Algorithmic Algebraic Number Theory

Algorithmic Algebraic Number Theory PDF
Author: M. Pohst
Publisher: Cambridge University Press
ISBN: 9780521596695
Size: 71.15 MB
Format: PDF, Docs
Category : Mathematics
Languages : en
Pages : 499
View: 5107

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Algorithmic Algebraic Number Theory

by M. Pohst, Algorithmic Algebraic Number Theory Books available in PDF, EPUB, Mobi Format. Download Algorithmic Algebraic Number Theory books, Classic book, addressed to all lovers of number theory.


A Course In Computational Algebraic Number Theory

A Course in Computational Algebraic Number Theory PDF
Author: Henri Cohen
Publisher: Springer Science & Business Media
ISBN: 3662029456
Size: 31.68 MB
Format: PDF, ePub
Category : Mathematics
Languages : en
Pages : 536
View: 5349

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A Course In Computational Algebraic Number Theory

by Henri Cohen, A Course In Computational Algebraic Number Theory Books available in PDF, EPUB, Mobi Format. Download A Course In Computational Algebraic Number Theory books, 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.


Algorithmic Algebra And Number Theory

Algorithmic Algebra and Number Theory PDF
Author: B.Heinrich Matzat
Publisher: Springer Science & Business Media
ISBN: 364259932X
Size: 33.84 MB
Format: PDF, Kindle
Category : Computers
Languages : en
Pages : 434
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Algorithmic Algebra And Number Theory

by B.Heinrich Matzat, Algorithmic Algebra And Number Theory Books available in PDF, EPUB, Mobi Format. Download Algorithmic Algebra And Number Theory books, This book contains 22 lectures presented at the final conference of the Ger man research program (Schwerpunktprogramm) Algorithmic Number The ory and Algebra 1991-1997, sponsored by the Deutsche Forschungsgemein schaft. The purpose of this research program and of the meeting was to bring together developers of computer algebra software and researchers using com putational methods to gain insight into experimental problems and theoret ical questions in algebra and number theory. The book gives an overview on algorithmic methods and on results ob tained during this period. This includes survey articles on the main research projects within the program: • algorithmic number theory emphasizing class field theory, constructive Galois theory, computational aspects of modular forms and of Drinfeld modules • computational algebraic geometry including real quantifier elimination and real algebraic geometry, and invariant theory of finite groups • computational aspects of presentations and representations of groups, especially finite groups of Lie type and their Heeke algebras, and of the isomorphism problem in group theory. Some of the articles illustrate the current state of computer algebra sys tems and program packages developed with support by the research pro gram, such as KANT and LiDIA for algebraic number theory, SINGULAR, RED LOG and INVAR for commutative algebra and invariant theory respec tively, and GAP, SYSYPHOS and CHEVIE for group theory and representation theory.


Algorithmic And Experimental Methods In Algebra Geometry And Number Theory

Algorithmic and Experimental Methods in Algebra  Geometry  and Number Theory PDF
Author: Gebhard Böckle
Publisher: Springer
ISBN: 3319705660
Size: 18.35 MB
Format: PDF, Mobi
Category : Mathematics
Languages : en
Pages : 763
View: 1149

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Algorithmic And Experimental Methods In Algebra Geometry And Number Theory

by Gebhard Böckle, Algorithmic And Experimental Methods In Algebra Geometry And Number Theory Books available in PDF, EPUB, Mobi Format. Download Algorithmic And Experimental Methods In Algebra Geometry And Number Theory books, This book presents state-of-the-art research and survey articles that highlight work done within the Priority Program SPP 1489 “Algorithmic and Experimental Methods in Algebra, Geometry and Number Theory”, which was established and generously supported by the German Research Foundation (DFG) from 2010 to 2016. The goal of the program was to substantially advance algorithmic and experimental methods in the aforementioned disciplines, to combine the different methods where necessary, and to apply them to central questions in theory and practice. Of particular concern was the further development of freely available open source computer algebra systems and their interaction in order to create powerful new computational tools that transcend the boundaries of the individual disciplines involved. The book covers a broad range of topics addressing the design and theoretical foundations, implementation and the successful application of algebraic algorithms in order to solve mathematical research problems. It offers a valuable resource for all researchers, from graduate students through established experts, who are interested in the computational aspects of algebra, geometry, and/or number theory.


Computational Algebra And Number Theory

Computational Algebra and Number Theory PDF
Author: Wieb Bosma
Publisher: Springer Science & Business Media
ISBN: 9401711089
Size: 51.80 MB
Format: PDF, ePub
Category : Mathematics
Languages : en
Pages : 322
View: 4797

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Computational Algebra And Number Theory

by Wieb Bosma, Computational Algebra And Number Theory Books available in PDF, EPUB, Mobi Format. Download Computational Algebra And Number Theory books, Computers have stretched the limits of what is possible in mathematics. More: they have given rise to new fields of mathematical study; the analysis of new and traditional algorithms, the creation of new paradigms for implementing computational methods, the viewing of old techniques from a concrete algorithmic vantage point, to name but a few. Computational Algebra and Number Theory lies at the lively intersection of computer science and mathematics. It highlights the surprising width and depth of the field through examples drawn from current activity, ranging from category theory, graph theory and combinatorics, to more classical computational areas, such as group theory and number theory. Many of the papers in the book provide a survey of their topic, as well as a description of present research. Throughout the variety of mathematical and computational fields represented, the emphasis is placed on the common principles and the methods employed. Audience: Students, experts, and those performing current research in any of the topics mentioned above.


Higher Arithmetic

Higher Arithmetic PDF
Author: Harold M. Edwards
Publisher: American Mathematical Soc.
ISBN: 9780821844397
Size: 46.57 MB
Format: PDF, Docs
Category : Mathematics
Languages : en
Pages : 210
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Higher Arithmetic

by Harold M. Edwards, Higher Arithmetic Books available in PDF, EPUB, Mobi Format. Download Higher Arithmetic books, Although number theorists have sometimes shunned and even disparaged computation in the past, today's applications of number theory to cryptography and computer security demand vast arithmetical computations. These demands have shifted the focus of studies in number theory and have changed attitudes toward computation itself. The important new applications have attracted a great many students to number theory, but the best reason for studying the subject remains what it was when Gauss published his classic Disquisitiones Arithmeticae in 1801: Number theory is the equal of Euclidean geometry--some would say it is superior to Euclidean geometry--as a model of pure, logical, deductive thinking. An arithmetical computation, after all, is the purest form of deductive argument. Higher Arithmetic explains number theory in a way that gives deductive reasoning, including algorithms and computations, the central role. Hands-on experience with the application of algorithms to computational examples enables students to master the fundamental ideas of basic number theory. This is a worthwhile goal for any student of mathematics and an essential one for students interested in the modern applications of number theory. Harold M. Edwards is Emeritus Professor of Mathematics at New York University. His previous books are Advanced Calculus (1969, 1980, 1993), Riemann's Zeta Function (1974, 2001), Fermat's Last Theorem (1977), Galois Theory (1984), Divisor Theory (1990), Linear Algebra (1995), and Essays in Constructive Mathematics (2005). For his masterly mathematical exposition he was awarded a Steele Prize as well as a Whiteman Prize by the American Mathematical Society.


Algorithmic Number Theory

Algorithmic Number Theory PDF
Author: Duncan Buell
Publisher: Springer
ISBN: 3540248471
Size: 48.61 MB
Format: PDF, Kindle
Category : Mathematics
Languages : en
Pages : 456
View: 1950

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Algorithmic Number Theory

by Duncan Buell, Algorithmic Number Theory Books available in PDF, EPUB, Mobi Format. Download Algorithmic Number Theory books, The sixth Algorithmic Number Theory Symposium was held at the University of Vermont, in Burlington, from 13–18 June 2004. The organization was a joint e?ort of number theorists from around the world. There were four invited talks at ANTS VI, by Dan Bernstein of the Univ- sity of Illinois at Chicago, Kiran Kedlaya of MIT, Alice Silverberg of Ohio State University, and Mark Watkins of Pennsylvania State University. Thirty cont- buted talks were presented, and a poster session was held. This volume contains the written versions of the contributed talks and three of the four invited talks. (Not included is the talk by Dan Bernstein.) ANTS in Burlington is the sixth in a series that began with ANTS I in 1994 at Cornell University, Ithaca, New York, USA and continued at Universit ́eB- deaux I, Bordeaux, France (1996), Reed College, Portland, Oregon, USA (1998), the University of Leiden, Leiden, The Netherlands (2000), and the University of Sydney, Sydney, Australia (2002). The proceedings have been published as volumes 877, 1122, 1423, 1838, and 2369 of Springer-Verlag’s Lecture Notes in Computer Science series. The organizers of the 2004 ANTS conference express their special gratitude and thanks to John Cannon and Joe Buhler for invaluable behind-the-scenes advice.