@Isabellatrix so for some reason you can’t tag questions with the holomorhpic-functions tag? That seems like a flaw in the tagging system regardless of synonyms. I should be able tag with either tag if only for the purpose of proper sorting of material. Not to mention that the terms are not synonymous and whoever thought that was a good idea should have their head put back on straight (cause it clearly wasn’t at the time).

Since the removal of the tag synonym is discussed here, I will add link to a previous exchange in tagging chatroom: chat.stackexchange.com/transcript/3740/2020/1/11

It contains some discussion about tag synonyms and their removals in general. (In particular, this answer might be useful for people who are not familiar with the details: What happens with the tagged questions when a tag-synonym is cancelled?)

And we were also trying to find out when the tag synonym was approved, according to this SEDE query it was in March 2019. (Notice that the date in the list of tag synonyms is the date when the synonym was proposed - see also my question on Meta Stack Exchange: What does the column “created” in the list of tag synonyms mean?)

@user64742 that's intended behavior. It is arguably true that "synonym" might be a bit of a misnomer, but the usage of having a more special tag as a "synonym" of a broader one is common, e.g., gcd is a synonym of gcd-and-lcm.

@quid so for questions that were tagged with holomorphic-function before the tag synonym linkage, did they all of a sudden all change tags to complex-analysis the moment someone hit the button? If not, then I really don't understand why one cannot or should not be able to tag with either at their choosing (or both!) as the software at least supports the ability to have it tagged that way even if the UI says no. The synonym aspect should only affect search-ability and the tag pop-up description.

@user64742 in this case, no. But indeed it is common to do what you said, too, that is change the tag on existing posts.

@quid I feel like that would be a horrible mistake, because what makes a certain function type directly related to complex analysis? surely there are real-world problems modeled by holomorphic-functions and questions about them would center purely around solving some equation or finding the right function for a specific use. It seems strange, and I would not go change all the tags, especially if this is going to be unlinked relatively soon-ish.

@user64742 "what makes a certain function type directly related to complex analysis" well arguably complex analysis is the study of holomorphic functions.

@user64742 There are two issues here: (1) How the software treats tag synonyms, and (2) the quality of the synonym (holomorphic-functions) $\to$ (complex-analysis).

@quid ah. did not know that. you learn something new every day!

Regarding the first point, the idea is that when a tag synonym is created, it means that the synonym conveys all of the same meaning as the original tag. Hence the synonym is automatically redirected to the original tag.

This means that new posts are tagged only with the original tag (and not the synonym).

hmmm

If a pre-existing tag is made a synonym of another tag, however, older posts will not be retagged; at least, not without further action.

perhaps then a button when creating a synonym to move all existing tagged posts to the "original" tag would be useful then.

Hence the synonym-ized tag can stick around on the website.

because not moving them all over conveys a strong amount of confusion

namely

"why can't I tag with that??? this other post did!"

@user64742 that exists.

However, it is only accessible to moderators. The current synonym was created by users.

Obligatory link to the FAQ post: What are merged tags?

AFAICT, the advantage of merging is that it changes all instance of the old tag to new tag. The disadvantage is that it is not reversible. (I am sure that quid will correct me if I got it wrong.)

Some brief comment on merging is also in the answer that I linked above: What happens with the tagged questions when a tag-synonym is cancelled?

Shog9's answer on another question seems to confirm that merging cannot be undone: There is no undo for tag merges; the process doesn't just retag the questions involved, it re-writes the history of each post that used the losing tag to use the winner

@MartinSleziak im not saying the history should be modified. I'm just proposing that tag synonyms should be something that nobody would have a problem with if every losing tag were (say by an approved bot account) changed to the winning tag. If you don't agree with that, perhaps the tag synonym should be reconsidered...

And when I mean having a problem I'm talking purely about the act of changing the tags. Issues with bumping 50 posts to the front page, sending many users an annoyingly high number of notifications about editing, etc. should be ignored for the purposes of that evaluation.

Sorry... I got a phone call and only finished half of what I was going to say:

regarding (2) (the quality of the synonym which maps (holomorphic-functions) to (complex-analysis), I can see an argument against this, but I come down on the side of "this is fine".

I mean, complex analysis is, essentially, the study of holomorphic functions.

ok

isn't a holomorphic function just a function that takens in a complex argument and returns a complex argument?

I cannot imagine a question which could be tagged (holomorphic-functions) but not (complex-analysis). The converse is a little trickier, but my feeling is that any question which could be tagged (complex-analysis) is ultimately going to be about holomorphic functions.

No, a holomorphic function is a function which is complex differentiable.

wouldn't that include all polynomials?

Yes, polynomials are holomorphic on $\mathbb{C}$.

so why would want to tag all questions about polynomials with complex-analysis?

as are $z \mapsto \mathrm{e}^z$ and $\sin(z)$ (for example).

@user64742 No, because not every polynomial is a function on $\mathbb{C}$.

We might only consider polynomials on $\mathbb{R}$ (these questions are usually algebra-precalculus questions), or abstract polynomial rings.

if I write $f(x) = x^2$ that's a holomorphic-function

should I not tag accordingly?

(1) A holomorphic function is a function $f : \mathbb{C} \supseteq D \to \mathbb{C}$ which is complex differentiable on its domain $D$. More generally, we could consider $D \subseteq \mathbb{C}^n$, or even $D$ a subset of some complex manifold.

However, the important point is that holomorphic functions are morphisms in a category where the objects are complex spaces.

So a function defined by the formula $f(x) = x^2$ is only holomorphic if $x$ is understood as a complex variable.

well ofc x would be a complex number

(2) Even if $f : \mathbb{C} \to \mathbb{C} : x \mapsto x^2$ is being considered, the tag complex-analysis may not be appropriate, because one may not be interested in the differential structure of that function. If that structure is not of interest, the tag is not relevant.

for starters all real numbers are complex numbers and even further all polynomials are functions of complex numbers

You know, I just explained why we can't assume that $x$ is complex without further context, and then you contradicted me by asserting that "of course it's complex!"

that is the largest set that can be validly applied to a polynomial function and all other sets are subsets of complex numbers

I disagree. Real numbers are not complex numbers. There is a canonical embedding of the real numbers into the complex numbers, but they are distinct sets.

all numbers are complex numbers

no

not all numbers are complex numbers

the $p$-adic numbers, for example, are not complex numbers

and polynomials can be defined over even more esoteric rings

ok

But, honestly, this is really not the point; if you tag something holomorphic-functions, then you are implicitly asking a question about the differential structure of that function, which means that you are asking about complex analysis.

@XanderHenderson I'm talking about the holomorphic-function tag. If you mention or include a a function that is holomorphic, you would tag as such, right? Just like any question including a polynomial should be tagged polynomial and any question including a sin should be tagged trigonometry.

@user64742 only if you care about holomorphic properties of that function

thats a very strange tag then

and no, not every question involving a sine should be tagged trigonometry, and not every question involving a polynomial should be tagged polynomials

tags should tell us what a question is about, not which objects are discussed in the question

tags are just to help searchability

anything in a question fitting a tag should warrant that tag being added

for example, a question about solving the differential equation $u'' + u = 0$ will likely involve sines and cosines, but should not be tagged trigonometry

@XanderHenderson I see...

@user64742 there is no problem. I can change all the instances of holomorphic-functions to complex-analysis without bumping or notifying anyone with a few clicks.

@quid yeah but it erases all of the history, right?

@user64742 yes.

regardless what does that have to do with my statement there...?

I'm just stating that unless it would be conceptually acceptable to completely change all the tags from one to other (ignoring any issues regarding red tape), they shouldn't be marked as synonyms.

@user64742 maybe I misunderstood you comment. I meant to point out that there is no need for a bot account etc as the features exist.

@quid it was just an example mechanism. The mechanism doesn't really matter.

the point is that I feel like changing the holomorphic function tags to complex analysis might actually be damaging to the posts and therefore making them synonyms was perhaps a bad idea.

ah

I see. so this an evaluation period.

Yes. Of course the duration of these evaluations periods vary wildly.

I feel like people need to make the equivalent of an alarm clock for that kind of stuff.

For the record, I am in favor of leaving (holomorphic-functions) as a synonym of (complex-analysis), and merging the tags. But if someone can give a convincing example of a class of questions which are about complex analysis but not holomorphic functions, I am willing to have my mind changed.

@XanderHenderson complex analysis on any function that is not continuous???

@user64742 That isn't complex analysis. As I said above, complex analysis is, essentially, the study of holomorphic functions.

@XanderHenderson complex analysis is the same as real analysis but with complex valued functions and it involves more than just studying differentiable functions.

Please look at any book on complex analysis. There is usually a very short introduction to complex variables, then an immediate leap to the definition of differentiation and integration.

What makes complex analysis an interesting and fruitful part of mathematics is the rigid structure provided by studying holomorphic functions. If you are not studying holomorphic functions, you aren't doing complex analysis.

You are, I suppose, engaged in the study of complex variables, which is more elementary.

@XanderHenderson please don't make such assumptions. I never claimed to be "engaged" in anything.