{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,22]],"date-time":"2026-04-22T13:19:01Z","timestamp":1776863941509,"version":"3.51.2"},"publisher-location":"Berlin, Heidelberg","reference-count":12,"publisher":"Springer Berlin Heidelberg","isbn-type":[{"value":"9783540878261","type":"print"},{"value":"9783540878278","type":"electronic"}],"license":[{"start":{"date-parts":[[2008,1,1]],"date-time":"2008-01-01T00:00:00Z","timestamp":1199145600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2008,1,1]],"date-time":"2008-01-01T00:00:00Z","timestamp":1199145600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2008]]},"DOI":"10.1007\/978-3-540-87827-8_20","type":"book-chapter","created":{"date-parts":[[2008,9,20]],"date-time":"2008-09-20T13:53:21Z","timestamp":1221918801000},"page":"236-245","source":"Crossref","is-referenced-by-count":6,"title":["An Algorithm for Transforming Regular Chain into Normal Chain"],"prefix":"10.1007","author":[{"given":"Banghe","family":"Li","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Dingkang","family":"Wang","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","reference":[{"key":"20_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., Maza, M.M.: On the Theories of Triangular Sets. J. Symbolic Computation\u00a028, 105\u2013124 (1999)","journal-title":"J. Symbolic Computation"},{"key":"20_CR2","doi-asserted-by":"publisher","first-page":"631","DOI":"10.1006\/jsco.1999.1562","volume":"31","author":"D. Bouziane","year":"2001","unstructured":"Bouziane, D., Kandri Rody, A.K., Maarouf, H.: Unmixed-dimensional Decomposition of a Finitely Generated Perfect Differential Ideal. J. Symbolic Computation.\u00a031, 631\u2013649 (2001)","journal-title":"J. Symbolic Computation."},{"key":"20_CR3","doi-asserted-by":"publisher","first-page":"335","DOI":"10.1145\/143242.143348","volume-title":"Proceedings ISSAC 1992","author":"X.S. Gao","year":"1992","unstructured":"Gao, X.S., Chou, S.C.: Solving parametric algebraic systems. In: Proceedings ISSAC 1992, Berkeley, July 27-29, pp. 335\u2013341. Association for Computing Machinery, New York (1992)"},{"key":"20_CR4","doi-asserted-by":"publisher","first-page":"143","DOI":"10.1006\/jsco.1993.1011","volume":"15","author":"M. Kalbrener","year":"1993","unstructured":"Kalbrener, M.: A Generalized Euclidean Algorithm for Computing Triangular Representations of Algebraic Varieties. J. Symbolic Computation\u00a015, 143\u2013167 (1993)","journal-title":"J. Symbolic Computation"},{"key":"20_CR5","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 demension. Discrete Appl. Math.\u00a033, 147\u2013160 (1991)","journal-title":"Discrete Appl. Math."},{"key":"20_CR6","unstructured":"Moreno, M.M.: On triangular decompositions of algebraic varieties. In: MEGA 2000, Bath, England (presented, 2000)"},{"key":"20_CR7","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4612-0129-8","volume-title":"Sturctured Matrices and Polynomials","author":"V.Y. Pan","year":"2001","unstructured":"Pan, V.Y.: Sturctured Matrices and Polynomials. Birkh\u00e4user, Boston (2001)"},{"issue":"10","key":"20_CR8","doi-asserted-by":"publisher","first-page":"1441","DOI":"10.1007\/s11425-007-0118-0","volume":"50","author":"D.K. Wang","year":"2007","unstructured":"Wang, D.K., Zhang, Y.: An algorithm for decomposing a polynomial system into normal ascending sets. Science in China, Series A: Mathematics\u00a050(10), 1441\u20131450 (2007)","journal-title":"Science in China, Series A: Mathematics"},{"key":"20_CR9","unstructured":"Wang, D.M.: Some Notes on Algebraic Method for Geometric Theorem Proving"},{"key":"20_CR10","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-7091-6202-6","volume-title":"Elimination Method","author":"D.M. Wang","year":"2001","unstructured":"Wang, D.M.: Elimination Method. Springer, New York (2001)"},{"key":"20_CR11","first-page":"20","volume":"4","author":"W.T. Wu","year":"1984","unstructured":"Wu, W.T.: Basic principles of mechanical theorem proving in elementray geometries. J. Syst. Sci. Math. Sci.\u00a04, 20\u2013235 (1984)","journal-title":"J. Syst. Sci. Math. Sci."},{"key":"20_CR12","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, Trieste (1991)"}],"container-title":["Lecture Notes in Computer Science","Computer Mathematics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-540-87827-8_20","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,5,9]],"date-time":"2024-05-09T07:13:14Z","timestamp":1715238794000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/978-3-540-87827-8_20"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2008]]},"ISBN":["9783540878261","9783540878278"],"references-count":12,"URL":"https:\/\/doi.org\/10.1007\/978-3-540-87827-8_20","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"value":"0302-9743","type":"print"},{"value":"1611-3349","type":"electronic"}],"subject":[],"published":{"date-parts":[[2008]]}}}