Binary Quadratic Forms: An Algorithmic Approach

Binary Quadratic Forms: An Algorithmic Approach

by Johannes Buchmann, Ulrich Vollmer
     
 

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

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Overview

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.

Editorial Reviews

From the Publisher
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 für Mathematik, Vol. 156 (3), March, 2009)

Product Details

ISBN-13:
9783642079719
Publisher:
Springer Berlin Heidelberg
Publication date:
11/23/2010
Series:
Algorithms and Computation in Mathematics Series, #20
Edition description:
Softcover reprint of hardcover 1st ed. 2007
Pages:
318
Product dimensions:
0.70(w) x 6.14(h) x 9.21(d)

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