{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,1,11]],"date-time":"2025-01-11T05:37:27Z","timestamp":1736573847791,"version":"3.32.0"},"publisher-location":"Berlin, Heidelberg","reference-count":26,"publisher":"Springer Berlin Heidelberg","isbn-type":[{"type":"print","value":"9783540397281"},{"type":"electronic","value":"9783540397304"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2006]]},"DOI":"10.1007\/11856290_9","type":"book-chapter","created":{"date-parts":[[2006,9,19]],"date-time":"2006-09-19T07:36:09Z","timestamp":1158651369000},"page":"82-93","source":"Crossref","is-referenced-by-count":5,"title":["Some Properties of Triangular Sets and Improvement Upon Algorithm CharSer"],"prefix":"10.1007","author":[{"given":"Yong-Bin","family":"Li","sequence":"first","affiliation":[]}],"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","doi-asserted-by":"publisher","first-page":"125","DOI":"10.1006\/jsco.1999.0270","volume":"28","author":"P. Aubry","year":"1999","unstructured":"Aubry, P., Moreno Maza, M.: Triangular sets for solving polynomial systems: a comparative implementation of four methods. J. Symb. Comput.\u00a028, 125\u2013154 (1999)","journal-title":"J. Symb. Comput."},{"key":"9_CR3","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"crossref","first-page":"207","DOI":"10.1007\/3-540-52885-7_89","volume-title":"10th International Conference on Automated Deduction","author":"S.-C. Chou","year":"1990","unstructured":"Chou, S.-C., Gao, X.-S.: Ritt-Wu\u2019s decomposition algorithm and geometry theorem proving. In: Stickel, M.E. (ed.) CADE 1990. LNCS, vol.\u00a0449, pp. 207\u2013220. Springer, Heidelberg (1990)"},{"key":"9_CR4","doi-asserted-by":"crossref","unstructured":"Chou, S.-C., Gao, X.-S.: Computations with parametric equations. In: Proceedings ISAAC 1991, pp. 122\u2013127 (1991)","DOI":"10.1145\/120694.120710"},{"key":"9_CR5","series-title":"Lecture Notes in Computer Science","first-page":"335","volume-title":"Algorithms and Computation","author":"S.-C. Chou","year":"1992","unstructured":"Chou, S.-C., Gao, X.-S.: Solving parametric algebraic systems. In: Ibaraki, T., Iwama, K., Yamashita, M., Inagaki, Y., Nishizeki, T. (eds.) ISAAC 1992. LNCS, vol.\u00a0650, pp. 335\u2013341. Springer, Heidelberg (1992)"},{"key":"9_CR6","doi-asserted-by":"crossref","unstructured":"Dahan, X., Moreno Maza, M., Schost, \u00c9., Wu, W., Xie, Y.: Lifting techniques for triangular decomposition. In: ISSAC 2005, pp. 108\u2013115 (2005)","DOI":"10.1145\/1073884.1073901"},{"key":"9_CR7","doi-asserted-by":"crossref","unstructured":"Gallo, G., Mishra, B.: Efficient algorithms and bounds for Wu-Ritt characteristic sets. In: Proceedings MEGA 1990, pp. 119\u2013142 (1990)","DOI":"10.1007\/978-1-4612-0441-1_8"},{"key":"9_CR8","doi-asserted-by":"crossref","unstructured":"Gallo, G., Mishra, B.: Wu-Ritt characteristic sets and their complexity. In: Goodman, J.E., Pollack, R., Steiger, W. (eds.) Discrete and Computational Geometry: Papers from the DIMACS Special Year. Dimacs Series in Discrete Mathematics and Theoretical Computer Science, vol.\u00a06, pp. 111\u2013136 (1991)","DOI":"10.1090\/dimacs\/006\/07"},{"key":"9_CR9","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_CR10","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_CR11","first-page":"1595","volume":"34","author":"Z.-M. Li","year":"1989","unstructured":"Li, Z.-M.: Determinant polynomial sequences. Chinese Sci. Bull.\u00a034, 1595\u20131599 (1989)","journal-title":"Chinese Sci. Bull."},{"key":"9_CR12","doi-asserted-by":"crossref","unstructured":"Li, Y.-B., Zhang, J.-Z., Yang, L.: Decomposing polynomial systems into strong regular sets. In: 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","doi-asserted-by":"publisher","first-page":"484","DOI":"10.1016\/j.amc.2005.04.087","volume":"173","author":"Y.-B. Li","year":"2006","unstructured":"Li, Y.-B.: An alternative algorithm for computing the pseudo-remainder of multivariate polynomials. Applied Mathematics and Computation\u00a0173, 484\u2013492 (2006)","journal-title":"Applied Mathematics and Computation"},{"key":"9_CR15","unstructured":"Wang, D.: Some improvements on Wu\u2019s method for solving systems of algebraic equations. In: Wen-Ts\u00fcn, W., Min-De, C. (eds.) Proc. of the Int. Workshop on Math. Mechanisation, Beijing, China (1992)"},{"key":"9_CR16","doi-asserted-by":"publisher","first-page":"83","DOI":"10.1006\/jsco.1993.1035","volume":"16","author":"D. Wang","year":"1993","unstructured":"Wang, D.: An elimination method for polynomial systems. J. Symb. Comput.\u00a016, 83\u2013114 (1993)","journal-title":"J. Symb. Comput."},{"key":"9_CR17","doi-asserted-by":"crossref","first-page":"187","DOI":"10.1007\/978-3-7091-6604-8_9","volume-title":"Automated Practical Reasoning: Algebraic Approaches","author":"D. Wang","year":"1995","unstructured":"Wang, D.: An implementation of the characteristic set method in Maple. In: Pfalzgraf, J., Wang, D. (eds.) Automated Practical Reasoning: Algebraic Approaches, pp. 187\u2013201. Springer, Wien (1995)"},{"key":"9_CR18","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, Wien (2001)"},{"key":"9_CR19","volume-title":"Elimination Practice","author":"D. Wang","year":"2003","unstructured":"Wang, D.: Elimination Practice. Imperial College Press, London (2003)"},{"key":"9_CR20","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_CR21","first-page":"1","volume":"31","author":"W.-T. Wu","year":"1986","unstructured":"Wu, W.-T.: On zeros of algebraic equations\u2013an application of Ritt principle. Kexue Tongbao\u00a031, 1\u20135 (1986)","journal-title":"Kexue Tongbao"},{"key":"9_CR22","first-page":"2","volume":"1","author":"W.-T. Wu","year":"1987","unstructured":"Wu, W.-T.: A zero structure theorem for polynomial equations solving. MM Research Preprints\u00a01, 2\u201312 (1987)","journal-title":"MM Research Preprints"},{"key":"9_CR23","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_CR24","volume-title":"Non-Linear equation systems and automated theorem proving","author":"L. Yang","year":"1996","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_CR25.1","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_CR25.2","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","Artificial Intelligence and Symbolic Computation"],"original-title":[],"link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/11856290_9.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,1,10]],"date-time":"2025-01-10T22:25:39Z","timestamp":1736547939000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/11856290_9"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2006]]},"ISBN":["9783540397281","9783540397304"],"references-count":26,"URL":"https:\/\/doi.org\/10.1007\/11856290_9","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"type":"print","value":"0302-9743"},{"type":"electronic","value":"1611-3349"}],"subject":[],"published":{"date-parts":[[2006]]}}}