{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,4,22]],"date-time":"2025-04-22T22:10:02Z","timestamp":1745359802738,"version":"3.40.4"},"reference-count":27,"publisher":"Springer Science and Business Media LLC","issue":"4","license":[{"start":{"date-parts":[[2012,11,28]],"date-time":"2012-11-28T00:00:00Z","timestamp":1354060800000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Math.Comput.Sci."],"published-print":{"date-parts":[[2012,12]]},"DOI":"10.1007\/s11786-012-0136-3","type":"journal-article","created":{"date-parts":[[2012,11,27]],"date-time":"2012-11-27T05:18:52Z","timestamp":1353993532000},"page":"457-473","source":"Crossref","is-referenced-by-count":7,"title":["On Solving Parametric Polynomial Systems"],"prefix":"10.1007","volume":"6","author":[{"given":"Marc","family":"Moreno Maza","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Bican","family":"Xia","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Rong","family":"Xiao","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2012,11,28]]},"reference":[{"issue":"1\u20132","key":"136_CR1","doi-asserted-by":"crossref","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. 28(1\u20132), 105\u2013124 (1999)","journal-title":"J. Symb. Comput."},{"key":"136_CR2","doi-asserted-by":"crossref","DOI":"10.1007\/3-540-33099-2","volume-title":"Algorithms in Real Algebraic Geometry","author":"S. Basu","year":"2006","unstructured":"Basu S., Pollack R., Roy M.-F.: Algorithms in Real Algebraic Geometry. Springer, Berlin (2006)"},{"key":"136_CR3","doi-asserted-by":"crossref","unstructured":"Chen, C., Davenport, J.H., May, J., Moreno Maza, M., Xia, B., Xiao, R.: Triangular decomposition of semi-algebraic systems. In: Proceedings of ISSAC 2010, pp. 187\u2013194. ACM, New York (2010)","DOI":"10.1145\/1837934.1837972"},{"key":"136_CR4","doi-asserted-by":"crossref","unstructured":"Chen, C., Davenport, J.H., Moreno Maza, M., Xia, B., Xiao, R.: Computing with semi-algebraic sets represented by triangular decomposition. In: Proceedings of ISSAC 2011, pp. 75\u201382. ACM, New York (2011)","DOI":"10.1145\/1993886.1993903"},{"key":"136_CR5","doi-asserted-by":"crossref","unstructured":"Chen, C., Golubitsky, O., Lemaire, F., Moreno Maza, M., Pan, W.: Comprehensive triangular decomposition. In: Proceedings of CASC\u201907, Lecture Notes in Computer Science, vol. 4770, pp. 73\u2013101 (2007)","DOI":"10.1007\/978-3-540-75187-8_7"},{"issue":"6","key":"136_CR6","doi-asserted-by":"crossref","first-page":"610","DOI":"10.1016\/j.jsc.2011.12.023","volume":"47","author":"C. Chen","year":"2012","unstructured":"Chen C., Moreno Maza M.: Algorithms for computing triangular decomposition of polynomial systems. J. Symb. Comput. 47(6), 610\u2013642 (2012)","journal-title":"J. Symb. Comput."},{"key":"136_CR7","doi-asserted-by":"crossref","unstructured":"Chou, S.C., Gao, X.S.: Solving parametric algebraic systems. In: Proceedings ISSAC\u201992, pp. 335\u2013341, Berkeley (1992)","DOI":"10.1145\/143242.143348"},{"key":"136_CR8","first-page":"515","volume":"33","author":"G.E. Collins","year":"1975","unstructured":"Collins G.E.: Quantifier elimination for real closed fields by cylindrical algebraic decomposition. Springer Lect. Notes Comput. Sci. 33, 515\u2013532 (1975)","journal-title":"Springer Lect. Notes Comput. Sci."},{"issue":"3","key":"136_CR9","doi-asserted-by":"crossref","first-page":"299","DOI":"10.1016\/S0747-7171(08)80152-6","volume":"12","author":"G.E. Collins","year":"1991","unstructured":"Collins G.E., Hong H.: Partial cylindrical algebraic decomposition. J. Symb. Comput. 12(3), 299\u2013328 (1991)","journal-title":"J. Symb. Comput."},{"key":"136_CR10","doi-asserted-by":"crossref","unstructured":"Dolzmann, A., Sturm, T., Weispfenning, V.: Real quantifier elimination in practice. In: Algorithmic Algebra and Number Theory, pp. 221\u2013247. Springer, New York (1998)","DOI":"10.1007\/978-3-642-59932-3_11"},{"key":"136_CR11","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/s002080050316","volume":"315","author":"Z. Jelonek","year":"1999","unstructured":"Jelonek Z.: Testing sets for properness of polynomial mappings. Math. Ann. 315, 1\u201335 (1999)","journal-title":"Math. Ann."},{"key":"136_CR12","doi-asserted-by":"crossref","first-page":"143","DOI":"10.1006\/jsco.1993.1011","volume":"15","author":"M. Kalkbrener","year":"1933","unstructured":"Kalkbrener M.: A generalized euclidean algorithm for computing triangular representations of algebraic varieties. J. Symb. Comput. 15, 143\u2013167 (1933)","journal-title":"J. Symb. Comput."},{"key":"136_CR13","unstructured":"Kapur, D.: An approach for solving systems of parametric polynomial equations (1993)"},{"key":"136_CR14","doi-asserted-by":"crossref","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. Discret. Appl. Math. 33, 147\u2013160 (1991)","journal-title":"Discret. Appl. Math."},{"issue":"6","key":"136_CR15","doi-asserted-by":"crossref","first-page":"636","DOI":"10.1016\/j.jsc.2007.01.007","volume":"42","author":"D. Lazard","year":"2007","unstructured":"Lazard D., Rouillier F.: Solving parametric polynomial systems. J. Symb. Comput. 42(6), 636\u2013667 (2007)","journal-title":"J. Symb. Comput."},{"key":"136_CR16","doi-asserted-by":"crossref","first-page":"463","DOI":"10.1016\/j.jsc.2007.07.022","volume":"44","author":"M. Manubens","year":"2009","unstructured":"Manubens M., Montes A.: Minimal canonical comprehensive Gr\u00f6bner systems. J. Symb. Comput. 44, 463\u2013478 (2009)","journal-title":"J. Symb. Comput."},{"key":"136_CR17","unstructured":"Moreno Maza, M., Xia, B., Xiao, R.: On solving parametric polynomial systems. In: Raschau, S. (ed.) Proceedings of the Fourth Internationa Conference on Mathematical Aspects of Computer Science and Information Sciences (MACIS 2011), pp. 205\u2013215, Beijing (2011)"},{"issue":"2","key":"136_CR18","doi-asserted-by":"crossref","first-page":"183","DOI":"10.1006\/jsco.2001.0504","volume":"33","author":"A. Montes","year":"2002","unstructured":"Montes A.: A new algorithm for discussing Gr\u00f6bner bases with parameters. J. Symb. Comput. 33(2), 183\u2013208 (2002)","journal-title":"J. Symb. Comput."},{"key":"136_CR19","doi-asserted-by":"crossref","first-page":"349","DOI":"10.1007\/s00200-002-0109-x","volume":"13","author":"\u00c9. Schost","year":"2003","unstructured":"Schost \u00c9.: Computing parametric geometric resolutions. Appl. Algebra Eng. Commun. Comput. 13, 349\u2013393 (2003)","journal-title":"Appl. Algebra Eng. Commun. Comput."},{"issue":"2\u20133","key":"136_CR20","doi-asserted-by":"crossref","first-page":"321","DOI":"10.1016\/S0022-4049(01)00063-9","volume":"169","author":"A. Stasica","year":"2002","unstructured":"Stasica A.: An effective description of the Jelonek set. J. Pure Appl. Algebra 169(2\u20133), 321\u2013326 (2002)","journal-title":"J. Pure Appl. Algebra"},{"key":"136_CR21","volume-title":"Elimination Methods","author":"D.M. Wang","year":"2000","unstructured":"Wang D.M.: Elimination Methods. Springer, New York (2000)"},{"key":"136_CR22","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/0747-7171(92)90023-W","volume":"14","author":"V. Weispfenning","year":"1992","unstructured":"Weispfenning V.: Comprehensive Gr\u00f6bner bases. J. Symb. Comput. 14, 1\u201329 (1992)","journal-title":"J. Symb. Comput."},{"key":"136_CR23","doi-asserted-by":"crossref","unstructured":"Weispfenning, V.: Canonical comprehensive Gr\u00f6bner bases. In: ISSAC 2002, pp. 270\u2013276. ACM Press, New York (2002)","DOI":"10.1145\/780506.780541"},{"key":"136_CR24","first-page":"2","volume":"1","author":"W.T. Wu","year":"1987","unstructured":"Wu W.T.: A zero structure theorem for polynomial equations solving. MM Res Preprints 1, 2\u201312 (1987)","journal-title":"MM Res Preprints"},{"key":"136_CR25","unstructured":"Xiao, R.: Parametric polynomial system solving. PhD thesis, Peking University, Beijing (2009)"},{"key":"136_CR26","doi-asserted-by":"crossref","unstructured":"Yang, L., Hou, X., Xia, B.: Automated discovering and proving for geometric inequalities. In: Proceedings of ADG\u201998, pp. 30\u201346 (1999)","DOI":"10.1007\/3-540-47997-X_3"},{"key":"136_CR27","unstructured":"Yang, L., Xia, B.: Real solution classifications of a class of parametric semi-algebraic systems. In: Proceedings of the A3L\u201905, pp. 281\u2013289 (2005)"}],"container-title":["Mathematics in Computer Science"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11786-012-0136-3.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s11786-012-0136-3\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11786-012-0136-3","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,4,22]],"date-time":"2025-04-22T21:37:57Z","timestamp":1745357877000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s11786-012-0136-3"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2012,11,28]]},"references-count":27,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2012,12]]}},"alternative-id":["136"],"URL":"https:\/\/doi.org\/10.1007\/s11786-012-0136-3","relation":{},"ISSN":["1661-8270","1661-8289"],"issn-type":[{"type":"print","value":"1661-8270"},{"type":"electronic","value":"1661-8289"}],"subject":[],"published":{"date-parts":[[2012,11,28]]}}}