Reasoning about the Elementary Functions of Complex Analysis

Authors:
Russell Bradford;Robert M. Corless;James H. Davenport;David J. Jeffrey;Stephen M. Watt
Affiliations:
Department of Computer Science, University of Bath, Bath BA2 7AY, England E-mails: R.J.Bradford@bath.ac.uk;Ontario Research Centre for Computer Algebra, Ontario, Canada URL: www.orcca.on.ca;Department of Computer Science, University of Bath, Bath BA2 7AY, England E-mails: J.H.Davenport@bath.ac.uk;Ontario Research Centre for Computer Algebra, Ontario, Canada URL: www.orcca.on.ca;Ontario Research Centre for Computer Algebra, Ontario, Canada URL: www.orcca.on.ca
Venue:
Annals of Mathematics and Artificial Intelligence
Year:
2002

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Abstract

There are many problems with the simplification of elementary functions, particularly over the complex plane, though not exclusively – see (20). Systems tend to make “howlers” or not to simplify enough. In this paper we outline the “unwinding number” approach to such problems, and show how it can be used to prevent errors and to systematise such simplification, even though we have not yet reduced the simplification process to a complete algorithm. The unsolved problems are probably more amenable to the techniques of artificial intelligence and theorem proving than the original problem of complex-variable analysis.