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Automated and semi-automated manipulation of so-called labelled transition systems has become an important means in discovering flaws in software and hardware systems. Process algebra has been developed to express such labelled transition systems algebraically, which enhances the ways of manipulation by means of equational logic and term rewriting.
The theory of process algebra has developed rapidly over the last twenty years, and verification tools have been developed on the basis of process algebra, often in cooperation with techniques related to model checking. This textbook gives a thorough introduction into the basics of process algebra and its applications. ... Read more

Customer Reviews (1)

Wondefully well written
This is a delightful new presentation of Process Algebra, which was much needed since the classic text by Baeten and Weijland is getting outdated. In comparison, I find Fokkink's text more easy to digest, more precise andgoing significantly further. Indeed, it should be for a theory that hasevolved rapidly in the last decade. Process Algebra is on its way to becomethe tool to build full-proof software that will lead us out of the presentday software jungle. I have used this text in my one semester class inTrier and can recommend it to any serious student of computer science. ... Read more

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The central problem considered in this book 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, i.e. its complete singularity structure, computing regular points of the curve in small coordinate fields, and constructing linear systems of curves with prescribed intersection multiplicities. Various optimality criteria for rational parametrizations of algebraic curves are discussed.

This book is mainly intended for graduate students and researchers in constructive algebraic curve geometry.

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This monograph-like anthology introduces the concepts and framework of Clifford algebra. It provides a rich source of examples of how to work with this formalism. Clifford or geometric algebra shows strong unifying aspects and turned out in the 1960s to be a most adequate formalism for describing different geometry-related algebraic systems as specializations of one "mother algebra" in various subfields of physics and engineering. Recent work shows that Clifford algebra provides a universal and powerful algebraic framework for an elegant and coherent representation of various problems occurring in computer science, signal processing, neural computing, image processing, pattern recognition, computer vision, and robotics. ... Read more

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Geometric algebra is still treated as an obscure branch of algebra and most books have been written by competent mathematicians in a very abstract style. This restricts the readership of such books especially by programmers working in computer graphics, who simply want guidance on algorithm design.

Geometric algebra provides a unified algebraic system for solving a wide variety of geometric problems. John Vince reveals the beauty of this algebraic framework and communicates to the reader new and unusual mathematical concepts using colour illustrations, tabulations, and easy-to-follow algebraic proofs.

The book includes many worked examples to show how the algebra works in practice and is essential reading for anyone involved in designing 3D geometric algorithms.

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Symbolic C++: An Introduction to Computer Algebra Using Object-Oriented Programming provides a concise introduction to C++ and object-oriented programming, using a step-by-step construction of a new object-oriented designed computer algebra system - Symbolic C++. It shows how object-oriented programming can be used to implement a symbolic algebra system and how this can then be applied to different areas in mathematics and physics. This second revised edition: - Explains the new powerful classes that have been added to Symbolic C++ - Includes the Standard Template Library - Extends the Java section - Contains useful classes in scientific computation - Contains extended coverage of Maple, Mathematica, Reduce and MuPAD Updated and extended code is available at http://issc. rau. ac. za . ... Read more

Customer Reviews (2)

a great object-oriented application
You will find this book fascinating if you are a computer science student intrigued by symbolic calculation systems such as Mathematica and Maple, and if you would like to see how such systems would be implemented in C++ (Mathematica and Maple are actually implemented in plain old C).

The C++ level required is just after CS2, the second C++ class that comprises data structures. If I were a CS2 instructor, I guess I would require students to read some parts of this book since it is a great means of reinforcing about all the concepts learned in C++, while building a nontrivial application; although some examples are taken from physics, physics knowledge is by no means required and the general math level called for reading this book remains comfortably low, and one can always skip the things one does not know or does not care about (such as quaternions, but hey, some people might be turned on by that stuff...).

It shows how to build classes that actually perform calculations using integers of arbitrary length, rational numbers of the a/b form, vectors, matrices, quaternions, symbolic variables, differentiation, integration, etc.

The system described in the book, SymbolicC++, can be used as a FREE alternative to Mathematica or Maple, less of course the graphing capabilities these great software products offer (less also zillions of functions available). SymbolicC++ may nevertheless be connected to Gnuplot to produce graphs. SymbolicC++ may also be of interest to the professional developer having to struggle with complex calculations, since its classes can be included in any C++ environment.

So in short, this book is great if you have the right background and the right interests.

I should also point out that Dr Steeb has written another great book that shows the system at work in problems from the physical sciences and finance ("The Nonlinear Workbook")

Eclectic but rich
A mixture of C++, group theory, and mathematical physics. Far from a polished treatment, but maybe worth perusing if these are topics of interest to you. ... Read more

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From the reviews of the first edition:

"It is certainly no exaggeration to say that … A Singular Introduction to Commutative Algebra aims to lead a further stage in the computational revolution in commutative algebra … . Among the great strengths and most distinctive features … is a new, completely unified treatment of the global and local theories. … making it one of the most flexible and most efficient systems of its type....another strength of Greuel and Pfister's book is its breadth of coverage of theoretical topics in the portions of commutative algebra closest to algebraic geometry, with algorithmic treatments of almost every topic....Greuel and Pfister have written a distinctive and highly useful book that should be in the library of every commutative algebraist and algebraic geometer, expert and novice alike."

J.B. Little, MAA, March 2004

The second edition is substantially enlarged by a chapter on Groebner bases in non-commtative rings, a chapter on characteristic and triangular sets with applications to primary decomposition and polynomial solving and an appendix on polynomial factorization including factorization over algebraic field extensions and absolute factorization, in the uni- and multivariate case.

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This Computer Algebra Handbook gives a comprehensive snapshot of this field at the intersection of mathematics and computer science with applications in physics, engineering and education. It contains both theory, systems and practice of the discipline of symbolic computation and computer algebra. With the wide angle of a "lense" of about 200 contributors it shows the state of computer algebra research and applications in the last decade of the twentieth century. Aside from discussing the foundations of computer algebra, the handbook describes 67 computer programs that perform tasks in symbolic computation. In addition, the handbook offers 100 pages on applications in physics, mathematics, computer science, engineering chemistry and education. This book will be very useful as a reference to graduate students and researchers in symbolic computation and computer algebra. ... Read more

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Hundreds of novel and innovative computer algebra ... Read more

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This book presents a step-by-step development of a rigorous framework for the specification and verification of concurrent systems. Petri Net Algebra takes its inspiration and methods from Process Algebra and Petri Nets, two prominent branches of concurrency theory. Added synergistic benefit is derived from combining their respective advantages.
Petri nets are treated as composable objects, and as such they are embedded in a general process algebra. On the other hand, a generic process algebra is given an automatic Petri net semantics so that net-based verification techniques, based on structural invariants and causal partial orders, can be applied to the process algebra.
The book contains full proofs, carefully chosen examples and several possible directions for further research. A unique aspect is that the development of the Petri net algebra is handled so as to allow for further application-oriented extensions and modifications. ... Read more

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This book integrates recent developments and related applications in $q$-series with a historical development of the field, focusing on major breakthroughs and the author's own research interests. The author develops both the important analytic topics (Bailey chains, integrals, and constant terms) and applications to additive number theory. He concludes with applications to physics and computer algebra and a section on results closely related to Ramanujan's ``Lost Notebook.'' With its wide range of applications, the book will interest researchers and students in combinatorics, additive number theory, special functions, statistical mechanics, and computer algebra. It is understandable to even a beginning graduate student in mathematics who has a background in advanced calculus and some mathematical maturity. ... Read more

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Hundreds of novel and innovative computer algebra "recipes" will enable readers starting at the second year undergraduate level to easily and rapidly solve and explore most problems they encounter in their classical mechanics studies. While the aim is not to try and teach the fundamentals of the subject, the recipes are organized to correlate with topics found in standard classical mechanics texts.Using the powerful computer algebra system MAPLE (Release 8) --- no prior knowledge of MAPLE is presumed --- the relevant command structures are explained on a need-to-know basis as the recipes are developed. This is a self-contained and standalone text, similar only in style and format to "Computer Algebra Recipes: A Gourmet's Guide to the Mathematical Models of Science," ISBN 0-387-95148-2, Springer New York. The computer algebra recipes are introduced in the context of interesting tales, a teaching approach that has been successfully classroom tested by the authors. For the reader's convenience, all recipes have been placed on a Windows Platform CD-ROM that comes with the book; MAC and UNIX systems are also compatible. The CD-ROM also includes computer algebra solutions to hundreds of problems.This new problem-solving guide can serve in a variety of ways: for use in the classroom or self-study, for reference, or as a text for an on-line course. Science professionals, engineers who need to quickly solve complex classical mechanics problems relevant to their work, and instructors seeking a modern approach to teaching this venerable subject will find this work an invaluable resource. ... Read more

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The Computer Algebra and Differential Equations meeting held in France in June 1992 (CADE-92) was the third of a series of biennial workshops devoted to recent developments in computer algebra systems. This book contains selected papers from that meeting. Three main topics are discussed. The first of these is the theory of D-modules. This offers an excellent way to effectively handle linear systems of partial differential equations. The second topic concerns the theoretical aspects of dynamical systems, with an introduction to Ecalle theory and perturbation analysis applied to differential equations and other nonlinear systems. The final topic is the theory of normal forms. Here recent improvements in the theory and computation of normal forms are discussed. ... Read more

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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

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. ... Read more

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Gives a careful account of the results and presents some applications of Fork algebras in computer science, particularly in system specification and program construction. Covers all the essentials in order to provide the reader with a better understanding. ... Read more

Customer Reviews (1)

Esta bueno ... pero ...
Yo le camviaria cosas. No se. Ustedes sabran. El final es muy opaco y quedan inconclusas muchas ideas. No se si Marselo penso en un final abierto pero ni siquiera eso es claro. Es muy confuso todo. Estoy escribiendo un libro con el y prometo que va a estar bueno. Van a quedar resolbidas muchas cosas que en este libro uno se quedo como que ¿que paso aca?. Bueno loco, despidome.
FREEDOM!! Peace out!

Charley ... Read more

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Written by an experienced physicist who is active in applying computer algebra to relativistic astrophysics and education, this is the resource for mathematical methods in physics using Maple and Mathematica. Through in-depth problems from core courses in the physics curriculum, the author guides students to apply analytical and numerical techniques in mathematical physics, and present the results in interactive graphics. Around 180 simulating exercises are included to facilitate learning by examples.

This book is a must-have for students of physics, electrical and mechanical engineering, materials scientists, lecturers in physics, and university libraries.

*Free online Maple material at http://www.wiley-vch.de/templates/pdf/maplephysics.zip

*Free online Mathematica material at http://www.wiley-vch.de/templates/pdf/physicswithmathematica.zip

*Solutions manual for lecturers available at www.wiley-vch.de/supplements/ ... Read more

Customer Reviews (2)

More than excellent.
This textbook combines Physics with Maple in a very suitable manner.
The students will find it very useful as they could learn how to apply computer algebra to Physical problems. It's really an excelnet book.

A superb textbook
The topics covered in this book form a very comprehensive look at the mathematics and types of problems that are encountered across the entire physics discipline.The author has done a nice job showing students how to use Maple for mathematical physics.The animation of several examples is a nice touch which really helps students what is going on with some of these solutions.This is a superb text. ... Read more

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This book gives a comprehensive introduction to computer algebra together with advanced topics in this field. It provides a detailed coverage of the mathematics of computer algebra as well as a step-by-step guide to implement a computer algebra system in the object-oriented language C++. The used tools from C++ are introduced in detail.

Numerous examples from mathematics, physics and engineering are presented to illustrate the system's capabilities. Computer algebra implementations in LISP and Haskell are also included. In addition, gene expression programming and multiexpression programming with applications to computer algebra are introduced.

Contents: Mathematics for Computer Algebra; Computer Algebra Systems; Tools in C++; String Class; Standard Template Library; Classes for Computer Algebra; Symbolic Class; Applications; LISP and Computer Algebra; Lisp Using C++; Gene Expression Programming; Program Listing. ... Read more

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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. ... Read more