{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,31]],"date-time":"2025-10-31T22:13:46Z","timestamp":1761948826534,"version":"3.40.3"},"publisher-location":"Cham","reference-count":38,"publisher":"Springer International Publishing","isbn-type":[{"type":"print","value":"9783031147876"},{"type":"electronic","value":"9783031147883"}],"license":[{"start":{"date-parts":[[2022,1,1]],"date-time":"2022-01-01T00:00:00Z","timestamp":1640995200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2022,1,1]],"date-time":"2022-01-01T00:00:00Z","timestamp":1640995200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2022]]},"DOI":"10.1007\/978-3-031-14788-3_8","type":"book-chapter","created":{"date-parts":[[2022,8,10]],"date-time":"2022-08-10T14:24:42Z","timestamp":1660141482000},"page":"124-142","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Analyses and\u00a0Implementations of\u00a0Chordality-Preserving Top-Down Algorithms for\u00a0Triangular Decomposition"],"prefix":"10.1007","author":[{"given":"Mingyu","family":"Dong","sequence":"first","affiliation":[]},{"given":"Chenqi","family":"Mou","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2022,8,11]]},"reference":[{"issue":"1\u20132","key":"8_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. 28(1\u20132), 105\u2013124 (1999)","journal-title":"J. Symb. Comput."},{"issue":"1","key":"8_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. 28(1), 125\u2013154 (1999)","journal-title":"J. Symb. Comput."},{"issue":"10","key":"8_CR3","doi-asserted-by":"publisher","first-page":"1233","DOI":"10.1016\/j.jsc.2011.12.043","volume":"47","author":"T B\u00e4chler","year":"2012","unstructured":"B\u00e4chler, T., Gerdt, V., Lange-Hegermann, M., Robertz, D.: Algorithmic Thomas decomposition of algebraic and differential systems. J. Symb. Comput. 47(10), 1233\u20131266 (2012)","journal-title":"J. Symb. Comput."},{"issue":"4","key":"8_CR4","doi-asserted-by":"publisher","first-page":"287","DOI":"10.1007\/s00453-004-1084-3","volume":"39","author":"A Berry","year":"2004","unstructured":"Berry, A., Blair, J., Heggernes, P., Peyton, B.: Maximum cardinality search for computing minimal triangulations of graphs. Algorithmica 39(4), 287\u2013298 (2004)","journal-title":"Algorithmica"},{"issue":"2","key":"8_CR5","doi-asserted-by":"publisher","first-page":"191","DOI":"10.1007\/s11424-008-9103-0","volume":"21","author":"F Chai","year":"2008","unstructured":"Chai, F., Gao, X.S., Yuan, C.: A characteristic set method for solving Boolean equations and applications in cryptanalysis of stream ciphers. J. Syst. Sci. Complex. 21(2), 191\u2013208 (2008)","journal-title":"J. Syst. Sci. Complex."},{"key":"8_CR6","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"27","DOI":"10.1007\/978-3-030-52200-1_3","volume-title":"Mathematical Software \u2013 ICMS 2020","author":"C Chen","year":"2020","unstructured":"Chen, C.: Chordality preserving incremental triangular decomposition and its implementation. In: Bigatti, A.M., Carette, J., Davenport, J.H., Joswig, M., de Wolff, T. (eds.) ICMS 2020. LNCS, vol. 12097, pp. 27\u201336. Springer, Cham (2020). https:\/\/doi.org\/10.1007\/978-3-030-52200-1_3"},{"key":"8_CR7","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., Moreno Maza, M., Pan, W.: Comprehensive triangular decomposition. In: Ganzha, V.G., Mayr, E.W., Vorozhtsov, E.V. (eds.) CASC 2007. LNCS, vol. 4770, pp. 73\u2013101. Springer, Heidelberg (2007). https:\/\/doi.org\/10.1007\/978-3-540-75187-8_7"},{"issue":"6","key":"8_CR8","doi-asserted-by":"publisher","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 decompositions of polynomial systems. J. Symb. Comput. 47(6), 610\u2013642 (2012)","journal-title":"J. Symb. Comput."},{"key":"8_CR9","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","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. 449, pp. 207\u2013220. Springer, Heidelberg (1990). https:\/\/doi.org\/10.1007\/3-540-52885-7_89"},{"issue":"1","key":"8_CR10","doi-asserted-by":"publisher","first-page":"73","DOI":"10.1137\/16M106995X","volume":"1","author":"D Cifuentes","year":"2017","unstructured":"Cifuentes, D., Parrilo, P.: Chordal networks of polynomial ideals. SIAM J. Appl. Algebra Geom. 1(1), 73\u2013110 (2017)","journal-title":"SIAM J. Appl. Algebra Geom."},{"key":"8_CR11","series-title":"Undergraduate Texts in Mathematics","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-319-16721-3","volume-title":"Ideals, Varieties, and Algorithms: An Introduction to Computational Algebraic Geometry and Commutative Algebra","author":"D Cox","year":"1997","unstructured":"Cox, D., Little, J., O\u2019Shea, D.: Ideals, Varieties, and Algorithms: An Introduction to Computational Algebraic Geometry and Commutative Algebra. Undergraduate Texts in Mathematics, Springer, New York (1997). https:\/\/doi.org\/10.1007\/978-3-319-16721-3"},{"key":"8_CR12","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"289","DOI":"10.1007\/3-540-15984-3_279","volume-title":"EUROCAL 1985","author":"J Della Dora","year":"1985","unstructured":"Della Dora, J., Dicrescenzo, C., Duval, D.: About a new method for computing in algebraic number fields. In: Caviness, B.F. (ed.) EUROCAL 1985. LNCS, vol. 204, pp. 289\u2013290. Springer, Heidelberg (1985). https:\/\/doi.org\/10.1007\/3-540-15984-3_279"},{"issue":"6","key":"8_CR13","doi-asserted-by":"publisher","first-page":"655","DOI":"10.1016\/j.jsc.2011.12.025","volume":"47","author":"XS Gao","year":"2012","unstructured":"Gao, X.S., Huang, Z.: Characteristic set algorithms for equation solving in finite fields. J. Symb. Comput. 47(6), 655\u2013679 (2012)","journal-title":"J. Symb. Comput."},{"key":"8_CR14","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-662-04963-1","volume-title":"A Singular Introduction to Commutative Algebra","author":"GM Greuel","year":"2002","unstructured":"Greuel, G.M., Pfister, G., Bachmann, O., Lossen, C., Sch\u00f6nemann, H.: A Singular Introduction to Commutative Algebra. Springer, Heidelberg (2002). https:\/\/doi.org\/10.1007\/978-3-662-04963-1"},{"key":"8_CR15","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"77","DOI":"10.1007\/978-3-642-21969-6_5","volume-title":"Progress in Cryptology \u2013 AFRICACRYPT 2011","author":"Z Huang","year":"2011","unstructured":"Huang, Z., Lin, D.: Attacking bivium and trivium with the characteristic set method. In: Nitaj, A., Pointcheval, D. (eds.) AFRICACRYPT 2011. LNCS, vol. 6737, pp. 77\u201391. Springer, Heidelberg (2011). https:\/\/doi.org\/10.1007\/978-3-642-21969-6_5"},{"key":"8_CR16","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/3-540-45084-X_1","volume-title":"Symbolic and Numerical Scientific Computation","author":"E Hubert","year":"2003","unstructured":"Hubert, E.: Notes on triangular sets and triangulation-decomposition algorithms I: polynomial systems. In: Winkler, F., Langer, U. (eds.) SNSC 2001. LNCS, vol. 2630, pp. 1\u201339. Springer, Heidelberg (2003). https:\/\/doi.org\/10.1007\/3-540-45084-X_1"},{"issue":"2","key":"8_CR17","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. 15(2), 143\u2013167 (1993)","journal-title":"J. Symb. Comput."},{"issue":"1\u20133","key":"8_CR18","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. Discret. Appl. Math. 33(1\u20133), 147\u2013160 (1991)","journal-title":"Discret. Appl. Math."},{"issue":"2","key":"8_CR19","doi-asserted-by":"publisher","first-page":"117","DOI":"10.1016\/S0747-7171(08)80086-7","volume":"13","author":"D Lazard","year":"1992","unstructured":"Lazard, D.: Solving zero-dimensional algebraic systems. J. Symb. Comput. 13(2), 117\u2013131 (1992)","journal-title":"J. Symb. Comput."},{"issue":"3","key":"8_CR20","doi-asserted-by":"publisher","first-page":"96","DOI":"10.1145\/1113439.1113456","volume":"39","author":"F Lemaire","year":"2005","unstructured":"Lemaire, F., Moreno Maza, M., Xie, Y.: The RegularChains library in MAPLE. ACM SIGSAM Bull. 39(3), 96\u201397 (2005)","journal-title":"ACM SIGSAM Bull."},{"key":"8_CR21","doi-asserted-by":"crossref","unstructured":"Li, H., Xia, B., Zhang, H., Zheng, T.: Choosing the variable ordering for cylindrical algebraic decomposition via exploiting chordal structure. In: Proceedings of ISSAC 2021, pp. 281\u2013288 (2021)","DOI":"10.1145\/3452143.3465520"},{"key":"8_CR22","doi-asserted-by":"crossref","unstructured":"Mou, C., Bai, Y.: On the chordality of polynomial sets in triangular decomposition in top-down style. In: Proceedings ISSAC 2018, pp. 287\u2013294 (2018)","DOI":"10.1145\/3208976.3208997"},{"key":"8_CR23","doi-asserted-by":"publisher","first-page":"108","DOI":"10.1016\/j.jsc.2019.10.011","volume":"102","author":"C Mou","year":"2021","unstructured":"Mou, C., Bai, Y., Lai, J.: Chordal graphs in triangular decomposition in top-down style. J. Symb. Comput. 102, 108\u2013131 (2021)","journal-title":"J. Symb. Comput."},{"key":"8_CR24","doi-asserted-by":"crossref","unstructured":"Mou, C., Ju, W.: Sparse triangular decomposition for computing equilibria of biological dynamic systems based on chordal graphs. In: IEEE\/ACM Transactions Computational Biology and Bioinformatics (2022)","DOI":"10.1109\/TCBB.2022.3156759"},{"key":"8_CR25","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"138","DOI":"10.1007\/978-3-030-43120-4_12","volume-title":"Mathematical Aspects of Computer and Information Sciences","author":"C Mou","year":"2020","unstructured":"Mou, C., Lai, J.: On the chordality of simple decomposition in top-down style. In: Slamanig, D., Tsigaridas, E., Zafeirakopoulos, Z. (eds.) MACIS 2019. LNCS, vol. 11989, pp. 138\u2013152. Springer, Cham (2020). https:\/\/doi.org\/10.1007\/978-3-030-43120-4_12"},{"key":"8_CR26","doi-asserted-by":"publisher","first-page":"102","DOI":"10.1016\/j.tcs.2012.11.009","volume":"468","author":"C Mou","year":"2013","unstructured":"Mou, C., Wang, D., Li, X.: Decomposing polynomial sets into simple sets over finite fields: the positive-dimensional case. Theoret. Comput. Sci. 468, 102\u2013113 (2013)","journal-title":"Theoret. Comput. Sci."},{"issue":"3","key":"8_CR27","doi-asserted-by":"publisher","first-page":"507","DOI":"10.1007\/s11786-007-0039-x","volume":"1","author":"W Niu","year":"2008","unstructured":"Niu, W., Wang, D.: Algebraic approaches to stability analysis of biological systems. Math. Comput. Sci. 1(3), 507\u2013539 (2008)","journal-title":"Math. Comput. Sci."},{"key":"8_CR28","doi-asserted-by":"crossref","unstructured":"Ritt, J.: Differential Equations from the Algebraic Standpoint. AMS (1932)","DOI":"10.1090\/coll\/014"},{"key":"8_CR29","doi-asserted-by":"crossref","unstructured":"Ritt, J.: Differential Algebra. AMS (1950)","DOI":"10.1090\/coll\/033"},{"issue":"2","key":"8_CR30","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. 16(2), 83\u2013114 (1993)","journal-title":"J. Symb. Comput."},{"issue":"3","key":"8_CR31","doi-asserted-by":"publisher","first-page":"295","DOI":"10.1006\/jsco.1997.0177","volume":"25","author":"D Wang","year":"1998","unstructured":"Wang, D.: Decomposing polynomial systems into simple systems. J. Symb. Comput. 25(3), 295\u2013314 (1998)","journal-title":"J. Symb. Comput."},{"key":"8_CR32","series-title":"Texts and Monographs in Symbolic Computation","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-7091-6202-6","volume-title":"Elimination Methods","author":"D Wang","year":"2001","unstructured":"Wang, D.: Elimination Methods. Texts and Monographs in Symbolic Computation, Springer Science & Business Media, New York (2001). https:\/\/doi.org\/10.1007\/978-3-7091-6202-6"},{"key":"8_CR33","doi-asserted-by":"crossref","unstructured":"Wang, D.: Epsilon: A library of software tools for polynomial elimination. In: Mathematical Software, pp. 379\u2013389. World Scientific (2002)","DOI":"10.1142\/9789812777171_0040"},{"key":"8_CR34","unstructured":"Wang, D.: wsolve: A Maple package for solving system of polynomial equations (2004). http:\/\/www.mmrc.iss.ac.cn"},{"key":"8_CR35","doi-asserted-by":"crossref","unstructured":"Wang, D., Xia, B.: Stability analysis of biological systems with real solution classification. In: Proceedings of ISSAC 2005, pp. 354\u2013361 (2005)","DOI":"10.1145\/1073884.1073933"},{"issue":"3","key":"8_CR36","doi-asserted-by":"publisher","first-page":"221","DOI":"10.1007\/BF02328447","volume":"2","author":"WT Wu","year":"1986","unstructured":"Wu, W.T.: Basic principles of mechanical theorem proving in elementary geometries. J. Autom. Reason. 2(3), 221\u2013252 (1986)","journal-title":"J. Autom. Reason."},{"key":"8_CR37","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"44","DOI":"10.1007\/3-540-51517-8_84","volume-title":"EUROCAL 1987","author":"WT Wu","year":"1989","unstructured":"Wu, W.T.: A zero structure theorem for polynomial-equations-solving and its applications. In: Davenport, J.H. (ed.) EUROCAL 1987. LNCS, vol. 378, pp. 44\u201344. Springer, Heidelberg (1989). https:\/\/doi.org\/10.1007\/3-540-51517-8_84"},{"key":"8_CR38","unstructured":"Yang, L., Zhang, J.: Searching dependency between algebraic equations: an algorithm applied to automated reasoning. In: Artificial Intelligence in Mathematics, pp. 147\u2013156 (1994)"}],"container-title":["Lecture Notes in Computer Science","Computer Algebra in Scientific Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-031-14788-3_8","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,8,11]],"date-time":"2022-08-11T23:15:52Z","timestamp":1660259752000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/978-3-031-14788-3_8"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022]]},"ISBN":["9783031147876","9783031147883"],"references-count":38,"URL":"https:\/\/doi.org\/10.1007\/978-3-031-14788-3_8","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"type":"print","value":"0302-9743"},{"type":"electronic","value":"1611-3349"}],"subject":[],"published":{"date-parts":[[2022]]},"assertion":[{"value":"11 August 2022","order":1,"name":"first_online","label":"First Online","group":{"name":"ChapterHistory","label":"Chapter History"}},{"value":"CASC","order":1,"name":"conference_acronym","label":"Conference Acronym","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"International Workshop on Computer Algebra in Scientific Computing","order":2,"name":"conference_name","label":"Conference Name","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Gebze","order":3,"name":"conference_city","label":"Conference City","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Turkey","order":4,"name":"conference_country","label":"Conference Country","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"2022","order":5,"name":"conference_year","label":"Conference Year","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"22 August 2022","order":7,"name":"conference_start_date","label":"Conference Start Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"26 August 2022","order":8,"name":"conference_end_date","label":"Conference End Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"24","order":9,"name":"conference_number","label":"Conference Number","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"casc2022","order":10,"name":"conference_id","label":"Conference ID","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"http:\/\/casc-conference.org\/","order":11,"name":"conference_url","label":"Conference URL","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Single-blind","order":1,"name":"type","label":"Type","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"EasyChair","order":2,"name":"conference_management_system","label":"Conference Management System","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"32","order":3,"name":"number_of_submissions_sent_for_review","label":"Number of Submissions Sent for Review","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"20","order":4,"name":"number_of_full_papers_accepted","label":"Number of Full Papers Accepted","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"0","order":5,"name":"number_of_short_papers_accepted","label":"Number of Short Papers Accepted","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"63% - The value is computed by the equation \"Number of Full Papers Accepted \/ Number of Submissions Sent for Review * 100\" and then rounded to a whole number.","order":6,"name":"acceptance_rate_of_full_papers","label":"Acceptance Rate of Full Papers","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"3.25","order":7,"name":"average_number_of_reviews_per_paper","label":"Average Number of Reviews per Paper","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"5.1","order":8,"name":"average_number_of_papers_per_reviewer","label":"Average Number of Papers per Reviewer","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"Yes","order":9,"name":"external_reviewers_involved","label":"External Reviewers Involved","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}}]}}