Zeros and Critical Points of Random Polynomials

This app computes and plots the zeros of a random polynomial
\( \quad f(z) = \displaystyle \sum_{j = 0}^n \alpha_j \; f_j(z) \)   where   \( \alpha_j \) are independent N(0,1) random variables and   \( f_j(z) \) = z^j z^j/j! z^j/sqrt(j!)
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 roots to make the 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 31