{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,1]],"date-time":"2026-05-01T14:17:57Z","timestamp":1777645077484,"version":"3.51.4"},"reference-count":0,"publisher":"SAGE Publications","issue":"4","license":[{"start":{"date-parts":[[2014,1,1]],"date-time":"2014-01-01T00:00:00Z","timestamp":1388534400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/journals.sagepub.com\/page\/policies\/text-and-data-mining-license"}],"content-domain":{"domain":["journals.sagepub.com"],"crossmark-restriction":true},"short-container-title":["Fundamenta Informaticae"],"published-print":{"date-parts":[[2014,8]]},"abstract":"<jats:p>\n                    We present combinatorial algorithms for solving three problems that appear in the study of the degeneration order \u2264\n                    <jats:sub>deg<\/jats:sub>\n                    for the variety of finite-dimensional modules over a k-algebra \u039b, where M \u2264\n                    <jats:sub>deg<\/jats:sub>\n                    N means that a module N belongs to an orbit closure $\\overline{\\cal{O}(M)}$ of a module M in the variety of \u039b-modules. In particular, we introduce algorithmic techniques for deciding whether or not the relation M \u2264\n                    <jats:sub>deg<\/jats:sub>\n                    N holds and for determining all predecessors (resp. succesors) of a given module M with respect to \u2264\n                    <jats:sub>deg<\/jats:sub>\n                    . The order \u2264\n                    <jats:sub>deg<\/jats:sub>\n                    plays an important role in modern algebraic geometry and module theory. Applications of our technique and experimental tests for particular classes of algebras are presented. The results show that a computer algebra technique and algorithmic computer calculations provide important tools in solving theoretical mathematics problems of high computational complexity. The algorithms are implemented and published as a part of an open source GAP package called QPA.\n                  <\/jats:p>","DOI":"10.3233\/fi-2014-1057","type":"journal-article","created":{"date-parts":[[2019,12,3]],"date-time":"2019-12-03T01:05:03Z","timestamp":1575335103000},"page":"519-532","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":0,"title":["Combinatorial Algorithms for Computing Degenerations of Modules of Finite Dimension"],"prefix":"10.1177","volume":"132","author":[{"given":"Andrzej","family":"Mr\u00f3z","sequence":"first","affiliation":[{"name":"Faculty of Mathematics and Computer Science, Nicolaus Copernicus University, Chopina 12\/18, 87-100 Toru\u0144, Poland. amroz@mat.umk.pl; gzwara@mat.umk.pl"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Grzegorz","family":"Zwara","sequence":"additional","affiliation":[{"name":"Faculty of Mathematics and Computer Science, Nicolaus Copernicus University, Chopina 12\/18, 87-100 Toru\u0144, Poland. amroz@mat.umk.pl; gzwara@mat.umk.pl"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"179","published-online":{"date-parts":[[2014,1,1]]},"container-title":["Fundamenta Informaticae"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.3233\/FI-2014-1057","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.3233\/FI-2014-1057","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,29]],"date-time":"2026-04-29T06:31:17Z","timestamp":1777444277000},"score":1,"resource":{"primary":{"URL":"https:\/\/journals.sagepub.com\/doi\/10.3233\/FI-2014-1057"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014,1,1]]},"references-count":0,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2014,8]]}},"alternative-id":["10.3233\/FI-2014-1057"],"URL":"https:\/\/doi.org\/10.3233\/fi-2014-1057","relation":{},"ISSN":["0169-2968","1875-8681"],"issn-type":[{"value":"0169-2968","type":"print"},{"value":"1875-8681","type":"electronic"}],"subject":[],"published":{"date-parts":[[2014,1,1]]}}}