TABLE OF CONTENTS In this appendix we recall several basic definitions and theorems concerning the different fields addressed by this book: functions of the complex variable, series expansions, algebraic structures, polynomials in the binary field, matrices. These reminders the choice of which remains arbitrary to a large extent are not required for the reading of this book. However, they may be of some help for various specific concepts, or preparation for the study of specialized textbooks.
Definition of the function of the complex variable. Let ? be an open set of the complex number field C. A function of the complex variable on ? is an application from ? to C, which for every z in ? yields a complex number denoted as:
This can always be written as:
The set ? is the function domain.
Uniform function. The function f( z) is said to be uniform (or single-valued) if every z in ? has a single image Z = f( z).
Continuity. Definitions about the limits of complex functions are identical to those concerning scalar functions.
Specifically, z being a continuous function in the complex plane, every polynomial in z is a continuous function on the whole plane. Similarly, every rational fraction of z is continuous on the plane, except in these points, where its denominator vanishes (these points...
