The Composition of Binary Quadratic Forms PDF Download
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Author: Edward Charles Zeiger
Publisher:
ISBN:
Category :
Languages : en
Pages :
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Author: Duncan A. Buell
Publisher: Springer Science & Business Media
ISBN: 1461245427
Category : Mathematics
Languages : en
Pages : 249
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Book Description
The first coherent exposition of the theory of binary quadratic forms was given by Gauss in the Disqnisitiones Arithmeticae. During the nine teenth century, as the theory of ideals and the rudiments of algebraic number theory were developed, it became clear that this theory of bi nary quadratic forms, so elementary and computationally explicit, was indeed just a special case of a much more elega,nt and abstract theory which, unfortunately, is not computationally explicit. In recent years the original theory has been laid aside. Gauss's proofs, which involved brute force computations that can be done in what is essentially a two dimensional vector space, have been dropped in favor of n-dimensional arguments which prove the general theorems of algebraic number the ory. In consequence, this elegant, yet pleasantly simple, theory has been neglected even as some of its results have become extremely useful in certain computations. I find this neglect unfortunate, because binary quadratic forms have two distinct attractions. First, the subject involves explicit computa tion and many of the computer programs can be quite simple. The use of computers in experimenting with examples is both meaningful and enjoyable; one can actually discover interesting results by com puting examples, noticing patterns in the "data," and then proving that the patterns result from the conclusion of some provable theorem.
Author: Edward Charles Zeiger
Publisher:
ISBN:
Category :
Languages : en
Pages :
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Author: Johannes Buchmann
Publisher: Springer Science & Business Media
ISBN: 3540463682
Category : Mathematics
Languages : en
Pages : 328
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Book Description
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.
Author: Bill J. Dulin
Publisher:
ISBN:
Category : Forms, Binary
Languages : en
Pages : 136
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Author: Constance Jane Boyd
Publisher:
ISBN:
Category : Forms, Binary
Languages : en
Pages : 60
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Author: C. S. Iliopoulos
Publisher:
ISBN:
Category : Applied mathematics
Languages : en
Pages :
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Author: Mary Virgilia Dragowski
Publisher:
ISBN:
Category : Forms, Binary
Languages : en
Pages : 44
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Author: George Ross Grainger
Publisher:
ISBN:
Category : Forms, Binary
Languages : en
Pages : 100
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Author: J. W. S. Cassels
Publisher: Courier Dover Publications
ISBN: 0486466701
Category : Mathematics
Languages : en
Pages : 429
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Book Description
Exploration of quadratic forms over rational numbers and rational integers offers elementary introduction. Covers quadratic forms over local fields, forms with integral coefficients, reduction theory for definite forms, more. 1968 edition.
Author: George Hoffman Cresse
Publisher:
ISBN:
Category : Forms, Binary
Languages : en
Pages : 117
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