Zeros and Critical Points of Random Polynomials

This app computes and plots the zeros of a random polynomial
\( \quad f(z) = \displaystyle \prod_{j = 0}^n \; (z - \zeta_j) \)   where   \( \zeta_j \) are independent uniformly distributed random variables in the complex plane
Inspired by discussions with my colleagues Amir Ali Ahmadi and Boris Hanin
it also computes and plots the roots of all of its derivatives.

Click here for a version that generates random coefficients to make a random polynomial.

Click here for a webpage that computes just zeros of random polynomials.

Provide the degree of the polynomial:       n =     and click     Compute

Select how many polynomials:       numpoly =

The zeros of the polynomial and its derivatives are shown in a rainbow of colors (ROYGBIV).

Updated 2024 July 29