7:17 AM
In the comments under my proposal in the tag management thread, @AlexanderGruber has suggested (in my view) a better way to resolve the issues with tagging questions about the gradient, namely, creating a [tag:grad-curl-div] tag that would subsume the intended scope of the [tag:gradient] tag and (presumably) would have [tag:gradient], [tag:curl], and [tag:divergence] tags as synonyms. My edit includes proposed a tag-excerpt and tag-wiki, and lists some advantages of implementing this proposal:
4

Proposal: Add the tag grad-curl-div; make gradient, curl and div aliases thereof. Edit 2: I've revised the proposal statement to Alexander Gruber's (in my view superior) suggestion in the comments. Implementing this proposal poses some advantages over the status quo: It would (productively) fr...

8:04 AM
You're right that divergence and curl have no business existing if gradient doesn't, but because they are so related pedagogically, my instinct is more to wrap them up into one tag than to emancipate gradient. Probably vector-analysis is not quite right, but how would y'all feel about something like div-grad-curl? — Alexander Gruber ♦ 1 hour ago
@AlexanderGruber and @TravisWillse It seems that this particular proposal has changed a few times.
1. Creating .
2. Removing synonym and leaving as a separate tag.
3. Creating .
There is no reasonable way of distingushing whether the upvotes count for the most recent suggestion or the upvoter agreed with the previous one but wouldn't agree with the new one.
I wonder what would be the best way to resolve this.

Probably: The alternative would be adding another question to the tag management thread, but it's potentially confusing to have two related but mutually exclusive suggestions in the thread, and deleting the old suggestion would discard/obscure some useful discussion.

I am aware that some users will almost immediately suggest closing that question as a duplicate of the tag management thread - so the question should explicitly explain that several options have been discussed in the answer from that thread and it is difficult to discuss various suggestions just in comments under the answer.
Although with a separate question would probably gain more attention than the answer in the long thread.

I'm happy to write up a separate question in meta about the new proposal, but if @AlexanderGruber prefers to propose the new tag himself (after all, the current iteration of the suggestion was his), I'm happy to defer to him.

Of course, if the moderators think that it is completely obvious that is the best option and they say that we should go with this, then it's not needed to discuss this further.

I would be content with that outcome, except that I strongly recommend that the tag list the operator names in the canonical order: .

8:13 AM
But the comment from Alexander Gruber seems more in the spirit "here is a suggestion, what do you think" than "I think this is better, I'm going to create the synonyms soon".

Right, I agree.

As a side not, I will point out that some thing (formatting, hyperlinks) don't work well in multiline messages: Markdown in Chat fails for Multi-Line Messages, a Reprise and Markdown in chat fails for multi-line messages.
That is the reason why [tag:tagname] syntax is not rendered in your previous message: chat.stackexchange.com/transcript/message/52799505#52799505

Will writing @{username} flag the user's attention if they haven't said anything in this chat room? More to the point, should I ask Alexander in the comments under the post in the tag management thread whether he'd prefer to write up a (separate) proposal himself or have someone else (me, or someone else if they wish) do it?
That's strange---it does render for me, albeit awkwardly: i.imgur.com/F9K3LKo.png

@TravisWillse The message in your screenshot renders for me just fine. I meant this message: chat.stackexchange.com/transcript/message/52799505#52799505

Ah, I see, thank you (yet again) for the information.

8:23 AM
Short answer is that the names which are offered in the autocomplete are users who can be pinged using @username. Alexander Gruber probably wasn't in this room for some time - so he isn't pingable in this way. But using direct reply to one of this older messages (as I did above) should give him notification.

Right, I see, and thank you.

1 hour later…
9:30 AM
A new tag was created by URL. There exists a tag called .
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The coefficient of similarity between two circles $C$ and $C’$ of radii $r$ and $r’$ is $$\frac{r}{r’}=\frac {k}{k_n},$$ where $k$ is the radius of inversion and $k_n$ is the square of the length of a tangent to $C’$. Why is this the case? I spent a lot of time trying to show it geometricall...

In geometry, inversive geometry is the study of those properties of figures that are preserved by a generalization of a type of transformation of the Euclidean plane, called inversion. These transformations preserve angles and map generalized circles into generalized circles, where a generalized circle means either a circle or a line (loosely speaking, a circle with infinite radius). Many difficult problems in geometry become much more tractable when an inversion is applied. The concept of inversion can be generalized to higher-dimensional spaces. == Circle inversion == === Inverse of a point... ===
A new tag was created by Trevor.
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Typically, Wilson's is given as $$(n-1)! \equiv -1 \pmod{n},$$ which is short and sweet, but I came up with an alternate presentation of it that's arguably needlessly complicated, but also arguably illustrative: $$\prod_{i=1}^{n}i \equiv \sum_{i=1}^{n}{1} \pmod{\sum_{i=1}^{n}{i}}.$$ This show...

In number theory, Wilson's theorem states that a natural number n > 1 is a prime number if and only if the product of all the positive integers less than n is one less than a multiple of n. That is (using the notations of modular arithmetic), the factorial ( n − 1 ) ! = 1 × 2 × 3 × ⋯ × ( n − 1 ) {\displaystyle (n-1)!=1\times 2\times 3\times \cdots \times (n-1)} satisfies (...
The tag Wilson's theorem has been created before: chat.stackexchange.com/transcript/3740/2019/8/21 There are two deleted posts with this tag: Proof of Wilson's theorem. and Proving no solutions to a Diophantine equation
(The results are currently empty - but unless that post gets deleted, it should appear there after the next update of the data in SEDE.)

1 hour later…
10:38 AM
Quasiperiodicity is the property of a system that displays irregular periodicity. Periodic behavior is defined as recurring at regular intervals, such as "every 24 hours". Quasiperiodic behavior is a pattern of recurrence with a component of unpredictability that does not lend itself to precise measurement. It is different from the mathematical concept of an almost periodic function, which has increasing regularity over multiple periods. The mathematical definition of quasiperiodic function is a completely different concept; the two should not be confused. == Climatology == In climatol...
1

According to the Scholarpedia defintion: a function $F$ of real variable $t$ such that $F(t) = f(\omega_1t,\cdots, \omega_m t)$ for some continuous function $f(\phi_1,\cdots,\phi_m)$ of $m$ variables $(m≥2)$, periodic on $\phi_1,\cdots,\phi_m$ with the period $2\pi$, and some set of posi...

3

Recently, I was investigating the following equation: $$p\pi = qe, p,q \in \Bbb{N}$$ I then plot the sets $\{p\pi\}$ in black,$\{qe\}$ in yellow and obtained the following plot: which apparently it has some kind of fringes that looks evenly spaced, suggesting some kind of periodicity. To inves...

4

Has anyone produced a quasiperiodic tiling of the hyperbolic plane? Or is there a reason it cannot be done? By quasiperiodic I mean that the structure is not strictly periodic (i.e. equal to itsef after translation) but that any arbitrary large neighbourhood of any point can be found identicall...

8

Sums of trigonometric functions may or may not be periodic functions; in particular, $\sin(ax)+\sin(bx)$ is periodic if $a/b$ is rational. If we consider the function $$f(x) = \sin(3x) + \sin(\pi x)$$ it surely looks periodic, even if it's not; to me it feels like the...

1

Define $$f(x)=\frac{\cos^2(\pi x)}{2+\cos(x)}$$ We know that $f(x)$ is not periodic. Is there any way to write $f(x)$ as the sum of two periodic functions. That is, find periodic functions $f_1(x)$ and $f_2(x)$ such that $f(x)=f_1(x)+f_2(x)$.

2

I am doing some work regarding quasiperiodic functions but I am not able to figure out the difference between almost periodic and quasiperiodic functions. Can anyone let me know about it?

0

I posted a question in such a garbled form that I thought I should repost separately. I have deleted the other post just to remove it from consideration. Apologies for that. I am playing with a complicated quasi-periodic equation, $f(x)$, which boils down to a summation of sines and cosines. I c...

Of course, since at the moment there are only a few questions in this newly created tag, this could be done manually simply by removing (quasiperdiodic-functions) and adding (quasiperiodicity) to those posts. (In that way you would bump the seven posts which have that tag at the moment - which is not that terrible.) — Martin Sleziak 1 min ago

5 hours later…
4:06 PM
@TravisWillse that's interesting, I always hear div grad curl (example)
is it regional?
I googled for "div grad curl" and "grad curl div" to see if there was a strong preference between the two and ended up seeing a mix of just about every permutation of the three

4:21 PM
If we did div-curl-grad then we could just name the tag 0

@AlexanderGruber What do you think about the issue discussed above.
Should there be a new post about the tag? (Since from the current one it's unclear which version of the post got the upvotes.)
Or is it enough if you discuss this with other moderators and the mods decide what should be done with the tag?

My view is we're pretty much ready to implement the change, I don't think a meta post is necessary, but if someone writes one I'll wait for the upvotes before making the synonyms.
Though if someone would like to write one in order to recruit people to help move over grad questions from vector-analysis, I've no problem with that
(I'm busy though-- definitely no problems with @TravisWillse writing stuff instead)

Well, if you think that additional post is unnecessary, it is all now up to the moderators, who can create the synonyms.

I'll wait a day or so to finalize in case of any unforseen objections or input on word order

2 hours later…
6:08 PM
in CRUDE, 2 hours ago, by Alexander Gruber
@BillDubuque can I get your opinion on info / usage guidelines on this tag? (context is resolving this discussion)
in CRUDE, 1 hour ago, by Bill Dubuque
@AlexanderGruber I just perused current usage and the current scheme seems to be working fine, i.e. gcd & lcm merged into gcd-and-lcm, separate from divisibility. What sparks the query, is there some impending action?
in CRUDE, 1 hour ago, by Alexander Gruber
@BillDubuque I just changed the tag info to discuss usage instead of some wikipedia excerpt that was there before. Just making sure there's nothing crucial that should be added since I don't really post in the tag.
7

Resolved (mostly) Creation of a tag gcd-and-lcm. Merge of the GCD part, not yet merged the LCM part, in case some objection emerges. The tag wiki might need some (more) attention. Proposal: merge gcd and lcm We tend to combine homologus objects into one tag, like supremum-and-infimum, limsup...

1 hour later…
7:09 PM
@AlexanderGruber I don't know whether there's any regional variation, though the book you cited might explain some of the use of div-grad-curl, at least in the U.S. But by canonical I really mean mathematically canonical, not just a predominant convention. On, e.g., an open subset U of R^3, the exterior derivative d defines maps

{0-forms on U} -> {1-forms on U} -> {2-forms on U} -> {3 forms on U}

Using the usual inner product (and orientation) on R^3 lets us regard this as a sequence of maps
(And the exterior derivative identity d^2 = 0 then specializes to the composition identities curl o grad = 0 and div o curl = 0.)