Give a generalized system of the form...
$$a_1 + a_2 + a_3 = x_1 + x_2 + x_3$$ $$a_1 a_2 + a_1 a_3 + a_2 a_3 = x_1 x_2 + x_1 x_3 + x_2 x_3$$ $$a_1 a_2 a_3 = x_1 x_2 x_3$$
... solvable in polynomial time?
By generalized I mean having $n$ of the $a_i$ and $x_i$ terms, with all the $a_i$ and $x_i$ being complex numbers.
See https://en.wikipedia.org/wiki/Elementary_symmetric_polynomial and https://en.wikipedia.org/wiki/Vieta%27s_formulas .
It is instant. The collection of $x_i$ is merely a permutation of the $a_j$