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Field name	Details
Dewey Class	512.7
Title	A Course in Computational Algebraic Number Theory ([EBook]) / by Henri Cohen.
Author	Cohen, Henri , 1947-
Other name(s)	SpringerLink (Online service)
Publication	Berlin, Heidelberg : Springer , 1993.
Physical Details	XXI, 536 pages : online resource.
Series	Graduate texts in mathematics 0072-5285 ; ; 138
ISBN	9783662029459
Summary Note	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.:
Contents note	1. Fundamental Number-Theoretic Algorithms -- 2. Algorithms for Linear Algebra and Lattices -- 3. Algorithms on Polynomials -- 4. Algorithms for Algebraic Number Theory I -- 5. Algorithms for Quadratic Fields -- 6. Algorithms for Algebraic Number Theory II -- 7. Introduction to Elliptic Curves -- 8. Factoring in the Dark Ages -- 9. Modern Primality Tests -- 10. Modern Factoring Methods -- Appendix A. Packages for Number Theory -- Appendix B. Some Useful Tables -- B.1. Table of Class Numbers of Complex Quadratic Fields -- B.2. Table of Class Numbers and Units of Real Quadratic Fields -- B.3. Table of Class Numbers and Units of Complex Cubic Fields -- B.4. Table of Class Numbers and Units of Totally Real Cubic Fields -- B.5. Table of Elliptic Curves.
System details note	Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users)
Internet Site	http://dx.doi.org/10.1007/978-3-662-02945-9
Links to Related Works	Subject References: Algebra . Algebraic number theory . Algorithm Analysis and Problem Complexity . Algorithms . Mathematics . Number Theory . Symbolic and Algebraic Manipulation . Theory of Computation . Authors: Cohen, Henri 1947- . Cohen, Henri, 1947- . Corporate Authors: SpringerLink (Online service) . Series: Graduate texts in mathematics . GTM . Classification: 512.7 .

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A Course in Computational Algebraic Number Theory

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