{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,3,28]],"date-time":"2025-03-28T01:45:41Z","timestamp":1743126341991,"version":"3.40.3"},"publisher-location":"Cham","reference-count":10,"publisher":"Springer Nature Switzerland","isbn-type":[{"type":"print","value":"9783031645280"},{"type":"electronic","value":"9783031645297"}],"license":[{"start":{"date-parts":[[2024,1,1]],"date-time":"2024-01-01T00:00:00Z","timestamp":1704067200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2024,1,1]],"date-time":"2024-01-01T00:00:00Z","timestamp":1704067200000},"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":[[2024]]},"DOI":"10.1007\/978-3-031-64529-7_3","type":"book-chapter","created":{"date-parts":[[2024,7,16]],"date-time":"2024-07-16T15:21:35Z","timestamp":1721143295000},"page":"29-35","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Computing the\u00a0Determinant of\u00a0a\u00a0Dense Matrix over\u00a0$${\\mathbb Z}$$"],"prefix":"10.1007","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-5608-3835","authenticated-orcid":false,"given":"John","family":"Abbott","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3420-1498","authenticated-orcid":false,"given":"Claus","family":"Fieker","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2024,7,17]]},"reference":[{"key":"3_CR1","doi-asserted-by":"crossref","unstructured":"Pauderis, C., Storjohann, A.: Computing the invariant structure of integer matrices: fast algorithms into practice. In: Proceedings International Symposium on Symbolic and Algebraic Computation, ACM Press, pp. 307\u2013314 (2013)","DOI":"10.1145\/2465506.2465955"},{"key":"3_CR2","unstructured":"Eberly, W., Giesbrecht, M., Villard, G.: On computing the determinant and Smith form of an integer matrix. In: Proceedings 41st Annual IEEE Symposium on Foundations of Computer Science, 2000, pp. 441\u2013458 (2000)"},{"key":"3_CR3","doi-asserted-by":"crossref","unstructured":"Abbott, J., Bronstein, M., Mulders, T.: Fast deterministic computation of determinants of dense matrices. In: Proceedings International Symposium on Symbolic and Algebraic Computation, ACM Press, 1999, pp. 197\u2013204 (1999)","DOI":"10.1145\/309831.309934"},{"key":"3_CR4","doi-asserted-by":"crossref","unstructured":"Fertin, G., Rusu, I., Vialette, S.: Obtaining a triangular matrix by independent row-column permutations. In: Proceedings 26th International Symposium on Algorithms and Computation, 2015, pp. 165\u2013175 (2015). https:\/\/hal.science\/hal-01189621","DOI":"10.1007\/978-3-662-48971-0_15"},{"key":"3_CR5","doi-asserted-by":"crossref","unstructured":"Pauderis, C., Storjohann, A.: Deterministic unimodularity certification. In: Proceedings International Symposium on Symbolic and Algebraic Computation, ACM Press, 2012, pp. 281\u2013288 (2012)","DOI":"10.1145\/2442829.2442870"},{"issue":"2","key":"3_CR6","doi-asserted-by":"publisher","first-page":"226","DOI":"10.1587\/nolta.2.226","volume":"2","author":"T Nishi","year":"2011","unstructured":"Nishi, T., Rump, S., Oishi, S.: On the generation of very ill-conditioned integer matrices. Nonlinear Theor. Appl. IEICE 2(2), 226\u2013245 (2011)","journal-title":"Nonlinear Theor. Appl. IEICE"},{"key":"3_CR7","unstructured":"Shoup, V.: NTL: a Library for doing Number Theory. Website https:\/\/www.libntl.org, version 11.5.1 (2024)"},{"key":"3_CR8","unstructured":"Abbott, J., Bigatti, A.: CoCoALib: a C++ library for doing Computations in Commutative Algebra. Available at https:\/\/cocoa.dima.unige.it\/, versions: CoCoALib-0.99820, CoCoA-5.4.1u (2024)"},{"key":"3_CR9","unstructured":"The FLINT team. Flint: fast library for number theory, Website https:\/\/flintlib.org, part of OSCAR 1.0.0 (2024)"},{"key":"3_CR10","unstructured":"The OSCAR team, Oscar \u2013 open source computer algebra research system, Website https:\/\/www.oscar-system.org, version 1.0.0 (2024)"}],"container-title":["Lecture Notes in Computer Science","Mathematical Software \u2013 ICMS 2024"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-031-64529-7_3","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,7,16]],"date-time":"2024-07-16T15:21:58Z","timestamp":1721143318000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/978-3-031-64529-7_3"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024]]},"ISBN":["9783031645280","9783031645297"],"references-count":10,"URL":"https:\/\/doi.org\/10.1007\/978-3-031-64529-7_3","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"type":"print","value":"0302-9743"},{"type":"electronic","value":"1611-3349"}],"subject":[],"published":{"date-parts":[[2024]]},"assertion":[{"value":"17 July 2024","order":1,"name":"first_online","label":"First Online","group":{"name":"ChapterHistory","label":"Chapter History"}},{"value":"ICMS","order":1,"name":"conference_acronym","label":"Conference Acronym","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"International Congress on Mathematical Software","order":2,"name":"conference_name","label":"Conference Name","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Durham","order":3,"name":"conference_city","label":"Conference City","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"United Kingdom","order":4,"name":"conference_country","label":"Conference Country","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"2024","order":5,"name":"conference_year","label":"Conference Year","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"22 July 2024","order":7,"name":"conference_start_date","label":"Conference Start Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"25 July 2024","order":8,"name":"conference_end_date","label":"Conference End Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"8","order":9,"name":"conference_number","label":"Conference Number","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"icms2024","order":10,"name":"conference_id","label":"Conference ID","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"https:\/\/maths.dur.ac.uk\/icms2024\/ICMS2024.html","order":11,"name":"conference_url","label":"Conference URL","group":{"name":"ConferenceInfo","label":"Conference Information"}}]}}