Abel's Theorem In Problems And Solutions Based ... Direct

When coefficients traverse certain loops, the roots of the polynomial undergo a non-trivial permutation.

Arnold’s proof centers on how the roots of a polynomial behave as its coefficients move along closed loops in complex space: Abel's theorem in problems and solutions based ...

The primary objective of this work is to present a of Abel's Impossibility Theorem. This theorem states that there is no general formula for the roots of a polynomial equation of degree five or higher using only arithmetic operations and radicals. When coefficients traverse certain loops, the roots of