Computing Hilbert class polynomials

Authors:
Juliana Belding;Reinier Bröker;Andreas Enge;Kristin Lauter
Affiliations:
Dept. of Mathematics, University of Maryland, College Park, MD;Microsoft Research, Redmond, WA;INRIA Futurs & Laboratoire d'Informatique, CNRS, UMR, ÉÉcole polytechnique, Palaiseau Cedex, France;Microsoft Research, Redmond, WA
Venue:
ANTS-VIII'08 Proceedings of the 8th international conference on Algorithmic number theory
Year:
2008

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Abstract

We present and analyze two algorithms for computing theHilbert class polynomial HD. The first is a p-adic lifting algorithm forinert primes p in the order of discriminant D HD, and weshow that all methods have comparable run times.