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Binary Quadratic Forms By Johannes Buchmann

Binary Quadratic Forms by Johannes Buchmann

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Summary

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.

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Binary Quadratic Forms Summary

Binary Quadratic Forms: An Algorithmic Approach 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. The book explains applications to cryptography and requires only basic mathematical knowledge. The author is a world leader in number theory.

Binary Quadratic Forms Reviews

From the reviews:

"Quadratic Field Theory is the best platform for the development of a computer viewpoint. Such 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 fur Mathematik, Vol. 156 (3), March, 2009)

About Johannes Buchmann


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.

Table of Contents

Binary Quadratic Forms.- Equivalence of Forms.- Constructing Forms.- Forms, Bases, Points, and Lattices.- Reduction of Positive Definite Forms.- Reduction of Indefinite Forms.- Multiplicative Lattices.- Quadratic Number Fields.- Class Groups.- Infrastructure.- Subexponential Algorithms.- Cryptographic Applications.

Additional information

NLS9783642079719
9783642079719
3642079717
Binary Quadratic Forms: An Algorithmic Approach by Johannes Buchmann
New
Paperback
Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
2010-11-25
318
N/A
Book picture is for illustrative purposes only, actual binding, cover or edition may vary.
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