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A Course in Computational Algebraic Number Theory 1993. 4th Print Edition
Contributor(s): Cohen, Henri (Author)

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 ISBN: 3540556400     ISBN-13: 9783540556404
Publisher: Springer
OUR PRICE: $85.49  

Binding Type: Hardcover
Published: August 1993
Qty:

Annotation: This book describes 148 algorithms which are fundamental for number-theoretic computations, in particular for computations related to algebraic number theory, elliptic curves, primality testing and factoring. The first seven chapters lead the reader 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. The last three chapters give a survey of factoring and primality testing methods, including a detailed description of the number field sieve algorithm. The book ends with a description of available computer packages and some useful tables. The book also contains a large number of exercises. Written by an authority in the field, and one with great practical and teaching experience it is sure to become the standard and indispensable reference on the subject.

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Additional Information
BISAC Categories:
- Mathematics | Number Theory
- Computers | Computer Science
- Computers | Programming - Algorithms
Dewey: 512.740
LCCN: 96044745
Series: Graduate Texts in Mathematics,
Physical Information: 1.4" H x 6.49" W x 9.3" L (2.08 lbs) 536 pages
 
Descriptions, Reviews, Etc.
Publisher Description:
With the advent of powerful computing tools and numerous advances in math- ematics, computer science and cryptography, algorithmic number theory has become an important subject in its own right. Both external and internal pressures gave a powerful impetus to the development of more powerful al- gorithms. These in turn led to a large number of spectacular breakthroughs. To mention but a few, the LLL algorithm which has a wide range of appli- cations, including real world applications to integer programming, primality testing and factoring algorithms, sub-exponential class group and regulator algorithms, etc ... Several books exist which treat parts of this subject. (It is essentially impossible for an author to keep up with the rapid pace of progress in all areas of this subject.) Each book emphasizes a different area, corresponding to the author's tastes and interests. The most famous, but unfortunately the oldest, is Knuth's Art of Computer Programming, especially Chapter 4. The present book has two goals. First, to give a reasonably comprehensive introductory course in computational number theory. In particular, although we study some subjects in great detail, others are only mentioned, but with suitable pointers to the literature. Hence, we hope that this book can serve as a first course on the subject. A natural sequel would be to study more specialized subjects in the existing literature.
 
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