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Evaluating Winding Numbers and Counting Complex Roots Through Cauchy Indices in Isabelle/HOL.

Published version
Peer-reviewed

Type

Article

Change log

Abstract

In complex analysis, the winding number measures the number of times a path (counter-clockwise) winds around a point, while the Cauchy index can approximate how the path winds. We formalise this approximation in the Isabelle theorem prover, and provide a tactic to evaluate winding numbers through Cauchy indices. By further combining this approximation with the argument principle, we are able to make use of remainder sequences to effectively count the number of complex roots of a polynomial within some domains, such as a rectangular box and a half-plane.

Description

Keywords

Computer Algebra, Winding Number, Isabelle/hol, Interactive Theorem Proving, Root Counting, Cauchy Index, The Routh–hurwitz Stability Criterion

Journal Title

Journal of automated reasoning

Conference Name

Journal ISSN

0168-7433

Volume Title

64

Publisher

Sponsorship
European Research Council (742178)