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Author : Benne M. M. De Weger
Publisher :
ISBN 13 :
Total Pages : 232 pages
Book Rating : 4.3/5 (91 download)
Download or read book Algorithms for Diophantine Equations written by Benne M. M. De Weger and published by . This book was released on 1989 with total page 232 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Nigel P. Smart
Publisher : Cambridge University Press
ISBN 13 : 9780521646338
Total Pages : 264 pages
Book Rating : 4.6/5 (463 download)
Download or read book The Algorithmic Resolution of Diophantine Equations written by Nigel P. Smart and published by Cambridge University Press. This book was released on 1998-11-12 with total page 264 pages. Available in PDF, EPUB and Kindle. Book excerpt: A coherent account of the computational methods used to solve diophantine equations.
Author : István Gaál
Publisher : Springer Nature
ISBN 13 : 3030238652
Total Pages : 326 pages
Book Rating : 4.0/5 (32 download)
Download or read book Diophantine Equations and Power Integral Bases written by István Gaál and published by Springer Nature. This book was released on 2019-09-03 with total page 326 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Istvan Gaal
Publisher : Springer Science & Business Media
ISBN 13 : 1461200857
Total Pages : 192 pages
Book Rating : 4.4/5 (612 download)
Download or read book Diophantine Equations and Power Integral Bases written by Istvan Gaal and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 192 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Nigel P. Smart
Publisher : Cambridge University Press
ISBN 13 : 9780521641562
Total Pages : 260 pages
Book Rating : 4.6/5 (415 download)
Download or read book The Algorithmic Resolution of Diophantine Equations written by Nigel P. Smart and published by Cambridge University Press. This book was released on 1998-11-12 with total page 260 pages. Available in PDF, EPUB and Kindle. Book excerpt: Beginning with a brief introduction to algorithms and diophantine equations, this volume provides a coherent modern account of the methods used to find all the solutions to certain diophantine equations, particularly those developed for use on a computer. The study is divided into three parts, emphasizing approaches with a wide range of applications. The first section considers basic techniques including local methods, sieving, descent arguments and the LLL algorithm. The second section explores problems that can be solved using Baker's theory of linear forms in logarithms. The final section looks at problems associated with curves, focusing on rational and integral points on elliptic curves. Each chapter concludes with a useful set of exercises. A detailed bibliography is included. This book will appeal to graduate students and research workers interested in solving diophantine equations using computational methods.
Author : R. C. Mason
Publisher : Cambridge University Press
ISBN 13 : 9780521269834
Total Pages : 142 pages
Book Rating : 4.2/5 (698 download)
Download or read book Diophantine Equations Over Function Fields written by R. C. Mason and published by Cambridge University Press. This book was released on 1984-04-26 with total page 142 pages. Available in PDF, EPUB and Kindle. Book excerpt: A self-contained account of a new approach to the subject.
Author : Joseph Tsu-wu Chou
Publisher :
ISBN 13 :
Total Pages : 264 pages
Book Rating : 4.:/5 (89 download)
Download or read book Algorithms for the Solution of Systems of Linear Diophantine Equations written by Joseph Tsu-wu Chou and published by . This book was released on 1979 with total page 264 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Titu Andreescu
Publisher : Springer Science & Business Media
ISBN 13 : 0817645497
Total Pages : 350 pages
Book Rating : 4.8/5 (176 download)
Download or read book An Introduction to Diophantine Equations written by Titu Andreescu and published by Springer Science & Business Media. This book was released on 2010-09-02 with total page 350 pages. Available in PDF, EPUB and Kindle. Book excerpt: This problem-solving book is an introduction to the study of Diophantine equations, a class of equations in which only integer solutions are allowed. The presentation features some classical Diophantine equations, including linear, Pythagorean, and some higher degree equations, as well as exponential Diophantine equations. Many of the selected exercises and problems are original or are presented with original solutions. An Introduction to Diophantine Equations: A Problem-Based Approach is intended for undergraduates, advanced high school students and teachers, mathematical contest participants — including Olympiad and Putnam competitors — as well as readers interested in essential mathematics. The work uniquely presents unconventional and non-routine examples, ideas, and techniques.
Author : Octavian Cira
Publisher : Infinite Study
ISBN 13 : 1599733072
Total Pages : 254 pages
Book Rating : 4.5/5 (997 download)
Download or read book Solving Diophantine Equations written by Octavian Cira and published by Infinite Study. This book was released on 2014 with total page 254 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this book a multitude of Diophantine equations and their partial or complete solutions are presented. How should we solve, for example, the equation η(π(x)) = π(η(x)), where η is the Smarandache function and π is Riemann function of counting the number of primes up to x, in the set of natural numbers? If an analytical method is not available, an idea would be to recall the empirical search for solutions. We establish a domain of searching for the solutions and then we check all possible situations, and of course we retain among them only those solutions that verify our equation. In other words, we say that the equation does not have solutions in the search domain, or the equation has n solutions in this domain. This mode of solving is called partial resolution. Partially solving a Diophantine equation may be a good start for a complete solving of the problem. The authors have identified 62 Diophantine equations that impose such approach and they partially solved them. For an efficient resolution it was necessarily that they have constructed many useful ”tools” for partially solving the Diophantine equations into a reasonable time. The computer programs as tools were written in Mathcad, because this is a good mathematical software where many mathematical functions are implemented. Transposing the programs into another computer language is facile, and such algorithms can be turned to account on other calculation systems with various processors.
Author : Benjamin M. de Weger
Publisher :
ISBN 13 :
Total Pages : 212 pages
Book Rating : 4.:/5 (63 download)
Download or read book Algorithms for diophantine equations written by Benjamin M. de Weger and published by . This book was released on 1989 with total page 212 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Henri Cohen
Publisher : Springer Science & Business Media
ISBN 13 : 0387499229
Total Pages : 673 pages
Book Rating : 4.3/5 (874 download)
Download or read book Number Theory written by Henri Cohen and published by Springer Science & Business Media. This book was released on 2007-05-23 with total page 673 pages. Available in PDF, EPUB and Kindle. Book excerpt: The central theme of this book is the solution of Diophantine equations, i.e., equations or systems of polynomial equations which must be solved in integers, rational numbers or more generally in algebraic numbers. This theme, in particular, is the central motivation for the modern theory of arithmetic algebraic geometry. In this text, this is considered through three of its most basic aspects. The book contains more than 350 exercises and the text is largely self-contained. Much more sophisticated techniques have been brought to bear on the subject of Diophantine equations, and for this reason, the author has included five appendices on these techniques.
Author : Alexander Schrijver
Publisher : John Wiley & Sons
ISBN 13 : 9780471982326
Total Pages : 488 pages
Book Rating : 4.9/5 (823 download)
Download or read book Theory of Linear and Integer Programming written by Alexander Schrijver and published by John Wiley & Sons. This book was released on 1998-06-11 with total page 488 pages. Available in PDF, EPUB and Kindle. Book excerpt: Als Ergänzung zu den mehr praxisorientierten Büchern, die auf dem Gebiet der linearen und Integerprogrammierung bereits erschienen sind, beschreibt dieses Werk die zugrunde liegende Theorie und gibt einen Überblick über wichtige Algorithmen. Der Autor diskutiert auch Anwendungen auf die kombinatorische Optimierung; neben einer ausführlichen Bibliographie finden sich umfangreiche historische Anmerkungen.
Author :
Publisher :
ISBN 13 :
Total Pages : 219 pages
Book Rating : 4.:/5 (781 download)
Download or read book Algorithms for Diophantine Equations written by and published by . This book was released on 1987 with total page 219 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Tsu-Wu J. Chou
Publisher :
ISBN 13 :
Total Pages : 117 pages
Book Rating : 4.:/5 (63 download)
Download or read book Algorithms for the solution of systems of linear diophantine equations written by Tsu-Wu J. Chou and published by . This book was released on 1981 with total page 117 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : T. N. Shorey
Publisher : Cambridge University Press
ISBN 13 : 9780521091701
Total Pages : 0 pages
Book Rating : 4.0/5 (917 download)
Download or read book Exponential Diophantine Equations written by T. N. Shorey and published by Cambridge University Press. This book was released on 2008-12-04 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a integrated presentation of the theory of exponential diophantine equations. The authors present, in a clear and unified fashion, applications to exponential diophantine equations and linear recurrence sequences of the Gelfond-Baker theory of linear forms in logarithms of algebraic numbers. Topics covered include the Thue equations, the generalised hyperelliptic equation, and the Fermat and Catalan equations. The necessary preliminaries are given in the first three chapters. Each chapter ends with a section giving details of related results.
Author : Hans Hermes
Publisher : Springer Science & Business Media
ISBN 13 : 3642461786
Total Pages : 260 pages
Book Rating : 4.6/5 (424 download)
Download or read book Enumerability · Decidability Computability written by Hans Hermes and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 260 pages. Available in PDF, EPUB and Kindle. Book excerpt: Once we have accepted a precise replacement of the concept of algo rithm, it becomes possible to attempt the problem whether there exist well-defined collections of problems which cannot be handled by algo rithms, and if that is the case, to give concrete cases of this kind. Many such investigations were carried out during the last few decades. The undecidability of arithmetic and other mathematical theories was shown, further the unsolvability of the word problem of group theory. Many mathematicians consider these results and the theory on which they are based to be the most characteristic achievements of mathe matics in the first half of the twentieth century. If we grant the legitimacy of the suggested precise replacements of the concept of algorithm and related concepts, then we can say that the mathematicians have shown by strictly mathematical methods that there exist mathematical problems which cannot be dealt with by the methods of calculating mathematics. In view of the important role which mathematics plays today in our conception of the world this fact is of great philosophical interest. Post speaks of a natural law about the "limitations of the mathematicizing power of Homo Sapiens". Here we also find a starting point for the discussion of the question, what the actual creative activity of the mathematician consists in. In this book we shall give an introduction to the theory of algorithms.
Author : Florentin Smarandache
Publisher : Infinite Study
ISBN 13 :
Total Pages : 9 pages
Book Rating : 4./5 ( download)
Download or read book ALGORITHMS FOR SOLVING LINEAR CONGRUENCES AND SYSTEMS OF LINEAR CONGRUENCES written by Florentin Smarandache and published by Infinite Study. This book was released on with total page 9 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this article we determine several theorems and methods for solving linear congruences and systems of linear congruences and we find the number of distinct solutions. Many examples of solving congruences are given.
