This question (now deleted) asked for a way to compute generators for $I \cap \mathbb{Z}[z_1,\ldots,z_n]$ as an ideal of $\mathbb{Z}[z_1,\ldots,z_n]$, given generators $f_1,\ldots,f_m \in \mathbb{Z}[z_1,\ldots,z_n]$ of an ideal $I$ of $\mathbb{Q}[z_1,\ldots,z_n]$.

This very much intrigued me (as the sort of problem I *definitely should* know the answer to, but do not). I found a paper relevant to the problem ("Ideal Memership in Polynomial Rings Over the Integers" by M. Aschenbrenner, *J. Amer. Math. Soc.* **17** (2004), 407–441) and suggested in a comment that the poster have a look at it. I then spent some time thinking about it myself and convinced myself that the answer can, indeed, be derived from the results in this paper (specifically, by combining corollary 3.5 and remark 4.5), but I'm not really happy with this answer, I wonder if there's a simpler one and I feel like I missed something.

I was just about to post an answer explaining this when the poster of the original question deleted the question. Now this makes me wonder even more, e.g., whether I missed something that made the answer obvious. To make things even more infuriating, the poster answered my comment before deleting the question, so I got a reply notification, which disappeared as soon as I clicked on it, leading me to the 404 page saying the question was gone, and now I can't read that answer either (I just got a glimpse of it).

Even though I'm tempted to do so, it's probably not appropriate to repost the question, considering that I have an answer, just to ask if somebody has a "better" one.

And of course there is no way to contact other users in StackExchange, which really adds insult to injury. Admittedly, this Meta question is something of a pretext to attempt to do precisely that.

(I should add that I know the poster's id and nickname, I won't copy them here in case they don't want to be associated with what they maybe decided was a stupid question.)

Can a moderator at least recover the comment that I didn't have the chance to read? (I assume it can be posted publicly: the author simply didn't realize that deleting the question would also delete the comment.)

Any other suggestions?

privately" would be more precise way of putting it. $\endgroup$ – Martin Sleziak Apr 1 '17 at 14:59