[{"_id":"35941","page":"1179-1186","dc":{"date":["1999"],"relation":["info:eu-repo/semantics/altIdentifier/issn/1088-6842","info:eu-repo/semantics/altIdentifier/issn/0025-5718"],"language":["eng"],"publisher":["American Mathematical Society (AMS)"],"type":["info:eu-repo/semantics/article","doc-type:article","text","http://purl.org/coar/resource_type/c_6501"],"source":["Klüners J, Acciaro V. Computing Automorphisms of Abelian Number Fields. *Mathematics of Computation*. 1999;68(227):1179-1186."],"description":["Let L = ℚ(α) be an abelian number field of degree n. Most\r\nalgorithms for computing the lattice of subfields of L require the computation\r\nof all the conjugates of α. This is usually achieved by factoring the minimal\r\npolynomial mα(x) of α over L. In practice, the existing algorithms for factoring\r\npolynomials over algebraic number fields can handle only problems of moderate\r\nsize. In this paper we describe a fast probabilistic algorithm for computing\r\nthe conjugates of α, which is based on p-adic techniques. Given mα(x) and a\r\nrational prime p which does not divide the discriminant disc(mα(x)) of mα(x),\r\nthe algorithm computes the Frobenius automorphism of p in time polynomial\r\nin the size of p and in the size of mα(x). By repeatedly applying the algorithm\r\nto randomly chosen primes it is possible to compute all the conjugates of α."],"title":["Computing Automorphisms of Abelian Number Fields"],"identifier":["https://ris.uni-paderborn.de/record/35941"],"creator":["Klüners, Jürgen","Acciaro, Vincenzo"],"rights":["info:eu-repo/semantics/closedAccess"]},"abstract":[{"lang":"eng"}],"intvolume":" 68","date_created":"2023-01-11T09:31:21Z","date_updated":"2023-03-06T10:28:52Z","dini_type":"doc-type:article","status":"public","type":"journal_article","language":[{}],"user_id":"93826","related_material":{"link":[{"url":"https://www.ams.org/journals/mcom/1999-68-227/S0025-5718-99-01084-4/S0025-5718-99-01084-4.pdf","relation":"confirmation"}]},"publication_status":"published","citation":{"mla":"Klüners, Jürgen, and Vincenzo Acciaro. “Computing Automorphisms of Abelian Number Fields.” *Mathematics of Computation*, vol. 68, no. 227, American Mathematical Society (AMS), 1999, pp. 1179–86.","bibtex":"@article{Klüners_Acciaro_1999, title={Computing Automorphisms of Abelian Number Fields}, volume={68}, number={227}, journal={Mathematics of Computation}, publisher={American Mathematical Society (AMS)}, author={Klüners, Jürgen and Acciaro, Vincenzo}, year={1999}, pages={1179–1186} }","apa":"Klüners, J., & Acciaro, V. (1999). Computing Automorphisms of Abelian Number Fields. *Mathematics of Computation*, *68*(227), 1179–1186.","ieee":"J. Klüners and V. Acciaro, “Computing Automorphisms of Abelian Number Fields,” *Mathematics of Computation*, vol. 68, no. 227, pp. 1179–1186, 1999.","chicago":"Klüners, Jürgen, and Vincenzo Acciaro. “Computing Automorphisms of Abelian Number Fields.” *Mathematics of Computation* 68, no. 227 (1999): 1179–86.","short":"J. Klüners, V. Acciaro, Mathematics of Computation 68 (1999) 1179–1186."},"publication":"Mathematics of Computation","creator":{"login":"ckoerber","id":"93826"},"issue":"227","volume":68,"publication_identifier":{"issn":[]},"department":[{"_id":"102","tree":[{"_id":"99"},{"_id":"10"},{"_id":"34"},{"_id":"44"},{"_id":"43"}]}],"author":[{"first_name":"Jürgen","id":"21202","last_name":"Klüners"},{"last_name":"Acciaro","first_name":"Vincenzo"}],"uri_base":"https://ris.uni-paderborn.de"}]