{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T01:58:18Z","timestamp":1760061498372,"version":"3.41.0"},"reference-count":9,"publisher":"Association for Computing Machinery (ACM)","issue":"4","license":[{"start":{"date-parts":[[2016,2,17]],"date-time":"2016-02-17T00:00:00Z","timestamp":1455667200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.acm.org\/publications\/policies\/copyright_policy#Background"}],"content-domain":{"domain":["dl.acm.org"],"crossmark-restriction":true},"short-container-title":["ACM Commun. Comput. Algebra"],"published-print":{"date-parts":[[2016,2,17]]},"abstract":"<jats:p>In this paper, we report on an implementation in the free software M<jats:sc>athemagix<\/jats:sc>[9] of lacunary factorization algorithms, distributed as a library called L<jats:sc>acunaryx<\/jats:sc>. These algorithms take as input a polynomial in sparse representation, that is as a list of nonzero monomials, and an integer<jats:italic>d<\/jats:italic>, and compute its degree-<jats:italic>d<\/jats:italic>factors.<jats:sup>2<\/jats:sup>The complexity of these algorithms is polynomial in the<jats:italic>sparse size<\/jats:italic>of the input polynomial and<jats:italic>d<\/jats:italic>: The sparse size of a polynomial [EQUATION] logwhere the<jats:italic>h<\/jats:italic>(\u00b7) denotes the<jats:italic>height<\/jats:italic>of a rational number, that is the maximum of the absolute values of its numerator and denominator.<\/jats:p>","DOI":"10.1145\/2893803.2893807","type":"journal-article","created":{"date-parts":[[2016,2,22]],"date-time":"2016-02-22T13:07:16Z","timestamp":1456146436000},"page":"121-124","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":1,"title":["Lacunaryx"],"prefix":"10.1145","volume":"49","author":[{"given":"Bruno","family":"Grenet","sequence":"first","affiliation":[{"name":"Universit\u00e9 de Montpellier"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"320","published-online":{"date-parts":[[2016,2,17]]},"reference":[{"key":"e_1_2_1_1_1","doi-asserted-by":"crossref","unstructured":"A. Chattopadhyay B. Grenet P. Koiran N. Portier and Y. Strozecki. Computing the multilinear factors of lacunary polynomials without heights. Manuscript (submitted) 2013. arXiv:1311.5694. A. Chattopadhyay B. Grenet P. Koiran N. Portier and Y. Strozecki. Computing the multilinear factors of lacunary polynomials without heights. Manuscript (submitted) 2013. arXiv:1311.5694.","DOI":"10.1145\/2465506.2465932"},{"key":"e_1_2_1_2_1","doi-asserted-by":"publisher","DOI":"10.1145\/2465506.2465932"},{"key":"e_1_2_1_3_1","doi-asserted-by":"publisher","DOI":"10.1006\/jsco.1998.0242"},{"key":"e_1_2_1_4_1","doi-asserted-by":"publisher","DOI":"10.1145\/2608628.2608649"},{"key":"e_1_2_1_5_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jsc.2015.11.013"},{"key":"e_1_2_1_6_1","doi-asserted-by":"publisher","DOI":"10.1145\/1073884.1073914"},{"key":"e_1_2_1_7_1","doi-asserted-by":"publisher","DOI":"10.1145\/1145768.1145798"},{"key":"e_1_2_1_8_1","doi-asserted-by":"crossref","first-page":"277","DOI":"10.1515\/9783110285581.277","volume-title":"Number theory in progress","author":"Lenstra H.","year":"1999"},{"key":"e_1_2_1_9_1","unstructured":"J. van der Hoeven etal Mathemagix from 2002. http:\/\/www.mathemagix.org. J. van der Hoeven et al. Mathemagix from 2002. http:\/\/www.mathemagix.org."}],"container-title":["ACM Communications in Computer Algebra"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/2893803.2893807","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/dl.acm.org\/doi\/pdf\/10.1145\/2893803.2893807","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,6,18]],"date-time":"2025-06-18T04:56:14Z","timestamp":1750222574000},"score":1,"resource":{"primary":{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/2893803.2893807"}},"subtitle":["computing bounded-degree factors of lacunary polynomials"],"short-title":[],"issued":{"date-parts":[[2016,2,17]]},"references-count":9,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2016,2,17]]}},"alternative-id":["10.1145\/2893803.2893807"],"URL":"https:\/\/doi.org\/10.1145\/2893803.2893807","relation":{},"ISSN":["1932-2240"],"issn-type":[{"type":"print","value":"1932-2240"}],"subject":[],"published":{"date-parts":[[2016,2,17]]},"assertion":[{"value":"2016-02-17","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}