Consider the following problem:
- Input: $n$ polynomial equations of degree $2$ in approximately $n$ variables.
- Each equation contains about $\sqrt{n}$ monomials.
- We would like to find one simultaneous real solution.
How large can $n$ be for today's software to solve this on a PC within reasonable time (we can define reasonable time as 24 hours).
I started to play with Matlab (MuPAD). I am using "numeric::polysysroots" and it seems that it does not return for $n=100$.
My motivation is that I'm going to have such a set of equations with $n\sim3000$. Is that hopeless?