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6:42 AM
@MartinSleziak Thanks for informing me about this discussion on meta. No doubt that factorization theory should not have a top-level tag. But concerning the use of "-theory", I beg to disagree: Please search for "Factorization" at commalg.org/surveys. For a relatively long time, this area of research has been viewed as a rather marginal subfield of commutative algebra, as it used to be almost entirely focuses on cancellative commutative monoids (the first source of examples being integral domains). But the situation has slightly changed in recent years. — Salvo Tringali 45 secs ago
Since Salvo Tringali is now aware of the discussion on meta, my comment on main is no longer needed, so I deleted it.
5 hours later…
11:33 AM
Hi @S.Carnahan. It's nice to see that mods occasionally visit this room, too.
1 hour later…
12:56 PM
What are the tags into which deprecated tags could possibly be merged (after clean-up)?
Apr 27 at 12:10, by YCor
If some merging should be made, it would rather be , which in a sense is more generic than the other two. I might then retag the group theory questions currently tagged then, and more generally those for which [ra.rings-and-algebras] wouldn't fit too well. (Tagging questions of pure commutative algebra being a minor side effect.)
For , YCor suggested . There are 178 questions tagged (abstract-algebra), 31 of them are also tagged ra.rings-and-algebras, which leaves 147 remaining questions.
For , the tag seems like an obvious choice. Of the 148 questions tagged (discrete-mathematics), 81 questions also have co.combinatorics tag, so only the remaining 67 questions need retagging. (Perhaps less, if (co.combinatorics) is suitable for some of those remaining question.)
For , the tag seems like a reasonable choice. There are 358 questions tagged (geometry), 65 of them have also the mg.metric-geometry tag, so there are 293 questions remaining.
For many of those remaining questions, is probably suitable. So I guess that there are less than 250 questions which have to be retagged, the rest could be solved by merging.
1 hour later…
1:59 PM
Q: How to prove that $\mathrm{Aut}(\mathcal{M})\cong\mathrm{Gal}(\bar{\mathbb{Q}}/\mathbb{Q})$?

Sylvain JULIENI want to study the structure of the rig of L-functions $\mathcal{M}$, which is defined as the maximal set of automorphic L-functions of $\mathrm{GL}_{n}(\mathbb{A}_{\mathbb{Q}})$ for some $n$ that be closed under the usual product and the tensor product corresponding to the Rankin-Selberg convol...

Semirings are sometimes called rigs. The "n" is removed from "ring" to indicate that negation is not necessarily a well-defined operation. That is, the additive structure is a commutative monoid instead of an abelian group.
2:14 PM
I have heard about rngs, rig is something I haven't seen before
> The term rig is also used occasionally—this originated as a joke, suggesting that rigs are rings without negative elements, similar to using rng to mean a ring without a multiplicative identity.
Interesting to know. I see I would found this if I tried Wikipedia: Rig: "rig (mathematics), a structure similar to rings without the requirement that elements should have additive inverses" en.wikipedia.org/w/…
I have added the suggested tag synonyms for , , and . Was this a reasonable course of action, or did you want to wait for more manual retagging to take place?
@S.Carnahan To be honest that was a bit unexpected. (And that wasn't what I was suggesting.)
However, I see that you have made a synonym without merging - which means that this can be undone (as far as I know) and also that the questions still have the original tags (until they are edited).
We'll see what other users who are active in tag-related issues think about this. (And at some point we might open a discussion on meta bout the issue.)
> Synonymsing without merging makes it possible to retain some older occurrences of the tag if the synonym is later removed. This is useful in cases where the two tags don't mean exactly the same thing and you want to leave the possibility to at least partially undo this action
The fact that I still see the old tags on the original posts suggests that a synonym was created, but the tags weren't merged.
Q: On the determination of ambiguous ideal class of the extension $\mathbb{Q}(\zeta_5,\sqrt[5]{m})/\mathbb{Q}(\zeta_5))$

Fouad Ellet $L=\mathbb{Q}(\sqrt[5]{n},\zeta_5)$ and $K=\mathbb{Q}(\zeta_5)$ the $5^{th}$ cyclotomic fields, we now that $[L:K] = 5$ and $ GAl(L/K) =\langle\sigma\rangle$ so we call $\mathcal{A}$ an ambigous ideal class of the extension $L/K$ if and only if $\mathcal{A}^{\sigma}= \mathcal{A}$. My questi...

Q: Minimum volume of intersection between two high-dim $\ell^1$-balls

AlanwangLet $B_1$ and $B_2$ be two balls with the same radius, in $\mathbb R^n$ with the $\ell^1$ norm. The distance between the centers of $B_1$ and $B_2$ is $d(B_1, B_2)$. Is there any deterministic method or probabilistic method to calculate the minimum volume of $B_1 \cap B_2$?

Q: Can I build infinitely many polytopes from only finitely many prescribed facets?

M. WinterGiven a finite set of convex $d$-dimensional polytopes $\mathcal P$, for some $d\ge 2$. Question: Is it true that there are only finitely many different convex $(d+1)$-dimensional polytopes whose facets are solely (scaled and rotated versions of) polytopes in $\mathcal P$? Some clarificat...

Until SEDE is updated in the next week, it is possible to get the list of questions also from SEDE: data.stackexchange.com/mathoverflow/query/1190392/… data.stackexchange.com/mathoverflow/query/1234513/…
Apr 27 at 12:21, by YCor
One question in any case is whether any mod is currently prone to deal with retagging. François Dorais used to do so but seems to have his last activity in the "help cleanup tags" thread in March 2019, in spite of many pending requests (including some obvious ones).
Apr 27 at 12:43, by Martin Sleziak
@YCor I suppose that retagging might take several months before it is cleaned-up sufficiently for merging. So it is more important whether the moderators will be active after that happens.
So it seems that some activity from the moderators came sooner than we expected.
@YCor If you're around - what do you think about the synonyms $\to$ , $\to$ , $\to$ which were just created?
One problematic aspect is that some questions which got and were originally tagged do not belong into the (ra.rings-and-algebras) tag.
2:59 PM
I think I see the problem: it is now difficult to search for the questions with the old tags, so it is difficult to check whether the synonyms are appropriate in each case.
OTOH, they were tagged incorrectly anyway - they had a deprecated tag. So they can still be cleaned up by users who are willing to do the retagging.
Only finding them is a bit more complicated than it used to be. (As S. Carnahan just said.)
3:22 PM
@S.Carnahan actually it was already checked and discussed that they were not appropriate in a number of cases (probably -> generating the largest number of wrong retagging). Nevertheless I think these tagging errors are quite harmless compared to the previous situation (forcing multiple manual retagging), so I'm really happy of the modification.
("in a number of cases: I'd say from memory and guess: 20% in ->, 35% in -> and 55% in ->)
@YCor Did you mean to say $\to$ rather then $\to$ ?
The percentages you wrote are percentages in which you expect the new tag to be wrong?
Oh indeed I mixed up. But I also believe is in more than 50% of the case, not the right tag to replace . Geometry is used for plenty of subjects from which the "metric" part has left long ago (algebraic geometry, algebraic geometry, symplectic geometry, a significant part of differential geometry, etc). It was a very incoherent tag.
So you suggest that the synonyms should stay (but without merging - so that the original tags are still visible)?
If the tag synonyms remain, at some point it might be useful to make a post on meta about that. (So that MO users are aware of the change and also how to find the posts which originally had these three tags.)
No I certainly didn't say this. I think that it's better now, and that manual retagging of the new errors can be made when we observe a clumsy choice of tags in bumped questions.
So what you're actually saying?
You want the synonym $\to$ to remain or to be cancelled? (Similarly for the other ones.)
3:33 PM
I don't want the synonym to be cancelled.
Still, as you say, this lead to some question being incorrectly tagged. (You estimated 50% in the case of .)
So it is a good thing that it is still visible which questions were originally tagged , isn't it?
Yes, if "incorrectly tagged" means "with at least one tag that is beyond the scope". But this is relatively harmless. Actually I retagged manually those questions with a single deprecated tag, a few months ago. So this avoids the worst possible cases.
So if you want to keep the current situation (that is still visible - rather than replaced with ), that means synonym without merging. (Which is what S. Carnahan has done, as far as I can tell.)
I don't understand what you're saying by "current situation that 'geometry' is still visible), since I don't see it as visible. What do you mean?
Q: Minimum volume of intersection between two high-dim $\ell^1$-balls

AlanwangLet $B_1$ and $B_2$ be two balls with the same radius, in $\mathbb R^n$ with the $\ell^1$ norm. The distance between the centers of $B_1$ and $B_2$ is $d(B_1, B_2)$. Is there any deterministic method or probabilistic method to calculate the minimum volume of $B_1 \cap B_2$?

You can still see the tag . (If somebody edits the question now, it will be changed to , but until that it stays like this.)
That is what I meant by "still visible". I think it's a bit useful - since we see that the questions was originally tagged .
If mods also merged the tags, all occurrences of would be replaced by - and we would no longer see from the question (or from the revision history) whether it originally had the tag.
3:41 PM
Oh I had misunderstood the change. Oh damn, no this is a real pity. So the bad tag is still there and there is no way (no easy way?) to search for it. Too bad :(
Yes, the fact that searching for the questions tagged is more difficult now is what both I and S. Carnahan mentioned above.
But what can be the interest of leaving the tag if it can't be searched?
I have mentioned some SEDE queries above: mathoverflow.net/questions/332819/… I am not sure whether they will still work after the next week or not.
@YCor Well, it is still at least visible.
One advantage of the fact that the tags weren't merged is that the process is reversible. If MO community (or mods) decide that creating the synonym wasn't a good decision, the synonym can be cancelled and the question which were tagged will still have the tag.
In this case, visibility is rather what we'd like to remove...
I see, reversibility is an important aspect.
The other advantage is that we can see that the question originally had tag. If you're estimating that 50% of questions in that tag are now tagged incorrectly, some clean-up will still be needed. For that, it is good that we see that a question is among those that likely need clean-up.
3:46 PM
I see two advantages to the current situation with the synonyms: (1) No new uses of the old tag, and automatic retagging on edit. (2) We can still search out the tag by hand (e.g., using a browser's "find" function on a page full of questions) and manually change them over time.
Of course, we also have the list of questions which were tagged - from there we can get questions which are likely in the need of retagging.
(1) Here one should think whether this might cause some problems or not. One more thing to keep in mind when creating these synonyms is also that it might possibly lead to some questions being incorrectly tagged. (E.g., some users might use and they do not notice that it was automatically changed to .)
(2) I think that SEDE makes searching easier than Ctrl+F. (If needed, I can create a list of all question which were currently tagged and post it on meta. Similarly for other tags.)
OK for (1). For (2), well I've worked browsing this list of 300 questions and it's already a lot of work. I don't feel doing the same with this list of question diluted in 3000 questions (61 pages of 50 listed questions).
Well, as I mentioned that list of questions with geometry tag is available here: data.stackexchange.com/mathoverflow/query/1190392/… (I am not sure whether that link will work after the next update of SEDE. But we'll see.)
And, as I said, it's not difficult to create a list. You both have sufficient reputation to see deleted posts, right?
But searching is often in combination with some keyword, choose some ranking... I found it not easy on but knowing that would be even harder. Probably merely retagging when bumping occurs will be enough.
I have posted this to clarify what I meant by list - it is not ordered by id, but I can clarify that later: Recent tag synonyms for deprecated tags.
@YCor I think that this would be argument in cancelling the synonyms. (At least until the tags are sufficiently cleaned-up for merging.)
Re: "(1) No new uses of the old tag". As I said a few times in the past, preventing tags from being added to new questions could be achieved by blacklisting them. That's what I suggested here: The existing deprecated tags should be blacklisted
I still think that it might be good to make a post on meta related to this - this changed tag on approximately 700 questions, so MO community should be aware of the change (or at least those users who do care about tags). And also other aspects of the issue could be discussed there.
3:58 PM
I agree that blacklisting seems to have the advantages and not the drawbacks of the synonym option.
I apologize, but I have to leave now.
I'll just add that I think that meta post could generate at least some discussion - today's discussion in this room shows that some aspects of this are not really that simple.
Thanks for making the meta post. Also, I agree that blacklisting is a better option.
I too must leave.
@S.Carnahan The post I linked on meta was just an example of what I meant by creating the list.
If nobody else decides to make a post on meta discussing the synonyms for the deprecated tags, I can try to do that later. (This post was not meant as the proper post, just a place which is quickly accessible to all three of us.)
I am not sure whether you want to discuss this with other MO mods before it is brought up on meta.
Regardless whether or not synonyms are created, I think list can be useful anyway.
For example, we could mark there which questions are already correctly retagged - as I did in one of the answers: "<s>Minimum volume of intersection between two high-dim $\ell^1$-balls</s> - fits"
The strikethrough signifies that the tags on the questions do not need additional attention (or that (geometry) can be safely replaced by (mg.metric-geometry) there).
This time I'm leaving for real.
But it's nice to see some people taking part in a tag-related discussion on MO.
1 hour later…
5:43 PM
A new tag was created. The question is also missing a top-level tag.
Q: Which curves and surfaces realizable by a linkages? references?

MirceaOk, so I try to formulate rigorously the question in the title, for which I am asking for references. My definitions may be flawed, so feel free to adjust/correct them! I care about dimensions 2 and 3 below, but feel free to mention general d as well. Let $d\ge 1$ be an integer, $G=(V,E)$ be a g...

6:12 PM
I removed the new tag (I think creating meta tags should be discussed beforehand, and this one is particularly opinion-based and of minor usefulness), and added two thematic tags including a top-level one (the only thematic one, "linkage", seems overly narrow)
2 hours later…

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