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?

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    $\begingroup$ The comment that was deleted said: "Thanks for the link to the nice paper. It turns out that I was not diligent enough about searching for an answer to this question and it has already been answered mathoverflow.net/questions/212653…. I'll delete my question soon" $\endgroup$
    – Yemon Choi
    Commented Mar 31, 2017 at 22:08
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    $\begingroup$ (10k rep is "all" that is needed to see deleted posts/answers) $\endgroup$
    – Yemon Choi
    Commented Mar 31, 2017 at 22:09
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    $\begingroup$ @YemonChoi Thanks! The answer to this older question is exactly the sort of thing I was hoping to see. $\endgroup$
    – Gro-Tsen
    Commented Apr 1, 2017 at 0:34
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    $\begingroup$ Somewhat related: Should we request a Private Message system? (The answers there explain how - at least in some cases - you can contact other users.) And in fact the same things are explained also in the thread you linked to. So probably saying that "there is no way to contact other users privately" would be more precise way of putting it. $\endgroup$ Commented Apr 1, 2017 at 14:59
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    $\begingroup$ There are also some possibilities which users below 10k can try to get some stuff from deleted posts. For example, some possibilities are mentioned here. Although in this specific case neither Google Cache nor SEDE were sufficient to get the comment you were looking for. $\endgroup$ Commented Apr 1, 2017 at 15:05
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    $\begingroup$ One way to attempt to contact the user is to leave a comment on another question/answer from the user. mathoverflow.net/users/77946/charlie $\endgroup$ Commented Apr 1, 2017 at 18:59
  • $\begingroup$ @FrançoisG.Dorais, maybe you should delete your comment, since Gro-Tsen expressed a desire not to identify the author of the original question? Also, such a use seems counter to the spirit of the question/answer system, except as a kludge towards a messaging system (and we all know how tolerant we are of the analogous situation of comments left as answers with the excuse that the poster can't leave comments yet :-) ). $\endgroup$
    – LSpice
    Commented Apr 4, 2017 at 21:16
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    $\begingroup$ @LSpice no, all posts on MathOverlow are subject to the CC-BY-SA license, regardless of whether they are deleted or not. Having 10k reputation doesn't allow anyone to get around the law, but the moderator agreement does prevent me from providing more information to Gro-Tsen. $\endgroup$ Commented Apr 4, 2017 at 21:32
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    $\begingroup$ @FrançoisG.Dorais, I don't think I expressed a view on anyone's fitness to evade the law. I was just suggesting that, since there is no particular need to identify the questioner (Gro-Tsen obviously knows who it is), it might be courteous, though not legally required, to follow Gro-Tsen's lead in not identifying him or her. $\endgroup$
    – LSpice
    Commented Apr 4, 2017 at 21:39
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    $\begingroup$ @LSpice looks like half of my earlier comment got deleted... Anyway, that's now besides the point. Since this post links to the deleted question, it doesn't seem that there is any desire to hide the author's identity. Moreover, it seems that would be counterproductive to the goal to hide the author's user name. $\endgroup$ Commented Apr 5, 2017 at 11:17


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