Eurocal 87
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| Author | : James H. Davenport |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 516 |
| Release | : 1989-08-09 |
| Genre | : Computers |
| ISBN | : 9783540515173 |
This is the sixth in a series of conference proceedings of international conferences on computer algebra held in Europe. All the preceding ones have also been published as Lecture Notes in Computer Science. They contain original research material not published elsewhere, and a few invited lectures summarising the state of the art. Computer algebra is the science of using computers to do algebraic calculations, rather than the purely arithmetic calculations which we all know computers can do. These calculations may be polynomial-like calculations - one thread of the conference was devoted to polynomial algorithms - or may relate to other areas of mathematics such as integration, the solution of differential equations, or geometry - a second thread was devoted to those topics. The calculations can be applied in a wide range of scientific and engineering subjects, and in branches of mathematics. Physics has benefitted especially from these calculations, and the proceedings contain many papers on this, and also papers on applications in computer aided design and robotics, to name but a few other applications. The third thread of the proceedings was devoted to these applications and to the computer algebra systems which perform these calculations.
| Author | : Thomas Becker |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 587 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 1461209137 |
The origins of the mathematics in this book date back more than two thou sand years, as can be seen from the fact that one of the most important algorithms presented here bears the name of the Greek mathematician Eu clid. The word "algorithm" as well as the key word "algebra" in the title of this book come from the name and the work of the ninth-century scientist Mohammed ibn Musa al-Khowarizmi, who was born in what is now Uzbek istan and worked in Baghdad at the court of Harun al-Rashid's son. The word "algorithm" is actually a westernization of al-Khowarizmi's name, while "algebra" derives from "al-jabr," a term that appears in the title of his book Kitab al-jabr wa'l muqabala, where he discusses symbolic methods for the solution of equations. This close connection between algebra and al gorithms lasted roughly up to the beginning of this century; until then, the primary goal of algebra was the design of constructive methods for solving equations by means of symbolic transformations. During the second half of the nineteenth century, a new line of thought began to enter algebra from the realm of geometry, where it had been successful since Euclid's time, namely, the axiomatic method.
| Author | : Edwin Kreuzer |
| Publisher | : Springer |
| Total Pages | : 265 |
| Release | : 2014-05-04 |
| Genre | : Technology & Engineering |
| ISBN | : 3709130107 |
The aim of this book is to present important software tools, basic concepts, methods, and highly sophisticated applications of computerized symbolic manipulation to mechanics problems. An overview about general-purpose symbolic software is followed by general guidelines how to develop and implement high-quality computer algebra code. The theoretical background including modeling techniques for mechanical systems is provided which allows for the computer aided generation of the symbolic equation of motion for multibody systems. It is shown how the governing equations for different types of problems in structural mechanics can be automatically derived and how to implement finite element techniques via computer algebra software. Perturbation methods as a very powerful approach for nonlinear problems are discussed in detail and are demonstrated for a number of applications. The applications covered in this book represent some of the most advanced topics in the rapidly growing field of research on symbolic computation.
| Author | : J.R. Rice |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 213 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 1468470744 |
Since scientific software is the fuel that drives today's computers to solve a vast range of problems, huge efforts are being put into the development of new software, systems and algorithms for scientific problem solving. This book explores how scientific software impacts the structure of mathematics, how it creates new subfields, and how new classes of mathematical problems arise. The focus is on five topics where the impact is currently being felt and where important new challenges exist, namely: the new subfield of parallel and geometric computations, the emergence of symbolic computation systems into "general" use, the potential emergence of new, high-level mathematical systems, and the crucial question of how to measure the performance of mathematical problem solving tools.
| Author | : Llorenc Huguet |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 428 |
| Release | : 1989-06-14 |
| Genre | : Computers |
| ISBN | : 9783540510826 |
The present volume contains the proceedings of the AAECC-5 Conference held at Menorca (Balearic Islands), June 15-19, 1987. The annual International AAECC Conference covers a range of topics related to Applied Algebra, Error-Correcting Codes, Finite Algebraic Structures, Computational Methods and Complexity in Algebra and Geometry. For the AAECC-5 Conference 73 papers were presented. Out of these thirty papers were selected for publication in the proceedings. They deal with topics such as error correcting codes (concerning problems of covering radius, decoding methods, expert systems and general results in coding theory), computational algebra, Gröbner basis, complexity, finite algebra and graphs. The proceedings of the 6th conference are published as Vol. 357 of the Lecture Notes in Computer Science.
| Author | : V A Rostovtsev |
| Publisher | : #N/A |
| Total Pages | : 467 |
| Release | : 1991-12-11 |
| Genre | : |
| ISBN | : 9814556092 |
Professor Nicholas N Govorun, corresponding member of the USSR Academy of Sciences, was the principal organizer of the precedent meetings held at Dubna (1979, 1983, 1985). Unfortunately, he passed away in 1989. This volume is to honor his support in Computer Algebra.This is perhaps the only meeting of the entire soviet union computer algebra community and foreign scientists. The meeting presented scientific results, plans for research facilities, and status reports of the basic areas of investigations. The fields covered include computer algebra systems and general algorithms as well as applied algorithms, programs and results in computer algebra applications (mainly in physics).
| Author | : Arjeh M. Cohen |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 374 |
| Release | : 1998-12-15 |
| Genre | : Computers |
| ISBN | : 9783540634805 |
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.
| Author | : Donald Sannella |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 280 |
| Release | : 1988-10-26 |
| Genre | : Computers |
| ISBN | : 9783540503255 |
The Fifth Workshop on Specification of Abstract Data Types took place 1-4 September 1987 in Gullane, near Edinburgh. This book contains papers based on selected talks presented at the workshop. The algebraic specification of abstract data types has been a flourishing topic in computer science since 1974. The main goal of work in this area is to evolve a methodology to support the design and formal development of reliable software. The particular approach taken builds upon concepts from universal algebra and elementary category theory. The core of this work has now stabilized to a great extent and is mature enough to find application in real-life software engineering and to related topics such as concurrency, databases, and even hardware design. Such applications are becoming more feasible because of the emergence of integrated specification/development environments which include tools such as theorem provers based on fast term rewriting engines. Researchers are also exploring ways of widening the scope of the theory to make it applicable to (for example) higher-order functions and non-deterministic programs. Another trend is toward taking a more general view which allows superficially different approaches having the same general aims and methods to be unified.
| Author | : Manuel Bronstein |
| Publisher | : Birkhäuser |
| Total Pages | : 291 |
| Release | : 2013-03-11 |
| Genre | : Computers |
| ISBN | : 3034888007 |
Symbolic rewriting techniques are methods for deriving consequences from systems of equations, and are of great use when investigating the structure of the solutions. Such techniques appear in many important areas of research within computer algebra: • the Knuth-Bendix completion for groups, monoids and general term-rewriting systems, • the Buchberger algorithm for Gröbner bases, • the Ritt-Wu characteristic set method for ordinary differential equations, and • the Riquier-Janet method for partial differential equations. This volume contains invited and contributed papers to the Symbolic Rewriting Techniques workshop, which was held at the Centro Stefano Franscini in Ascona, Switzerland, from April 30 to May 4, 1995. That workshop brought together 40 researchers from various areas of rewriting techniques, the main goal being the investigation of common threads and methods. Following the workshops, each contribution was formally refereed and 14 papers were selected for publication.
| Author | : Keith O. Geddes |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 594 |
| Release | : 2007-06-30 |
| Genre | : Computers |
| ISBN | : 0585332479 |
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.
