Algorithms For Computer Algebra. Download and Read online Algorithms For Computer Algebra ebooks in PDF, epub, Tuebl Mobi, Kindle Book. Get Free Algorithms For Computer Algebra Textbook and unlimited access to our library by created an account. What I envisage for computer algebra for the next few decades is a continuation of the trend we al-ready see. Among the major computer algebra systems, this trend was taken into account earliest and most fruitfully by Mathematica, which has as a result achieved the largest market share of the ma-jor computer algebra systems. The book assumes that the students will have access to a computer algebra sys-tem.AppendixC describesthefeaturesofMapleTM,Mathematica, Sage,andother computer algebra systems that are most relevant to the text. We do not assume any prior experience with computer science. However, many of the algorithms in the vii.
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Algorithms for Computer Algebra
| Author | : Keith O. Geddes,Stephen R. Czapor,George Labahn |
| Publsiher | : Springer Science & Business Media |
| Total Pages | : 586 |
| Release | : 2007-06-30 |
| ISBN 10 | : 0585332479 |
| ISBN 13 | : 9780585332475 |
| Language | : EN, FR, DE, ES & NL |
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.
Polynomial Algorithms in Computer Algebra
| Author | : Franz Winkler |
| Publsiher | : Springer Science & Business Media |
| Total Pages | : 270 |
| Release | : 1996-08-02 |
| ISBN 10 | : 9783211827598 |
| ISBN 13 | : 3211827595 |
| Language | : EN, FR, DE, ES & NL |
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.
Computer Algebra Handbook
| Author | : Johannes Grabmeier,Erich Kaltofen,Volker Weispfenning |
| Publsiher | : Springer Science & Business Media |
| Total Pages | : 637 |
| Release | : 2012-12-06 |
| ISBN 10 | : 3642558267 |
| ISBN 13 | : 9783642558269 |
| Language | : EN, FR, DE, ES & NL |
This Handbook gives a comprehensive snapshot of a field at the intersection of mathematics and computer science with applications in physics, engineering and education. Reviews 67 software systems and offers 100 pages on applications in physics, mathematics, computer science, engineering chemistry and education.
Computer Algebra and Symbolic Computation
| Author | : Joel S. Cohen |
| Publsiher | : CRC Press |
| Total Pages | : 323 |
| Release | : 2002-07-19 |
| ISBN 10 | : 1439863695 |
| ISBN 13 | : 9781439863695 |
| Language | : EN, FR, DE, ES & NL |
This book provides a systematic approach for the algorithmic formulation and implementation of mathematical operations in computer algebra programming languages. The viewpoint is that mathematical expressions, represented by expression trees, are the data objects of computer algebra programs, and by using a few primitive operations that analyze and
Computer Algebra
| Author | : James Harold Davenport,Y. Siret,F. Tournier,E. Tournier |
| Publsiher | : Anonim |
| Total Pages | : 298 |
| Release | : 1993 |
| ISBN 10 | : |
| ISBN 13 | : UOM:39015029950279 |
| Language | : EN, FR, DE, ES & NL |
This book still remains the best introduction to computer algebra, catering to both the interested beginner and the experienced pure mathematician and computer scientist. This updated Second Edition provides a comprehensive review, and contains excellent references to fundamental papers and worked examples. In addition to being a general text on the subject, the book includes an appendix describing the use of one particular algebra system-REDUCE.
Some Tapas of Computer Algebra
| Author | : Arjeh M. Cohen,Hans Cuypers,Hans Sterk |
| Publsiher | : Springer Science & Business Media |
| Total Pages | : 352 |
| Release | : 1998-12-15 |
| ISBN 10 | : 9783540634805 |
| ISBN 13 | : 3540634800 |
| Language | : EN, FR, DE, ES & NL |
This book presents the basic concepts and algorithms of computer algebra using practical examples that illustrate their actual use in symbolic computation. A wide range of topics are presented, including: Groebner bases, real algebraic geometry, lie algebras, factorization of polynomials, integer programming, permutation groups, differential equations, coding theory, automatic theorem proving, and polyhedral geometry. This book is a must read for anyone working in the area of computer algebra, symbolic computation, and computer science.
Modern Computer Algebra
| Author | : Joachim von zur Gathen,Jürgen Gerhard |
| Publsiher | : Cambridge University Press |
| Total Pages | : 329 |
| Release | : 2013-04-25 |
| ISBN 10 | : 1107245257 |
| ISBN 13 | : 9781107245259 |
| Language | : EN, FR, DE, ES & NL |
Computer algebra systems are now ubiquitous in all areas of science and engineering. This highly successful textbook, widely regarded as the 'bible of computer algebra', gives a thorough introduction to the algorithmic basis of the mathematical engine in computer algebra systems. Designed to accompany one- or two-semester courses for advanced undergraduate or graduate students in computer science or mathematics, its comprehensiveness and reliability has also made it an essential reference for professionals in the area. Special features include: detailed study of algorithms including time analysis; implementation reports on several topics; complete proofs of the mathematical underpinnings; and a wide variety of applications (among others, in chemistry, coding theory, cryptography, computational logic, and the design of calendars and musical scales). A great deal of historical information and illustration enlivens the text. In this third edition, errors have been corrected and much of the Fast Euclidean Algorithm chapter has been renovated.
Computer algebra design of algorithms implementations and applications
| Author | : Anonim |
| Publsiher | : Anonim |
| Total Pages | : 329 |
| Release | : 2006 |
| ISBN 10 | : |
| ISBN 13 | : OCLC:255949045 |
| Language | : EN, FR, DE, ES & NL |
Computer Algebra
| Author | : Edmund A. Lamagna |
| Publsiher | : CRC Press |
| Total Pages | : 350 |
| Release | : 2019-01-15 |
| ISBN 10 | : 1351605836 |
| ISBN 13 | : 9781351605830 |
| Language | : EN, FR, DE, ES & NL |
The goal of Computer Algebra: Concepts and Techniques is to demystify computer algebra systems for a wide audience including students, faculty, and professionals in scientific fields such as computer science, mathematics, engineering, and physics. Unlike previous books, the only prerequisites are knowledge of first year calculus and a little programming experience — a background that can be assumed of the intended audience. The book is written in a lean and lively style, with numerous examples to illustrate the issues and techniques discussed. It presents the principal algorithms and data structures, while also discussing the inherent and practical limitations of these systems
Algorithmic Algebra
| Author | : Bhubaneswar Mishra |
| Publsiher | : Springer Science & Business Media |
| Total Pages | : 420 |
| Release | : 1993-09-29 |
| ISBN 10 | : 9780387940908 |
| ISBN 13 | : 0387940901 |
| Language | : EN, FR, DE, ES & NL |
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.
Computing in Algebraic Geometry
| Author | : Wolfram Decker,Christoph Lossen |
| Publsiher | : Springer Science & Business Media |
| Total Pages | : 328 |
| Release | : 2006-03-02 |
| ISBN 10 | : 3540289925 |
| ISBN 13 | : 9783540289920 |
| Language | : EN, FR, DE, ES & NL |
This book provides a quick access to computational tools for algebraic geometry, the mathematical discipline which handles solution sets of polynomial equations. Originating from a number of intense one week schools taught by the authors, the text is designed so as to provide a step by step introduction which enables the reader to get started with his own computational experiments right away. The authors present the basic concepts and ideas in a compact way.
Rational Algebraic Curves
| Author | : J. Rafael Sendra,Franz Winkler,Sonia Pérez-Diaz |
| Publsiher | : Springer Science & Business Media |
| Total Pages | : 270 |
| Release | : 2007-12-10 |
| ISBN 10 | : 3540737251 |
| ISBN 13 | : 9783540737254 |
| Language | : EN, FR, DE, ES & NL |
The central problem considered in this introduction for graduate students is the determination of rational parametrizability of an algebraic curve and, in the positive case, the computation of a good rational parametrization. This amounts to determining the genus of a curve: its complete singularity structure, computing regular points of the curve in small coordinate fields, and constructing linear systems of curves with prescribed intersection multiplicities. The book discusses various optimality criteria for rational parametrizations of algebraic curves.
Mathematics for Computer Algebra
| Author | : Maurice Mignotte |
| Publsiher | : Springer Science & Business Media |
| Total Pages | : 346 |
| Release | : 2012-12-06 |
| ISBN 10 | : 1461391717 |
| ISBN 13 | : 9781461391715 |
| Language | : EN, FR, DE, ES & NL |
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.
Involution
| Author | : Werner M. Seiler |
| Publsiher | : Springer Science & Business Media |
| Total Pages | : 650 |
| Release | : 2009-10-26 |
| ISBN 10 | : 3642012876 |
| ISBN 13 | : 9783642012877 |
| Language | : EN, FR, DE, ES & NL |
The book provides a self-contained account of the formal theory of general, i.e. also under- and overdetermined, systems of differential equations which in its central notion of involution combines geometric, algebraic, homological and combinatorial ideas.
Handbook of Computer Vision Algorithms in Image Algebra
| Author | : Joseph N. Wilson,Gerhard X. Ritter |
| Publsiher | : CRC Press |
| Total Pages | : 448 |
| Release | : 2000-09-21 |
| ISBN 10 | : 1420042386 |
| ISBN 13 | : 9781420042382 |
| Language | : EN, FR, DE, ES & NL |
Image algebra is a comprehensive, unifying theory of image transformations, image analysis, and image understanding. In 1996, the bestselling first edition of the Handbook of Computer Vision Algorithms in Image Algebra introduced engineers, scientists, and students to this powerful tool, its basic concepts, and its use in the concise representation of computer vision algorithms. Updated to reflect recent developments and advances, the second edition continues to provide an outstanding introduction to image algebra. It describes more than 80 fundamental computer vision techniques and introduces the portable iaC++ library, which supports image algebra programming in the C++ language. Revisions to the first edition include a new chapter on geometric manipulation and spatial transformation, several additional algorithms, and the addition of exercises to each chapter. The authors-both instrumental in the groundbreaking development of image algebra-introduce each technique with a brief discussion of its purpose and methodology, then provide its precise mathematical formulation. In addition to furnishing the simple yet powerful utility of image algebra, the Handbook of Computer Vision Algorithms in Image Algebra supplies the core of knowledge all computer vision practitioners need. It offers a more practical, less esoteric presentation than those found in research publications that will soon earn it a prime location on your reference shelf.
Computer Algebra
| Author | : B. Buchberger,G.E. Collins,R. Loos |
| Publsiher | : Springer Science & Business Media |
| Total Pages | : 284 |
| Release | : 2013-06-29 |
| ISBN 10 | : 3709134064 |
| ISBN 13 | : 9783709134061 |
| Language | : EN, FR, DE, ES & NL |
The journal Computing has established a series of supplement volumes the fourth of which appears this year. Its purpose is to provide a coherent presentation of a new topic in a single volume. The previous subjects were Computer Arithmetic 1977, Fundamentals of Numerical Computation 1980, and Parallel Processes and Related Automata 1981; the topic of this 1982 Supplementum to Computing is Computer Algebra. This subject, which emerged in the early nineteen sixties, has also been referred to as 'symbolic and algebraic computation' or 'formula manipulation'. Algebraic algorithms have been receiving increasing interest as a result of the recognition of the central role of algorithms in computer science. They can be easily specified in a formal and rigorous way and provide solutions to problems known and studied for a long time. Whereas traditional algebra is concerned with constructive methods, computer algebra is furthermore interested in efficiency, in implementation, and in hardware and software aspects of the algorithms. It develops that in deciding effectiveness and determining efficiency of algebraic methods many other tools - recursion theory, logic, analysis and combinatorics, for example - are necessary. In the beginning of the use of computers for symbolic algebra it soon became apparent that the straightforward textbook methods were often very inefficient. Instead of turning to numerical approximation methods, computer algebra studies systematically the sources of the inefficiency and searches for alternative algebraic methods to improve or even replace the algorithms.
Computational Commutative Algebra 1
| Author | : Martin Kreuzer,Lorenzo Robbiano |
| Publsiher | : Springer Science & Business Media |
| Total Pages | : 322 |
| Release | : 2008-07-15 |
| ISBN 10 | : 354067733X |
| ISBN 13 | : 9783540677338 |
| Language | : EN, FR, DE, ES & NL |
This introduction to polynomial rings, Gröbner bases and applications bridges the gap in the literature between theory and actual computation. It details numerous applications, covering fields as disparate as algebraic geometry and financial markets. To aid in a full understanding of these applications, more than 40 tutorials illustrate how the theory can be used. The book also includes many exercises, both theoretical and practical.
Planning Algorithms
| Author | : Steven M. LaValle |
| Publsiher | : Cambridge University Press |
| Total Pages | : 329 |
| Release | : 2006-05-29 |
| ISBN 10 | : 1139455176 |
| ISBN 13 | : 9781139455176 |
| Language | : EN, FR, DE, ES & NL |
Planning algorithms are impacting technical disciplines and industries around the world, including robotics, computer-aided design, manufacturing, computer graphics, aerospace applications, drug design, and protein folding. This coherent and comprehensive book unifies material from several sources, including robotics, control theory, artificial intelligence, and algorithms. The treatment is centered on robot motion planning, but integrates material on planning in discrete spaces. A major part of the book is devoted to planning under uncertainty, including decision theory, Markov decision processes, and information spaces, which are the 'configuration spaces' of all sensor-based planning problems. The last part of the book delves into planning under differential constraints that arise when automating the motions of virtually any mechanical system. This text and reference is intended for students, engineers, and researchers in robotics, artificial intelligence, and control theory as well as computer graphics, algorithms, and computational biology.
Applied Algebra
| Author | : Darel W. Hardy,Fred Richman,Carol L. Walker |
| Publsiher | : CRC Press |
| Total Pages | : 410 |
| Release | : 2011-08-10 |
| ISBN 10 | : 1420071432 |
| ISBN 13 | : 9781420071436 |
| Language | : EN, FR, DE, ES & NL |
Using mathematical tools from number theory and finite fields, Applied Algebra: Codes, Ciphers, and Discrete Algorithms, Second Edition presents practical methods for solving problems in data security and data integrity. It is designed for an applied algebra course for students who have had prior classes in abstract or linear algebra. While the content has been reworked and improved, this edition continues to cover many algorithms that arise in cryptography and error-control codes. New to the Second Edition A CD-ROM containing an interactive version of the book that is powered by Scientific Notebook®, a mathematical word processor and easy-to-use computer algebra system New appendix that reviews prerequisite topics in algebra and number theory Double the number of exercises Instead of a general study on finite groups, the book considers finite groups of permutations and develops just enough of the theory of finite fields to facilitate construction of the fields used for error-control codes and the Advanced Encryption Standard. It also deals with integers and polynomials. Explaining the mathematics as needed, this text thoroughly explores how mathematical techniques can be used to solve practical problems. About the Authors Darel W. Hardy is Professor Emeritus in the Department of Mathematics at Colorado State University. His research interests include applied algebra and semigroups. Fred Richman is a professor in the Department of Mathematical Sciences at Florida Atlantic University. His research interests include Abelian group theory and constructive mathematics. Carol L. Walker is Associate Dean Emeritus in the Department of Mathematical Sciences at New Mexico State University. Her research interests include Abelian group theory, applications of homological algebra and category theory, and the mathematics of fuzzy sets and fuzzy logic.
Computer Algebra and Symbolic Computation
| Author | : Joel S. Cohen |
| Publsiher | : CRC Press |
| Total Pages | : 472 |
| Release | : 2003-01-03 |
| ISBN 10 | : 1439863709 |
| ISBN 13 | : 9781439863701 |
| Language | : EN, FR, DE, ES & NL |
Mathematica, Maple, and similar software packages provide programs that carry out sophisticated mathematical operations. Applying the ideas introduced in Computer Algebra and Symbolic Computation: Elementary Algorithms, this book explores the application of algorithms to such methods as automatic simplification, polynomial decomposition, and polyno
Author: Keith O. GeddesPublisher: Springer Science & Business Media
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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.
Computer Algebra System Online