A description of 148 algorithms fundamental to number-theoretic
computations, in particular for computations related to algebraic number
theory, elliptic curves, primality testing and factoring. The first
seven chapters guide readers to the heart of current research in
computational algebraic number theory, including recent algorithms for
computing class groups and units, as well as elliptic curve
computations, while the last three chapters survey factoring and
primality testing methods, including a detailed description of the
number field sieve algorithm. The whole is rounded off with a
description of available computer packages and some useful tables,
backed by numerous exercises. Written by an authority in the field, and
one with great practical and teaching experience, this is certain to
become the standard and indispensable reference on the subject.

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