{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,7]],"date-time":"2025-10-07T12:07:38Z","timestamp":1759838858380},"reference-count":18,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2021,1,12]],"date-time":"2021-01-12T00:00:00Z","timestamp":1610409600000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2021,1,12]],"date-time":"2021-01-12T00:00:00Z","timestamp":1610409600000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J Syst Sci Complex"],"published-print":{"date-parts":[[2021,6]]},"DOI":"10.1007\/s11424-020-9314-6","type":"journal-article","created":{"date-parts":[[2021,1,13]],"date-time":"2021-01-13T03:31:44Z","timestamp":1610508704000},"page":"1189-1206","update-policy":"http:\/\/dx.doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Computing \u03bc-Bases of Univariate Polynomial Matrices Using Polynomial Matrix Factorization"],"prefix":"10.1007","volume":"34","author":[{"given":"Bingru","family":"Huang","sequence":"first","affiliation":[]},{"given":"Falai","family":"Chen","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2021,1,12]]},"reference":[{"issue":"8","key":"9314_CR1","doi-asserted-by":"publisher","first-page":"803","DOI":"10.1016\/S0167-8396(98)00014-4","volume":"15","author":"D Cox","year":"1998","unstructured":"Cox D, Sederberg T W, and Chen F L, The moving line ideal basis of planar rational curves, Computer Aided Geometric Design, 1998, 15(8): 803\u2013827.","journal-title":"Computer Aided Geometric Design"},{"issue":"6","key":"9314_CR2","doi-asserted-by":"publisher","first-page":"687","DOI":"10.1016\/0167-8396(94)90059-0","volume":"11","author":"T W Sederberg","year":"1994","unstructured":"Sederberg T W, Saito T, Qi D, et al., Curve implicitization using moving lines, Computer Aided Geometric Design, 1994, 11(6): 687\u2013706.","journal-title":"Computer Aided Geometric Design"},{"key":"9314_CR3","doi-asserted-by":"crossref","unstructured":"Sederberg T W and Chen F L, Implicitization using moving curves and surfaces, Proceedings of SIGGRAPH, 1995, 301\u2013308.","DOI":"10.1145\/218380.218460"},{"issue":"2","key":"9314_CR4","doi-asserted-by":"publisher","first-page":"217","DOI":"10.1016\/j.cagd.2008.04.001","volume":"26","author":"N Song","year":"2009","unstructured":"Song N and Goldman R, \u03bc-bases for polynomial systems in one variable, Computer Aided Geometric Design, 2009, 26(2): 217\u2013230.","journal-title":"Computer Aided Geometric Design"},{"issue":"1","key":"9314_CR5","doi-asserted-by":"publisher","first-page":"61","DOI":"10.1016\/S0167-8396(01)00012-7","volume":"18","author":"F L Chen","year":"2001","unstructured":"Chen F L, Zheng J M, and Sederberg T W, The \u03bc-basis of a rational ruled surface, Computer Aided Geometric Design, 2001, 18(1): 61\u201372.","journal-title":"Computer Aided Geometric Design"},{"issue":"5","key":"9314_CR6","first-page":"699","volume":"36","author":"F L Chen","year":"2003","unstructured":"Chen F L and Wang W P, Revisiting the \u03bc-basis of a rational ruled surface, Computer Aided Geometric Design, 2003, 36(5): 699\u2013716.","journal-title":"Computer Aided Geometric Design"},{"issue":"6","key":"9314_CR7","doi-asserted-by":"publisher","first-page":"689","DOI":"10.1016\/j.jsc.2005.01.003","volume":"39","author":"F L Chen","year":"2005","unstructured":"Chen F L, Cox D, and Liu Y, The \u03bc-basis and implicitization of a rational parametric surface, Journal of Symbolic Computation, 2005, 39(6): 689\u2013706.","journal-title":"Journal of Symbolic Computation"},{"issue":"2","key":"9314_CR8","doi-asserted-by":"publisher","first-page":"92","DOI":"10.1016\/j.jsc.2007.10.003","volume":"43","author":"F L Chen","year":"2008","unstructured":"Chen F L, Wang W P, and Liu Y, Computing singular points of plane rational curves, Journal of Symbolic Computation, 2008, 43(2): 92\u2013117.","journal-title":"Journal of Symbolic Computation"},{"issue":"9","key":"9314_CR9","doi-asserted-by":"publisher","first-page":"970","DOI":"10.1016\/j.cagd.2009.08.001","volume":"26","author":"X H Jia","year":"2009","unstructured":"Jia X H and Goldman R, \u03bc-bases and singularities of rational planar curves, Computer Aided Geometric Design, 2009, 26(9): 970\u2013988.","journal-title":"Computer Aided Geometric Design"},{"issue":"6","key":"9314_CR10","doi-asserted-by":"publisher","first-page":"296","DOI":"10.1016\/j.cagd.2012.02.001","volume":"29","author":"X H Jia","year":"2012","unstructured":"Jia X H and Goldman R, Using Smith normal forms and \u03bc-bases to compute all the singularities of rational planar curves, Computer Aided Geometric Design, 2012, 29(6): 296\u2013314.","journal-title":"Computer Aided Geometric Design"},{"issue":"3","key":"9314_CR11","doi-asserted-by":"publisher","first-page":"287","DOI":"10.1016\/j.cagd.2008.09.005","volume":"26","author":"X H Jia","year":"2009","unstructured":"Jia X H, Chen F L, and Deng J S, Computing self-intersection curves of rational ruled surfaces, Computer Aided Geometric Design, 2009, 26(3): 287\u2013299.","journal-title":"Computer Aided Geometric Design"},{"issue":"1","key":"9314_CR12","doi-asserted-by":"publisher","first-page":"11","DOI":"10.1016\/S0167-8396(02)00191-7","volume":"20","author":"F L Chen","year":"2003","unstructured":"Chen F L, Reparametrization of a rational ruled surface using the \u03bc-basis, Computer Aided Geometric Design, 2003, 20(1): 11\u201317.","journal-title":"Computer Aided Geometric Design"},{"key":"9314_CR13","doi-asserted-by":"crossref","unstructured":"Wang X H, Chen F L, and Deng J S, Implicitization and parametrization of quadratic surfaces with one simple base point, Proceedings of International Symposium on Symbolic and Algebraic Computation (ISSAC), 2008, 31\u201338.","DOI":"10.1145\/1390768.1390776"},{"issue":"5","key":"9314_CR14","doi-asserted-by":"publisher","first-page":"619","DOI":"10.1006\/jsco.2001.0437","volume":"31","author":"J M Zheng","year":"2001","unstructured":"Zheng J M and Sederberg T W, A direct approach to computing the \u03bc-basis of planar rational curves, Journal of Symbolic Computation, 2001, 31(5): 619\u2013629.","journal-title":"Journal of Symbolic Computation"},{"issue":"6","key":"9314_CR15","doi-asserted-by":"publisher","first-page":"368","DOI":"10.1016\/S1077-3169(02)00017-5","volume":"64","author":"F L Chen","year":"2003","unstructured":"Chen F L and Wang W P, The \u03bc-basis of a planar rational curve \u2014 Properties and computation, Graphical Models, 2003, 64(6): 368\u2013381.","journal-title":"Graphical Models"},{"key":"9314_CR16","doi-asserted-by":"publisher","first-page":"844","DOI":"10.1016\/j.jsc.2016.08.013","volume":"80","author":"H Hong","year":"2017","unstructured":"Hong H, Hough Z, and Kogan I A, Algorithm for computing \u03bc-bases of univariate polynomials, Journal of Symbolic Computation, 2017, 80: 844\u2013874.","journal-title":"Journal of Symbolic Computation"},{"key":"9314_CR17","unstructured":"Deng J S, Chen F L, and Shen L Y, Computing \u03bc-bases of rational curves and surfaces using polynomial matrix factorization, Proceedings of International Symposium on Symbolic and Algebraic Computation (ISSAC), 2008, 132\u2013139."},{"key":"9314_CR18","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4757-6911-1","volume-title":"Using Algebraic Geomety","author":"D Cox","year":"1998","unstructured":"Cox D, Little J, and O\u2019shea D, Using Algebraic Geomety, Springer, New York, 1998."}],"container-title":["Journal of Systems Science and Complexity"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11424-020-9314-6.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s11424-020-9314-6\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11424-020-9314-6.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,3,10]],"date-time":"2021-03-10T17:08:16Z","timestamp":1615396096000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s11424-020-9314-6"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,1,12]]},"references-count":18,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2021,6]]}},"alternative-id":["9314"],"URL":"https:\/\/doi.org\/10.1007\/s11424-020-9314-6","relation":{},"ISSN":["1009-6124","1559-7067"],"issn-type":[{"value":"1009-6124","type":"print"},{"value":"1559-7067","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,1,12]]},"assertion":[{"value":"14 November 2019","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"30 March 2020","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"12 January 2021","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}