Download or read book Algorithmic Algebraic Number Theory written by M. Pohst and published by Cambridge University Press. This book was released on 1997-09-25 with total page 520 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book A Course in Computational Algebraic Number Theory written by Henri Cohen and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 556 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Algorithmic Number Theory Efficient algorithms written by Eric Bach and published by MIT Press. This book was released on 1996 with total page 536 pages. Available in PDF, EPUB and Kindle. Book excerpt: Volume 1.
Download or read book Algorithmic Algebra written by Bhubaneswar Mishra and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 427 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Algorithmic Number Theory written by Joe P. Buhler and published by Springer. This book was released on 2003-06-29 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Computational Algebra and Number Theory written by Wieb Bosma and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 326 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book A Brief Guide to Algebraic Number Theory written by H. P. F. Swinnerton-Dyer and published by Cambridge University Press. This book was released on 2001-02-22 with total page 164 pages. Available in PDF, EPUB and Kindle. Book excerpt: Broad graduate-level account of Algebraic Number Theory, first published in 2001, including exercises, by a world-renowned author.
Download or read book Algorithms in Real Algebraic Geometry written by Saugata Basu and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 602 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Computational Number Theory written by Abhijit Das and published by CRC Press. This book was released on 2016-04-19 with total page 614 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
Download or read book Algebraic Complexity Theory written by Peter Bürgisser and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 630 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Computational Algebraic Number Theory written by M.E. Pohst and published by Springer Science & Business Media. This book was released on 1993-09 with total page 108 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 Dusseldorf. 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. The workshops organized by the Gesselschaft fur mathematische Forschung in cooperation with the Deutsche Mathematiker-Vereinigung (German Mathematics Society) are intended to help, in particular, students and younger mathematicians, to obtain an introduction to fields of current research. Through the means of these well-organized seminars, scientists from other fields can also be introduced to new mathematical ideas. The publication of these workshops in the series DMV SEMINAR will make the material available to an even larger audience.
Download or read book Algorithmic and Combinatorial Algebra written by L.A. Bokut' and published by Springer Science & Business Media. This book was released on 1994-05-31 with total page 406 pages. Available in PDF, EPUB and Kindle. Book excerpt: Even three decades ago, the words 'combinatorial algebra' contrasting, for in stance, the words 'combinatorial topology,' were not a common designation for some branch of mathematics. The collocation 'combinatorial group theory' seems to ap pear first as the title of the book by A. Karras, W. Magnus, and D. Solitar [182] and, later on, it served as the title of the book by R. C. Lyndon and P. Schupp [247]. Nowadays, specialists do not question the existence of 'combinatorial algebra' as a special algebraic activity. The activity is distinguished not only by its objects of research (that are effectively given to some extent) but also by its methods (ef fective to some extent). To be more exact, we could approximately define the term 'combinatorial algebra' for the purposes of this book, as follows: So we call a part of algebra dealing with groups, semi groups , associative algebras, Lie algebras, and other algebraic systems which are given by generators and defining relations {in the first and particular place, free groups, semigroups, algebras, etc. )j a part in which we study universal constructions, viz. free products, lINN-extensions, etc. j and, finally, a part where specific methods such as the Composition Method (in other words, the Diamond Lemma, see [49]) are applied. Surely, the above explanation is far from covering the full scope of the term (compare the prefaces to the books mentioned above).
Download or read book Number Theory for Computing written by Song Y. Yan and published by Springer Science & Business Media. This book was released on 2013-11-11 with total page 454 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a good introduction to the classical elementary number theory and the modern algorithmic number theory, and their applications in computing and information technology, including computer systems design, cryptography and network security. In this second edition proofs of many theorems have been provided, further additions and corrections were made.
Download or read book Algorithms for Computer Algebra written by Keith O. Geddes and published by Springer Science & Business Media. This book was released on 2007-06-30 with total page 594 pages. Available in PDF, EPUB and Kindle. Book excerpt: Algorithms for Computer Algebra is the first comprehensive textbook to be published on the topic of computational symbolic mathematics. The book first develops the foundational material from modern algebra that is required for subsequent topics. It then presents a thorough development of modern computational algorithms for such problems as multivariate polynomial arithmetic and greatest common divisor calculations, factorization of multivariate polynomials, symbolic solution of linear and polynomial systems of equations, and analytic integration of elementary functions. Numerous examples are integrated into the text as an aid to understanding the mathematical development. The algorithms developed for each topic are presented in a Pascal-like computer language. An extensive set of exercises is presented at the end of each chapter. Algorithms for Computer Algebra is suitable for use as a textbook for a course on algebraic algorithms at the third-year, fourth-year, or graduate level. Although the mathematical development uses concepts from modern algebra, the book is self-contained in the sense that a one-term undergraduate course introducing students to rings and fields is the only prerequisite assumed. The book also serves well as a supplementary textbook for a traditional modern algebra course, by presenting concrete applications to motivate the understanding of the theory of rings and fields.
Download or read book Fundamental Problems of Algorithmic Algebra written by Chee-Keng Yap and published by Oxford University Press on Demand. This book was released on 2000 with total page 511 pages. Available in PDF, EPUB and Kindle. Book excerpt: Popular computer algebra systems such as Maple, Macsyma, Mathematica, and REDUCE are now basic tools on most computers. Efficient algorithms for various algebraic operations underlie all these systems. Computer algebra, or algorithmic algebra, studies these algorithms and their properties and represents a rich intersection of theoretical computer science with classical mathematics. Fundamental Problems of Algorithmic Algebra provides a systematic and focused treatment of a collection of core problemsthe computational equivalents of the classical Fundamental Problem of Algebra and its derivatives. Topics covered include the GCD, subresultants, modular techniques, the fundamental theorem of algebra, roots of polynomials, Sturm theory, Gaussian lattice reduction, lattices and polynomial factorization, linear systems, elimination theory, Grobner bases, and more. Features · Presents algorithmic ideas in pseudo-code based on mathematical concepts and can be used with any computer mathematics system · Emphasizes the algorithmic aspects of problems without sacrificing mathematical rigor · Aims to be self-contained in its mathematical development · Ideal for a first course in algorithmic or computer algebra for advanced undergraduates or beginning graduate students
Download or read book The Development of the Number Field Sieve written by Arjen K. Lenstra and published by Springer. This book was released on 2006-11-15 with total page 138 pages. Available in PDF, EPUB and Kindle. Book excerpt: The number field sieve is an algorithm for finding the prime factors of large integers. It depends on algebraic number theory. Proposed by John Pollard in 1988, the method was used in 1990 to factor the ninth Fermat number, a 155-digit integer. The algorithm is most suited to numbers of a special form, but there is a promising variant that applies in general. This volume contains six research papers that describe the operation of the number field sieve, from both theoretical and practical perspectives. Pollard's original manuscript is included. In addition, there is an annotated bibliography of directly related literature.
Download or read book Completeness and Reduction in Algebraic Complexity Theory written by Peter Bürgisser and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 174 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a thorough and comprehensive treatment of the theory of NP-completeness in the framework of algebraic complexity theory. Coverage includes Valiant's algebraic theory of NP-completeness; interrelations with the classical theory as well as the Blum-Shub-Smale model of computation, questions of structural complexity; fast evaluation of representations of general linear groups; and complexity of immanants.
