{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,31]],"date-time":"2025-10-31T22:14:28Z","timestamp":1761948868190,"version":"3.40.3"},"publisher-location":"Cham","reference-count":19,"publisher":"Springer Nature Switzerland","isbn-type":[{"type":"print","value":"9783031417238"},{"type":"electronic","value":"9783031417245"}],"license":[{"start":{"date-parts":[[2023,1,1]],"date-time":"2023-01-01T00:00:00Z","timestamp":1672531200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2023,1,1]],"date-time":"2023-01-01T00:00:00Z","timestamp":1672531200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2023]]},"DOI":"10.1007\/978-3-031-41724-5_1","type":"book-chapter","created":{"date-parts":[[2023,8,23]],"date-time":"2023-08-23T07:02:38Z","timestamp":1692774158000},"page":"1-20","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Computing GCDs of\u00a0Multivariate Polynomials over\u00a0Algebraic Number Fields Presented with\u00a0Multiple Extensions"],"prefix":"10.1007","author":[{"given":"Mahsa","family":"Ansari","sequence":"first","affiliation":[]},{"given":"Michael","family":"Monagan","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2023,8,24]]},"reference":[{"key":"1_CR1","doi-asserted-by":"crossref","unstructured":"Ben-Or, M., Tiwari, P.: A deterministic algorithm for sparse multivariate polynomial interpolation. In: Proceedings of STOC 1988, pp. 301\u2013309. ACM (1988)","DOI":"10.1145\/62212.62241"},{"key":"1_CR2","doi-asserted-by":"publisher","first-page":"478","DOI":"10.1145\/321662.321664","volume":"18","author":"WS Brown","year":"1971","unstructured":"Brown, W.S.: On Euclid\u2019s algorithm and the computation of polynomial greatest common divisors. J. ACM 18, 478\u2013504 (1971)","journal-title":"J. ACM"},{"key":"1_CR3","doi-asserted-by":"publisher","first-page":"128","DOI":"10.1145\/321371.321381","volume":"14","author":"GE Collins","year":"1967","unstructured":"Collins, G.E.: Subresultants and reduced polynomial remainder sequences. J. ACM 14, 128\u2013142 (1967)","journal-title":"J. ACM"},{"key":"1_CR4","doi-asserted-by":"publisher","first-page":"299","DOI":"10.1006\/jsco.1995.1052","volume":"20","author":"MJ Encarnaci\u00f3n","year":"1995","unstructured":"Encarnaci\u00f3n, M.J.: Computing GCDs of polynomials over algebraic number fields. J. Symb. Comput. 20, 299\u2013313 (1995)","journal-title":"J. Symb. Comput."},{"issue":"1","key":"1_CR5","doi-asserted-by":"publisher","first-page":"4","DOI":"10.1145\/844076.844080","volume":"37","author":"R Fateman","year":"2003","unstructured":"Fateman, R.: Comparing the speed of programs for sparse polynomial multiplication. SIGSAM Bull. 37(1), 4\u201315 (2003)","journal-title":"SIGSAM Bull."},{"issue":"1","key":"1_CR6","first-page":"28","volume":"105","author":"H Jiaxiong","year":"2021","unstructured":"Jiaxiong, H., Monagan, M.: A fast parallel sparse polynomial GCD algorithm. Symb. Comput. 105(1), 28\u201363 (2021)","journal-title":"Symb. Comput."},{"issue":"5","key":"1_CR7","doi-asserted-by":"publisher","first-page":"429","DOI":"10.1016\/S0747-7171(89)80053-7","volume":"8","author":"L Langemyr","year":"1989","unstructured":"Langemyr, L., McCallum, S.: The computation of polynomial greatest common divisors over an algebraic number field. J. Symb. Comput. 8(5), 429\u2013448 (1989)","journal-title":"J. Symb. Comput."},{"issue":"7","key":"1_CR8","doi-asserted-by":"publisher","first-page":"891","DOI":"10.1016\/j.jsc.2008.04.019","volume":"44","author":"X Lin","year":"2009","unstructured":"Lin, X., Maza, M.M., Schost, \u00c9.: Fast arithmetic for triangular sets: from theory to practice. J. Symb. Comput. 44(7), 891\u2013907 (2009)","journal-title":"J. Symb. Comput."},{"key":"1_CR9","doi-asserted-by":"crossref","unstructured":"Monagan, M.: Maximal quotient rational reconstruction: an almost optimal algorithm for rational reconstruction. In: Proceedings of ISSAC 2004, pp. 243\u2013249. ACM (2004)","DOI":"10.1145\/1005285.1005321"},{"key":"1_CR10","unstructured":"Monagan, M., et al.: Maple 8 Introductory Programming Guide (2003)"},{"key":"1_CR11","doi-asserted-by":"publisher","first-page":"463","DOI":"10.1007\/s00037-013-0063-y","volume":"22","author":"A Poteaux","year":"2013","unstructured":"Poteaux, A., Schost, \u00c9.: Modular composition modulo triangular sets and applications. Comput. Complex. 22, 463\u2013516 (2013)","journal-title":"Comput. Complex."},{"key":"1_CR12","doi-asserted-by":"publisher","first-page":"110","DOI":"10.1016\/j.jsc.2012.05.008","volume":"50","author":"A Poteaux","year":"2013","unstructured":"Poteaux, A., Schost, \u00c9.: On the complexity of computing with zero-dimensional triangular sets. J. Symb. Comput. 50, 110\u2013138 (2013)","journal-title":"J. Symb. Comput."},{"key":"1_CR13","doi-asserted-by":"crossref","unstructured":"Smedley, T.: A new modular algorithm for computation of algebraic number polynomial GCDs. In: Proceedings of ISSAC 1989, pp. 91\u201394. ACM (1989)","DOI":"10.1145\/74540.74552"},{"key":"1_CR14","doi-asserted-by":"crossref","unstructured":"Trager, B.M.: Algebraic factoring and rational function integration. In: Proceedings of the Third ACM Symposium on Symbolic and Algebraic Computation, SYMSAC 1976, pp. 219\u2013226. ACM (1976)","DOI":"10.1145\/800205.806338"},{"key":"1_CR15","doi-asserted-by":"publisher","first-page":"101402","DOI":"10.1016\/j.jco.2019.03.002","volume":"55","author":"J van der Hoeven","year":"2019","unstructured":"van der Hoeven, J., Lecerf, G.: Accelerated tower arithmetic. J. Complex. 55, 101402 (2019)","journal-title":"J. Complex."},{"key":"1_CR16","doi-asserted-by":"publisher","first-page":"101498","DOI":"10.1016\/j.jco.2020.101498","volume":"60","author":"J van der Hoeven","year":"2020","unstructured":"van der Hoeven, J., Lecerf, G.: Directed evaluation. J. Complex. 60, 101498 (2020)","journal-title":"J. Complex."},{"key":"1_CR17","doi-asserted-by":"crossref","unstructured":"van Hoeij, M., Monagan, M.: A modular GCD algorithm over number fields presented with multiple extensions. In: Proceedings of the 2002 International Symposium on Symbolic and Algebraic Computation, ISSAC 2002, pp. 109\u2013116. ACM (2002)","DOI":"10.1145\/780506.780520"},{"issue":"2","key":"1_CR18","doi-asserted-by":"publisher","first-page":"2","DOI":"10.1145\/1089292.1089293","volume":"16","author":"P Wang","year":"1982","unstructured":"Wang, P., Guy, M.J.T., Davenport, J.H.: P-adic reconstruction of rational numbers. SIGSAM Bull. 16(2), 2\u20133 (1982)","journal-title":"SIGSAM Bull."},{"key":"1_CR19","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"216","DOI":"10.1007\/3-540-09519-5_73","volume-title":"Symbolic and Algebraic Computation","author":"R Zippel","year":"1979","unstructured":"Zippel, R.: Probabilistic algorithms for sparse polynomials. In: Ng, E.W. (ed.) Symbolic and Algebraic Computation. LNCS, vol. 72, pp. 216\u2013226. Springer, Heidelberg (1979). https:\/\/doi.org\/10.1007\/3-540-09519-5_73"}],"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\/978-3-031-41724-5_1","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,8,23]],"date-time":"2023-08-23T07:04:24Z","timestamp":1692774264000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/978-3-031-41724-5_1"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023]]},"ISBN":["9783031417238","9783031417245"],"references-count":19,"URL":"https:\/\/doi.org\/10.1007\/978-3-031-41724-5_1","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"type":"print","value":"0302-9743"},{"type":"electronic","value":"1611-3349"}],"subject":[],"published":{"date-parts":[[2023]]},"assertion":[{"value":"24 August 2023","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":"Havana","order":3,"name":"conference_city","label":"Conference City","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Cuba","order":4,"name":"conference_country","label":"Conference Country","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"2023","order":5,"name":"conference_year","label":"Conference Year","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"28 August 2023","order":7,"name":"conference_start_date","label":"Conference Start Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"1 September 2023","order":8,"name":"conference_end_date","label":"Conference End Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"25","order":9,"name":"conference_number","label":"Conference Number","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"casc2023","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":"29","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":"22","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":"76% - 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":"3.17","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":"1.41","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)"}}]}}