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\title{Evaluate Winding Numbers through Cauchy Indices}
\author{Wenda Li}
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\begin{abstract}
	In complex analysis, the winding number measures the number of times a path (counterclockwise) winds around a point, while the Cauchy index can approximate how the path winds. This entry provides a formalisation of the Cauchy index, which is then shown to be related to the winding number. In addition, this entry also offers a tactic that enables users to evaluate the winding number by calculating Cauchy indices. The connection between the winding number and the Cauchy index can be found in the literature \cite{eisermann2012fundamental} \cite[Chapter 11]{rahman2002analytic}.
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\section{Acknowledgements}
The work was supported by the ERC Advanced Grant ALEXANDRIA (Project 742178), funded by the European Research Council
and led by Professor Lawrence Paulson at the University of Cambridge, UK.

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