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Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.78.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.


Generating random factored ideals in number fields
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by Zachary Charles PDF
Math. Comp. 87 (2018), 2047-2056 Request permission


We present a randomized polynomial-time algorithm to generate an ideal and its factorization uniformly at random in a given number field. We do this by generating a random integer and its factorization according to the distribution of norms of ideals at most $N$ in the given number field. Using this randomly generated norm, we can produce a random factored ideal in the ring of algebraic integers uniformly at random among ideals with norm up to $N$, in randomized polynomial time. We also present a variant of this algorithm for generating random factored ideals in function fields.
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Additional Information
  • Zachary Charles
  • Affiliation: Department of Mathematics, University of Wisconsin-Madison, Madison, Wisconsin 53706
  • MR Author ID: 1002462
  • Email:
  • Received by editor(s): December 14, 2016
  • Received by editor(s) in revised form: February 8, 2017
  • Published electronically: October 17, 2017
  • © Copyright 2017 American Mathematical Society
  • Journal: Math. Comp. 87 (2018), 2047-2056
  • MSC (2010): Primary 11Y16; Secondary 68Q25
  • DOI:
  • MathSciNet review: 3787402