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# Binary Quadratic Forms: An Algorithmic Approach

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ISBN: 9783540463672 Publisher: Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
Year of publishing: 2007 Format: Hardcover
No of Pages: 332 Language: English

This book deals with algorithmic problems related to binary quadratic forms, such as finding the representations of an integer by a form with integer coefficients, finding the minimum of a form with real...Read more

This book deals with algorithmic problems related to binary quadratic forms, such as finding the representations of an integer by a form with integer coefficients, finding the minimum of a form with real coefficients and deciding equivalence of two forms. In order to solve those problems, 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. It requires only basic mathematical knowledge.

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**About the author:**Johannes Buchmann

**Review**:

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...Read more

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)

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