A Course in Computational Algebraic Number Theory (Graduate Texts in Mathematics, 138)

by: Henri Cohen (Author)

Publisher: Springer

Edition: 1993. 4th Print

Publication Date: 1993/8/5

Language: English

Print Length: 557 pages

ISBN-10: 3540556400

ISBN-13: 9783540556404

Book 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 exteal and inteal pressures gave a powerful impetus to the development of more powerful al­ gorithms. These in tu 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.

About the Author

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 exteal and inteal pressures gave a powerful impetus to the development of more powerful al­ gorithms. These in tu 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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