Suppose I have a vector of unknowns $x_i$, with $i=1,...,N$, where $N$ is symbolic, and I have some nonlinear system of $M$ equations, $$f_m(x_1,...,x_N) = 0\quad \forall m,$$ with $f_m: \mathbb{R}^N \rightarrow \mathbb{R}$ the family of (possibly nonlinear) equations in this system. How should I approach this problem with Sympy?
To make things more concrete and simple, suppose I have the system $$x_i+\sum_{j=1}^Nx_j^2 = 0, \forall i$$
I could describe this typical equation in Sympy as follows:
N = Symbol('N', integer = True)
i = Idx('i', (1,N))
j = Idx('j', (1,N))
x = IndexedBase('x')
eq = x[i] + Sum(x[j]**2, j) # This is a generic equation, valid for all i
How to state this problem to the computer? Thanks in advance.