{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,9,5]],"date-time":"2024-09-05T19:38:46Z","timestamp":1725565126566},"publisher-location":"Berlin, Heidelberg","reference-count":22,"publisher":"Springer Berlin Heidelberg","isbn-type":[{"type":"print","value":"9783540221562"},{"type":"electronic","value":"9783540248477"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2004]]},"DOI":"10.1007\/978-3-540-24847-7_4","type":"book-chapter","created":{"date-parts":[[2010,9,10]],"date-time":"2010-09-10T22:33:04Z","timestamp":1284157984000},"page":"57-71","source":"Crossref","is-referenced-by-count":3,"title":["Binary GCD Like Algorithms for Some Complex Quadratic Rings"],"prefix":"10.1007","author":[{"given":"Saurabh","family":"Agarwal","sequence":"first","affiliation":[]},{"given":"Gudmund Skovbjerg","family":"Frandsen","sequence":"additional","affiliation":[]}],"member":"297","reference":[{"key":"4_CR1","doi-asserted-by":"crossref","unstructured":"Agarwal, S.: Binary gcd like algorithms in some number rings. Department of Computer Science, University of Aarhus (2004)","DOI":"10.1007\/978-3-540-24847-7_4"},{"key":"4_CR2","series-title":"Foundations of Computing Series","volume-title":"Algorithmic number theory","author":"E. Bach","year":"1996","unstructured":"Bach, E., Shallit, J.: Algorithmic number theory. Foundations of Computing Series, vol.\u00a01. MIT Press, Cambridge (1996)"},{"issue":"216","key":"4_CR3","doi-asserted-by":"publisher","first-page":"1681","DOI":"10.1090\/S0025-5718-96-00766-1","volume":"65","author":"H. Cohen","year":"1996","unstructured":"Cohen, H.: Hermite and Smith normal form algorithms over Dedekind domains. Math. Comp.\u00a065(216), 1681\u20131699 (1996)","journal-title":"Math. Comp."},{"issue":"4","key":"4_CR4","doi-asserted-by":"publisher","first-page":"385","DOI":"10.1006\/jsco.2001.0518","volume":"33","author":"G.E. Collins","year":"2002","unstructured":"Collins, G.E.: A fast Euclidean algorithm for Gaussian integers. J. Symbolic Comput.\u00a033(4), 385\u2013392 (2002)","journal-title":"J. Symbolic Comput."},{"key":"4_CR5","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"109","DOI":"10.1007\/978-3-540-45077-1_11","volume-title":"Fundamentals of Computation Theory","author":"I.B. Damg\u00e5rd","year":"2003","unstructured":"Damg\u00e5rd, I.B., Frandsen, G.S.: Efficient algorithms for gcd and cubic residuosity in the ring of Eisenstein integers. In: Lingas, A., Nilsson, B.J. (eds.) FCT 2003. LNCS, vol.\u00a02751, pp. 109\u2013117. Springer, Heidelberg (2003)"},{"key":"4_CR6","series-title":"Graduate Texts in Mathematics","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4612-6101-8","volume-title":"Algebra","author":"T.W. Hungerford","year":"1980","unstructured":"Hungerford, T.W.: Algebra. Graduate Texts in Mathematics, vol.\u00a073. Springer, New York (1980); Reprint of the 1974 original"},{"key":"4_CR7","series-title":"Graduate Texts in Mathematics","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4757-2103-4","volume-title":"A classical introduction to modern number theory","author":"K. Ireland","year":"1990","unstructured":"Ireland, K., Rosen, M.: A classical introduction to modern number theory, 2nd edn. Graduate Texts in Mathematics, vol.\u00a084. Springer, New York (1990)","edition":"2"},{"issue":"188","key":"4_CR8","first-page":"697","volume":"53","author":"E. Kaltofen","year":"1989","unstructured":"Kaltofen, E., Rolletschek, H.: Computing greatest common divisors and factorizations in quadratic number fields. Math. Comp.\u00a053(188), 697\u2013720 (1989)","journal-title":"Math. Comp."},{"key":"4_CR9","volume-title":"The art of computer programming","author":"D.E. Knuth","year":"1981","unstructured":"Knuth, D.E.: The art of computer programming, 2nd edn., vol.\u00a02. Addison-Wesley Publishing Co., Reading (1981)","edition":"2"},{"key":"4_CR10","volume-title":"Algebra","author":"S. Lang","year":"1993","unstructured":"Lang, S.: Algebra, 3rd edn. Addison-Wesley Publishing Company, Reading (1993)","edition":"3"},{"key":"4_CR11","doi-asserted-by":"crossref","unstructured":"Lehmer, D.H.: Euclid\u2019s algorithm for large numbers. \u00a045, 227\u2013233 (1938)","DOI":"10.1080\/00029890.1938.11990797"},{"issue":"5","key":"4_CR12","first-page":"385","volume":"13","author":"F. Lemmermeyer","year":"1995","unstructured":"Lemmermeyer, F.: The Euclidean algorithm in algebraic number fields. Exposition. Math.\u00a013(5), 385\u2013416 (1995); An updated version is available at the webpage, http:\/\/www.rzuser.uni-heidelberg.de\/~hb3\/prep.html","journal-title":"Exposition. Math."},{"issue":"4","key":"4_CR13","doi-asserted-by":"publisher","first-page":"457","DOI":"10.1112\/jlms\/s2-10.4.457","volume":"10","author":"H.W. Lenstra Jr.","year":"1975","unstructured":"Lenstra Jr., H.W.: Euclid\u2019s algorithm in cyclotomic fields. J. London Math. Soc (2)\u00a010(4), 457\u2013465 (1975)","journal-title":"J. London Math. Soc. (2)"},{"issue":"3","key":"4_CR14","doi-asserted-by":"publisher","first-page":"261","DOI":"10.1016\/S0747-7171(86)80027-X","volume":"2","author":"H. Rolletschek","year":"1986","unstructured":"Rolletschek, H.: On the number of divisions of the Euclidean algorithm applied to Gaussian integers. J. Symbolic Comput.\u00a02(3), 261\u2013291 (1986)","journal-title":"J. Symbolic Comput."},{"issue":"2","key":"4_CR15","doi-asserted-by":"publisher","first-page":"117","DOI":"10.1007\/BF01398010","volume":"6","author":"R. Scheidler","year":"1995","unstructured":"Scheidler, R., Williams, H.C.: A public-key cryptosystem utilizing cyclotomic fields. Des. Codes Cryptogr.\u00a06(2), 117\u2013131 (1995)","journal-title":"Des. Codes Cryptogr."},{"key":"4_CR16","doi-asserted-by":"publisher","first-page":"139","DOI":"10.1007\/BF00289520","volume":"1","author":"A. Sch\u00f6nhage","year":"1971","unstructured":"Sch\u00f6nhage, A.: Schnelle Berechnung von Kettenbruchentwilungen. Acta Informatica\u00a01, 139\u2013144 (1971)","journal-title":"Acta Informatica"},{"issue":"1","key":"4_CR17","doi-asserted-by":"publisher","first-page":"110","DOI":"10.1006\/jagm.1994.1006","volume":"16","author":"J. Sorenson","year":"1994","unstructured":"Sorenson, J.: Two fast GCD algorithms. J. Algorithms\u00a016(1), 110\u2013144 (1994)","journal-title":"J. Algorithms"},{"key":"4_CR18","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1307\/mmj\/1028999653","volume":"14","author":"H.M. Stark","year":"1967","unstructured":"Stark, H.M.: A complete determination of the complex quadratic fields of classnumber one. Michigan Math. J.\u00a014, 1\u201327 (1967)","journal-title":"Michigan Math. J."},{"key":"4_CR19","doi-asserted-by":"crossref","unstructured":"Stein, J.: Computational problems associated with Racah algebra. J. Comput. Phys.\u00a0(1), 397\u2013405 (1967)","DOI":"10.1016\/0021-9991(67)90047-2"},{"key":"4_CR20","unstructured":"Weilert, A.: Effiziente Algorithmen zur Berechnung von Idealsummen in Quadratischen Ornungen. Dissertation, Universitaet Bonn (2000)"},{"issue":"5","key":"4_CR21","doi-asserted-by":"publisher","first-page":"605","DOI":"10.1006\/jsco.2000.0422","volume":"30","author":"A. Weilert","year":"2000","unstructured":"Weilert, A.: (1 + i)-ary GCD computation in Z[i] as an analogue to the binary GCD algorithm. J. Symbolic Comput.\u00a030(5), 605\u2013617 (2000)","journal-title":"J. Symbolic Comput."},{"key":"4_CR22","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"595","DOI":"10.1007\/10722028_40","volume-title":"Algorithmic number theory (Leiden, 2000)","author":"A. Weilert","year":"2000","unstructured":"Weilert, A.: Asymptotically fast GCD computation in Z[i]. In: Algorithmic number theory (Leiden, 2000). LNCS, vol.\u00a01838, pp. 595\u2013613. Springer, Berlin (2000)"}],"container-title":["Lecture Notes in Computer Science","Algorithmic Number Theory"],"original-title":[],"link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-540-24847-7_4.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,11,19]],"date-time":"2020-11-19T04:57:32Z","timestamp":1605761852000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/978-3-540-24847-7_4"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2004]]},"ISBN":["9783540221562","9783540248477"],"references-count":22,"URL":"https:\/\/doi.org\/10.1007\/978-3-540-24847-7_4","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"type":"print","value":"0302-9743"},{"type":"electronic","value":"1611-3349"}],"subject":[],"published":{"date-parts":[[2004]]}}}