Evaluating Winding Numbers and Counting Complex Roots Through Cauchy Indices in Isabelle/HOL.
Published version
Peer-reviewed
Repository URI
Repository DOI
Change log
Authors
Li, Wenda https://orcid.org/0000-0002-9886-9542
Paulson, Lawrence C https://orcid.org/0000-0003-0288-4279
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
Publisher DOI
Sponsorship
European Research Council (742178)