I have some affine varieties whose cohomology (topological, with $\mathbb{C}$ coefficients) I would like to know. They are very nice, they are all of the form $\mathbb{A}^n \setminus \{ f=0 \}$ for some hypersurface $f$. (In particular, they are smooth.) If I needed to write them as closed subvarieties, I could just write $y f(x_1, \ldots, x_n)=1$.
I want software where I type in $f$ and get back the betti numbers. Or at least directions for how to reasonably hack existing software into doing this. Thanks!