Structure of the Class Group of Positive Binary Quadratic Forms Under Composition PDF Download
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Author: Mary Virgilia Dragowski
Publisher:
ISBN:
Category : Forms, Binary
Languages : en
Pages : 44
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Book Description
Author: Mary Virgilia Dragowski
Publisher:
ISBN:
Category : Forms, Binary
Languages : en
Pages : 44
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Book Description
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: George Ross Grainger
Publisher:
ISBN:
Category : Forms, Binary
Languages : en
Pages : 100
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Author: George Hoffman Cresse
Publisher:
ISBN:
Category : Forms, Binary
Languages : en
Pages : 117
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Author: Edward Charles Zeiger
Publisher:
ISBN:
Category :
Languages : en
Pages :
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Author: Caroline G. MacGillivray
Publisher:
ISBN:
Category : Class groups (Mathematics)
Languages : en
Pages : 52
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Author: Johannes Buchmann
Publisher: Algorithms and Computation in Mathematics
ISBN:
Category : Computers
Languages : en
Pages : 354
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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: 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: John William Scott Cassels
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 444
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Book Description
