{"citation":{"short":"J. Klüners, V. Acciaro, Mathematics of Computation 68 (1999) 1179–1186.","ama":"Klüners J, Acciaro V. Computing Automorphisms of Abelian Number Fields. *Mathematics of Computation*. 1999;68(227):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.","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} }"},"publication":"Mathematics of Computation","issue":"227","volume":68,"publication_identifier":{"issn":["1088-6842","0025-5718"]},"department":[{"_id":"102"}],"publisher":"American Mathematical Society (AMS)","author":[{"id":"21202","first_name":"Jürgen","last_name":"Klüners","full_name":"Klüners, Jürgen"},{"full_name":"Acciaro, Vincenzo","last_name":"Acciaro","first_name":"Vincenzo"}],"_id":"35941","page":"1179-1186","abstract":[{"lang":"eng","text":"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."}],"intvolume":" 68","date_created":"2023-01-11T09:31:21Z","date_updated":"2023-03-06T10:28:52Z","status":"public","title":"Computing Automorphisms of Abelian Number Fields","year":"1999","type":"journal_article","language":[{"iso":"eng"}],"user_id":"93826","publication_status":"published","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"}]}}