.54 (1973).","DOI":"10.1515\/crll.1973.261.29"},{"key":"e_1_2_1_5_1","first-page":"213","volume-title":"Iwami: Analytic Factorization of the Multivariate Polynomial. Proceedings of the Sixth International Workshop on Computer Algebra in Scientific Computing.","author":"M.","year":"2003"},{"key":"e_1_2_1_6_1","first-page":"269","volume-title":"Proceedings of the Seventh International Workshop on Computer Algebra in Scientific Computing.","author":"Iwami M.","year":"2004"},{"key":"e_1_2_1_7_1","doi-asserted-by":"publisher","DOI":"10.4153\/CJM-1989-048-7"},{"key":"e_1_2_1_8_1","doi-asserted-by":"publisher","DOI":"10.1006\/jsco.1997.0150"},{"key":"e_1_2_1_9_1","doi-asserted-by":"publisher","DOI":"10.1145\/373500.373502"},{"key":"e_1_2_1_10_1","doi-asserted-by":"publisher","DOI":"10.1007\/BF03167329"},{"key":"e_1_2_1_11_1","unstructured":"{Sas00} T. Sasaki: Properties of Extended Hensel Factors and Application to Approximate Factorization. Preprint Univ. Tsukuba (2000).  {Sas00} T. Sasaki: Properties of Extended Hensel Factors and Application to Approximate Factorization. Preprint Univ. Tsukuba (2000)."}],"container-title":["ACM SIGSAM Bulletin"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/1140378.1140383","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/dl.acm.org\/doi\/pdf\/10.1145\/1140378.1140383","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,6,18]],"date-time":"2025-06-18T15:06:24Z","timestamp":1750259184000},"score":1,"resource":{"primary":{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/1140378.1140383"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2005,12]]},"references-count":11,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2005,12]]}},"alternative-id":["10.1145\/1140378.1140383"],"URL":"https:\/\/doi.org\/10.1145\/1140378.1140383","relation":{},"ISSN":["0163-5824"],"issn-type":[{"type":"print","value":"0163-5824"}],"subject":[],"published":{"date-parts":[[2005,12]]},"assertion":[{"value":"2005-12-01","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}