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Multiple-valued complex functions and computer algebra

Summary: Multiple-valued complex functions
and computer algebra
Helmer Aslaksen
Department of Mathematics
National University of Singapore
Singapore 117543
1 Introduction
I recently taught a course on complex analysis. That forced me to think more
carefully about branches. Being interested in computer algebra, it was only natural
that I wanted to see how such programs dealt with these problems. I was also
inspired by a paper by Stoutemyer ([3]).
While programs like Derive, Maple, Mathematica and Reduce are very pow-
erful, they also have their fair share of problems. In particular, branches are some-
what of an Achilles' heel for them. As is well-known, the complex logarithm
function is properly defined as a multiple-valued function. And since the general
power and exponential functions are defined in terms of the logarithm function,
they are also multiple valued. But for actual computations, we need to make them


Source: Aslaksen, Helmer - Department of Mathematics, National University of Singapore


Collections: Mathematics