Binary Quadratic Forms

Name: Binary Quadratic Forms
Brand: Springer-Verlag New York Inc.
SKU: 9780387970370
Price: 824.66 RON
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Classical Theory and Modern Computations

Autor: Duncan A. Buell

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Legare: Copertă tare

Editura: Springer-Verlag New York Inc.

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The first coherent exposition of the theory of binary quadratic forms was given by Gauss in the Disq...

Informații despre carte

Autor

Duncan A. Buell

Limbă

engleză

Legare

Carte - Copertă tare

Pagini

248

EAN

9780387970370

ISBN

0387970371

Enbook ID

01385047

Editura

Springer-Verlag New York Inc.

Greutate

1210

Dimensiuni

155 x 235 x 19

Descriere completă

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.

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Binary Quadratic Forms

Classical Theory and Modern Computations

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