{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,9,5]],"date-time":"2024-09-05T17:49:18Z","timestamp":1725558558203},"publisher-location":"Berlin, Heidelberg","reference-count":22,"publisher":"Springer Berlin Heidelberg","isbn-type":[{"type":"print","value":"9783642141270"},{"type":"electronic","value":"9783642141287"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2010]]},"DOI":"10.1007\/978-3-642-14128-7_9","type":"book-chapter","created":{"date-parts":[[2010,6,29]],"date-time":"2010-06-29T10:45:36Z","timestamp":1277808336000},"page":"89-100","source":"Crossref","is-referenced-by-count":1,"title":["Some Notes upon \u201cWhen Does $&lt;{\\mathbb T}&gt;$ Equal Sat $({\\mathbb T})$ ?\u201d"],"prefix":"10.1007","author":[{"given":"Yongbin","family":"Li","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","reference":[{"key":"9_CR1","doi-asserted-by":"publisher","first-page":"105","DOI":"10.1006\/jsco.1999.0269","volume":"28","author":"P. Aubry","year":"1999","unstructured":"Aubry, P., Lazard, D., Moreno Maza, M.: On the theories of triangular sets. J. Symb. Comput.\u00a028, 105\u2013124 (1999)","journal-title":"J. Symb. Comput."},{"key":"9_CR2","unstructured":"Boulier, F., Lemaire, F., Moreno Maza, M.: Well known theorems on triangular systems and the D5 principle. In: Proc. of Transgressive Computing 2006 (2006)"},{"key":"9_CR3","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"73","DOI":"10.1007\/978-3-540-75187-8_7","volume-title":"Computer Algebra in Scientific Computing","author":"C. Chen","year":"2007","unstructured":"Chen, C., Golubitsky, O., Lemaire, F., Maza, M.M., Pan, W.: Comprehensive triangular decomposition. In: Ganzha, V.G., Mayr, E.W., Vorozhtsov, E.V. (eds.) CASC 2007. LNCS, vol.\u00a04770, pp. 73\u2013101. Springer, Heidelberg (2007)"},{"key":"9_CR4","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4757-2181-2","volume-title":"Ideals, Varieties, and algorithms","author":"D. Cox","year":"1992","unstructured":"Cox, D., Little, J., O\u2019Shea, D.: Ideals, Varieties, and algorithms. Springer, Heidelberg (1992)"},{"key":"9_CR5","doi-asserted-by":"crossref","unstructured":"Dahan, X., Maza, M.M., Schost, E., Wu, W., Xie, Y.: Lifting techniques for triangular decompositions. In: Proceedings ISSAC 2005, Beijing, China (2005)","DOI":"10.1145\/1073884.1073901"},{"key":"9_CR6","doi-asserted-by":"publisher","first-page":"207","DOI":"10.1145\/1390768.1390798","volume-title":"Proceedings ISSAC 2008","author":"F. Lemaire","year":"2008","unstructured":"Lemaire, F., Moreno Maza, M., Pan, W., Xie, Y.: When does $<{{\\mathbb T}}> = { \\rm sat}({\\mathbb T})$ ? In: Proceedings ISSAC 2008, pp. 207\u2013214. ACM Press, New York (2008)"},{"key":"9_CR7","doi-asserted-by":"crossref","unstructured":"Gao, X.-S., Chou, S.-C.: Computations with parametric equations. In: Proceedings ISAAC 1991, pp. 122\u2013127 (1991)","DOI":"10.1145\/120694.120710"},{"key":"9_CR8","first-page":"799","volume":"38","author":"X.-S. Gao","year":"1993","unstructured":"Gao, X.-S., Chou, S.-C.: On the dimension of an arbitray ascending chain. Chin. Sci. Bull.\u00a038, 799\u2013804 (1993)","journal-title":"Chin. Sci. Bull."},{"key":"9_CR9","unstructured":"Huang, F.-J.: Researches on Algorithms of Decomposition of Polynomial System. Ph.D. Thesis. Chengdu Institute of Computer Applications, China (2007)"},{"key":"9_CR10","doi-asserted-by":"publisher","first-page":"143","DOI":"10.1006\/jsco.1993.1011","volume":"15","author":"M. Kalkbrener","year":"1993","unstructured":"Kalkbrener, M.: A generalized Euclidean algorithm for computing triangular representations of algebraic varieties. J. Symb. Comput.\u00a015, 143\u2013167 (1993)","journal-title":"J. Symb. Comput."},{"key":"9_CR11","doi-asserted-by":"publisher","first-page":"147","DOI":"10.1016\/0166-218X(91)90113-B","volume":"33","author":"D. Lazard","year":"1991","unstructured":"Lazard, D.: A new method for solving algebraic systems of positive dimension. Discrete Appl. Math.\u00a033, 147\u2013160 (1991)","journal-title":"Discrete Appl. Math."},{"key":"9_CR12","doi-asserted-by":"crossref","unstructured":"Li, Y.-B., Zhang, J.-Z., Yang, L.: Decomposing polynomial systems into strong regular sets. In: Cohen, A.M., Gao, X.-S., Takayama, N. (eds.) Proceedings ICMS 2002, pp. 361\u2013371 (2002)","DOI":"10.1142\/9789812777171_0038"},{"key":"9_CR13","doi-asserted-by":"publisher","first-page":"815","DOI":"10.1016\/j.jsc.2003.10.004","volume":"38","author":"Y.-B. Li","year":"2004","unstructured":"Li, Y.-B.: Applications of the theory of weakly nondegenerate conditions to zero decomposition for polynomial systems. J. Symb. Comput.\u00a038, 815\u2013832 (2004)","journal-title":"J. Symb. Comput."},{"key":"9_CR14","series-title":"Lecture Notes in Artificial Intelligence","doi-asserted-by":"publisher","first-page":"82","DOI":"10.1007\/11856290_9","volume-title":"Artificial Intelligence and Symbolic Computation","author":"Y.-B. Li","year":"2006","unstructured":"Li, Y.-B.: Some Properties of Triangular Sets and Improvement Upon Algorithm CharSer. In: Calmet, J., Ida, T., Wang, D. (eds.) AISC 2006. LNCS (LNAI), vol.\u00a04120, pp. 82\u201393. Springer, Heidelberg (2006)"},{"key":"9_CR15","doi-asserted-by":"publisher","first-page":"221","DOI":"10.1006\/jsco.1999.0355","volume":"30","author":"D. Wang","year":"2000","unstructured":"Wang, D.: Computing triangular systems and regular systems. J. Symb. Comput.\u00a030, 221\u2013236 (2000)","journal-title":"J. Symb. Comput."},{"key":"9_CR16","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-7091-6202-6","volume-title":"Elimination Methods","author":"D. Wang","year":"2001","unstructured":"Wang, D.: Elimination Methods. Springer, New York (2001)"},{"key":"9_CR17","first-page":"159","volume":"21","author":"W.-T. Wu","year":"1978","unstructured":"Wu, W.-T.: On the decision problem and the mechanization of theorem-proving in elementary geometry. Scientia Sinica\u00a021, 159\u2013172 (1978)","journal-title":"Scientia Sinica"},{"key":"9_CR18","first-page":"1","volume":"31","author":"W.-T. Wu","year":"1986","unstructured":"Wu, W.-T.: On zeros of algebraic equations \u2014 An application of Ritt principle. Kexue Tongbao\u00a031, 1\u20135 (1986)","journal-title":"Kexue Tongbao"},{"key":"9_CR19","unstructured":"Yang, L., Zhang, J.-Z.: Search dependency between algebraic equations: An algorithm applied to automated reasoning. Technical Report ICTP\/91\/6, International Center For Theoretical Physics, International Atomic Energy Agency, Miramare, Trieste (1991)"},{"key":"9_CR20","unstructured":"Yang, L., Zhang, J.-Z., Hou, X.-R.: Non-Linear Equation Systems and Automated Theorem Proving. Shanghai Sci. & Tech. Education Publ. House, Shanghai (1996) (in Chinese)"},{"key":"#cr-split#-9_CR21.1","unstructured":"Zhang, J.-Z., Yang, L., Hou, X.-R.: A note on Wu Wen-Ts??n???s nondegenerate condition. Technical Report ICTP\/91\/160, International Center For Theoretical Physics, International Atomic Energy Agency, Miramare, Trieste (1991);"},{"key":"#cr-split#-9_CR21.2","doi-asserted-by":"crossref","unstructured":"Also in Chinese Science Bulletin, 38(1), 86???87 (1993)","DOI":"10.1037\/032978"}],"container-title":["Lecture Notes in Computer Science","Intelligent Computer Mathematics"],"original-title":[],"link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-642-14128-7_9.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,11,24]],"date-time":"2020-11-24T02:47:53Z","timestamp":1606186073000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/978-3-642-14128-7_9"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2010]]},"ISBN":["9783642141270","9783642141287"],"references-count":22,"URL":"https:\/\/doi.org\/10.1007\/978-3-642-14128-7_9","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"type":"print","value":"0302-9743"},{"type":"electronic","value":"1611-3349"}],"subject":[],"published":{"date-parts":[[2010]]}}}