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Subexponential class group and unit group computation in large degree number fields

Published online by Cambridge University Press:  01 August 2014

Jean-François Biasse
Computer Science Department and Mathematics Department, University of Calgary, 2500 University Drive NW, Calgary, Alberta T2N 1N4, Canada email
Claus Fieker
University of Kaiserslautern, Fachbereich Mathematik, Postfach 3049, 67653 Kaiserslautern, Germany email


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We describe how to compute the ideal class group and the unit group of an order in a number field in subexponential time. Our method relies on the generalized Riemann hypothesis and other usual heuristics concerning the smoothness of ideals. It applies to arbitrary classes of number fields, including those for which the degree goes to infinity.

Research Article
© The Author(s) 2014 


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