{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,23]],"date-time":"2026-08-23T18:30:23Z","timestamp":1787509823115,"version":"build-2736575974"},"reference-count":32,"publisher":"Elsevier BV","issue":"1","license":[{"start":{"date-parts":[[2004,1,1]],"date-time":"2004-01-01T00:00:00Z","timestamp":1072915200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/tdm\/userlicense\/1.0\/"},{"start":{"date-parts":[[2013,7,17]],"date-time":"2013-07-17T00:00:00Z","timestamp":1374019200000},"content-version":"vor","delay-in-days":3485,"URL":"https:\/\/www.elsevier.com\/open-access\/userlicense\/1.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Journal of Symbolic Computation"],"published-print":{"date-parts":[[2004,1]]},"DOI":"10.1016\/s0747-7171(03)00071-3","type":"journal-article","created":{"date-parts":[[2003,6,30]],"date-time":"2003-06-30T13:29:20Z","timestamp":1056979760000},"page":"35-81","source":"Crossref","is-referenced-by-count":12,"title":["Efficient decomposition of separable algebras"],"prefix":"10.1016","volume":"37","author":[{"given":"W.","family":"Eberly","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"M.","family":"Giesbrecht","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"78","reference":[{"key":"10.1016\/S0747-7171(03)00071-3_B1","series-title":"The Probabilistic Method","author":"Alon","year":"1992"},{"key":"10.1016\/S0747-7171(03)00071-3_B2","doi-asserted-by":"crossref","first-page":"231","DOI":"10.1090\/S0025-5718-1974-0331751-8","article-title":"Triangular factorization and inversion by fast matrix multiplication","volume":"28","author":"Bunch","year":"1974","journal-title":"Math. Comp."},{"key":"10.1016\/S0747-7171(03)00071-3_B3","article-title":"Algebraic Complexity Theory","volume":"vol. 315","author":"B\u00fcrgisser","year":"1997"},{"key":"10.1016\/S0747-7171(03)00071-3_B4","doi-asserted-by":"crossref","first-page":"177","DOI":"10.1016\/S0022-4049(97)00010-8","article-title":"Finding the radical of an algebra of linear transformations","volume":"117\u2013118","author":"Cohen","year":"1997","journal-title":"J. Pure Appl. Algebra"},{"key":"10.1016\/S0747-7171(03)00071-3_B5","doi-asserted-by":"crossref","first-page":"472","DOI":"10.1137\/0211038","article-title":"On the asymptotic complexity of matrix multiplication","volume":"11","author":"Coppersmith","year":"1982","journal-title":"SIAM J. Comput."},{"key":"10.1016\/S0747-7171(03)00071-3_B6","series-title":"Representation Theory of Finite Groups and Associative Algebras","author":"Curtis","year":"1962"},{"key":"10.1016\/S0747-7171(03)00071-3_B7","doi-asserted-by":"crossref","first-page":"193","DOI":"10.1016\/0020-0190(78)90067-4","article-title":"A probabilistic remark on algebraic program testing","volume":"7","author":"DeMillo","year":"1978","journal-title":"Inform. Process. Lett."},{"key":"10.1016\/S0747-7171(03)00071-3_B8","first-page":"179","article-title":"Decompositions of algebras over finite fields and number fields","volume":"1","author":"Eberly","year":"1991","journal-title":"Comput. Complexity"},{"key":"10.1016\/S0747-7171(03)00071-3_B9","doi-asserted-by":"crossref","unstructured":"Eberly, W., Giesbrecht, M., 1996. Efficient decomposition of associative algebras. Proceedings, 1996 International Symposium on Symbolic and Algebraic Computation, Zurich, Switzerland, pp.\u00a0170\u2013178","DOI":"10.1145\/236869.236931"},{"key":"10.1016\/S0747-7171(03)00071-3_B10","doi-asserted-by":"crossref","first-page":"441","DOI":"10.1006\/jsco.1999.0308","article-title":"Efficient decomposition of associative algebras over finite fields","volume":"29","author":"Eberly","year":"2000","journal-title":"J. Symbolic. Comput."},{"key":"10.1016\/S0747-7171(03)00071-3_B11","doi-asserted-by":"crossref","unstructured":"Friedl, K., R\u00f3nyai, L., 1985. Polynomial time solutions of some problems in computational algebra. In: Proceedings, 7th ACM Symposium on Theory of Computing. Providence, RI, USA, pp.\u00a0153\u2013162","DOI":"10.1145\/22145.22162"},{"key":"10.1016\/S0747-7171(03)00071-3_B12","doi-asserted-by":"crossref","first-page":"948","DOI":"10.1137\/S0097539793252687","article-title":"Nearly optimal algorithms for canonical matrix forms","volume":"24","author":"Giesbrecht","year":"1995","journal-title":"SIAM J. Comput."},{"key":"10.1016\/S0747-7171(03)00071-3_B13","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1017\/S1446788700036016","article-title":"Testing modules for irreducibility","volume":"57","author":"Holt","year":"1994","journal-title":"J. Aust. Math. Soc."},{"key":"10.1016\/S0747-7171(03)00071-3_B14","doi-asserted-by":"crossref","first-page":"45","DOI":"10.1016\/0196-6774(82)90007-4","article-title":"A generalization of the fast LUP matrix decomposition algorithm and applications","volume":"3","author":"Ibarra","year":"1982","journal-title":"J. Algorithms"},{"key":"10.1016\/S0747-7171(03)00071-3_B15","doi-asserted-by":"crossref","first-page":"159","DOI":"10.1016\/S0022-4049(99)00010-9","article-title":"Finding the radical of matrix algebras using Fitting decompositions","volume":"139","author":"Ivanyos","year":"1999","journal-title":"J. Pure Appl. Algebra"},{"key":"10.1016\/S0747-7171(03)00071-3_B16","series-title":"Proceedings, 2000 International Symposium on Symbolic and Algebraic Computation","first-page":"175","article-title":"Fast randomized algorithms for the structure of matrix algebras over finite fields (extended abstract)","author":"Ivanyos","year":"2000"},{"key":"10.1016\/S0747-7171(03)00071-3_B17","doi-asserted-by":"crossref","first-page":"245","DOI":"10.1007\/BF01271370","article-title":"Finding maximal orders in semisimple algebras over Q","volume":"3","author":"Ivanyos","year":"1993","journal-title":"Comput. Complexity"},{"key":"10.1016\/S0747-7171(03)00071-3_B18","doi-asserted-by":"crossref","first-page":"189","DOI":"10.1016\/0024-3795(90)90028-B","article-title":"Parallel algorithms for matrix normal forms","volume":"136","author":"Kaltofen","year":"1990","journal-title":"Linear Algebra and its Applications"},{"key":"10.1016\/S0747-7171(03)00071-3_B19","doi-asserted-by":"crossref","first-page":"309","DOI":"10.1016\/0304-3975(85)90049-0","article-title":"Fast algorithms for the characteristic polynomial","volume":"36","author":"Keller-Gehrig","year":"1985","journal-title":"Theoret. Comput. Sci."},{"key":"10.1016\/S0747-7171(03)00071-3_B20","series-title":"Computational Group Theory: Proceedings of the London Mathematical Society Symposium on Computational Group Theory","first-page":"267","article-title":"The computer calculation of modular characters (the meat-axe)","author":"Parker","year":"1984"},{"key":"10.1016\/S0747-7171(03)00071-3_B21","series-title":"Associative Algebras","author":"Pierce","year":"1982"},{"key":"10.1016\/S0747-7171(03)00071-3_B22","doi-asserted-by":"crossref","unstructured":"R\u00f3nyai, L., 1987. Simple algebras are difficult. In: Proceedings, 19th ACM Symposium on Theory of Computing. New York, pp.\u00a0398\u2013408","DOI":"10.1145\/28395.28438"},{"key":"10.1016\/S0747-7171(03)00071-3_B23","doi-asserted-by":"crossref","first-page":"494","DOI":"10.1016\/0196-6774(88)90014-4","article-title":"Zero divisors in quaternion algebras","volume":"9","author":"R\u00f3nyai","year":"1988","journal-title":"J. Algorithms"},{"key":"10.1016\/S0747-7171(03)00071-3_B24","doi-asserted-by":"crossref","first-page":"355","DOI":"10.1016\/S0747-7171(08)80017-X","article-title":"Computing the structure of finite algebras","volume":"9","author":"R\u00f3nyai","year":"1990","journal-title":"J. Symbolic Comput."},{"key":"10.1016\/S0747-7171(03)00071-3_B25","doi-asserted-by":"crossref","first-page":"225","DOI":"10.1007\/BF01272075","article-title":"Algorithmic properties of maximal orders in simple algebras over Q","volume":"2","author":"R\u00f3nyai","year":"1992","journal-title":"Comput. Complexity"},{"key":"10.1016\/S0747-7171(03)00071-3_B26","doi-asserted-by":"crossref","first-page":"607","DOI":"10.1016\/S0747-7171(08)80078-8","article-title":"Computing with endomorphism rings of modular representations","volume":"9","author":"Schneider","year":"1990","journal-title":"J. Symbolic Comput."},{"key":"10.1016\/S0747-7171(03)00071-3_B27","doi-asserted-by":"crossref","first-page":"395","DOI":"10.1007\/BF00289470","article-title":"Schnelle multiplikation von polynomen \u00fcber k\u00f6rpern der charakteristik\u00a02","volume":"7","author":"Sch\u00f6nhage","year":"1977","journal-title":"Acta Inform."},{"key":"10.1016\/S0747-7171(03)00071-3_B28","doi-asserted-by":"crossref","first-page":"281","DOI":"10.1007\/BF02242355","article-title":"Schnelle Multiplikation gro\u00dfer Zahlen","volume":"7","author":"Sch\u00f6nhage","year":"1971","journal-title":"Computing"},{"key":"10.1016\/S0747-7171(03)00071-3_B29","doi-asserted-by":"crossref","first-page":"701","DOI":"10.1145\/322217.322225","article-title":"Fast probabilistic algorithms for verification of polynomial identities","volume":"27","author":"Schwartz","year":"1980","journal-title":"J. Assoc. Comput. Mach."},{"key":"10.1016\/S0747-7171(03)00071-3_B30","series-title":"Modern Computer Algebra","author":"von zur Gathen","year":"1999"},{"issue":"2","key":"10.1016\/S0747-7171(03)00071-3_B31","first-page":"77","article-title":"On hypercomplex numbers","volume":"6","author":"Wedderburn","year":"1907","journal-title":"Proc. London Math. Soc."},{"key":"10.1016\/S0747-7171(03)00071-3_B32","series-title":"Proc. EUROSAM\u00a079","first-page":"216","article-title":"Probabilistic algorithms for sparse polynomials","author":"Zippel","year":"1979"}],"container-title":["Journal of Symbolic Computation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0747717103000713?httpAccept=text\/xml","content-type":"text\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0747717103000713?httpAccept=text\/plain","content-type":"text\/plain","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2019,3,18]],"date-time":"2019-03-18T10:21:39Z","timestamp":1552904499000},"score":1,"resource":{"primary":{"URL":"https:\/\/linkinghub.elsevier.com\/retrieve\/pii\/S0747717103000713"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2004,1]]},"references-count":32,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2004,1]]}},"alternative-id":["S0747717103000713"],"URL":"https:\/\/doi.org\/10.1016\/s0747-7171(03)00071-3","relation":{},"ISSN":["0747-7171"],"issn-type":[{"value":"0747-7171","type":"print"}],"subject":[],"published":{"date-parts":[[2004,1]]}}}