A Course in Computational Algebraic Number Theory

Description

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 Front Matter....Pages I-XXI Fundamental Number-Theoretic Algorithms....Pages 1-44 Algorithms for Linear Algebra and Lattices....Pages 45-107 Algorithms on Polynomials....Pages 108-150 Algorithms for Algebraic Number Theory I....Pages 151-217 Algorithms for Quadratic Fields....Pages 218-296 Algorithms for Algebraic Number Theory II....Pages 297-359 Introduction to Elliptic Curves....Pages 360-411 Factoring in the Dark Ages....Pages 412-436 Modern Primality Tests....Pages 437-468 Modern Factoring Methods....Pages 469-497 Back Matter....Pages 498-536