{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,1]],"date-time":"2026-05-01T14:14:48Z","timestamp":1777644888559,"version":"3.51.4"},"reference-count":0,"publisher":"SAGE Publications","issue":"3","license":[{"start":{"date-parts":[[2013,1,1]],"date-time":"2013-01-01T00:00:00Z","timestamp":1356998400000},"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":[[2013,5]]},"abstract":"<jats:p>\n                    We study the complexity of Bongartz's algorithm for determining a maximal common direct summand of a pair of modules M, N over k-algebra \u039b; in particular, we estimate its pessimistic computational complexity \ud835\udcaa(rm\n                    <jats:sup>6<\/jats:sup>\n                    n\n                    <jats:sup>2<\/jats:sup>\n                    (n + m log n)), where m = dim\n                    <jats:sub>k<\/jats:sub>\n                    M \u2264 n = dim\n                    <jats:sub>k<\/jats:sub>\n                    N and r is a number of common indecomposable direct summands of M and N. We improve the algorithm to another one of complexity \ud835\udcaa(rm\n                    <jats:sup>4<\/jats:sup>\n                    n\n                    <jats:sup>2<\/jats:sup>\n                    (n+m log m)) and we show that it applies to the isomorphism problem (having at least an exponential complexity in a direct approach). Moreover, we discuss a performance of both algorithms in practice and show that the \u201caverage\u201d complexity is much lower, especially for the improved one (which becomes a part of QPA package for GAP computer algebra system).\n                  <\/jats:p>","DOI":"10.3233\/fi-2013-813","type":"journal-article","created":{"date-parts":[[2019,12,3]],"date-time":"2019-12-03T00:22:08Z","timestamp":1575332528000},"page":"317-329","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":0,"title":["On the Computational Complexity of Bongartz's Algorithm"],"prefix":"10.1177","volume":"123","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"}]}],"member":"179","published-online":{"date-parts":[[2013,1,1]]},"container-title":["Fundamenta Informaticae"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.3233\/FI-2013-813","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.3233\/FI-2013-813","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,29]],"date-time":"2026-04-29T06:30:29Z","timestamp":1777444229000},"score":1,"resource":{"primary":{"URL":"https:\/\/journals.sagepub.com\/doi\/10.3233\/FI-2013-813"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013,1,1]]},"references-count":0,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2013,5]]}},"alternative-id":["10.3233\/FI-2013-813"],"URL":"https:\/\/doi.org\/10.3233\/fi-2013-813","relation":{},"ISSN":["0169-2968","1875-8681"],"issn-type":[{"value":"0169-2968","type":"print"},{"value":"1875-8681","type":"electronic"}],"subject":[],"published":{"date-parts":[[2013,1,1]]}}}