{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,7]],"date-time":"2025-10-07T11:47:50Z","timestamp":1759837670658,"version":"3.40.4"},"reference-count":17,"publisher":"Springer Science and Business Media LLC","issue":"4","license":[{"start":{"date-parts":[[2012,12,1]],"date-time":"2012-12-01T00:00:00Z","timestamp":1354320000000},"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\/s11786-012-0131-8","type":"journal-article","created":{"date-parts":[[2012,12,12]],"date-time":"2012-12-12T06:59:21Z","timestamp":1355295561000},"page":"361-374","source":"Crossref","is-referenced-by-count":6,"title":["Rational General Solutions of Trivariate Rational Differential Systems"],"prefix":"10.1007","volume":"6","author":[{"given":"Yanli","family":"Huang","sequence":"first","affiliation":[]},{"given":"L. X. Ch\u00e2u","family":"Ng\u00f4","sequence":"additional","affiliation":[]},{"given":"Franz","family":"Winkler","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2012,12,13]]},"reference":[{"issue":"4","key":"131_CR1","doi-asserted-by":"crossref","first-page":"325","DOI":"10.1145\/77269.77273","volume":"8","author":"S.S. Abhyankar","year":"1989","unstructured":"Abhyankar S.S., Bajaj C.L.: Automatic parametrization of rational curves and surfaces IV: algebraic space curves. ACM Trans. Graph. 8(4), 325\u2013334 (1989)","journal-title":"ACM Trans. Graph."},{"key":"131_CR2","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, 105\u2013124 (1999)","journal-title":"J. Symb. Comput."},{"key":"131_CR3","doi-asserted-by":"crossref","first-page":"289","DOI":"10.2307\/2118601","volume":"140","author":"M.M. Carnicer","year":"1994","unstructured":"Carnicer M.M.: The Poincar\u00e9 problem in the nondicritical case. Ann. Math. 140, 289\u2013294 (1994)","journal-title":"Ann. Math."},{"key":"131_CR4","doi-asserted-by":"crossref","first-page":"739","DOI":"10.1016\/j.jsc.2006.02.002","volume":"41","author":"R.Y. Feng","year":"2006","unstructured":"Feng R.Y., Gao X.S.: A polynomial time algorithm for finding rational general solutions of first order autonomous ODEs. J. Symb. Comput. 41, 739\u2013762 (2006)","journal-title":"J. Symb. Comput."},{"key":"131_CR5","doi-asserted-by":"crossref","unstructured":"Feng, R.Y., Gao, X.S.: Rational general solutions of algebraic ordinary differential equations. In: Proceedings of the 2004 International Symposium on Symbolic and Algebraic Computation (ISSAC\u20192004), pp. 155\u2013162. ACM Press, New York (2004)","DOI":"10.1145\/1005285.1005309"},{"key":"131_CR6","doi-asserted-by":"crossref","first-page":"641","DOI":"10.1006\/jsco.1999.0344","volume":"29","author":"E. Hubert","year":"2000","unstructured":"Hubert E.: Factorization-free decomposition algorithms in differential algebra. J. Symb. Comput. 29, 641\u2013662 (2000)","journal-title":"J. Symb. Comput."},{"key":"131_CR7","doi-asserted-by":"crossref","unstructured":"Hubert, E.: The general solution of an ordinary differential equation. In: Proceedings of the 1996 International Symposium on Symbolic and Algebraic Computation (ISSAC\u20191996), pp. 189\u2013195. ACM Press, New York (1996)","DOI":"10.1145\/236869.237073"},{"key":"131_CR8","volume-title":"Differential algebra and algebraic groups","author":"E.R. Kolchin","year":"1973","unstructured":"Kolchin E.R.: Differential algebra and algebraic groups. Academic Press, New York (1973)"},{"key":"131_CR9","doi-asserted-by":"crossref","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. 15, 143\u2013167 (1993)","journal-title":"J. Symb. Comput."},{"key":"131_CR10","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 algbebraic systems of positive dimension. Discret. Apll. Math. 33, 147\u2013160 (1991)","journal-title":"Discret. Apll. Math."},{"key":"131_CR11","doi-asserted-by":"crossref","unstructured":"Lemaire, F., Moreno Maza, M., Pan, W., Xie, Y.: When does $${\\langle T \\rangle}$$ equal sat(T)? In: Proceedings of the 2008 International Symposium on Symbolic and Algebraic Computation (ISSAC\u20192008), pp. 207\u2013214, ACM Press, New York (2008)","DOI":"10.1145\/1390768.1390798"},{"key":"131_CR12","doi-asserted-by":"crossref","first-page":"1426","DOI":"10.1016\/j.jsc.2010.06.018","volume":"45","author":"L.X.C. Ng\u00f4","year":"2010","unstructured":"Ng\u00f4 L.X.C., Winkler F.: Rational general solutions of first order non-autonomous parametrizable ODEs. J. Symb. Comput. 45, 1426\u20131441 (2010)","journal-title":"J. Symb. Comput."},{"key":"131_CR13","doi-asserted-by":"crossref","first-page":"1173","DOI":"10.1016\/j.jsc.2011.06.002","volume":"46","author":"L.X.C. Ng\u00f4","year":"2011","unstructured":"Ng\u00f4 L.X.C., Winkler F.: Rational general solutions of planar rational systems of autonomous ODEs. J. Symb. Comput. 46, 1173\u20131186 (2011)","journal-title":"J. Symb. Comput."},{"key":"131_CR14","doi-asserted-by":"crossref","DOI":"10.1090\/coll\/033","volume-title":"Differential algebra","author":"J.F. Ritt","year":"1950","unstructured":"Ritt J.F.: Differential algebra. American Mathematical Society, Colloquium Publications, New York (1950)"},{"key":"131_CR15","doi-asserted-by":"crossref","first-page":"191","DOI":"10.1006\/jsco.1996.0083","volume":"23","author":"J.R. Sendra","year":"1997","unstructured":"Sendra J.R., Winkler F.: Parametrization of algebraic curves over optimal field extensions. J. Symb. Comput. 23, 191\u2013207 (1997)","journal-title":"J. Symb. Comput."},{"key":"131_CR16","doi-asserted-by":"crossref","first-page":"771","DOI":"10.1016\/S0167-8396(01)00069-3","volume":"18","author":"J.R. Sendra","year":"2001","unstructured":"Sendra J.R., Winkler F.: Tracing index of rational curve parametrization. Comput. Aided Geom. Des. 18, 771\u2013795 (2001)","journal-title":"Comput. Aided Geom. Des."},{"key":"131_CR17","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-540-73725-4","volume-title":"Rational algebraic curves: a computer algebra approach","author":"J.R. Sendra","year":"2008","unstructured":"Sendra J.R., Winkler F., P\u00e9rez-D\u00edaz S.: Rational algebraic curves: a computer algebra approach. Springer, Berlin (2008)"}],"container-title":["Mathematics in Computer Science"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11786-012-0131-8.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s11786-012-0131-8\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11786-012-0131-8","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,4,23]],"date-time":"2025-04-23T14:56:35Z","timestamp":1745420195000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s11786-012-0131-8"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2012,12]]},"references-count":17,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2012,12]]}},"alternative-id":["131"],"URL":"https:\/\/doi.org\/10.1007\/s11786-012-0131-8","relation":{},"ISSN":["1661-8270","1661-8289"],"issn-type":[{"type":"print","value":"1661-8270"},{"type":"electronic","value":"1661-8289"}],"subject":[],"published":{"date-parts":[[2012,12]]}}}