  We solve the problem of determining under which conditions the monodromy of a
vanishing cycle generates the whole homology of a regular fiber for a
polynomial $f(x,y)=g(x)+h(y)$ where $h$ and $g$ are polynomials with real
coefficients having real critical points and satisfying
$\text{deg}(g)\cdot\text{deg}(h)\leq 2500 $ and
$\text{gcd}(\text{deg}(g),\text{deg}(h))\leq 2$. As an application, under the
same assumptions we solve the tangential-center problem which is known to be
linked to the weak 16th Hilbert problem.
