Binary Quadratic Forms
Binary Quadratic Forms
Summary
This book deals with algorithmic problems concerning binary quadratic forms 2 2 f(X,Y)= aX +bXY +cY with integer coe?cients a, b, c, the mathem- ical theories that permit the solution of these problems, and applications to cryptography.
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Binary Quadratic Forms by Johannes Buchmann
The book deals with algorithmic problems related to binary quadratic forms. It uniquely focuses on the algorithmic aspects of the theory. The book introduces the reader to important areas of number theory such as diophantine equations, reduction theory of quadratic forms, geometry of numbers and algebraic number theory.From the reviews:
"Quadratic Field Theory is the best platform for the development of a computer viewpointSuch an idea is not dominant in earlier texts on quadratic forms … . this book reads like a continuous program with major topics occurring as subroutines. The theory appears as ‘program comments,’ accompanied by numerical examples. … An appendix explaining linear algebra (bases and matrices) helps make this work ideal as a self-contained well-motivated textbook for computer-oriented students at any level and as a reference book." (Harvey Cohn, Zentralblatt MATH, Vol. 1125 (2), 2008)
“The book under discussion contains the classical Gauß -Dirichlet representation theory of integral binary quadric forms. … Many of the algorithms presented in this book are described in full detail. The whole text is very carefully written. It is therefore also well suited for beginners as in addition no special knowledge on Number Theory is necessary to understand the text. It can also be recommended to teachers who give courses in Number Theory or Computational Algebra.” (J. Schoissengeier, Monatshefte für Mathematik, Vol. 156 (3), March, 2009)
Buchmann: Professor of Computer Science and Mathematics
special areas number theory, computer algebra, cryptography
associate editor Journal of Cryptology
Leibniz Award of the Deutsche Forschungsgemeinschaft
Author of "Introduction to cryptography" UTM, translated into seven languages
Member of Berlin-Brandenburg Academy of Sciences
Member of Academy of Sciences and Literature, Mainz
Vollmer: Thesis and several articles on algorithms for Class Group and Regulator computation in quadratic fields.
| SKU | Unavailable |
| ISBN 13 | 9783642079719 |
| ISBN 10 | 3642079717 |
| Title | Binary Quadratic Forms |
| Author | Johannes Buchmann |
| Series | Algorithms And Computation In Mathematics |
| Condition | Unavailable |
| Binding Type | Paperback |
| Publisher | Springer |
| Year published | 2010-11-25 |
| Number of pages | 318 |
| Cover note | Book picture is for illustrative purposes only, actual binding, cover or edition may vary. |
| Note | Unavailable |