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Author : David R. Musser
Publisher :
ISBN 13 :
Total Pages : 376 pages
Book Rating : 4.:/5 (89 download)
Download or read book Algorithms for Polynomial Factorization written by David R. Musser and published by . This book was released on 1971 with total page 376 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Peter L. A. Roelse
Publisher :
ISBN 13 :
Total Pages : 70 pages
Book Rating : 4.E/5 ( download)
Download or read book Linear Methods for Polynomial Factorization Over Finite Fields written by Peter L. A. Roelse and published by . This book was released on 1997 with total page 70 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Franz Winkler
Publisher : Springer Science & Business Media
ISBN 13 : 3709165717
Total Pages : 284 pages
Book Rating : 4.7/5 (91 download)
Download or read book Polynomial Algorithms in Computer Algebra written by Franz Winkler and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 284 pages. Available in PDF, EPUB and Kindle. Book excerpt: For several years now I have been teaching courses in computer algebra at the Universitat Linz, the University of Delaware, and the Universidad de Alcala de Henares. In the summers of 1990 and 1992 I have organized and taught summer schools in computer algebra at the Universitat Linz. Gradually a set of course notes has emerged from these activities. People have asked me for copies of the course notes, and different versions of them have been circulating for a few years. Finally I decided that I should really take the time to write the material up in a coherent way and make a book out of it. Here, now, is the result of this work. Over the years many students have been helpful in improving the quality of the notes, and also several colleagues at Linz and elsewhere have contributed to it. I want to thank them all for their effort, in particular I want to thank B. Buchberger, who taught me the theory of Grabner bases nearly two decades ago, B. F. Caviness and B. D. Saunders, who first stimulated my interest in various problems in computer algebra, G. E. Collins, who showed me how to compute in algebraic domains, and J. R. Sendra, with whom I started to apply computer algebra methods to problems in algebraic geometry. Several colleagues have suggested improvements in earlier versions of this book. However, I want to make it clear that I am responsible for all remaining mistakes.
Author : Richard Zippel
Publisher : Springer Science & Business Media
ISBN 13 : 1461531888
Total Pages : 364 pages
Book Rating : 4.4/5 (615 download)
Download or read book Effective Polynomial Computation written by Richard Zippel and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 364 pages. Available in PDF, EPUB and Kindle. Book excerpt: Effective Polynomial Computation is an introduction to the algorithms of computer algebra. It discusses the basic algorithms for manipulating polynomials including factoring polynomials. These algorithms are discussed from both a theoretical and practical perspective. Those cases where theoretically optimal algorithms are inappropriate are discussed and the practical alternatives are explained. Effective Polynomial Computation provides much of the mathematical motivation of the algorithms discussed to help the reader appreciate the mathematical mechanisms underlying the algorithms, and so that the algorithms will not appear to be constructed out of whole cloth. Preparatory to the discussion of algorithms for polynomials, the first third of this book discusses related issues in elementary number theory. These results are either used in later algorithms (e.g. the discussion of lattices and Diophantine approximation), or analogs of the number theoretic algorithms are used for polynomial problems (e.g. Euclidean algorithm and p-adic numbers). Among the unique features of Effective Polynomial Computation is the detailed material on greatest common divisor and factoring algorithms for sparse multivariate polynomials. In addition, both deterministic and probabilistic algorithms for irreducibility testing of polynomials are discussed.
Author : Phong Q. Nguyen
Publisher : Springer Science & Business Media
ISBN 13 : 3642022952
Total Pages : 503 pages
Book Rating : 4.6/5 (42 download)
Download or read book The LLL Algorithm written by Phong Q. Nguyen and published by Springer Science & Business Media. This book was released on 2009-12-02 with total page 503 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first book to offer a comprehensive view of the LLL algorithm, this text surveys computational aspects of Euclidean lattices and their main applications. It includes many detailed motivations, explanations and examples.
Author : Elwyn R Berlekamp
Publisher : World Scientific
ISBN 13 : 981463591X
Total Pages : 501 pages
Book Rating : 4.8/5 (146 download)
Download or read book Algebraic Coding Theory (Revised Edition) written by Elwyn R Berlekamp and published by World Scientific. This book was released on 2015-03-26 with total page 501 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the revised edition of Berlekamp's famous book, 'Algebraic Coding Theory', originally published in 1968, wherein he introduced several algorithms which have subsequently dominated engineering practice in this field. One of these is an algorithm for decoding Reed-Solomon and Bose-Chaudhuri-Hocquenghem codes that subsequently became known as the Berlekamp-Massey Algorithm. Another is the Berlekamp algorithm for factoring polynomials over finite fields, whose later extensions and embellishments became widely used in symbolic manipulation systems. Other novel algorithms improved the basic methods for doing various arithmetic operations in finite fields of characteristic two. Other major research contributions in this book included a new class of Lee metric codes, and precise asymptotic results on the number of information symbols in long binary BCH codes.Selected chapters of the book became a standard graduate textbook.Both practicing engineers and scholars will find this book to be of great value.
Author : Alicia Dickenstein
Publisher : Springer Science & Business Media
ISBN 13 : 3540243267
Total Pages : 433 pages
Book Rating : 4.5/5 (42 download)
Download or read book Solving Polynomial Equations written by Alicia Dickenstein and published by Springer Science & Business Media. This book was released on 2005-04-27 with total page 433 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a general introduction to modern mathematical aspects in computing with multivariate polynomials and in solving algebraic systems. It presents the state of the art in several symbolic, numeric, and symbolic-numeric techniques, including effective and algorithmic methods in algebraic geometry and computational algebra, complexity issues, and applications ranging from statistics and geometric modelling to robotics and vision. Graduate students, as well as researchers in related areas, will find an excellent introduction to currently interesting topics. These cover Groebner and border bases, multivariate resultants, residues, primary decomposition, multivariate polynomial factorization, homotopy continuation, complexity issues, and their applications.
Author : Arjen Klaas Lenstra
Publisher :
ISBN 13 :
Total Pages : 132 pages
Book Rating : 4.:/5 (256 download)
Download or read book Polynomial-time Algorithms for the Factorization of Polynomials written by Arjen Klaas Lenstra and published by . This book was released on 1984 with total page 132 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Samuel S. Wagstaff (Jr.)
Publisher : American Mathematical Soc.
ISBN 13 : 1470410486
Total Pages : 311 pages
Book Rating : 4.4/5 (74 download)
Download or read book The Joy of Factoring written by Samuel S. Wagstaff (Jr.) and published by American Mathematical Soc.. This book was released on 2013-10-24 with total page 311 pages. Available in PDF, EPUB and Kindle. Book excerpt: "This book is about the theory and practice of integer factorization presented in a historic perspective. It describes about twenty algorithms for factoring and a dozen other number theory algorithms that support the factoring algorithms. Most algorithms are described both in words and in pseudocode to satisfy both number theorists and computer scientists. Each of the ten chapters begins with a concise summary of its contents. This book is written for readers who want to learn more about the best methods of factoring integers, many reasons for factoring, and some history of this fascinating subject. It can be read by anyone who has taken a first course in number theory." -- Publisher website.
Author : J.M. McNamee
Publisher : Elsevier Inc. Chapters
ISBN 13 : 0128077050
Total Pages : 94 pages
Book Rating : 4.1/5 (28 download)
Download or read book Numerical Methods for Roots of Polynomials - Part II written by J.M. McNamee and published by Elsevier Inc. Chapters. This book was released on 2013-07-19 with total page 94 pages. Available in PDF, EPUB and Kindle. Book excerpt: The zeros of a polynomial can be readily recovered from its linear factors. The linear factors can be approximated by first splitting a polynomial numerically into the product of its two nonconstant factors and then recursively splitting every computed nonlinear factor in similar fashion. For both the worst and average case inputs the resulting algorithms solve the polynomial factorization and root-finding problems within fixed sufficiently small error bounds by using nearly optimal arithmetic and Boolean time, that is using nearly optimal numbers of arithmetic and bitwise operations; in the case of a polynomial with integer coefficients and simple roots we can immediately extend factorization to root isolation, that is to computing disjoint covering discs, one for every root on the complex plane. The presented algorithms compute highly accurate approximations to all roots nearly as fast as one reads the input coefficients. Furthermore, our algorithms allow processor efficient parallel acceleration, which enables root-finding, factorization, and root isolation in polylogarithmic arithmetic and Boolean time. The chapter thoroughly covers the design and analysis of these algorithms, including auxiliary techniques of independent interest. At the end we compare the presented polynomial root-finders with alternative ones, in particular with the popular algorithms adopted by users based on supporting empirical information. We also comment on some promising directions to further progress.
Author : J.M. Selig
Publisher : Springer Science & Business Media
ISBN 13 : 0387272747
Total Pages : 402 pages
Book Rating : 4.3/5 (872 download)
Download or read book Geometric Fundamentals of Robotics written by J.M. Selig and published by Springer Science & Business Media. This book was released on 2007-12-13 with total page 402 pages. Available in PDF, EPUB and Kindle. Book excerpt: * Provides an elegant introduction to the geometric concepts that are important to applications in robotics * Includes significant state-of-the art material that reflects important advances, connecting robotics back to mathematical fundamentals in group theory and geometry * An invaluable reference that serves a wide audience of grad students and researchers in mechanical engineering, computer science, and applied mathematics
Author : Cristina Bertone
Publisher :
ISBN 13 :
Total Pages : 109 pages
Book Rating : 4.:/5 (69 download)
Download or read book Polynomial Factorization and Curve Decomposition Algorithms written by Cristina Bertone and published by . This book was released on 2010 with total page 109 pages. Available in PDF, EPUB and Kindle. Book excerpt: Affine algebraic curves are a tool applied in different fields, for instance CAGD. They are defined using polynomials, but they often have several different irreducible components. In this thesis we develop efficient algorithms to decompose a curve defined by rational polynomials. In the first part we present an absolute factorization algorithm for bivariate polynomials (this problem is equivalent to the decomposition of a curve in the plane). We start from the existing algorithm TKTD and we improve the definition of the algebraic extension needed for the factorization, using modular techniques and the LLL algorithm to identify an algebraic number form its p-adic approximation. In the second part we pass to the problem of decomposing a curve in the three-dimensional space: the corresponding technique of the factorization for the case of the plan is the primary decomposition of an ideal for the three-dimensional case. At first, we show some bounds on the degrees of the surfaces separating the different components, using some classical results of algebraic geometry, as the "Lifting problem" or the Castelnuovo-Mumford regularity. After this, we apply consider a classical algorithm of decomposition, which is not efficient for computations, and we apply on it the modular techniques. We obtain a modular algorithm giving the Hilbert function for the reduced components of the curve. The two main algorithms were tested on several examples and compared with the executions times of other softwares.
Author : Henri Cohen
Publisher : Springer Science & Business Media
ISBN 13 : 3662029456
Total Pages : 556 pages
Book Rating : 4.6/5 (62 download)
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.
Author : Keith O. Geddes
Publisher : Springer Science & Business Media
ISBN 13 : 0585332479
Total Pages : 594 pages
Book Rating : 4.5/5 (853 download)
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.
Author : Maurice Mignotte
Publisher : Springer Science & Business Media
ISBN 13 : 1461391717
Total Pages : 357 pages
Book Rating : 4.4/5 (613 download)
Download or read book Mathematics for Computer Algebra written by Maurice Mignotte and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 357 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book corresponds to a mathematical course given in 1986/87 at the University Louis Pasteur, Strasbourg. This work is primarily intended for graduate students. The following are necessary prerequisites : a few standard definitions in set theory, the definition of rational integers, some elementary facts in Combinatorics (maybe only Newton's binomial formula), some theorems of Analysis at the level of high schools, and some elementary Algebra (basic results about groups, rings, fields and linear algebra). An important place is given to exercises. These exercises are only rarely direct applications of the course. More often, they constitute complements to the text. Mostly, hints or references are given so that the reader should be able to find solutions. Chapters one and two deal with elementary results of Number Theory, for example : the euclidean algorithm, the Chinese remainder theorem and Fermat's little theorem. These results are useful by themselves, but they also constitute a concrete introduction to some notions in abstract algebra (for example, euclidean rings, principal rings ... ). Algorithms are given for arithmetical operations with long integers. The rest of the book, chapters 3 through 7, deals with polynomials. We give general results on polynomials over arbitrary rings. Then polynomials with complex coefficients are studied in chapter 4, including many estimates on the complex roots of polynomials. Some of these estimates are very useful in the subsequent chapters.
Author : Alec Sobeck
Publisher :
ISBN 13 :
Total Pages : 0 pages
Book Rating : 4.:/5 (14 download)
Download or read book Issues in the Implementation of Multiplication and Factoring Algorithms in Galois Fields written by Alec Sobeck and published by . This book was released on 2020 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Cryptography in finite fields often requires factoring polynomials. As a result, there is value to understanding the different approaches to polynomial factoring algorithms and their performance. First, several of the approaches to univariate polynomial multiplication are explored. These polynomial factoring algorithms are then used to solve the problem of univariate polynomial factorization in a Galois field. An emphasis is placed on the theoretical running time and memory requirements of these algorithms, as well as the actual running time (in seconds) of some sample problems. This is done to give an idea of the real computing costs of running these algorithms. After covering univariate polynomial multiplication and factoring, the more complex problem of factoring with a field extension is explored. One approach to this problem is to modify the univariate polynomial factoring algorithms (such as Cantor-Zassenhaus) to account for the more complicated finite field structure. Finally, a novel application of the Cantor-Zassenhaus algorithm is developed.
Author : Robert Thomas Moenck
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (223 download)
Download or read book Algorithms for Factoring Polynomials written by Robert Thomas Moenck and published by . This book was released on 1971 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
