A Course In Computational Algebraic Number Theory

Author : Henri Cohen
Publisher : Springer Science & Business Media
Page : 556 pages
File Size : 51,8 Mb
Release : 2013-04-17
Category : Mathematics
ISBN : 9783662029459

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A Course in Computational Algebraic Number Theory by Henri Cohen Pdf

A description of 148 algorithms fundamental to number-theoretic computations, in particular for computations related to algebraic number theory, elliptic curves, primality testing and factoring. The first seven chapters guide readers to the heart of current research in computational algebraic number theory, including recent algorithms for computing class groups and units, as well as elliptic curve computations, while the last three chapters survey factoring and primality testing methods, including a detailed description of the number field sieve algorithm. The whole is rounded off with a description of available computer packages and some useful tables, backed by numerous exercises. Written by an authority in the field, and one with great practical and teaching experience, this is certain to become the standard and indispensable reference on the subject.

Author : Henri Cohen
Publisher : Springer Science & Business Media
Page : 580 pages
File Size : 46,7 Mb
Release : 2000-08-01
Category : Mathematics
ISBN : 3540556400

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A Course in Computational Algebraic Number Theory by Henri Cohen Pdf

A description of 148 algorithms fundamental to number-theoretic computations, in particular for computations related to algebraic number theory, elliptic curves, primality testing and factoring. The first seven chapters guide readers to the heart of current research in computational algebraic number theory, including recent algorithms for computing class groups and units, as well as elliptic curve computations, while the last three chapters survey factoring and primality testing methods, including a detailed description of the number field sieve algorithm. The whole is rounded off with a description of available computer packages and some useful tables, backed by numerous exercises. Written by an authority in the field, and one with great practical and teaching experience, this is certain to become the standard and indispensable reference on the subject.

Author : Henri Cohen
Publisher : Springer Science & Business Media
Page : 591 pages
File Size : 51,9 Mb
Release : 2012-10-29
Category : Mathematics
ISBN : 9781441984890

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Advanced Topics in Computational Number Theory by Henri Cohen Pdf

Written by an authority with great practical and teaching experience in the field, this book addresses a number of topics in computational number theory. Chapters one through five form a homogenous subject matter suitable for a six-month or year-long course in computational number theory. The subsequent chapters deal with more miscellaneous subjects.

Author : M. Pohst,H. Zassenhaus
Publisher : Cambridge University Press
Page : 520 pages
File Size : 44,6 Mb
Release : 1997-09-25
Category : Mathematics
ISBN : 0521596696

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Algorithmic Algebraic Number Theory by M. Pohst,H. Zassenhaus Pdf

Now in paperback, this classic book is addresssed to all lovers of number theory. On the one hand, it gives a comprehensive introduction to constructive algebraic number theory, and is therefore especially suited as a textbook for a course on that subject. On the other hand many parts go beyond an introduction an make the user familliar with recent research in the field. For experimental number theoreticians new methods are developed and new results are obtained which are of great importance for them. Both computer scientists interested in higher arithmetic and those teaching algebraic number theory will find the book of value.

Author : Victor Shoup
Publisher : Cambridge University Press
Page : 544 pages
File Size : 45,6 Mb
Release : 2005-04-28
Category : Computers
ISBN : 0521851548

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A Computational Introduction to Number Theory and Algebra by Victor Shoup Pdf

This introductory book emphasises algorithms and applications, such as cryptography and error correcting codes.

Author : H. P. F. Swinnerton-Dyer
Publisher : Cambridge University Press
Page : 164 pages
File Size : 41,7 Mb
Release : 2001-02-22
Category : Mathematics
ISBN : 0521004233

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A Brief Guide to Algebraic Number Theory by H. P. F. Swinnerton-Dyer Pdf

Broad graduate-level account of Algebraic Number Theory, first published in 2001, including exercises, by a world-renowned author.

Author : Ian Stewart,David Tall
Publisher : CRC Press
Page : 334 pages
File Size : 49,6 Mb
Release : 2001-12-12
Category : Mathematics
ISBN : 9781439864081

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Algebraic Number Theory and Fermat's Last Theorem by Ian Stewart,David Tall Pdf

First published in 1979 and written by two distinguished mathematicians with a special gift for exposition, this book is now available in a completely revised third edition. It reflects the exciting developments in number theory during the past two decades that culminated in the proof of Fermat's Last Theorem. Intended as a upper level textbook, it

Author : Abhijit Das
Publisher : CRC Press
Page : 614 pages
File Size : 45,5 Mb
Release : 2016-04-19
Category : Computers
ISBN : 9781482205824

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Computational Number Theory by Abhijit Das Pdf

Developed from the author's popular graduate-level course, Computational Number Theory presents a complete treatment of number-theoretic algorithms. Avoiding advanced algebra, this self-contained text is designed for advanced undergraduate and beginning graduate students in engineering. It is also suitable for researchers new to the field and pract

Author : David Bressoud,Stan Wagon
Publisher : Wiley
Page : 0 pages
File Size : 52,6 Mb
Release : 2008-06-10
Category : Mathematics
ISBN : 0470412151

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A Course in Computational Number Theory by David Bressoud,Stan Wagon Pdf

A Course in Computational Number Theory uses the computer as a tool for motivation and explanation. The book is designed for the reader to quickly access a computer and begin doing personal experiments with the patterns of the integers. It presents and explains many of the fastest algorithms for working with integers. Traditional topics are covered, but the text also explores factoring algorithms, primality testing, the RSA public-key cryptosystem, and unusual applications such as check digit schemes and a computation of the energy that holds a salt crystal together. Advanced topics include continued fractions, Pell’s equation, and the Gaussian primes.

Author : Neal Koblitz
Publisher : Springer Science & Business Media
Page : 245 pages
File Size : 47,8 Mb
Release : 2012-09-05
Category : Mathematics
ISBN : 9781441985927

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A Course in Number Theory and Cryptography by Neal Koblitz Pdf

This is a substantially revised and updated introduction to arithmetic topics, both ancient and modern, that have been at the centre of interest in applications of number theory, particularly in cryptography. As such, no background in algebra or number theory is assumed, and the book begins with a discussion of the basic number theory that is needed. The approach taken is algorithmic, emphasising estimates of the efficiency of the techniques that arise from the theory, and one special feature is the inclusion of recent applications of the theory of elliptic curves. Extensive exercises and careful answers are an integral part all of the chapters.

Author : Anonim
Publisher : Unknown
Page : 534 pages
File Size : 45,5 Mb
Release : 1993
Category : Algebraic number theory
ISBN : OCLC:503757438

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COURSE IN COMPUTATIONAL ALGEBRAIC NUMBER THEORY by Anonim Pdf

Author : Robert B. Ash
Publisher : Courier Corporation
Page : 130 pages
File Size : 50,9 Mb
Release : 2010-01-01
Category : Mathematics
ISBN : 9780486477541

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A Course in Algebraic Number Theory by Robert B. Ash Pdf

This text for a graduate-level course covers the general theory of factorization of ideals in Dedekind domains as well as the number field case. It illustrates the use of Kummer's theorem, proofs of the Dirichlet unit theorem, and Minkowski bounds on element and ideal norms. 2003 edition.

Author : Wolfram Decker,Gerhard Pfister
Publisher : Cambridge University Press
Page : 127 pages
File Size : 52,7 Mb
Release : 2013-02-07
Category : Computers
ISBN : 9781107612532

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A First Course in Computational Algebraic Geometry by Wolfram Decker,Gerhard Pfister Pdf

A quick guide to computing in algebraic geometry with many explicit computational examples introducing the computer algebra system Singular.

Author : M.E. Pohst
Publisher : Birkhäuser
Page : 99 pages
File Size : 47,9 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783034885898

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Computational Algebraic Number Theory by M.E. Pohst Pdf

Computational algebraic number theory has been attracting broad interest in the last few years due to its potential applications in coding theory and cryptography. For this reason, the Deutsche Mathematiker Vereinigung initiated an introductory graduate seminar on this topic in Düsseldorf. The lectures given there by the author served as the basis for this book which allows fast access to the state of the art in this area. Special emphasis has been placed on practical algorithms - all developed in the last five years - for the computation of integral bases, the unit group and the class group of arbitrary algebraic number fields. Contents: Introduction • Topics from finite fields • Arithmetic and polynomials • Factorization of polynomials • Topics from the geometry of numbers • Hermite normal form • Lattices • Reduction • Enumeration of lattice points • Algebraic number fields • Introduction • Basic Arithmetic • Computation of an integral basis • Integral closure • Round-Two-Method • Round-Four-Method • Computation of the unit group • Dirichlet's unit theorem and a regulator bound • Two methods for computing r independent units • Fundamental unit computation • Computation of the class group • Ideals and class number • A method for computing the class group • Appendix • The number field sieve • KANT • References • Index

Author : Peter Borwein
Publisher : Springer Science & Business Media
Page : 220 pages
File Size : 44,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9780387216522

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Computational Excursions in Analysis and Number Theory by Peter Borwein Pdf

This introduction to computational number theory is centered on a number of problems that live at the interface of analytic, computational and Diophantine number theory, and provides a diverse collection of techniques for solving number- theoretic problems. There are many exercises and open research problems included.