TABLE OF CONTENTS In this chapter we summarize the background material that provides a framework for the mathematical and computational discussions in the book. A more detailed discussion of this material can be found on the CD that accompanies this book and in our companion book, Computer Algebra and Symbolic Computation, Elementary Algorithms , (Cohen [24]). Readers who are familiar with this material may wish to skim this chapter and refer to it as needed.
A computer algebra system (CAS) or symbol manipulation system is a computer program that performs symbolic mathematical operations. In this book we refer to the computer algebra capabilities of the following three systems which are readily available and support a programming style that is most similar to the one used here:
Maple a very large CAS originally developed by the Symbolic Computation Group at the University of Waterloo (Canada) and now distributed by Waterloo Maple Inc. Information about Maple is found in Heck [45] or at the web site http://www.maplesoft.com.
Mathematica a very large CAS developed by Wolfram Research Inc. Information about Mathematica can be found in Wolfram [102] or at the web site http://www.wolfram.com.
MuPAD a large CAS developed by the University of Paderborn (Germany) and SciFace Software GmbH & Co. KG. Information about MuPAD can be found in Gerhard et al. [40] or at the web site http://www.mupad.com.
Mathematical pseudo-language (MPL) is an algorithmic language that is used throughout this book...
