
A Course in Computational Algebraic Number Theory
Henri Cohen(Author)
Springer (Publisher)
1st Edition
Published on 8. December 2010
Book
Paperback/Softback
XXI, 536 pages
978-3-642-08142-2 (ISBN)
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.
Reviews / Votes
H. Cohen A Course in Computational Algebraic Number Theory "With numerous advances in mathematics, computer science, and cryptography, algorithmic number theory has become an important subject. Undoubtedly, this book, written by one of the leading authorities in the field, is one of the most beautiful books available on the market." -ACTA SCIENTIARUM MATHEMATICARUMMore details
Product info
Previously published in hardcover
Series
Band 138
Edition
1st ed. 1993. 4th printing. Softcover version of original hardcover edition 1993
Language
English
Place of publication
Berlin, Heidelberg
Germany
Target group
Research
Product notice
Paperback (trade)
Illustrations
biography
Dimensions
Height: 235 mm
Width: 155 mm
Thickness: 29 mm
Weight
836 gr
ISBN-13
978-3-642-08142-2 (9783642081422)
DOI
10.1007/978-3-662-02945-9
Schweitzer Classification
Other editions
Additional editions

E-Book
04/2013
Springer
€64.19
Available for download

Book
08/2000
1st Edition
Springer
€90.94
Shipment within 10-15 days
Content
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.