Computer Algebra Systems

Author : Keith O. Geddes,Stephen R. Czapor,George Labahn
Publisher : Springer Science & Business Media
Page : 594 pages
File Size : 40,9 Mb
Release : 2007-06-30
Category : Computers
ISBN : 9780585332475

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Algorithms for Computer Algebra by Keith O. Geddes,Stephen R. Czapor,George Labahn Pdf

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 : Michael J. Wester
Publisher : Wiley-Blackwell
Page : 464 pages
File Size : 51,5 Mb
Release : 1999-07-16
Category : Computers
ISBN : UVA:X004339714

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Computer Algebra Systems by Michael J. Wester Pdf

This thorough overview of the major computer algebra (symbolic mathematical) systems compares and contrasts their strengths and weaknesses, and gives tutorial information for using these systems in various ways. * Compares different packages quantitatively using standard 'test suites' * Ideal for assessing the most appropriate package for a particular user or application * Examines the performance and future developments from a user's and developer's viewpoint Internationally recognized specialists overview both the general and special purpose systems and discuss issues such as denesting nested roots, complex number calculations, efficiently computing special polynomials, solving single equations and systems of polynomial equations, computing limits, multiple integration, solving ordinary differential and nonlinear evolution equations, code generation, evaluation and computer algebra in education. The historical origins, computer algebra resources and equivalents for many common operations in seven major packages are also covered. By providing such a comprehensive survey, the experienced user is able to make an informed decision on which system(s) he or she might like to use. It also allows a user new to computer algebra to form an idea of where to begin. Since each system looked at in this book uses a different language, many examples are included to aid the user in adapting to these language differences. These examples can be used as a guide to using the various systems once one understands the basic principles of one CAS. The book also includes contributions which look at the broad issues of the needs of various users and future developments, both from the user's and the developer's viewpoint. The author is a leading figure in the development and analysis of mathematical software and is well known through the 'Wester test suite' of problems which provide a bench mark for measuring the performance of mathematical software systems. The book will help develop our range of titles for applied mathematcians. The book will provide a unique, fully up-to-date and independent assessment of particular systems and will be of interest to users and purchasers of CAS's.

Author : Joachim von zur Gathen,Jürgen Gerhard
Publisher : Cambridge University Press
Page : 811 pages
File Size : 48,6 Mb
Release : 2013-04-25
Category : Computers
ISBN : 9781107039032

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Modern Computer Algebra by Joachim von zur Gathen,Jürgen Gerhard Pdf

Now in its third edition, this highly successful textbook is widely regarded as the 'bible of computer algebra'.

Author : Edmund A. Lamagna
Publisher : CRC Press
Page : 350 pages
File Size : 44,5 Mb
Release : 2019-01-15
Category : Mathematics
ISBN : 9781351605830

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Computer Algebra by Edmund A. Lamagna Pdf

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

Author : Johannes Grabmeier,Erich Kaltofen,Volker Weispfenning
Publisher : Springer Science & Business Media
Page : 656 pages
File Size : 43,9 Mb
Release : 2012-12-06
Category : Computers
ISBN : 9783642558269

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Computer Algebra Handbook by Johannes Grabmeier,Erich Kaltofen,Volker Weispfenning Pdf

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.

Author : James Harold Davenport,Y. Siret,E. Tournier
Publisher : Unknown
Page : 328 pages
File Size : 52,5 Mb
Release : 1993
Category : Computers
ISBN : UOM:39015029950279

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Computer Algebra by James Harold Davenport,Y. Siret,E. Tournier Pdf

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.

Author : Joel S. Cohen
Publisher : CRC Press
Page : 323 pages
File Size : 41,6 Mb
Release : 2002-07-19
Category : Computers
ISBN : 9781439863695

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Computer Algebra and Symbolic Computation by Joel S. Cohen Pdf

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

Author : Joel S. Cohen
Publisher : CRC Press
Page : 472 pages
File Size : 55,6 Mb
Release : 2003-01-03
Category : Computers
ISBN : 9781439863701

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Computer Algebra and Symbolic Computation by Joel S. Cohen Pdf

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 : John M. Stewart
Publisher : Cambridge University Press
Page : 272 pages
File Size : 45,5 Mb
Release : 2017-07-20
Category : Computers
ISBN : 9781316641231

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Python for Scientists by John M. Stewart Pdf

Scientific Python is taught from scratch in this book via copious, downloadable, useful and adaptable code snippets. Everything the working scientist needs to know is covered, quickly providing researchers and research students with the skills to start using Python effectively.

Author : James Taylor Fey
Publisher : National Council of Teachers of English
Page : 336 pages
File Size : 44,9 Mb
Release : 2003
Category : Algebra
ISBN : 0873535316

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Computer Algebra Systems in Secondary School Mathematics Education by James Taylor Fey Pdf

Author : R. Albrecht,B. Buchberger,G.E. Collins,R. Loos
Publisher : Springer Science & Business Media
Page : 282 pages
File Size : 55,6 Mb
Release : 2013-06-29
Category : Computers
ISBN : 9783709134061

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Computer Algebra by R. Albrecht,B. Buchberger,G.E. Collins,R. Loos Pdf

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.

Author : Richard Pavelle
Publisher : Springer Science & Business Media
Page : 443 pages
File Size : 46,5 Mb
Release : 2012-12-06
Category : Computers
ISBN : 9781468468885

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Applications of Computer Algebra by Richard Pavelle Pdf

Today, certain computer software systems exist which surpass the computational ability of researchers when their mathematical techniques are applied to many areas of science and engineering. These computer systems can perform a large portion of the calculations seen in mathematical analysis. Despite this massive power, thousands of people use these systems as a routine resource for everyday calculations. These software programs are commonly called "Computer Algebra" systems. They have names such as MACSYMA, MAPLE, muMATH, REDUCE and SMP. They are receiving credit as a computational aid with in creasing regularity in articles in the scientific and engineering literature. When most people think about computers and scientific research these days, they imagine a machine grinding away, processing numbers arithmetically. It is not generally realized that, for a number of years, computers have been performing non-numeric computations. This means, for example, that one inputs an equa tion and obtains a closed form analytic answer. It is these Computer Algebra systems, their capabilities, and applications which are the subject of the papers in this volume.

Author : James Harold Davenport,Y. Siret,E. Tournier
Publisher : Unknown
Page : 0 pages
File Size : 45,8 Mb
Release : 1993
Category : Algebra
ISBN : 0122092325

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Computer Algebra by James Harold Davenport,Y. Siret,E. Tournier Pdf

Author : Ilias S. Kotsireas,Edgar Martínez-Moro
Publisher : Springer
Page : 515 pages
File Size : 53,5 Mb
Release : 2017-07-26
Category : Mathematics
ISBN : 9783319569321

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Applications of Computer Algebra by Ilias S. Kotsireas,Edgar Martínez-Moro Pdf

The Applications of Computer Algebra (ACA) conference covers a wide range of topics from Coding Theory to Differential Algebra to Quantam Computing, focusing on the interactions of these and other areas with the discipline of Computer Algebra. This volume provides the latest developments in the field as well as its applications in various domains, including communications, modelling, and theoretical physics. The book will appeal to researchers and professors of computer algebra, applied mathematics, and computer science, as well as to engineers and computer scientists engaged in research and development.

Author : Joachim von zur Gathen,Jürgen Gerhard
Publisher : Cambridge University Press
Page : 811 pages
File Size : 40,6 Mb
Release : 2013-04-25
Category : Computers
ISBN : 9781107245259

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Modern Computer Algebra by Joachim von zur Gathen,Jürgen Gerhard Pdf

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.