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!

comme on imagine), by results of Grothendieck, Hartshorne and probably others, no? Since $\Omega^1$ can be constructed easily in Macaulay2, you need to compute its exterior powers and the exterior differential, which should be "easy". $\endgroup$ – Mariano Suárez-Álvarez Nov 16 '11 at 21:28