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Book review

Author(s) Geddes, Keith O.
Czapor, Stephen R.
Labahn, George
Title Algorithms for Computer Algebra
Publisher Kluwer Academic Publishers
Year of publication 1992
Reviewed by Mihai Postolache

The computational symbolic mathematics has found in the last decade various applications in classical mathematics and other bits of science and technology. Is possible to mention here symbolic integration, linear systems solving using symbolic computation, numeric computation and other specific mathematical computations. The aim of this book is to present basic information about computer algebra systems (tools which can manipulate symbolic mathematical objects) and the corresponding mathematical algorithms as well as some problems of implementation of computer algebra systems.

This book is suitable for more advanced students in mathematics and computers, applied mathematicians as well as for scientists interested in the topic of computer representation of algebraic objects. An introductory course to linear algebra and to computers science is assumed. Also the reader must be familiar with data structures (lists, arrays representation and all) and with some notions from the algorithms theory.

The authors' aim have been to provide new results concerning backgrounds of computational symbolic mathematics with examples drawn from various areas of applications. The range of topics covered is from algebra of polynomials and arithmetic algorithms to advanced concepts such as homomorphic images, advanced computations in polynomial domains, indefinite integration. In this book can be found numerous examples and pictures, carefully plotted, which illustrate the ideas and the concepts. Also the exercises at end of each chapter lead to individual research work. The main algorithms are presented in a specific computer language.

There exists a table of index and the table of contents is aufficiently detailed. Also a list of algorithms, a list of figures and a list of tables are included. Every chapter contains a comprehensive bibliographical list. The book is very well produced like all books produced by KAP.

Generally, the presentation is rigorous and reflects the experience of the authors in the difficult field of the computational symbolic mathematics and the computers research work. The book is sufficiently self contained to enable independent research. Consequently a large area of readers can use it. Purchasing this book is a good investment for individuals and libraries alike.