skip to content
Binary Quadratic Forms : Classical Theory and Modern Computations Preview this item
ClosePreview this item
Checking...

Binary Quadratic Forms : Classical Theory and Modern Computations

Author: Duncan A Buell
Publisher: New York, NY : Springer New York, 1989.
Edition/Format:   eBook : Document : EnglishView all editions and formats
Summary:
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  Read more...
Rating:

(not yet rated) 0 with reviews - Be the first.

Subjects
More like this

 

Find a copy online

Links to this item

Find a copy in the library

&AllPage.SpinnerRetrieving; Finding libraries that hold this item...

Details

Genre/Form: Electronic books
Additional Physical Format: Print version:
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Duncan A Buell
ISBN: 9781461245421 1461245427
OCLC Number: 852790476
Description: 1 online resource (x, 247 pages)
Contents: 1 Elementary Concepts --
2 Reduction of Positive Definite Forms --
3 Indefinite Forms --
3.1 Reduction, Cycles --
3.2 Automorphs, Pell's Equation --
3.3 Continued Fractions and Indefinite Forms --
4 The Class Group --
4.1 Representation and Genera --
4.2 Composition Algorithms --
4.3 Generic Characters Revisited --
4.4 Representation of Integers --
5 Miscellaneous Facts --
5.1 Class Number Computations --
5.2 Extreme Cases and Asymptotic Results --
6 Quadratic Number Fields --
6.1 Basic Algebraic Definitions --
6.2 Algebraic Numbers and Quadratic Fields --
6.3 Ideals in Quadratic Fields --
6.4 Binary Quadratic Forms and Classes of Ideals --
6.5 History --
7 Composition of Forms --
7.1 Nonfundamental Discriminants --
7.2 The General Problem of Composition --
7.3 Composition in Different Orders --
8 Miscellaneous Facts II --
8.1 The Cohen-Lenstra Heuristics --
8.2 Decomposing Class Groups --
8.3 Specifying Subgroups of Class Groups --
9 The 2-Sylow Subgroup --
9.1 Classical Results on the Pell Equation --
9.2 Modern Results --
9.3 Reciprocity Laws --
9.4 Special References for Chapter 9 --
10 Factoring with Binary Quadratic Forms --
10.1 Classical Methods --
10.2 SQUFOF --
10.3 CLASNO --
10.4 SPAR --
10.5 CFRAC --
10.6 A General Analysis --
Appendix 1:Tables, Negative Discriminants --
Appendix 2:Tables, Positive Discriminants.
Responsibility: by Duncan A. Buell.

Abstract:

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.

Reviews

User-contributed reviews
Retrieving GoodReads reviews...
Retrieving DOGObooks reviews...

Tags

Be the first.

Similar Items

Confirm this request

You may have already requested this item. Please select Ok if you would like to proceed with this request anyway.

Linked Data


Primary Entity

<http://www.worldcat.org/oclc/852790476> # Binary Quadratic Forms : Classical Theory and Modern Computations
    a schema:CreativeWork, schema:Book, schema:MediaObject ;
   library:oclcnum "852790476" ;
   library:placeOfPublication <http://experiment.worldcat.org/entity/work/data/890482018#Place/new_york_ny> ; # New York, NY
   library:placeOfPublication <http://id.loc.gov/vocabulary/countries/nyu> ;
   schema:about <http://id.worldcat.org/fast/868961> ; # Combinatorial analysis
   schema:about <http://id.worldcat.org/fast/1041214> ; # Number theory
   schema:about <http://id.worldcat.org/fast/1012163> ; # Mathematics
   schema:about <http://dewey.info/class/512.7/e23/> ;
   schema:bookFormat schema:EBook ;
   schema:creator <http://viaf.org/viaf/291274> ; # Duncan A. Buell
   schema:datePublished "1989" ;
   schema: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."@en ;
   schema:description "1 Elementary Concepts -- 2 Reduction of Positive Definite Forms -- 3 Indefinite Forms -- 3.1 Reduction, Cycles -- 3.2 Automorphs, Pell's Equation -- 3.3 Continued Fractions and Indefinite Forms -- 4 The Class Group -- 4.1 Representation and Genera -- 4.2 Composition Algorithms -- 4.3 Generic Characters Revisited -- 4.4 Representation of Integers -- 5 Miscellaneous Facts -- 5.1 Class Number Computations -- 5.2 Extreme Cases and Asymptotic Results -- 6 Quadratic Number Fields -- 6.1 Basic Algebraic Definitions -- 6.2 Algebraic Numbers and Quadratic Fields -- 6.3 Ideals in Quadratic Fields -- 6.4 Binary Quadratic Forms and Classes of Ideals -- 6.5 History -- 7 Composition of Forms -- 7.1 Nonfundamental Discriminants -- 7.2 The General Problem of Composition -- 7.3 Composition in Different Orders -- 8 Miscellaneous Facts II -- 8.1 The Cohen-Lenstra Heuristics -- 8.2 Decomposing Class Groups -- 8.3 Specifying Subgroups of Class Groups -- 9 The 2-Sylow Subgroup -- 9.1 Classical Results on the Pell Equation -- 9.2 Modern Results -- 9.3 Reciprocity Laws -- 9.4 Special References for Chapter 9 -- 10 Factoring with Binary Quadratic Forms -- 10.1 Classical Methods -- 10.2 SQUFOF -- 10.3 CLASNO -- 10.4 SPAR -- 10.5 CFRAC -- 10.6 A General Analysis -- Appendix 1:Tables, Negative Discriminants -- Appendix 2:Tables, Positive Discriminants."@en ;
   schema:exampleOfWork <http://worldcat.org/entity/work/id/890482018> ;
   schema:genre "Electronic books"@en ;
   schema:inLanguage "en" ;
   schema:isSimilarTo <http://worldcat.org/entity/work/data/890482018#CreativeWork/> ;
   schema:name "Binary Quadratic Forms : Classical Theory and Modern Computations"@en ;
   schema:productID "852790476" ;
   schema:publication <http://www.worldcat.org/title/-/oclc/852790476#PublicationEvent/new_york_ny_springer_new_york_1989> ;
   schema:publisher <http://experiment.worldcat.org/entity/work/data/890482018#Agent/springer_new_york> ; # Springer New York
   schema:url <http://link.springer.com/10.1007/978-1-4612-4542-1> ;
   schema:url <https://link.springer.com/openurl?genre=book&isbn=978-0-387-97037-0> ;
   schema:url <http://dx.doi.org/10.1007/978-1-4612-4542-1> ;
   schema:workExample <http://dx.doi.org/10.1007/978-1-4612-4542-1> ;
   schema:workExample <http://worldcat.org/isbn/9781461245421> ;
   wdrs:describedby <http://www.worldcat.org/title/-/oclc/852790476> ;
    .


Related Entities

<http://experiment.worldcat.org/entity/work/data/890482018#Agent/springer_new_york> # Springer New York
    a bgn:Agent ;
   schema:name "Springer New York" ;
    .

<http://id.worldcat.org/fast/1012163> # Mathematics
    a schema:Intangible ;
   schema:name "Mathematics"@en ;
    .

<http://id.worldcat.org/fast/1041214> # Number theory
    a schema:Intangible ;
   schema:name "Number theory"@en ;
    .

<http://id.worldcat.org/fast/868961> # Combinatorial analysis
    a schema:Intangible ;
   schema:name "Combinatorial analysis"@en ;
    .

<http://link.springer.com/10.1007/978-1-4612-4542-1>
   rdfs:comment "from Springer" ;
   rdfs:comment "(Unlimited Concurrent Users)" ;
    .

<http://viaf.org/viaf/291274> # Duncan A. Buell
    a schema:Person ;
   schema:familyName "Buell" ;
   schema:givenName "Duncan A." ;
   schema:name "Duncan A. Buell" ;
    .

<http://worldcat.org/entity/work/data/890482018#CreativeWork/>
    a schema:CreativeWork ;
   schema:description "Print version:" ;
   schema:isSimilarTo <http://www.worldcat.org/oclc/852790476> ; # Binary Quadratic Forms : Classical Theory and Modern Computations
    .

<http://worldcat.org/isbn/9781461245421>
    a schema:ProductModel ;
   schema:isbn "1461245427" ;
   schema:isbn "9781461245421" ;
    .


Content-negotiable representations

Close Window

Please sign in to WorldCat 

Don't have an account? You can easily create a free account.