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Testing the Julia's package RootsAndPoles.jl v2.0.0 for the (complex) logarithm f(z)=log(z) with standard (default) parameters as described on GitHub by Piotr Kowalczyk I obtain the following result in a moderate domain around the origin

number of roots: 1
number of poles: 1

enter image description here

While the result for the root z=1 is clear I do not understand the meaning/outcome of the pole at z=-1. Even for a non-standard branch cut, the Log 'function' has no pole at z=-1 in contrast to the findings in the figure.

Is there a bug in the Julia package or do I overlook anything?

Bernd
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  • you're better off asking the question in that github repository than here... – jling Mar 01 '23 at 00:53
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    It looks like the algorithm as implemented calculates the complex quadrant by [comparing the real and imaginary parts to zero](https://github.com/fgasdia/RootsAndPoles.jl/blob/b3d3bd8715eeddaca78fb7a8e21bd98df3dd9b2e/src/RootsAndPoles.jl#L144) rather than computing the argument of the complex number (see equation (1) in https://arxiv.org/pdf/1806.06522.pdf). That means it will incorrectly find quadrant changes at branch cuts. I can't be sure, but it's likely a bug, and you should probably notify the authors. – PaSTE Mar 01 '23 at 02:31
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    Thanks all for the answer - I have created an issue on GitHub. – Bernd Mar 01 '23 at 07:03

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