{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,16]],"date-time":"2026-03-16T22:34:02Z","timestamp":1773700442676,"version":"3.50.1"},"publisher-location":"New York, NY, USA","reference-count":52,"publisher":"ACM","license":[{"start":{"date-parts":[[2024,7,24]],"date-time":"2024-07-24T00:00:00Z","timestamp":1721779200000},"content-version":"vor","delay-in-days":366,"URL":"http:\/\/www.acm.org\/publications\/policies\/copyright_policy#Background"}],"funder":[{"DOI":"10.13039\/501100001665","name":"Agence Nationale de la Recherche","doi-asserted-by":"publisher","award":["ANR-18-CE33-0011, ANR-19-CE40-0018"],"award-info":[{"award-number":["ANR-18-CE33-0011, ANR-19-CE40-0018"]}],"id":[{"id":"10.13039\/501100001665","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Forschungsinitiative Rheinland-Pfalz"},{"DOI":"10.13039\/501100000781","name":"European Research Council","doi-asserted-by":"publisher","award":["101040794"],"award-info":[{"award-number":["101040794"]}],"id":[{"id":"10.13039\/501100000781","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Agence Nationale de la Recherche, Austrian Science Fund FWF","award":["ANR-19-CE48-0015, ANR-22-CE91-0007"],"award-info":[{"award-number":["ANR-19-CE48-0015, ANR-22-CE91-0007"]}]},{"DOI":"10.13039\/100015464","name":"European Office of Aerospace Research and Development","doi-asserted-by":"publisher","award":["FA8665-20-1-7029"],"award-info":[{"award-number":["FA8665-20-1-7029"]}],"id":[{"id":"10.13039\/100015464","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001659","name":"Deutsche Forschungsgemeinschaft","doi-asserted-by":"publisher","award":["TRR 195"],"award-info":[{"award-number":["TRR 195"]}],"id":[{"id":"10.13039\/501100001659","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["dl.acm.org"],"crossmark-restriction":true},"short-container-title":[],"published-print":{"date-parts":[[2023,7,24]]},"DOI":"10.1145\/3597066.3597069","type":"proceedings-article","created":{"date-parts":[[2023,7,5]],"date-time":"2023-07-05T18:15:27Z","timestamp":1688580927000},"page":"260-269","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":3,"title":["A Direttissimo Algorithm for Equidimensional Decomposition"],"prefix":"10.1145","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-8814-8493","authenticated-orcid":false,"given":"Christian","family":"Eder","sequence":"first","affiliation":[{"name":"RPTU Kaiserslautern-Landau, Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3756-0151","authenticated-orcid":false,"given":"Pierre","family":"Lairez","sequence":"additional","affiliation":[{"name":"Inria, Universit\u00e9 Paris-Saclay, France"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0009-0000-9869-7122","authenticated-orcid":false,"given":"Rafael","family":"Mohr","sequence":"additional","affiliation":[{"name":"Sorbonne Universit\u00e9, France and RPTU Kaiserslautern-Landau, Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9463-1257","authenticated-orcid":false,"given":"Mohab","family":"Safey El Din","sequence":"additional","affiliation":[{"name":"Sorbonne Universit\u00e9, France"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"320","published-online":{"date-parts":[[2023,7,24]]},"reference":[{"key":"e_1_3_2_1_1_1","unstructured":"M. Asadi A. Brandt C. Chen S. Covanov M. Kazemi F. Mansouri D. Mohajerani R.\u00a0H.\u00a0C. Moir M. Moreno\u00a0Maza D. Talaashrafi Linxiao Wang Ning Xie and Yuzhen Xie. 2021. Basic Polynomial Algebra Subprograms (BPAS) (Version 1.791)."},{"key":"e_1_3_2_1_2_1","doi-asserted-by":"publisher","DOI":"10.5555\/2947511.2947551"},{"key":"e_1_3_2_1_3_1","doi-asserted-by":"publisher","DOI":"10.1006\/jsco.2002.0563"},{"key":"e_1_3_2_1_4_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jsc.2014.09.025"},{"key":"e_1_3_2_1_5_1","doi-asserted-by":"crossref","unstructured":"Daniel\u00a0J. Bates Jonathan\u00a0D. Hauenstein Andrew\u00a0J. Sommese and Charles\u00a0W. Wampler. 2013. Numerically Solving Polynomial Systems with Bertini. SIAM.","DOI":"10.1137\/1.9781611972702"},{"key":"e_1_3_2_1_6_1","volume-title":"Vol.\u00a0141","author":"Becker Thomas","unstructured":"Thomas Becker and Volker Weispfenning. 1993. Gr\u00f6bner Bases. Graduate Texts in Mathematics, Vol.\u00a0141. Springer-Verlag."},{"key":"e_1_3_2_1_7_1","doi-asserted-by":"publisher","DOI":"10.1145\/3452143.3465545"},{"key":"e_1_3_2_1_8_1","unstructured":"J\u00e9r\u00e9my Berthomieu Christian Eder and Mohab Safey El\u00a0Din. 2022. New Efficient Algorithms for Computing Gr\u00f6bner Bases of Saturation Ideals (F4SAT) and Colon Ideals (Sparse-FGLM-colon). arxiv:2202.13387"},{"key":"e_1_3_2_1_9_1","doi-asserted-by":"publisher","DOI":"10.1137\/141000671"},{"key":"e_1_3_2_1_10_1","doi-asserted-by":"publisher","DOI":"10.1006\/jsco.1996.0125"},{"key":"e_1_3_2_1_11_1","first-page":"30","article-title":"3264 Conics in a Second","volume":"67","author":"Breiding Paul","year":"2020","unstructured":"Paul Breiding, Bernd Sturmfels, and Sascha Timme. 2020. 3264 Conics in a Second. Not. Am. Math. Soc. 67, 1 (2020), 30\u201337.","journal-title":"Not. Am. Math. Soc."},{"key":"e_1_3_2_1_12_1","volume-title":"Yet Another Ideal Decomposition Algorithm. In AAECC 1997(Lecture Notes in Computer Science). Springer, 39\u201354","author":"Caboara Massimo","year":"1997","unstructured":"Massimo Caboara, Pasqualina Conti, and Carlo Traverse. 1997. Yet Another Ideal Decomposition Algorithm. In AAECC 1997(Lecture Notes in Computer Science). Springer, 39\u201354."},{"key":"e_1_3_2_1_13_1","doi-asserted-by":"publisher","DOI":"10.1142\/S021812741350154X"},{"key":"e_1_3_2_1_14_1","volume-title":"Efficient Computations of Irredundant Triangular Decompositions with the Regularchains Library. In Int. Conf. Comput. Sci. Springer, 268\u2013271","author":"Chen Changbo","year":"2007","unstructured":"Changbo Chen, Fran\u00e7ois Lemaire, Marc Moreno\u00a0Maza, Wei Pan, and Yuzhen Xie. 2007. Efficient Computations of Irredundant Triangular Decompositions with the Regularchains Library. In Int. Conf. Comput. Sci. Springer, 268\u2013271."},{"key":"e_1_3_2_1_15_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jsc.2011.12.023"},{"key":"e_1_3_2_1_16_1","volume-title":"Ritt-Wu\u2019s Decomposition Algorithm and Geometry Theorem Proving. In 10th Int. Conf. Autom. Deduc.(Lecture Notes in Computer Science). Springer, 207\u2013220","author":"Chou Shang-Ching","year":"1990","unstructured":"Shang-Ching Chou and Xiao-Shan Gao. 1990. Ritt-Wu\u2019s Decomposition Algorithm and Geometry Theorem Proving. In 10th Int. Conf. Autom. Deduc.(Lecture Notes in Computer Science). Springer, 207\u2013220."},{"key":"e_1_3_2_1_17_1","unstructured":"David\u00a0A. Cox John Little and Donal O\u2019Shea. 2015. Ideals Varieties and Algorithms (4 ed.). Springer."},{"key":"e_1_3_2_1_18_1","volume-title":"Primary Decomposition: Algorithms and Comparisons. In Algorithmic Algebra Number Theory","author":"Decker Wolfram","year":"1999","unstructured":"Wolfram Decker, Gert-Martin Greuel, and Gerhard Pfister. 1999. Primary Decomposition: Algorithms and Comparisons. In Algorithmic Algebra Number Theory. Springer, 187\u2013220."},{"key":"e_1_3_2_1_19_1","unstructured":"Wolfram Decker Gert-Martin Greuel Gerhard Pfister and Hans Sch\u00f6nemann. 2021. Singular 4-2-1 \u2014 A computer algebra system for polynomial computations. http:\/\/www.singular.uni-kl.de."},{"key":"e_1_3_2_1_20_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jsc.2023.02.001"},{"key":"e_1_3_2_1_21_1","doi-asserted-by":"publisher","DOI":"10.1007\/BF01231331"},{"key":"e_1_3_2_1_22_1","volume-title":"Effective Methods in Algebraic Geometry","author":"Gallo Giovanni","unstructured":"Giovanni Gallo and Bhubaneswar Mishra. 1991. Efficient Algorithms and Bounds for Wu-Ritt Characteristic Sets. In Effective Methods in Algebraic Geometry. Birkh\u00e4user, 119\u2013142."},{"key":"e_1_3_2_1_23_1","doi-asserted-by":"publisher","DOI":"10.1007\/s11263-021-01567-4"},{"key":"e_1_3_2_1_24_1","doi-asserted-by":"publisher","DOI":"10.1016\/S0747-7171(88)80040-3"},{"key":"e_1_3_2_1_25_1","doi-asserted-by":"publisher","DOI":"10.1145\/3087604.3087624"},{"key":"e_1_3_2_1_26_1","first-page":"1","article-title":"Notes on Triangular Sets and Triangulation-Decomposition Algorithms I. In Symb","author":"Hubert Evelyne","year":"2003","unstructured":"Evelyne Hubert. 2003. Notes on Triangular Sets and Triangulation-Decomposition Algorithms I. In Symb. Numer. Sci. Comput.(Lecture Notes in Computer Science). Springer, 1\u201339.","journal-title":"Numer. Sci. Comput.(Lecture Notes in Computer Science). Springer"},{"key":"e_1_3_2_1_27_1","doi-asserted-by":"publisher","DOI":"10.1145\/3476446.3535488"},{"key":"e_1_3_2_1_28_1","doi-asserted-by":"publisher","DOI":"10.1016\/S0022-4049(01)00083-4"},{"key":"e_1_3_2_1_29_1","doi-asserted-by":"publisher","DOI":"10.1006\/jsco.1993.1011"},{"key":"e_1_3_2_1_30_1","doi-asserted-by":"publisher","DOI":"10.1006\/jsco.1994.1052"},{"key":"e_1_3_2_1_31_1","doi-asserted-by":"publisher","DOI":"10.1007\/3-540-54522-0_108"},{"key":"e_1_3_2_1_32_1","doi-asserted-by":"publisher","DOI":"10.1016\/0166-218X(91)90113-B"},{"key":"e_1_3_2_1_33_1","doi-asserted-by":"publisher","DOI":"10.1145\/345542.345633"},{"key":"e_1_3_2_1_34_1","doi-asserted-by":"publisher","DOI":"10.1016\/S0885-064X(03)00031-1"},{"key":"e_1_3_2_1_35_1","doi-asserted-by":"publisher","DOI":"10.1145\/1113439.1113456"},{"key":"e_1_3_2_1_36_1","unstructured":"Yang Lu and Zhang Jingzhong. 1994. Searching Dependency between Algebraic Equations: An Algorithm Applied to Automated Reasoning. In Artificial Intelligence in Mathematics."},{"key":"e_1_3_2_1_37_1","first-page":"263","article-title":"Regular Decompositions. In","author":"Moroz Guillaume","year":"2008","unstructured":"Guillaume Moroz. 2008. Regular Decompositions. In Comput. Math.(Lecture Notes in Computer Science). Springer, 263\u2013277.","journal-title":"Comput. Math.(Lecture Notes in Computer Science). Springer"},{"key":"e_1_3_2_1_38_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jsc.2003.08.004"},{"key":"e_1_3_2_1_39_1","doi-asserted-by":"publisher","DOI":"10.1007\/s11263-020-01420-0"},{"key":"e_1_3_2_1_40_1","unstructured":"Joseph\u00a0Fels Ritt. 1950. Differential Algebra. AMS."},{"key":"e_1_3_2_1_41_1","doi-asserted-by":"publisher","DOI":"10.1007\/s00454-004-1107-5"},{"key":"e_1_3_2_1_42_1","volume-title":"Proc. ISSAC 2018(ISSAC \u201918)","author":"El\u00a0Din Mohab Safey","year":"2018","unstructured":"Mohab Safey El\u00a0Din, Zhi-Hong Yang, and Lihong Zhi. 2018. On the Complexity of Computing Real Radicals of Polynomial Systems. In Proc. ISSAC 2018(ISSAC \u201918). Association for Computing Machinery, 351\u2013358."},{"key":"e_1_3_2_1_43_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jsc.2019.10.018"},{"key":"e_1_3_2_1_44_1","volume-title":"Introduction to Numerical Algebraic Geometry","author":"Sommese J.","unstructured":"Andrew\u00a0J. Sommese, Jan Verschelde, and Charles\u00a0W. Wampler. 2005. Introduction to Numerical Algebraic Geometry. In Solving Polynomial Equations, Manuel Bronstein, Arjeh\u00a0M. Cohen, Henri Cohen, David Eisenbud, Bernd Sturmfels, Alicia Dickenstein, and Ioannis\u00a0Z. Emiris (Eds.). Springer, 301\u2013337."},{"key":"e_1_3_2_1_45_1","unstructured":"The OSCAR team. 2023. OSCAR \u2013 Open Source Computer Algebra Research System."},{"key":"e_1_3_2_1_46_1","doi-asserted-by":"publisher","DOI":"10.1006\/jsco.1993.1035"},{"key":"e_1_3_2_1_47_1","volume-title":"Elimination Methods","author":"Wang Dongming","unstructured":"Dongming Wang. 2001. Elimination Methods. Springer."},{"key":"e_1_3_2_1_48_1","doi-asserted-by":"publisher","DOI":"10.1007\/s11704-007-0001-8"},{"key":"e_1_3_2_1_49_1","doi-asserted-by":"publisher","DOI":"10.1007\/BF02328447"},{"key":"e_1_3_2_1_50_1","volume-title":"Automated Discovering and Proving for Geometric Inequalities. In Int. Workshop Autom. Deduc. Geom. Springer, 30\u201346","author":"Yang Lu","year":"1998","unstructured":"Lu Yang, Xiaorong Hou, and Bican Xia. 1998. Automated Discovering and Proving for Geometric Inequalities. In Int. Workshop Autom. Deduc. Geom. Springer, 30\u201346."},{"key":"e_1_3_2_1_51_1","doi-asserted-by":"publisher","DOI":"10.1007\/BF02713938"},{"key":"e_1_3_2_1_52_1","doi-asserted-by":"crossref","unstructured":"Kazuhiro Yokoyama. 2002. Prime Decomposition of Polynomial Ideals over Finite Fields. In Mathematical Software. World Scientific 217\u2013227.","DOI":"10.1142\/9789812777171_0022"}],"event":{"name":"ISSAC 2023: International Symposium on Symbolic and Algebraic Computation 2023","location":"Troms\u00f8 Norway","acronym":"ISSAC 2023"},"container-title":["Proceedings of the 2023 International Symposium on Symbolic and Algebraic Computation"],"original-title":[],"link":[{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/3597066.3597069","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/dl.acm.org\/doi\/pdf\/10.1145\/3597066.3597069","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"https:\/\/dl.acm.org\/doi\/pdf\/10.1145\/3597066.3597069","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,8,22]],"date-time":"2025-08-22T09:37:14Z","timestamp":1755855434000},"score":1,"resource":{"primary":{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/3597066.3597069"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,7,24]]},"references-count":52,"alternative-id":["10.1145\/3597066.3597069","10.1145\/3597066"],"URL":"https:\/\/doi.org\/10.1145\/3597066.3597069","relation":{},"subject":[],"published":{"date-parts":[[2023,7,24]]},"assertion":[{"value":"2023-07-24","order":3,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}