{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,6,19]],"date-time":"2025-06-19T04:30:11Z","timestamp":1750307411086,"version":"3.41.0"},"reference-count":8,"publisher":"Association for Computing Machinery (ACM)","issue":"3\/4","license":[{"start":{"date-parts":[[2010,6,24]],"date-time":"2010-06-24T00:00:00Z","timestamp":1277337600000},"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":["ACM Commun. Comput. Algebra"],"published-print":{"date-parts":[[2010,6,24]]},"abstract":"<jats:p>\n            We provide a method of determining whether there exist some\n            <jats:italic>p 2 P<\/jats:italic>\n            and\n            <jats:italic>f 2 F<\/jats:italic>\n            such that p is divisible by\n            <jats:italic>f<\/jats:italic>\n            for a pair of real multivariate interval polynomials,\n            <jats:italic>P<\/jats:italic>\n            and\n            <jats:italic>F<\/jats:italic>\n            . Although this problem is written as a feasibility problem for a system of nonlinear algebraic equations, it is an NP-hard problem and is thus difficult to solve. Our approach is iterative based on interval analyses, which outputs the regions containing the solutions if the system is feasible; otherwise, it outputs the fact of infeasibility. We also propose two methods for where the system of algebraic equations is underdetermined, the first obtains the regions that enclose all solutions, and the second obtains the solution that minimizes error in the Euclidean norm.\n          <\/jats:p>","DOI":"10.1145\/1823931.1823944","type":"journal-article","created":{"date-parts":[[2010,6,29]],"date-time":"2010-06-29T13:02:22Z","timestamp":1277816542000},"page":"91-94","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":0,"title":["Determining divisibility between polynomials with inexact coefficients"],"prefix":"10.1145","volume":"43","author":[{"given":"Hiroki","family":"Nakayama","sequence":"first","affiliation":[{"name":"Nippon Telegraph and Telephone Corporation"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Hiroshi","family":"Sekigawa","sequence":"additional","affiliation":[{"name":"Nippon Telegraph and Telephone Corporation"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"320","published-online":{"date-parts":[[2010,6,24]]},"reference":[{"key":"e_1_2_1_1_1","first-page":"36","volume-title":"INTERVAL '94","author":"Andrade M. V. A.","year":"1994"},{"key":"e_1_2_1_2_1","doi-asserted-by":"crossref","unstructured":"S. Basu R. Pollack and M.-F. Roy Algorithms in Real Algebraic Geometry Springer-Verlag 2nd Edition 2006.   S. Basu R. Pollack and M.-F. Roy Algorithms in Real Algebraic Geometry Springer-Verlag 2nd Edition 2006.","DOI":"10.1007\/3-540-33099-2"},{"key":"e_1_2_1_3_1","first-page":"79","volume-title":"Springer","author":"Frommer A.","year":"2001"},{"volume-title":"2nd Edition","year":"2003","author":"Hansen E.","key":"e_1_2_1_4_1"},{"key":"e_1_2_1_5_1","first-page":"5","article-title":"An algorithm for iteratively refining the interval including the solution set of parameter dependent nonlinear equations","volume":"83","author":"Kanzawa Y.","year":"2000","journal-title":"IEICE Trans. Fundamentals (Jpn. Ed.)"},{"key":"e_1_2_1_6_1","first-page":"3","article-title":"On the best multiplication of the affine arithmetic","volume":"86","author":"Miyajima S.","year":"2003","journal-title":"IEICE Trans. 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