Is there any algorithm that finds all zeros(roots) of a continuous function $F:\mathbb R^n\to\mathbb R^n$?
I've seen some algorithms that find one zero, such as Newton's method. But I need to find all zeros (I need this because I want my computer to use Lagrange's mutiplier theorem).
If that's impossible, then adding the following restriction is okay:
$F$ is composed only of polynomial functions. For example, $F:(x_1,x_2)\mapsto(x_1x_2+1,x_1^2+x_2^2)$.