The authors focus on the five most popular computer algebra systems--Derive, Macsyma, Maple, Mathematica, and Reduce. Their goal is to describe what commercial software is available, summarize the facilities provided by each system, and evaluate the relative merits of each system.
The book is divided into three parts. The first part (chapters 2 through 7) describes and compares the basic capabilities of each system. Topics include the mathematical operations in algebra (simplification, solution of equations, vectors, matrices, tensors, and so on) and calculus (differentiation, integration, limits, differential equations, series, and so on), interactive and graphical capabilities, and programming language capabilities to extend the software. In addition, the authors discuss facilities for translating symbolic expressions to conventional languages (FORTRAN or C) and mathematical word processing languages (TEX and eqn). The second part of the book (chapter 8) includes seven case studies with programs in various symbolic languages. It is intended to illustrate some of the capabilities of the systems on more involved and realistic problems. The final part of the book (chapter 9) is an annotated bibliography about computer algebra; it includes books, review papers, journals, conferences, newsletters, and software libraries.
This introductory guide summarizes the basic capabilities of five commercial computer algebra systems. In a general way, it describes some of the mathematical operations one can expect to see in this software, and it includes a number of tables that compare the capabilities of the various systems. Computer algebra software is concerned with involved mathematical operations, some of which are difficult to describe in a simple way. Therefore, it is not surprising (but is unfortunate) that the book does not describe the more subtle mathematical capabilities and limitations of the software. (A useful description of the limits of computer algebra software is given by Stoutemyer [1].) In addition, since updated versions of the various systems are frequently released, the comparisons in the book will soon be dated.
The book will be useful to those who want a brief summary and evaluation of the elementary capabilities of current commercial computer algebra software.
