A Topological Analysis Research and Demonstration Computer Program Library.

摘要

This report describes a computer program designed to operate in either batch mode or interactive conversational mode, created for the purposes of demonstrating certain aspects of the foundations of complex function theory and of facilitating research therein. The program is built around the concept of winding number which it relates to the concept of integer valued analogue of the complex analytic logarithm function. This number counts the number of times a closed path in the plane 'winds' about a point. It can be expressed in terms of concepts of combinatorial topology or analytically in terms of complex contour integrals or complex logarithm functions. A detailed set of instructions on how to use the program as well as a listing of the program coding is included.