{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,23]],"date-time":"2026-01-23T12:09:20Z","timestamp":1769170160612,"version":"3.49.0"},"publisher-location":"New York, NY, USA","reference-count":21,"publisher":"ACM","license":[{"start":{"date-parts":[[2008,7,20]],"date-time":"2008-07-20T00:00:00Z","timestamp":1216512000000},"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":[],"published-print":{"date-parts":[[2008,7,20]]},"DOI":"10.1145\/1390768.1390798","type":"proceedings-article","created":{"date-parts":[[2008,7,22]],"date-time":"2008-07-22T13:46:39Z","timestamp":1216734399000},"page":"207-214","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":6,"title":["When does (\n            <i>T<\/i>\n            ) equal sat(\n            <i>T<\/i>\n            )?"],"prefix":"10.1145","author":[{"given":"Francois","family":"Lemaire","sequence":"first","affiliation":[{"name":"University of Lille 1, Lille, France"}]},{"given":"Marc Moreno","family":"Maza","sequence":"additional","affiliation":[{"name":"University of Western Ontario, London, ON, Canada"}]},{"given":"Wei","family":"Pan","sequence":"additional","affiliation":[{"name":"University of Western Ontario, London, ON, Canada"}]},{"given":"Yuzhen","family":"Xie","sequence":"additional","affiliation":[{"name":"University of Western Ontario, London, ON, Canada"}]}],"member":"320","published-online":{"date-parts":[[2008,7,20]]},"reference":[{"key":"e_1_3_2_1_1_1","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9939-1970-0252360-3"},{"key":"e_1_3_2_1_2_1","doi-asserted-by":"publisher","DOI":"10.1006\/jsco.1999.0269"},{"key":"e_1_3_2_1_3_1","doi-asserted-by":"publisher","DOI":"10.1006\/jsco.1999.0270"},{"key":"e_1_3_2_1_4_1","first-page":"2006","article-title":"Well known theorems on triangular systems and the d5 principle","author":"Boulier F.","year":"2006","unstructured":"F. Boulier , F. Lemaire , and M. Moreno Maza . Well known theorems on triangular systems and the d5 principle . In Transgressive Computing 2006 , 2006 . F. Boulier, F. Lemaire, and M. Moreno Maza. Well known theorems on triangular systems and the d5 principle. In Transgressive Computing 2006, 2006.","journal-title":"Transgressive Computing"},{"key":"e_1_3_2_1_5_1","series-title":"Lecture Notes in Computer Science","first-page":"73","volume-title":"Comprehensive triangular decomposition","author":"Chen C.","year":"2007","unstructured":"C. Chen , F. Lemaire , O. Golubitsky , M. Moreno Maza , and W. Pan . Comprehensive triangular decomposition . In Lecture Notes in Computer Science , volume 4770 , pages 73 -- 101 . Springer-Verlag , 2007 . C. Chen, F. Lemaire, O. Golubitsky, M. Moreno Maza, and W. Pan. Comprehensive triangular decomposition. In Lecture Notes in Computer Science, volume 4770, pages 73--101. Springer-Verlag, 2007."},{"key":"e_1_3_2_1_6_1","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-540-72586-2_38"},{"key":"e_1_3_2_1_7_1","first-page":"799","article-title":"On the dimension of an arbitrary ascending chain","volume":"38","author":"Chou S.C.","year":"1991","unstructured":"S.C. Chou and X.S. Gao . On the dimension of an arbitrary ascending chain . Chinese Bull. of Sci. , 38 : 799 -- 804 , 1991 . S.C. Chou and X.S. Gao. On the dimension of an arbitrary ascending chain. Chinese Bull. of Sci., 38:799--804, 1991.","journal-title":"Chinese Bull. of Sci."},{"key":"e_1_3_2_1_8_1","volume-title":"L'id\u00e9al des coefficients du produit de deux polyn\u00f4mes. Revue des Math\u00e9matiques de l'enseignement Sup\u00e9rieur, 113(3):25--39","author":"Coquand T.","year":"2003","unstructured":"T. Coquand , L. Ducos , H. Lombardi , and C. Quitt\u00e9 . L'id\u00e9al des coefficients du produit de deux polyn\u00f4mes. Revue des Math\u00e9matiques de l'enseignement Sup\u00e9rieur, 113(3):25--39 , 2003 . T. Coquand, L. Ducos, H. Lombardi, and C. Quitt\u00e9. L'id\u00e9al des coefficients du produit de deux polyn\u00f4mes. Revue des Math\u00e9matiques de l'enseignement Sup\u00e9rieur, 113(3):25--39, 2003."},{"key":"e_1_3_2_1_9_1","doi-asserted-by":"publisher","DOI":"10.1016\/S0022-4049(97)80001-1"},{"key":"e_1_3_2_1_10_1","doi-asserted-by":"crossref","unstructured":"D. Eisenbud. Commutative Algebra. Springer-Verlag 1994.  D. Eisenbud. Commutative Algebra. Springer-Verlag 1994.","DOI":"10.1007\/978-1-4612-5350-1"},{"key":"e_1_3_2_1_11_1","first-page":"1","volume-title":"SNSC","author":"Hubert E.","year":"2001","unstructured":"E. Hubert . Notes on triangular sets and triangulation-decomposition algorithms i: Polynomial systems . In SNSC , pages 1 -- 39 , 2001 . E. Hubert. Notes on triangular sets and triangulation-decomposition algorithms i: Polynomial systems. In SNSC, pages 1--39, 2001."},{"key":"e_1_3_2_1_12_1","volume-title":"Ideals and reality. Projective modules and number of generators of ideals","author":"Ischebeck F.","year":"2005","unstructured":"F. Ischebeck and R. A. Rao . Ideals and reality. Projective modules and number of generators of ideals . Springer-Verlag , 2005 . F. Ischebeck and R. A. Rao. Ideals and reality. Projective modules and number of generators of ideals. Springer-Verlag, 2005."},{"key":"e_1_3_2_1_13_1","doi-asserted-by":"publisher","DOI":"10.1006\/jsco.1993.1011"},{"key":"e_1_3_2_1_14_1","doi-asserted-by":"publisher","DOI":"10.1006\/jsco.1998.0227"},{"key":"e_1_3_2_1_15_1","first-page":"355","volume-title":"Maple Conference 2005","author":"Lemaire F.","year":"2005","unstructured":"F. Lemaire , M. Moreno Maza , and Y. Xie . The RegularChains library. In Ilias S. Kotsireas, editor , Maple Conference 2005 , pages 355 -- 368 , 2005 . F. Lemaire, M. Moreno Maza, and Y. Xie. The RegularChains library. In Ilias S. Kotsireas, editor, Maple Conference 2005, pages 355--368, 2005."},{"key":"e_1_3_2_1_16_1","doi-asserted-by":"publisher","DOI":"10.1145\/1145768.1145809"},{"key":"e_1_3_2_1_18_1","first-page":"365","volume-title":"Proc. AAECC-11","author":"Moreno Maza M.","year":"1995","unstructured":"M. Moreno Maza and R. Rioboo . Polynomial gcd computations over towers of algebraic extensions . In Proc. AAECC-11 , pages 365 -- 382 . Springer , 1995 . M. Moreno Maza and R. Rioboo. Polynomial gcd computations over towers of algebraic extensions. In Proc. AAECC-11, pages 365--382. Springer, 1995."},{"key":"e_1_3_2_1_19_1","doi-asserted-by":"publisher","DOI":"10.1090\/cbms\/097"},{"key":"e_1_3_2_1_20_1","doi-asserted-by":"publisher","DOI":"10.1006\/jsco.1999.0355"},{"issue":"1","key":"e_1_3_2_1_21_1","first-page":"1","article-title":"On zeros of algebraic equations -- an application of Ritt principle","volume":"31","author":"Wu W.T.","year":"1986","unstructured":"W.T. Wu . On zeros of algebraic equations -- an application of Ritt principle . Kexue Tongbao , 31 ( 1 ): 1 - 5 , 1986 . W.T. Wu. On zeros of algebraic equations -- an application of Ritt principle. Kexue Tongbao, 31(1):1-5, 1986.","journal-title":"Kexue Tongbao"},{"key":"e_1_3_2_1_22_1","volume-title":"Miramare","author":"Yang L.","year":"1991","unstructured":"L. Yang and J. Zhang . Searching dependency between algebraic equations: an algorithm applied to automated reasoning. Technical report ic\/91\/6, International Atomic Engery Angency , Miramare , Trieste, Italy , 1991 . L. Yang and J. Zhang. Searching dependency between algebraic equations: an algorithm applied to automated reasoning. Technical report ic\/91\/6, International Atomic Engery Angency, Miramare, Trieste, Italy, 1991."}],"event":{"name":"ISSAC '08: International Symposium on Symbolic and Algebraic Computation","location":"Linz\/Hagenberg Austria","acronym":"ISSAC '08","sponsor":["ACM Association for Computing Machinery","SIGSAM ACM Special Interest Group on Symbolic and Algebraic Manipulation"]},"container-title":["Proceedings of the twenty-first international symposium on Symbolic and algebraic computation"],"original-title":[],"link":[{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/1390768.1390798","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/dl.acm.org\/doi\/pdf\/10.1145\/1390768.1390798","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,6,18]],"date-time":"2025-06-18T14:47:11Z","timestamp":1750258031000},"score":1,"resource":{"primary":{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/1390768.1390798"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2008,7,20]]},"references-count":21,"alternative-id":["10.1145\/1390768.1390798","10.1145\/1390768"],"URL":"https:\/\/doi.org\/10.1145\/1390768.1390798","relation":{},"subject":[],"published":{"date-parts":[[2008,7,20]]},"assertion":[{"value":"2008-07-20","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}