{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,6,18]],"date-time":"2025-06-18T04:17:35Z","timestamp":1750220255693,"version":"3.41.0"},"publisher-location":"New York, NY, USA","reference-count":36,"publisher":"ACM","license":[{"start":{"date-parts":[[2022,7,4]],"date-time":"2022-07-04T00:00:00Z","timestamp":1656892800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.acm.org\/publications\/policies\/copyright_policy#Background"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["12001030, 12171469"],"award-info":[{"award-number":["12001030, 12171469"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100012226","name":"Fundamental Research Funds for the Central Universities","doi-asserted-by":"publisher","award":["2682022CX048"],"award-info":[{"award-number":["2682022CX048"]}],"id":[{"id":"10.13039\/501100012226","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100012166","name":"National Key Research and Development Program of China","doi-asserted-by":"publisher","award":["2020YFA0712300"],"award-info":[{"award-number":["2020YFA0712300"]}],"id":[{"id":"10.13039\/501100012166","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["dl.acm.org"],"crossmark-restriction":true},"short-container-title":[],"published-print":{"date-parts":[[2022,7,4]]},"DOI":"10.1145\/3476446.3535470","type":"proceedings-article","created":{"date-parts":[[2022,7,5]],"date-time":"2022-07-05T13:16:01Z","timestamp":1657026961000},"page":"343-350","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":0,"title":["A Property of Modules Over a Polynomial Ring With an Application in Multivariate Polynomial Matrix Factorizations"],"prefix":"10.1145","author":[{"given":"Dong","family":"Lu","sequence":"first","affiliation":[{"name":"Southwest Jiaotong University, Chengdu, China"}]},{"given":"Dingkang","family":"Wang","sequence":"additional","affiliation":[{"name":"KLMM, Academy of Mathematics and Systems Science, Chinese Academy of Sciences &amp; University of Chinese Academy of Sciences, Beijing, China"}]},{"given":"Fanghui","family":"Xiao","sequence":"additional","affiliation":[{"name":"Hunan Normal University, Changsha, China"}]},{"given":"Xiaopeng","family":"Zheng","sequence":"additional","affiliation":[{"name":"KLMM, Academy of Mathematics and Systems Science, Chinese Academy of Sciences &amp; University of Chinese Academy of Sciences, Beijing, China"}]}],"member":"320","published-online":{"date-parts":[[2022,7,5]]},"reference":[{"volume-title":"Multidimensional Systems Theory and Applications","author":"Bose N.K.","key":"e_1_3_2_1_1_1","unstructured":"N.K. Bose . 2003. Multidimensional Systems Theory and Applications second ed.). Kluwer Academic Publishers , Dordrecht . With contributions by B. Buchberger and J.P. Guiver. N.K. Bose. 2003. Multidimensional Systems Theory and Applications second ed.). Kluwer Academic Publishers, Dordrecht. With contributions by B. Buchberger and J.P. Guiver."},{"volume-title":"Applied Multidimensional Systems Theory","author":"Bose N.K.","key":"e_1_3_2_1_2_1","unstructured":"N.K. Bose . 2017. Applied Multidimensional Systems Theory . Springer , Cham . Second edition, With a preface by W.K. Jenkins, C. Lagoa and U. Srinivas. N.K. Bose. 2017. Applied Multidimensional Systems Theory .Springer, Cham. Second edition, With a preface by W.K. Jenkins, C. Lagoa and U. Srinivas."},{"key":"e_1_3_2_1_3_1","doi-asserted-by":"publisher","DOI":"10.1109\/82.809533"},{"volume-title":"Using Algebraic Geometry","author":"Cox D.","key":"e_1_3_2_1_4_1","unstructured":"D. Cox , J. Little , and D. O'shea . 2005. Using Algebraic Geometry . Springer , New York . D. Cox, J. Little, and D. O'shea. 2005. Using Algebraic Geometry .Springer, New York."},{"volume-title":"Proceedings of the 2005 ACM International Symposium on Symbolic and Algebraic Computation. ACM","author":"Deng J.","key":"e_1_3_2_1_5_1","unstructured":"J. Deng , F. Chen , and L. Shen . 2005. Computing \u03bc-bases of rational curves and surfaces using polynomial matrix factorization . In Proceedings of the 2005 ACM International Symposium on Symbolic and Algebraic Computation. ACM , New York, 132--139. J. Deng, F. Chen, and L. Shen. 2005. Computing \u03bc-bases of rational curves and surfaces using polynomial matrix factorization. In Proceedings of the 2005 ACM International Symposium on Symbolic and Algebraic Computation. ACM, New York, 132--139."},{"key":"e_1_3_2_1_6_1","unstructured":"D. Eisenbud. 2013. Commutative Algebra: with a view toward algebraic geometry .New York: Springer.  D. Eisenbud. 2013. Commutative Algebra: with a view toward algebraic geometry .New York: Springer."},{"key":"e_1_3_2_1_7_1","first-page":"23","article-title":"Applications of the Quillen-Suslin theorem to multidimensional systems theory. https:\/\/wwwb.math.rwth-aachen.de\/QuillenSuslin\/. In: H. Park and G. Regensburger, (Eds.), gr Bases in Control Theory and Signal Processing","volume":"3","author":"Fabia'nska A.","year":"2007","unstructured":"A. Fabia'nska and A. Quadrat . 2007 . Applications of the Quillen-Suslin theorem to multidimensional systems theory. https:\/\/wwwb.math.rwth-aachen.de\/QuillenSuslin\/. In: H. Park and G. Regensburger, (Eds.), gr Bases in Control Theory and Signal Processing , Radon Series on Computational and Applied Mathematics , Vol. 3 (2007), 23 -- 106 . A. Fabia'nska and A. Quadrat. 2007. Applications of the Quillen-Suslin theorem to multidimensional systems theory. https:\/\/wwwb.math.rwth-aachen.de\/QuillenSuslin\/. In: H. Park and G. Regensburger, (Eds.), gr Bases in Control Theory and Signal Processing, Radon Series on Computational and Applied Mathematics, Vol. 3 (2007), 23--106.","journal-title":"Radon Series on Computational and Applied Mathematics"},{"key":"e_1_3_2_1_8_1","doi-asserted-by":"publisher","DOI":"10.1023\/A:1008256224288"},{"key":"e_1_3_2_1_9_1","doi-asserted-by":"crossref","unstructured":"G. Greuel and G. Pfister. 2002. A SINGULAR Introduction to Commutative Algebra .Springer-Verlag.  G. Greuel and G. Pfister. 2002. A SINGULAR Introduction to Commutative Algebra .Springer-Verlag.","DOI":"10.1007\/978-3-662-04963-1"},{"key":"e_1_3_2_1_10_1","doi-asserted-by":"publisher","DOI":"10.1007\/s11424-018-7446-8"},{"key":"e_1_3_2_1_11_1","doi-asserted-by":"publisher","DOI":"10.1007\/s11045-018-0566-4"},{"key":"e_1_3_2_1_12_1","doi-asserted-by":"publisher","DOI":"10.1109\/TCS.1982.1085085"},{"key":"e_1_3_2_1_13_1","doi-asserted-by":"publisher","DOI":"10.1109\/31.7606"},{"key":"e_1_3_2_1_14_1","doi-asserted-by":"publisher","DOI":"10.1023\/A:1008427830183"},{"key":"e_1_3_2_1_15_1","doi-asserted-by":"publisher","DOI":"10.1016\/S0024-3795(01)00370-6"},{"volume-title":"Proceedings of the 2006 IEEE International Symposium on Circuits and Systems. 4911--4914","author":"Lin Z.","key":"e_1_3_2_1_16_1","unstructured":"Z. Lin , M.S. Boudellioua , and L. Xu . 2006. On the equivalence and factorization of multivariate polynomial matrices . In Proceedings of the 2006 IEEE International Symposium on Circuits and Systems. 4911--4914 . Z. Lin, M.S. Boudellioua, and L. Xu. 2006. On the equivalence and factorization of multivariate polynomial matrices. In Proceedings of the 2006 IEEE International Symposium on Circuits and Systems. 4911--4914."},{"key":"e_1_3_2_1_17_1","doi-asserted-by":"publisher","DOI":"10.1109\/TCSII.2005.850516"},{"key":"e_1_3_2_1_18_1","doi-asserted-by":"publisher","DOI":"10.1007\/s00034-010-9229-x"},{"key":"e_1_3_2_1_19_1","doi-asserted-by":"publisher","DOI":"10.1007\/s11045-009-0089-0"},{"key":"e_1_3_2_1_20_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.laa.2012.08.012"},{"key":"e_1_3_2_1_21_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.laa.2014.09.027"},{"volume-title":"Proceedings of the 2017 ACM International Symposium on Symbolic and Algebraic Computation. ACM","author":"Lu D.","key":"e_1_3_2_1_22_1","unstructured":"D. Lu , X. Ma , and D. Wang . 2017. A new algorithm for general factorizations of multivariate polynomial matrices . In Proceedings of the 2017 ACM International Symposium on Symbolic and Algebraic Computation. ACM , New York, 277--284. D. Lu, X. Ma, and D. Wang. 2017. A new algorithm for general factorizations of multivariate polynomial matrices. In Proceedings of the 2017 ACM International Symposium on Symbolic and Algebraic Computation. ACM, New York, 277--284."},{"key":"e_1_3_2_1_23_1","doi-asserted-by":"publisher","DOI":"10.1007\/s11045-019-00694-z"},{"key":"e_1_3_2_1_24_1","doi-asserted-by":"publisher","DOI":"10.1007\/s11045-021-00768-x"},{"key":"e_1_3_2_1_25_1","doi-asserted-by":"publisher","DOI":"10.1109\/PROC.1977.10582"},{"key":"e_1_3_2_1_26_1","doi-asserted-by":"publisher","DOI":"10.1080\/0025570X.1999.11996730"},{"key":"e_1_3_2_1_27_1","doi-asserted-by":"publisher","DOI":"10.23919\/ECC.2001.7076157"},{"key":"e_1_3_2_1_28_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jalgebra.2003.10.035"},{"key":"e_1_3_2_1_29_1","doi-asserted-by":"publisher","DOI":"10.1137\/S036301299122027X"},{"key":"e_1_3_2_1_30_1","doi-asserted-by":"publisher","DOI":"10.1109\/TCSI.2007.897720"},{"key":"e_1_3_2_1_31_1","doi-asserted-by":"publisher","DOI":"10.1109\/TCSII.2007.909866"},{"key":"e_1_3_2_1_32_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.laa.2004.04.020"},{"key":"e_1_3_2_1_33_1","doi-asserted-by":"publisher","DOI":"10.1007\/s00498-005-0155-6"},{"key":"e_1_3_2_1_34_1","doi-asserted-by":"publisher","DOI":"10.1007\/BF02741885"},{"key":"e_1_3_2_1_35_1","doi-asserted-by":"publisher","DOI":"10.1007\/s11424-021-0072-x"},{"key":"e_1_3_2_1_36_1","doi-asserted-by":"publisher","DOI":"10.1109\/TCS.1979.1084614"}],"event":{"name":"ISSAC '22: International Symposium on Symbolic and Algebraic Computation","sponsor":["SIGSAM ACM Special Interest Group on Symbolic and Algebraic Manipulation"],"location":"Villeneuve-d'Ascq France","acronym":"ISSAC '22"},"container-title":["Proceedings of the 2022 International Symposium on Symbolic and Algebraic Computation"],"original-title":[],"link":[{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/3476446.3535470","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/dl.acm.org\/doi\/pdf\/10.1145\/3476446.3535470","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,6,17]],"date-time":"2025-06-17T19:30:46Z","timestamp":1750188646000},"score":1,"resource":{"primary":{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/3476446.3535470"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,7,4]]},"references-count":36,"alternative-id":["10.1145\/3476446.3535470","10.1145\/3476446"],"URL":"https:\/\/doi.org\/10.1145\/3476446.3535470","relation":{},"subject":[],"published":{"date-parts":[[2022,7,4]]},"assertion":[{"value":"2022-07-05","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}