{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,6,18]],"date-time":"2025-06-18T04:28:21Z","timestamp":1750220901981,"version":"3.41.0"},"reference-count":8,"publisher":"Association for Computing Machinery (ACM)","issue":"4","license":[{"start":{"date-parts":[[2019,5,30]],"date-time":"2019-05-30T00:00:00Z","timestamp":1559174400000},"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":[[2019,5,30]]},"abstract":"<jats:p>\n            <jats:bold>Overview.<\/jats:bold>\n            Computing the Gr\u00f6bner basis of an ideal with respect to a term ordering is an essential step in solving systems of polynomials; in what follows, we restrict our attention to systems with finitely many solutions. Certain term orderings, such as the degree reverse lexicographical ordering (\n            <jats:italic>degrevlex<\/jats:italic>\n            ), make the computation of the Gr\u00f6bner basis faster, while other orderings, such as the lexicographical ordering (\n            <jats:italic>lex<\/jats:italic>\n            ), make it easier to find the coordinates of the solutions. Thus, one typically first computes a Gr\u00f6bner basis for the degrevlex ordering, and then converts it to either a lex Gr\u00f6bner basis or a related representation, such as Rouillier's Rational Univariate Representation [8].\n          <\/jats:p>","DOI":"10.1145\/3338637.3338641","type":"journal-article","created":{"date-parts":[[2019,5,31]],"date-time":"2019-05-31T12:37:11Z","timestamp":1559306231000},"page":"123-125","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":0,"title":["Sparse FGLM using the block Wiedemann algorithm"],"prefix":"10.1145","volume":"52","author":[{"given":"Seung Gyu","family":"Hyun","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Vincent","family":"Neiger","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Hamid","family":"Rahkooy","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"\u00c9ric","family":"Schost","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"320","published-online":{"date-parts":[[2019,5,30]]},"reference":[{"key":"e_1_2_1_1_1","first-page":"239","article-title":"Fast algorithms for zero-dimensional polynomial systems using duality. Applicable Algebra in Engineering","volume":"14","author":"Bostan A.","year":"2003","journal-title":"Communication and Computing"},{"key":"e_1_2_1_2_1","doi-asserted-by":"publisher","DOI":"10.1016\/0024-3795(93)90235-G"},{"key":"e_1_2_1_3_1","unstructured":"J.-C. Faug\u00e8re P. Gaudry L. Huot and G. Renault. Polynomial Systems Solving by Fast Linear Algebra. https:\/\/hal.archives-ouvertes.fr\/hal-00816724 2013.  J.-C. Faug\u00e8re P. Gaudry L. Huot and G. Renault. Polynomial Systems Solving by Fast Linear Algebra. https:\/\/hal.archives-ouvertes.fr\/hal-00816724 2013."},{"key":"e_1_2_1_4_1","doi-asserted-by":"publisher","DOI":"10.1006\/jsco.1993.1051"},{"key":"e_1_2_1_5_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jsc.2016.07.025"},{"key":"e_1_2_1_6_1","doi-asserted-by":"publisher","DOI":"10.1007\/s00037-004-0185-3"},{"key":"e_1_2_1_7_1","unstructured":"V. Neiger. Bases of relations in one or several variables: fast algorithms and applications. PhD thesis \u00c9cole Normale Sup\u00e9rieure de Lyon November 2016.  V. Neiger. Bases of relations in one or several variables: fast algorithms and applications. PhD thesis \u00c9cole Normale Sup\u00e9rieure de Lyon November 2016."},{"issue":"5","key":"e_1_2_1_8_1","first-page":"433","article-title":"Solving zero-dimensional systems through the rational univariate representation. Applicable Algebra in Engineering","volume":"9","author":"Rouillier F.","year":"1999","journal-title":"Communication and Computing"}],"container-title":["ACM Communications in Computer Algebra"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/3338637.3338641","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/dl.acm.org\/doi\/pdf\/10.1145\/3338637.3338641","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,6,17]],"date-time":"2025-06-17T23:44:47Z","timestamp":1750203887000},"score":1,"resource":{"primary":{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/3338637.3338641"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,5,30]]},"references-count":8,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2019,5,30]]}},"alternative-id":["10.1145\/3338637.3338641"],"URL":"https:\/\/doi.org\/10.1145\/3338637.3338641","relation":{},"ISSN":["1932-2240"],"issn-type":[{"type":"print","value":"1932-2240"}],"subject":[],"published":{"date-parts":[[2019,5,30]]},"assertion":[{"value":"2019-05-30","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}