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:
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.
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.
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:
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.
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.
Download or read book Polynominal time Algorithms for the Factorization of Polynomials written by A. Lenstra and published by . This book was released on 1984 with total page 132 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Primality Testing in Polynomial Time written by Martin Dietzfelbinger and published by Springer Science & Business Media. This book was released on 2004-06-29 with total page 153 pages. Available in PDF, EPUB and Kindle. Book excerpt: A self-contained treatment of theoretically and practically important efficient algorithms for the primality problem. The text covers the randomized algorithms by Solovay-Strassen and Miller-Rabin from the late 1970s as well as the recent deterministic algorithm of Agrawal, Kayal and Saxena. The volume is written for students of computer science, in particular those with a special interest in cryptology, and students of mathematics, and it may be used as a supplement for courses or for self-study.
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.
Download or read book Mathematics of Public Key Cryptography written by Steven D. Galbraith and published by Cambridge University Press. This book was released on 2012-03-15 with total page 631 pages. Available in PDF, EPUB and Kindle. Book excerpt: This advanced graduate textbook gives an authoritative and insightful description of the major ideas and techniques of public key cryptography.
Download or read book EUROCAL 85 European Conference on Computer Algebra Linz Austria April 1 3 1985 Proceedings written by Bob F. Caviness and published by Springer Science & Business Media. This book was released on 1985 with total page 676 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Algorithmic Number Theory written by Wieb Bosma and published by Springer Science & Business Media. This book was released on 2000-06-21 with total page 610 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the 4th International Algorithmic Number Theory Symposium, ANTS-IV, held in Leiden, The Netherlands, in July 2000. The book presents 36 contributed papers which have gone through a thorough round of reviewing, selection and revision. Also included are 4 invited survey papers. Among the topics addressed are gcd algorithms, primality, factoring, sieve methods, cryptography, linear algebra, lattices, algebraic number fields, class groups and fields, elliptic curves, polynomials, function fields, and power sums.
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
Download or read book The Concise Handbook of Algebra written by Alexander V. Mikhalev and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 629 pages. Available in PDF, EPUB and Kindle. Book excerpt: It is by no means clear what comprises the "heart" or "core" of algebra, the part of algebra which every algebraist should know. Hence we feel that a book on "our heart" might be useful. We have tried to catch this heart in a collection of about 150 short sections, written by leading algebraists in these areas. These sections are organized in 9 chapters A, B, . . . , I. Of course, the selection is partly based on personal preferences, and we ask you for your understanding if some selections do not meet your taste (for unknown reasons, we only had problems in the chapter "Groups" to get enough articles in time). We hope that this book sets up a standard of what all algebraists are supposed to know in "their" chapters; interested people from other areas should be able to get a quick idea about the area. So the target group consists of anyone interested in algebra, from graduate students to established researchers, including those who want to obtain a quick overview or a better understanding of our selected topics. The prerequisites are something like the contents of standard textbooks on higher algebra. This book should also enable the reader to read the "big" Handbook (Hazewinkel 1999-) and other handbooks. In case of multiple authors, the authors are listed alphabetically; so their order has nothing to do with the amounts of their contributions.
Download or read book Proceedings of the Ninth Annual ACM SIAM Symposium on Discrete Algorithms written by Howard Karloff and published by SIAM. This book was released on 1998-01-01 with total page 726 pages. Available in PDF, EPUB and Kindle. Book excerpt: This symposium is jointly sponsored by the ACM Special Interest Group on Algorithms and Computation Theory and the SIAM Activity Group on Discrete Mathematics.
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:
Download or read book Proceedings of the Seventh Annual ACM SIAM Symposium on Discrete Algorithms written by and published by SIAM. This book was released on 1996-01-01 with total page 608 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text covers the proceedings of the Seventh Annual ACM-SIAM Symposium on Discrete Algorithms, which was held in Atlanta, Georgia, in January 1996.
