Introduction

xxm

We have included descriptions of many special cases and summarized

the results of many calculations. Most of the nontrivial calculations used

the symbolic manipulation programs MATHEMATICA and/or MAPLE. In

order to excite the reader about the flowers in the beautiful garden we are

cultivating here, we start each chapter with (what we regard as) a handsome

example of what will follow. We have included a number of accessible exer-

cises and research level problems. The latter may be quite challenging and

are at times only conjectures. The reader should also approach the many

special cases we have included as challenges to obtain independent solutions.

They are presented in the spirit of exercises, with solutions supplied by the

authors.

Numbering systems. The book consists of seven chapters and a set of bib-

liographical notes that will be maintained and updated on the web. Chapters

are subdivided into sections; these into subsections. Definitions, lemmas,

propositions, theorems, exercises, problems and remarks are labeled consec-

utively as a single group within each section. A typical item is Theorem

section.number; number starts with 1 for the first item in the section. Thus,

for example, in Chapter 2, Definition 2.32 (in section 2) in our numbering

scheme is followed by Lemma 4.1 (in section 4). Equations that will be ref-

erenced subsequently in the text are labeled by a decimal: chapter.number;

number starts with 1 for the first numbered equation in the chapter. Tables

and figures are numbered consecutively in the book.

Acknowledgments. We thank

1. the mathematicians who have had the patience to listen to our lectures

on the subject of this book: whether our students at the Hebrew University

in Jerusalem or the State University of New York in Stony Brook, who at

times have provided us with constructive criticism, or colleagues at various

institutions who have invited us to speak about this subject;

2. our graduate students who read previous drafts of the book and pointed

out errors and ambiguities (needless to say, the remaining errors and ambi-

guities are the authors' responsibilities);

3. our undergraduate students who helped with the MATHEMATICA cal-

culations and the figures;

4. the editorial and technical staff of the American Mathematical Society,

especially Deborah Smith and Janet Pecorelli who guided us through the

final preparation of the manuscript; and most importantly,