Algorithmic Algebraic Number Theory
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Author | : M. Pohst |
Publisher | : Cambridge University Press |
Total Pages | : 520 |
Release | : 1997-09-25 |
Genre | : Mathematics |
ISBN | : 9780521596695 |
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 | : Henri Cohen |
Publisher | : Springer Science & Business Media |
Total Pages | : 556 |
Release | : 2013-04-17 |
Genre | : Mathematics |
ISBN | : 3662029456 |
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 | : Eric Bach |
Publisher | : MIT Press |
Total Pages | : 536 |
Release | : 1996 |
Genre | : Computers |
ISBN | : 9780262024051 |
Author | : Bhubaneswar Mishra |
Publisher | : Springer Science & Business Media |
Total Pages | : 427 |
Release | : 2012-12-06 |
Genre | : Computers |
ISBN | : 1461243440 |
Algorithmic Algebra studies some of the main algorithmic tools of computer algebra, covering such topics as Gröbner bases, characteristic sets, resultants and semialgebraic sets. The main purpose of the book is to acquaint advanced undergraduate and graduate students in computer science, engineering and mathematics with the algorithmic ideas in computer algebra so that they could do research in computational algebra or understand the algorithms underlying many popular symbolic computational systems: Mathematica, Maple or Axiom, for instance. Also, researchers in robotics, solid modeling, computational geometry and automated theorem proving community may find it useful as symbolic algebraic techniques have begun to play an important role in these areas. The book, while being self-contained, is written at an advanced level and deals with the subject at an appropriate depth. The book is accessible to computer science students with no previous algebraic training. Some mathematical readers, on the other hand, may find it interesting to see how algorithmic constructions have been used to provide fresh proofs for some classical theorems. The book also contains a large number of exercises with solutions to selected exercises, thus making it ideal as a textbook or for self-study.
Author | : Joe P. Buhler |
Publisher | : Springer |
Total Pages | : 0 |
Release | : 2003-06-29 |
Genre | : Computers |
ISBN | : 3540691138 |
This book constitutes the refereed proceedings of the Third International Symposium on Algorithmic Number Theory, ANTS-III, held in Portland, Oregon, USA, in June 1998. The volume presents 46 revised full papers together with two invited surveys. The papers are organized in chapters on gcd algorithms, primality, factoring, sieving, analytic number theory, cryptography, linear algebra and lattices, series and sums, algebraic number fields, class groups and fields, curves, and function fields.
Author | : Saugata Basu |
Publisher | : Springer Science & Business Media |
Total Pages | : 602 |
Release | : 2013-03-09 |
Genre | : Mathematics |
ISBN | : 3662053551 |
In this first-ever graduate textbook on the algorithmic aspects of real algebraic geometry, the main ideas and techniques presented form a coherent and rich body of knowledge, linked to many areas of mathematics and computing. Mathematicians already aware of real algebraic geometry will find relevant information about the algorithmic aspects. Researchers in computer science and engineering will find the required mathematical background. This self-contained book is accessible to graduate and undergraduate students.
Author | : Wieb Bosma |
Publisher | : Springer Science & Business Media |
Total Pages | : 326 |
Release | : 2013-03-09 |
Genre | : Mathematics |
ISBN | : 9401711089 |
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.
Author | : H. P. F. Swinnerton-Dyer |
Publisher | : Cambridge University Press |
Total Pages | : 164 |
Release | : 2001-02-22 |
Genre | : Mathematics |
ISBN | : 9780521004237 |
Broad graduate-level account of Algebraic Number Theory, first published in 2001, including exercises, by a world-renowned author.
Author | : Abhijit Das |
Publisher | : CRC Press |
Total Pages | : 614 |
Release | : 2016-04-19 |
Genre | : Computers |
ISBN | : 1482205823 |
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 | : Peter Bürgisser |
Publisher | : Springer Science & Business Media |
Total Pages | : 630 |
Release | : 2013-03-14 |
Genre | : Mathematics |
ISBN | : 3662033380 |
The algorithmic solution of problems has always been one of the major concerns of mathematics. For a long time such solutions were based on an intuitive notion of algorithm. It is only in this century that metamathematical problems have led to the intensive search for a precise and sufficiently general formalization of the notions of computability and algorithm. In the 1930s, a number of quite different concepts for this purpose were pro posed, such as Turing machines, WHILE-programs, recursive functions, Markov algorithms, and Thue systems. All these concepts turned out to be equivalent, a fact summarized in Church's thesis, which says that the resulting definitions form an adequate formalization of the intuitive notion of computability. This had and continues to have an enormous effect. First of all, with these notions it has been possible to prove that various problems are algorithmically unsolvable. Among of group these undecidable problems are the halting problem, the word problem theory, the Post correspondence problem, and Hilbert's tenth problem. Secondly, concepts like Turing machines and WHILE-programs had a strong influence on the development of the first computers and programming languages. In the era of digital computers, the question of finding efficient solutions to algorithmically solvable problems has become increasingly important. In addition, the fact that some problems can be solved very efficiently, while others seem to defy all attempts to find an efficient solution, has called for a deeper under standing of the intrinsic computational difficulty of problems.