Email Gateway (Aug 22 2022 at 16:17): Email Gateway (Aug 22 2022 at 16:17):From: "Thiemann, Rene" <Rene.Thiemann@uibk.ac.at>
Dear all,
it is my pleasure to announce two strongly related and interesting AFP entries
on complex analysis by Wenda Li.
Evaluate winding numbers through Cauchy indices
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.
Count the Number of Complex Roots
Based on evaluating Cauchy indices through remainder sequences, this
entry provides an effective procedure to count the number of complex
roots (with multiplicity) of a polynomial within a rectangle box or a
half-plane. Potential applications of this entry include certified
complex root isolation (of a polynomial) and testing the Routh-Hurwitz
stability criterion (i.e., to check whether all the roots of some
characteristic polynomial have negative real parts).
For more information, have a look at:
https://www.isa-afp.org/entries/Winding_Number_Eval.html
https://www.isa-afp.org/entries/Count_Complex_Roots.html
Cheers,
René
Last updated: Apr 23 2024 at 08:19 UTC