For rings such as $\mathbb{Z}[x,y]$ is there software to compute any of:

1.) The integral closure of $\mathbb{Z}[x,y]/(f)$. de Jong has a very general algorithm that works in this context (http://arxiv.org/abs/alg-geom/9704017)

2.) The radical of an ideal $I$.

3.) Minimal primes of an ideal/the primary decomposition.

4.) The dimension of $\mathbb{Z}[x,y]/I$

5.) Any invariants of a singularity on such a scheme.

Over fields $\mathbb{Q}, \mathbb{F}_p$ I think Sage, Macaulay 2 etc., implement 1-4. Are 1-4 difficult to compute for such rings, or are there just no implementations yet?