Algorithmic Number Theory: Efficient algorithms, Volume 1

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MIT Press, 1996 - 512 pages
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Algorithmic Number Theory provides a thorough introduction to the design and analysisof algorithms for problems from the theory of numbers. Although not an elementary textbook, itincludes over 300 exercises with suggested solutions. Every theorem not proved in the text or leftas an exercise has a reference in the notes section that appears at the end of each chapter. Thebibliography contains over 1,750 citations to the literature. Finally, it successfully blendscomputational theory with practice by covering some of the practical aspects of algorithmimplementations.The subject of algorithmic number theory represents the marriage of number theorywith the theory of computational complexity. It may be briefly defined as finding integer solutionsto equations, or proving their non-existence, making efficient use of resources such as time andspace. Implicit in this definition is the question of how to efficiently represent the objects inquestion on a computer. The problems of algorithmic number theory are important both for theirintrinsic mathematical interest and their application to random number generation, codes forreliable and secure information transmission, computer algebra, and other areas.Publisher's Note:Volume 2 was not written. Volume 1 is, therefore, a stand-alone publication.

 

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Table des matières

Introduction
1
Intractable Problems will cover the following topics
3
Fundamentals of Number Theory
19
A Survey of Complexity Theory
41
The Greatest Common Divisor
67
Computing in Zn
101
Finite Fields
125
Solving Equations over Finite Fields
155
Discrete Logarithms
162
Open Problems
194
Facts and Heuristics
203
Basic Algorithms
265
A Solutions to Exercises
319
Droits d'auteur

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Expressions et termes fréquents

Fréquemment cités

Page 394 - Rosier, Algorithms and Complexity Concerning the Preemptive Scheduling of Periodic Real-Time Tasks on One Processor.
Page 468 - On the normal density of primes in small intervals, and the difference between consecutive primes. Arch.

Informations bibliographiques