東華大學圖書館 |

Language: English

Help

回圖書館首頁

手機版館藏查詢

Back

Switch To: Labeled | MARC Mode | ISBD

Diophantine equations and power inte...

Gaal, Istvan.

Linked to FindBook

Google Book

Amazon

博客來

Diophantine equations and power integral bases = theory and algorithms /

Record Type:	Electronic resources : Monograph/item
Title/Author:	Diophantine equations and power integral bases/ by Istvan Gaal.
Reminder of title:	theory and algorithms /
Author:	Gaal, Istvan.
Published:	Cham :Springer International Publishing : : 2019.,
Description:	xxii, 326 p. :ill., digital ;24 cm.
[NT 15003449]:	Introduction -- Auxiliary results, tools -- Thue equations -- Inhomogeneous Thue equations -- Relative Thue equations -- The resolution of norm form equations -- Index form equations in general -- Cubic fields -- Quartic fields -- Quintic fields -- Sextic fields -- Pure fields -- Cubic relative extensions -- Quartic relative extensions -- Some higher degree fields -- Tables.
Contained By:	Springer Nature eBook
Subject:	Diophantine equations. -
Online resource:	https://doi.org/10.1007/978-3-030-23865-0
ISBN:	9783030238650

Diophantine equations and power integral bases = theory and algorithms /
Gaal, Istvan.

Diophantine equations and power integral basestheory and algorithms /[electronic resource] :by Istvan Gaal. - Second edition. - Cham :Springer International Publishing :2019. - xxii, 326 p. :ill., digital ;24 cm.

Introduction -- Auxiliary results, tools -- Thue equations -- Inhomogeneous Thue equations -- Relative Thue equations -- The resolution of norm form equations -- Index form equations in general -- Cubic fields -- Quartic fields -- Quintic fields -- Sextic fields -- Pure fields -- Cubic relative extensions -- Quartic relative extensions -- Some higher degree fields -- Tables.

This monograph outlines the structure of index form equations, and makes clear their relationship to other classical types of Diophantine equations. In order to more efficiently determine generators of power integral bases, several algorithms and methods are presented to readers, many of which are new developments in the field. Additionally, readers are presented with various types of number fields to better facilitate their understanding of how index form equations can be solved. By introducing methods like Baker-type estimates, reduction methods, and enumeration algorithms, the material can be applied to a wide variety of Diophantine equations. This new edition provides new results, more topics, and an expanded perspective on algebraic number theory and Diophantine Analysis. Notations, definitions, and tools are presented before moving on to applications to Thue equations and norm form equations. The structure of index forms is explained, which allows readers to approach several types of number fields with ease. Detailed numerical examples, particularly the tables of data calculated by the presented methods at the end of the book, will help readers see how the material can be applied. Diophantine Equations and Power Integral Bases will be ideal for graduate students and researchers interested in the area. A basic understanding of number fields and algebraic methods to solve Diophantine equations is required.

ISBN: 9783030238650

Standard No.: 10.1007/978-3-030-23865-0doiSubjects--Topical Terms:

596233
Diophantine equations.

LC Class. No.: QA242 / .G22 2019

Dewey Class. No.: 512.72

Diophantine equations and power integral bases = theory and algorithms /
LDR:02836nmm a2200337 a 4500 001 2243199
003 DE-He213
005 20200703124759.0
006 m d
007 cr nn 008maaau
008 211207s2019 sz s 0 eng d
020 $a 9783030238650 $q (electronic bk.)
020 $a 9783030238643 $q (paper)
024 7 $a 10.1007/978-3-030-23865-0 $2 doi
035 $a 978-3-030-23865-0
040 $a GP $c GP
041 0 $a eng
050 4 $a QA242 $b .G22 2019
072 7 $a PBH $2 bicssc
072 7 $a MAT022000 $2 bisacsh
072 7 $a PBH $2 thema
082 0 4 $a 512.72 $2 23
090 $a QA242 $b .G111 2019
100 1 $a Gaal, Istvan. $3 3503113
245 1 0 $a Diophantine equations and power integral bases $h [electronic resource] : $b theory and algorithms / $c by Istvan Gaal.
250 $a Second edition.
260 $a Cham : $b Springer International Publishing : $b Imprint: Birkhauser, $c 2019.
300 $a xxii, 326 p. : $b ill., digital ; $c 24 cm.
505 0 $a Introduction -- Auxiliary results, tools -- Thue equations -- Inhomogeneous Thue equations -- Relative Thue equations -- The resolution of norm form equations -- Index form equations in general -- Cubic fields -- Quartic fields -- Quintic fields -- Sextic fields -- Pure fields -- Cubic relative extensions -- Quartic relative extensions -- Some higher degree fields -- Tables.
520 $a This monograph outlines the structure of index form equations, and makes clear their relationship to other classical types of Diophantine equations. In order to more efficiently determine generators of power integral bases, several algorithms and methods are presented to readers, many of which are new developments in the field. Additionally, readers are presented with various types of number fields to better facilitate their understanding of how index form equations can be solved. By introducing methods like Baker-type estimates, reduction methods, and enumeration algorithms, the material can be applied to a wide variety of Diophantine equations. This new edition provides new results, more topics, and an expanded perspective on algebraic number theory and Diophantine Analysis. Notations, definitions, and tools are presented before moving on to applications to Thue equations and norm form equations. The structure of index forms is explained, which allows readers to approach several types of number fields with ease. Detailed numerical examples, particularly the tables of data calculated by the presented methods at the end of the book, will help readers see how the material can be applied. Diophantine Equations and Power Integral Bases will be ideal for graduate students and researchers interested in the area. A basic understanding of number fields and algebraic methods to solve Diophantine equations is required.
650 0 $a Diophantine equations. $3 596233
650 0 $a Algebraic fields. $3 532032
650 0 $a Bases (Linear topological spaces) $3 907355
650 1 4 $a Number Theory. $3 891078
710 2 $a SpringerLink (Online service) $3 836513
773 0 $t Springer Nature eBook
856 4 0 $u https://doi.org/10.1007/978-3-030-23865-0
950 $a Mathematics and Statistics (SpringerNature-11649)