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Binary Quadratic Forms: An Algorithmic Approach: Book by Johannes Buchmann

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
Buchmann: Professor of Computer Science and Mathematics special areas number theory, computer algebra, cryptography associate editor Journal of Cryptology... Read more
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.
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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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