Binary Quadratic Forms: Classical Theory and Modern Computations
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
New York, NY
Springer New York
1989
|
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | The first coherent exposition of the theory of binary quadratic forms was given by Gauss in the Disqnisitiones Arithmeticae. During the nineteenth century, as the theory of ideals and the rudiments of algebraic number theory were developed, it became clear that this theory of binary 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 twodimensional vector space, have been dropped in favor of n-dimensional arguments which prove the general theorems of algebraic number theory. 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 computation 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 |
| Beschreibung: | 1 Online-Ressource (X, 248 p) |
| ISBN: | 9781461245421 9781461288701 |
| DOI: | 10.1007/978-1-4612-4542-1 |
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| 500 | |a The first coherent exposition of the theory of binary quadratic forms was given by Gauss in the Disqnisitiones Arithmeticae. During the nineteenth century, as the theory of ideals and the rudiments of algebraic number theory were developed, it became clear that this theory of binary 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 twodimensional vector space, have been dropped in favor of n-dimensional arguments which prove the general theorems of algebraic number theory. 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 computation 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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Datensatz im Suchindex
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| discipline | Mathematik |
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| format | Electronic eBook |
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| indexdate | 2024-07-10T01:21:06Z |
| institution | BVB |
| isbn | 9781461245421 9781461288701 |
| language | English |
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| spelling | Buell, Duncan A. Verfasser aut Binary Quadratic Forms Classical Theory and Modern Computations by Duncan A. Buell New York, NY Springer New York 1989 1 Online-Ressource (X, 248 p) txt rdacontent c rdamedia cr rdacarrier The first coherent exposition of the theory of binary quadratic forms was given by Gauss in the Disqnisitiones Arithmeticae. During the nineteenth century, as the theory of ideals and the rudiments of algebraic number theory were developed, it became clear that this theory of binary 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 twodimensional vector space, have been dropped in favor of n-dimensional arguments which prove the general theorems of algebraic number theory. 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 computation 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 Mathematics Combinatorics Number theory Number Theory Mathematik Binäre quadratische Form (DE-588)4145538-1 gnd rswk-swf Binäre quadratische Form (DE-588)4145538-1 s 1\p DE-604 https://doi.org/10.1007/978-1-4612-4542-1 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Buell, Duncan A. Binary Quadratic Forms Classical Theory and Modern Computations Mathematics Combinatorics Number theory Number Theory Mathematik Binäre quadratische Form (DE-588)4145538-1 gnd |
| subject_GND | (DE-588)4145538-1 |
| title | Binary Quadratic Forms Classical Theory and Modern Computations |
| title_auth | Binary Quadratic Forms Classical Theory and Modern Computations |
| title_exact_search | Binary Quadratic Forms Classical Theory and Modern Computations |
| title_full | Binary Quadratic Forms Classical Theory and Modern Computations by Duncan A. Buell |
| title_fullStr | Binary Quadratic Forms Classical Theory and Modern Computations by Duncan A. Buell |
| title_full_unstemmed | Binary Quadratic Forms Classical Theory and Modern Computations by Duncan A. Buell |
| title_short | Binary Quadratic Forms |
| title_sort | binary quadratic forms classical theory and modern computations |
| title_sub | Classical Theory and Modern Computations |
| topic | Mathematics Combinatorics Number theory Number Theory Mathematik Binäre quadratische Form (DE-588)4145538-1 gnd |
| topic_facet | Mathematics Combinatorics Number theory Number Theory Mathematik Binäre quadratische Form |
| url | https://doi.org/10.1007/978-1-4612-4542-1 |
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