Author: Nigel P. Smart
Publisher: Cambridge University Press
ISBN: 9780521646338
Category : Mathematics
Languages : en
Pages : 264

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Book Description
A coherent account of the computational methods used to solve diophantine equations.

Author: Benne M. M. De Weger
Publisher:
ISBN:
Category : Algebra
Languages : en
Pages : 232

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Book Description

Author: R. C. Mason
Publisher: Cambridge University Press
ISBN: 9780521269834
Category : Mathematics
Languages : en
Pages : 142

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Book Description
A self-contained account of a new approach to the subject.

Author: Jan-Hendrik Evertse
Publisher: Cambridge University Press
ISBN: 1107097606
Category : Mathematics
Languages : en
Pages : 381

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Book Description
A comprehensive, graduate-level treatment of unit equations and their various applications.

Author: István Gaál
Publisher: Springer Nature
ISBN: 3030238652
Category : Mathematics
Languages : en
Pages : 335

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Book Description
Work examines the latest algorithms and tools to solve classical types of diophantine equations.; Unique book---closest competitor, Smart, Cambridge, does not treat index form equations.; Author is a leading researcher in the field of computational algebraic number theory.; The text is illustrated with several tables of various number fields, including their data on power integral bases.; Several interesting properties of number fields are examined.; Some infinite parametric families of fields are also considered as well as the resolution of the corresponding infinite parametric families of diophantine equations.

Author: Jan-Hendrik Evertse
Publisher: Cambridge University Press
ISBN: 1107097614
Category : Mathematics
Languages : en
Pages : 477

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Book Description
The first comprehensive and up-to-date account of discriminant equations and their applications. For graduate students and researchers.

Author: Istvan Gaal
Publisher: Springer Science & Business Media
ISBN: 1461200857
Category : Mathematics
Languages : en
Pages : 192

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Book Description
Work examines the latest algorithms and tools to solve classical types of diophantine equations.; Unique book---closest competitor, Smart, Cambridge, does not treat index form equations.; Author is a leading researcher in the field of computational algebraic number theory.; The text is illustrated with several tables of various number fields, including their data on power integral bases.; Several interesting properties of number fields are examined.; Some infinite parametric families of fields are also considered as well as the resolution of the corresponding infinite parametric families of diophantine equations.

Author: Bogdan Grechuk
Publisher: Springer Nature
ISBN: 3031629493
Category :
Languages : en
Pages : 824

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Book Description

Author: Nikos Tzanakis
Publisher: Walter de Gruyter
ISBN: 3110281147
Category : Mathematics
Languages : en
Pages : 196

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Book Description
This book presents in a unified and concrete way the beautiful and deep mathematics - both theoretical and computational - on which the explicit solution of an elliptic Diophantine equation is based. It collects numerous results and methods that are scattered in the literature. Some results are hidden behind a number of routines in software packages, like Magma and Maple; professional mathematicians very often use these routines just as a black-box, having little idea about the mathematical treasure behind them. Almost 20 years have passed since the first publications on the explicit solution of elliptic Diophantine equations with the use of elliptic logarithms. The "art" of solving this type of equation has now reached its full maturity. The author is one of the main persons that contributed to the development of this art. The monograph presents a well-balanced combination of a variety of theoretical tools (from Diophantine geometry, algebraic number theory, theory of linear forms in logarithms of various forms - real/complex and p-adic elliptic - and classical complex analysis), clever computational methods and techniques (LLL algorithm and de Weger's reduction technique, AGM algorithm, Zagier's technique for computing elliptic integrals), ready-to-use computer packages. A result is the solution in practice of a large general class of Diophantine equations.

Author: Jan-Hendrik Evertse
Publisher: Cambridge University Press
ISBN: 1009050036
Category : Mathematics
Languages : en
Pages : 242

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Book Description
This book provides the first thorough treatment of effective results and methods for Diophantine equations over finitely generated domains. Compiling diverse results and techniques from papers written in recent decades, the text includes an in-depth analysis of classical equations including unit equations, Thue equations, hyper- and superelliptic equations, the Catalan equation, discriminant equations and decomposable form equations. The majority of results are proved in a quantitative form, giving effective bounds on the sizes of the solutions. The necessary techniques from Diophantine approximation and commutative algebra are all explained in detail without requiring any specialized knowledge on the topic, enabling readers from beginning graduate students to experts to prove effective finiteness results for various further classes of Diophantine equations.