Evaluate Winding Numbers through Cauchy Indices


Title: Evaluate Winding Numbers through Cauchy Indices
Author: Wenda Li
Submission date: 2017-10-17
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.
  author  = {Wenda Li},
  title   = {Evaluate Winding Numbers through Cauchy Indices},
  journal = {Archive of Formal Proofs},
  month   = oct,
  year    = 2017,
  note    = {\url{http://isa-afp.org/entries/Winding_Number_Eval.html},
            Formal proof development},
  ISSN    = {2150-914x},
License: BSD License
Depends on: Budan_Fourier, Sturm_Tarski
Used by: Count_Complex_Roots, Zeta_Function
Status: [ok] This is a development version of this entry. It might change over time and is not stable. Please refer to release versions for citations.