{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,8,7]],"date-time":"2024-08-07T21:53:40Z","timestamp":1723067620830},"reference-count":31,"publisher":"Elsevier BV","license":[{"start":{"date-parts":[[2018,3,1]],"date-time":"2018-03-01T00:00:00Z","timestamp":1519862400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/tdm\/userlicense\/1.0\/"},{"start":{"date-parts":[[2022,3,1]],"date-time":"2022-03-01T00:00:00Z","timestamp":1646092800000},"content-version":"vor","delay-in-days":1461,"URL":"http:\/\/www.elsevier.com\/open-access\/userlicense\/1.0\/"}],"funder":[{"DOI":"10.13039\/501100001665","name":"ANR","doi-asserted-by":"publisher","award":["ANR-13-BS02-0003"],"id":[{"id":"10.13039\/501100001665","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["elsevier.com","sciencedirect.com"],"crossmark-restriction":true},"short-container-title":["Journal of Symbolic Computation"],"published-print":{"date-parts":[[2018,3]]},"DOI":"10.1016\/j.jsc.2017.07.004","type":"journal-article","created":{"date-parts":[[2017,7,17]],"date-time":"2017-07-17T12:47:20Z","timestamp":1500295640000},"page":"72-107","update-policy":"http:\/\/dx.doi.org\/10.1016\/elsevier_cm_policy","source":"Crossref","is-referenced-by-count":2,"special_numbering":"C","title":["The Brun gcd algorithm in high dimensions is almost always subtractive"],"prefix":"10.1016","volume":"85","author":[{"given":"Val\u00e9rie","family":"Berth\u00e9","sequence":"first","affiliation":[]},{"given":"Lo\u00efck","family":"Lhote","sequence":"additional","affiliation":[]},{"given":"Brigitte","family":"Vall\u00e9e","sequence":"additional","affiliation":[]}],"member":"78","reference":[{"key":"10.1016\/j.jsc.2017.07.004_br0010","doi-asserted-by":"crossref","first-page":"645","DOI":"10.24033\/asens.1682","article-title":"Mesures de Gauss pour des algorithmes de fractions continues multidimensionnelles","volume":"26","author":"Arnoux","year":"1993","journal-title":"Ann. Sci. \u00c9c. Norm. Sup\u00e9r."},{"key":"10.1016\/j.jsc.2017.07.004_br0020","article-title":"Positive Transfer Operators and Decay of Correlations","volume":"vol. 16","author":"Baladi","year":"2000"},{"key":"10.1016\/j.jsc.2017.07.004_br0030","doi-asserted-by":"crossref","first-page":"331","DOI":"10.1016\/j.jnt.2004.08.008","article-title":"Euclidean algorithms are Gaussian","volume":"110","author":"Baladi","year":"2006","journal-title":"J. Number Theory"},{"key":"10.1016\/j.jsc.2017.07.004_br0040","series-title":"Combinatorics on Words","first-page":"58","article-title":"Generating discrete planes with substitutions","volume":"vol. 8079","author":"Berth\u00e9","year":"2013"},{"key":"10.1016\/j.jsc.2017.07.004_br0050","series-title":"Proceedings of the ACM on International Symposium on Symbolic and Algebraic Computation","first-page":"87","article-title":"Analysis of the Brun gcd algorithm","author":"Berth\u00e9","year":"2016"},{"key":"10.1016\/j.jsc.2017.07.004_br0060","doi-asserted-by":"crossref","first-page":"425","DOI":"10.1016\/j.jsc.2015.08.007","article-title":"Probabilistic analyses of the plain multiple gcd algorithm","volume":"74","author":"Berth\u00e9","year":"2016","journal-title":"J. Symb. Comput."},{"key":"10.1016\/j.jsc.2017.07.004_br0070","first-page":"1","article-title":"Transformations dilatantes de l'intervalle et th\u00e9or\u00e8mes limites","volume":"238","author":"Broise","year":"1996","journal-title":"Ast\u00e9risque"},{"issue":"3","key":"10.1016\/j.jsc.2017.07.004_br0080","doi-asserted-by":"crossref","first-page":"565","DOI":"10.5802\/aif.1832","article-title":"Exposants caract\u00e9ristiques de l'algorithme de Jacobi\u2013Perron et de la transformation associ\u00e9e","volume":"51","author":"Broise-Alamichel","year":"2001","journal-title":"Ann. Inst. Fourier"},{"key":"10.1016\/j.jsc.2017.07.004_br0090","series-title":"13e Congr\u00e8s des Math\u00e9maticiens Scandinaves","first-page":"45","article-title":"Algorithmes euclidiens pour trois et quatre nombres","author":"Brun","year":"1958"},{"key":"10.1016\/j.jsc.2017.07.004_br0100","series-title":"Advances in Cryptology, EUROCRYPT '94 Proceedings","first-page":"389","article-title":"Efficient exponentiation using precomputation and vector addition chains","volume":"vol. 950","author":"de Rooij","year":"1995"},{"issue":"2","key":"10.1016\/j.jsc.2017.07.004_br0110","doi-asserted-by":"crossref","first-page":"357","DOI":"10.2307\/121012","article-title":"On decay of correlations in Anosov flows","volume":"147","author":"Dolgopyat","year":"1998","journal-title":"Ann. Math."},{"key":"10.1016\/j.jsc.2017.07.004_br0120","series-title":"Analytic Combinatorics","author":"Flajolet","year":"2009"},{"key":"10.1016\/j.jsc.2017.07.004_br0130","first-page":"53","article-title":"Continued fractions, comparison algorithms, and fine structure constants","volume":"vol. 27","author":"Flajolet","year":"2000"},{"issue":"6","key":"10.1016\/j.jsc.2017.07.004_br0140","doi-asserted-by":"crossref","first-page":"1711","DOI":"10.1017\/S014338570000095X","article-title":"On almost everywhere strong convergence of multi-dimensional continued fraction algorithms","volume":"20","author":"Hardcastle","year":"2000","journal-title":"Ergod. Theory Dyn. Syst."},{"issue":"1","key":"10.1016\/j.jsc.2017.07.004_br0150","doi-asserted-by":"crossref","first-page":"119","DOI":"10.1080\/10586458.2002.10504474","article-title":"The d-dimensional Gauss transformation: strong convergence and Lyapunov exponents","volume":"11","author":"Hardcastle","year":"2002","journal-title":"Exp. Math."},{"issue":"2","key":"10.1016\/j.jsc.2017.07.004_br0160","first-page":"627","article-title":"Sur un th\u00e9or\u00e8me spectral et son application aux noyaux lipchitziens","volume":"118","author":"Hennion","year":"1993","journal-title":"Proc. Am. Math. Soc."},{"key":"10.1016\/j.jsc.2017.07.004_br0170","doi-asserted-by":"crossref","first-page":"140","DOI":"10.2307\/1969514","article-title":"Th\u00e9orie ergodique pour des classes d'op\u00e9rations non compl\u00e8tement continues","volume":"52","author":"Ionescu Tulcea","year":"1950","journal-title":"Ann. Math. (2)"},{"key":"10.1016\/j.jsc.2017.07.004_br0180","series-title":"Discrete Geometry for Computer Imagery","first-page":"45","article-title":"Generation of digital planes using generalized continued-fractions algorithms","volume":"vol. 9647","author":"Jamet","year":"2016"},{"key":"10.1016\/j.jsc.2017.07.004_br0190","article-title":"Perturbation Theory for Linear Operators","volume":"vol. 132","author":"Kato","year":"1976"},{"key":"10.1016\/j.jsc.2017.07.004_br0200","article-title":"Seminumerical Algorithms","volume":"vol. 2","author":"Knuth","year":"1998"},{"key":"10.1016\/j.jsc.2017.07.004_br0210","doi-asserted-by":"crossref","first-page":"299","DOI":"10.1007\/BF01667310","article-title":"The quality of the diophantine approximations found by the Jacobi\u2013Perron algorithm, and related algorithms","volume":"115","author":"Lagarias","year":"1993","journal-title":"Monatshefte Math."},{"key":"10.1016\/j.jsc.2017.07.004_br0220","series-title":"Proceedings of an International Conference on Coding Theory, Cryptography and Related Areas","first-page":"156","article-title":"Worst-case analysis of an algorithm for computing the greatest common divisor of n inputs","author":"Lam","year":"1998"},{"issue":"4","key":"10.1016\/j.jsc.2017.07.004_br0230","doi-asserted-by":"crossref","first-page":"497","DOI":"10.1007\/s00453-007-9009-6","article-title":"Gaussian laws for the main parameters of the Euclid algorithms","volume":"50","author":"Lhote","year":"2008","journal-title":"Algorithmica"},{"key":"10.1016\/j.jsc.2017.07.004_br0240","series-title":"Algorithmic Number Theory","first-page":"184","article-title":"The complexity of greatest common divisor computations","volume":"vol. 877","author":"Majewski","year":"1994"},{"issue":"184\u2013194","key":"10.1016\/j.jsc.2017.07.004_br0250","first-page":"227","article-title":"A generalization of the continued fraction algorithm that is related to the Viggo Brun algorithm","volume":"67","author":"Podsypanin","year":"1977","journal-title":"Zap. Nau\u010d. Semin. Leningrad. Otdel. Mat. Inst. Steklov. (LOMI)"},{"key":"10.1016\/j.jsc.2017.07.004_br0260","series-title":"2017 Proceedings of the Fourteenth Workshop on Analytic Algorithmics and Combinatorics","first-page":"100","article-title":"The recurrence function of a random sturmian word","author":"Rotondo","year":"2017"},{"issue":"8\u20139","key":"10.1016\/j.jsc.2017.07.004_br0270","first-page":"325","article-title":"Ergodische Eigenschaften der Algorithmen von Brun und Selmer","volume":"191","author":"Schweiger","year":"1982","journal-title":"\u00d6sterreich. Akad. Wiss. Math.-Natur. Kl. Sitzungsber. II"},{"key":"10.1016\/j.jsc.2017.07.004_br0280","series-title":"Multidimensional Continued Fractions","author":"Schweiger","year":"2000"},{"key":"10.1016\/j.jsc.2017.07.004_br0290","series-title":"Diophantine Approximation","first-page":"371","article-title":"A note on Lyapunov theory for Brun algorithm","volume":"vol. 16","author":"Schweiger","year":"2008"},{"issue":"15","key":"10.1016\/j.jsc.2017.07.004_br0300","doi-asserted-by":"crossref","first-page":"281","DOI":"10.3934\/dcds.2006.15.281","article-title":"Euclidean dynamics","volume":"1","author":"Vall\u00e9e","year":"2006","journal-title":"Discrete Contin. Dyn. Syst."},{"issue":"2","key":"10.1016\/j.jsc.2017.07.004_br0310","doi-asserted-by":"crossref","first-page":"288","DOI":"10.1016\/0022-247X(77)90109-3","article-title":"A Jacobi algorithm and metric theory for greatest common divisors","volume":"59","author":"Waterman","year":"1977","journal-title":"J. Math. Anal. Appl."}],"container-title":["Journal of Symbolic Computation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0747717117300688?httpAccept=text\/xml","content-type":"text\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0747717117300688?httpAccept=text\/plain","content-type":"text\/plain","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2022,2,28]],"date-time":"2022-02-28T20:55:20Z","timestamp":1646081720000},"score":1,"resource":{"primary":{"URL":"https:\/\/linkinghub.elsevier.com\/retrieve\/pii\/S0747717117300688"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,3]]},"references-count":31,"alternative-id":["S0747717117300688"],"URL":"https:\/\/doi.org\/10.1016\/j.jsc.2017.07.004","relation":{},"ISSN":["0747-7171"],"issn-type":[{"value":"0747-7171","type":"print"}],"subject":[],"published":{"date-parts":[[2018,3]]},"assertion":[{"value":"Elsevier","name":"publisher","label":"This article is maintained by"},{"value":"The Brun gcd algorithm in high dimensions is almost always subtractive","name":"articletitle","label":"Article Title"},{"value":"Journal of Symbolic Computation","name":"journaltitle","label":"Journal Title"},{"value":"https:\/\/doi.org\/10.1016\/j.jsc.2017.07.004","name":"articlelink","label":"CrossRef DOI link to publisher maintained version"},{"value":"article","name":"content_type","label":"Content Type"},{"value":"\u00a9 2017 Elsevier Ltd.","name":"copyright","label":"Copyright"}]}}