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Algebra Comput."],"published-print":{"date-parts":[[2024,11]]},"abstract":"<jats:p> We suggest that straight-line programs designed for algebraic computations should be accompanied by a comprehensive complexity analysis that takes into account both the number of fundamental algebraic operations needed, as well as memory requirements arising during evaluation. We introduce an approach for formalizing this idea and, as illustration, construct and analyze straight-line programs for the Bruhat decomposition of [Formula: see text] matrices with determinant 1 over a finite field of order q that have length [Formula: see text] and require storing only [Formula: see text] matrices during evaluation. <\/jats:p>","DOI":"10.1142\/s0218196724500413","type":"journal-article","created":{"date-parts":[[2024,7,27]],"date-time":"2024-07-27T03:52:43Z","timestamp":1722052363000},"page":"1059-1090","source":"Crossref","is-referenced-by-count":0,"title":["Showcasing straight-line programs with memory via matrix Bruhat decomposition"],"prefix":"10.1142","volume":"34","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-2163-3240","authenticated-orcid":false,"given":"Alice C.","family":"Niemeyer","sequence":"first","affiliation":[{"name":"Chair for Algebra and Representation Theory, RWTH Aachen University, Pontdriesch 10-16, Aachen 52062, Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2974-1470","authenticated-orcid":false,"given":"Tomasz","family":"Popiel","sequence":"additional","affiliation":[{"name":"School of Mathematics, Monash University, 9 Rainforest Walk, Clayton, VIC 3800, Australia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0881-7336","authenticated-orcid":false,"given":"Cheryl E.","family":"Praeger","sequence":"additional","affiliation":[{"name":"Centre for the Mathematics of Symmetry and Computation, The University of Western Australia, 35 Stirling Highway, Crawley, WA 6009, Australia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0009-0004-0638-0873","authenticated-orcid":false,"given":"Daniel","family":"Rademacher","sequence":"additional","affiliation":[{"name":"Chair for Algebra and Representation Theory, RWTH Aachen University, Pontdriesch 10-16, Aachen 52062, Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2024,10,11]]},"reference":[{"key":"S0218196724500413BIB001","doi-asserted-by":"publisher","DOI":"10.1016\/j.jsc.2011.08.017"},{"key":"S0218196724500413BIB002","doi-asserted-by":"publisher","DOI":"10.1109\/SFCS.1984.715919"},{"key":"S0218196724500413BIB003","series-title":"Institute for Systems and Technologies of Information, Control and Communication","first-page":"41","volume-title":"ICEC 2010: Proc. 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