Effective Algorithm of Analysis of Integrability via the Ziglin’s Method

In this paper, we continue the description of the possibilities to use numerical simulations for mathematically rigorous computer-assisted analysis of integrability of
dynamical systems. We sketch some of the algebraic methods of studying the integrability
and present a constructive algorithm issued from the Ziglin’s approach. We provide some
examples of successful applications of the constructed algorithm to physical systems.