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Book Cover
E-book
Author Cohen, Henri

Title A Course in Computational Algebraic Number Theory / by Henri Cohen
Published Berlin, Heidelberg : Springer Berlin Heidelberg, 1993

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Description 1 online resource (xxi, 536 pages)
Series Graduate Texts in Mathematics, 0072-5285 ; 138
Graduate texts in mathematics ; 138
Contents 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
Summary 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
Bibliography Includes bibliographical references (pages 527-539) and index
Notes English
Subject Mathematics.
Computer software.
Algebra -- Data processing
Algorithms.
Number theory.
Mathematics
Software
Algorithms
software.
algorithms.
Algebra -- Data processing
Algorithms
Computer software
Mathematics
Number theory
Form Electronic book
ISBN 9783662029459
3662029456