Wikipedia talk:WikiProject Mathematics/Archive/2019/May

Placing the Iterated function and Tetration pages on more solid mathematical ground

Folks, please check out my recent edits on the Iterated_function and Tetration pages as well as my comments at Talk:Tetration#Moving_towards_a_verifiable_article. Both pages suffer from liberal edits including non-attributable and nonverifiable mathematical content that have never been peer reviewed or published. I have five-year-old comments asking for people to fix their entries that have never been responded to. The content of the pages is ruled by politics, not Wikipedia policy. I would like to hear of better options than what I have offered. Thanks.

Daniel Geisler (talk) 19:04, 30 April 2019 (UTC)

Please disregard. Wikipedia is not the appropriate place for me to benefit people.

Daniel Geisler (talk) 08:10, 2 May 2019 (UTC)

Two-dimensional graph

This article is linked to in Curve (mathematics). I came to it because its title does not indicate what is the subject. The first sentence is "A two-dimensional graph is a set of points in two-dimensional space". For me, a set of points in two-dimensional space is called a plane figure. The content and the figures suggest that it what is intended by this title. The article does not contain any reference, and is tagged as such. What should be done with this article? My opinion is that it should be either deleted or redirected to graph of a function. But other advices would be useful. D.Lazard (talk) 17:00, 30 April 2019 (UTC)

It sounds both vague and non-standard. "Two-dimensional graph" could refer to a plane curve, a planar graph, a 2D plot, etc. In the absence of a uniquely good redirect, and without evidence that it is a common search term, I'd be inclined to delete it. XOR'easter (talk) 18:03, 30 April 2019 (UTC)

I second the deletion suggestion. Currently too ambiguous. — MarkH21 (talk) 18:25, 30 April 2019 (UTC)

I have prodded the article. D.Lazard (talk) 08:41, 2 May 2019 (UTC)

How about turning it into a disambig page? For me, the issue seems that the term can be ambiguous without context. -- Taku (talk) 23:53, 2 May 2019 (UTC)

Taku's suggestion done. D.Lazard (talk) 09:37, 3 May 2019 (UTC)

RD: Goro Shimura

Goro Shimura just passed away yesterday, so I have updated the article and made an RD nomination at ITN/Candidates. Comments and article improvements would be most welcome! — MarkH21 (talk) 10:45, 4 May 2019 (UTC)

Geometry of an algebraic curve

(Note there is Wikipedia:Articles for deletion/Geometry of an algebraic curve.) I have split-off some of content to separate articles (Severi variety (Hilbert scheme) and Hurwitz scheme) and merged the rest into Draft:Complete algebraic curve and its talkpage. This should solve the issue that the page looks too unfocused and for me, this seems like the most constructive steps instead of arguing about the page. I just sincerely hope we focus on the discussion and development of the content (not the history or the procedure). —- Taku (talk) 13:19, 22 April 2019 (UTC)

I never saw this article before it was deleted, so I cannot judge on what was there, but I find it alarming that some other editors seem to be ganging up on Taku and being mean to him. Taku's one of ur finest math editors, he's been here for over a decade, his work is top-notch, and I find it disturbing that some editors, who have never-ever contributed to any math articles, can just pop up and commit these kinds of drive-by vandalism-by-deletion. I don't like this, I don't like it at all. I think its deeply and fundamentally wrong. 67.198.37.16 (talk) 18:09, 4 May 2019 (UTC)

A typesetting software bug

In Nowhere-zero flow we find this code:

0&nbsp;<&nbsp;|''φ''(''e'')|&nbsp;<&nbsp;''k''

With a certain window geometry, one sees this:

0 < |

φ(e)| < k

To say the least, the line-break is in a very very bad place. But "&nbsp;" is supposed to prevent that. Michael Hardy (talk) 18:29, 5 May 2019 (UTC)

@Michael Hardy: not at all – “|” is a punctuation mark, that is, line break is allowed after it. Unfortunately, some faction of en.Wikipedians persists with the use of bare text as mathematical formulas. Such thing could be acceptable for certain special kinds of notation—such as A ∨ ¬A—but leads to misery for common mathematics. For the latter, importantly, sans-serif fonts are ill-advised. Incnis Mrsi (talk) 21:57, 5 May 2019 (UTC)

@Incnis Mrsi: What do you take to be the pros and cons of A ∨ ¬A versus ${\textstyle A\vee \lnot A}$? Michael Hardy (talk) 00:59, 6 May 2019 (UTC)

“A” and “A” and “$A$” have not much difference between each other. But, while both “ln x” and “$\ln x$” look more or less good, “ln x” is strikingly unprofessional, not only with ugly letters but overextended whitespace also. Modern students perhaps are more accommodated to illegible letters, than myself, because developers of Beamer supplied the class with sans font—by default—for some bizarre reason. Incnis Mrsi (talk) 05:54, 6 May 2019 (UTC)

Your third capital A looks a lot bigger than the other two. Michael Hardy (talk) 23:13, 6 May 2019 (UTC)

You could possibly try surronding the whole expressions in {{Nowrap}}. You will need to use {{abs}} or {{pipe}} to replace the verticle bars. Using the {{abs}} template might work without the nowrap as the remplate adds some hair-spaces which might prevent line breaking. --Salix alba (talk): 14:21, 6 May 2019 (UTC)

Alternatively to escaping the vertical bars one could use {{nowrap begin}} and {{nowrap end}} directly. – Tea2min (talk) 14:58, 6 May 2019 (UTC)

An “expert” on spinors and tensor algebra

Hi.
Wrote a wall of text on talk:Spin group #Incorrect use of “⊗” while their notation is clearly wrong. Incnis Mrsi (talk) 18:18, 3 May 2019 (UTC)

I wrote a wall of text since, apparently, you do not actually know how to construct a quotient algebra of a tensor algebra. I really do not want to get into a hostile argument over this stuff -- there are plenty of published textbooks in representation theory that explain this -- and also pretty much any text that explains how to construct the symmetric algebra or the exterior algebra or the clifford algebra, etc. out of the tensor algebra. This is quite wide-spread, and foundational for lots of math/physics applications. 67.198.37.16 (talk) 20:37, 3 May 2019 (UTC)

Whether do I know how to make quotient stuff is irrelevant. The point is that a mathematician reading allegations that e₁ ⊗ e₂ = −e₂ ⊗ e₁ is somewhere a true statement becomes confused. Should a student learn what does “⊗” mean to subsequently solve such quizzes? Incnis Mrsi (talk) 20:55, 3 May 2019 (UTC)

See talk page. It's been removed. For a long-term solution, I think a low-brow article on the construction of quotients of tensor algebras is in order; lets continue conversation at Talk:Spin group. 67.198.37.16 (talk) 18:13, 4 May 2019 (UTC)

I'm not sure about "low-brow" but we certainly lack an algebra-version of presentation of a group and presentation of a module, which should probably be called a presentation of an algebra. -- Taku (talk) 23:43, 4 May 2019 (UTC)

@TakuyaMurata: I don’t think that anything like free presentation would be helpful to explain how to construct an associative algebra (such as Clifford algebra) off tensor algebra as a quotient. My proposal is to render references to “quotient algebra” as a link to quotient ring for the time being. Writing a new article for the case grazes the domain of original research, whereas quotient algebra considers a way abstract stuff having little in common with quotient over ideals. Incnis Mrsi (talk) 16:39, 5 May 2019 (UTC)

Constructing an algebra out of generators and relations is definitely not an original research; I do agree with User 67.'s assessment that Wikipedia seems to lack an article on the subject. A separate article is appropriate just as presentation of a group is not part of quotient group. Maybe a better article title is "algebra defined by generators and relations" (and we're allowed to rename it as we like).

About quotient algebra: I don't believe "quotient algebra" in the sense in universal algebra is a primary topic and therefore the page should be redirected to quotient ring (and the current article be moved to quotient algebra (universal algebra).) -- Taku (talk) 22:59, 5 May 2019 (UTC)

A disambiguation page on “quotient algebra”, perhaps? Incnis Mrsi (talk) 05:54, 6 May 2019 (UTC)

A disambig page is fine too but I just did a Google search and very few instances of the use in universal algebra came up and that suggests a redirect is better. -- Taku (talk) 23:05, 6 May 2019 (UTC)

We do have algebra extension, which is closely related but is a still *somehow different* notion (different, in the same way, we distinguish between group presentation and group extension) -- Taku (talk) 00:46, 5 May 2019 (UTC)

Please can an expert disambiguate the incoming links to the new disambiguation page Quotient algebra? As the meanings are easily confused, I'd rather not guess. Thanks, Certes (talk) 11:25, 8 May 2019 (UTC)

 Done I have disambiguated all these links. Not surprisingly (for me), when the links was intended to quotient (universal algebra), I had generally to further edit the article for fixing some errors, such as "the kernel of a homomorphism" is a subalgebra. D.Lazard (talk) 14:40, 8 May 2019 (UTC)

RfC, of a sort

Smarandache came up at Talk:Jean-Pierre Petit2021/December#Request for comment (which came to my attention here), so it may be of interest to the community here. XOR'easter (talk) 17:57, 8 May 2019 (UTC)

"of a sort", indeed! --JBL (talk) 18:58, 8 May 2019 (UTC)

I tried to come up with a more precise description, but nothing quite did it justice.

There may also be WP:BLP issues with that article, with claims and counter-claims about academic misconduct cited to unreliable primary sources. This isn't a good week for me to put time into sorting out a mess like that, though. XOR'easter (talk) 20:44, 8 May 2019 (UTC)

Unknown Symbol

Hey, WikiProject Math,

I was reading an article and came across a mathematical symbol that looks like a fork or trident, placed on its side like an "E". Can anyone tell me what this is? I wasn't even sure where to look for an explanation and the article didn't explain what it meant. Thanks, anyone. Liz ^{Read! Talk!} 03:01, 9 May 2019 (UTC)

Never mind. I found it at Table of mathematical symbols and it has to do with set membership (although that doesn't explain the equation I read). Liz ^{Read! Talk!} 03:10, 9 May 2019 (UTC)

Either copy the symbol over here (in context) or link to the article in which it appeared and tell us the section and line number. JRSpriggs (talk) 03:14, 9 May 2019 (UTC)

Watch out for the mob of angry villagers with $\pitchfork$ s! –Deacon Vorbis (carbon • videos) 03:28, 9 May 2019 (UTC)

@Liz: Presumably this is about the symbol $\in$ (indicating that an element is a member of a set)? (As opposed to $\subseteq$, indicating that one set is contained in another, or the Greek letter $\epsilon$, sometimes rendered less trident-like as $\varepsilon$.) Often it is easy to replace that symbol in context with English words. Can you point out the article where you found it? --JBL (talk) 11:42, 9 May 2019 (UTC)

What is a curve?

See Talk:Curve#What is a curve? for a discussion that concerns several articles.

See also Talk:Plane curve#Merge with algebraic curve? and Talk:Curve#Sections on differentiable curves for recent related discussions]]. D.Lazard (talk) 15:31, 9 May 2019 (UTC)

Interior solution

Members of this project may be able to assist at WP:Redirects for discussion/Log/2019 May 9#Interior solution. Certes (talk) 21:40, 9 May 2019 (UTC)

"Ramanujan prime corollary", possible OR

A few months ago, I had a brief exchange here with Reddwarf2956 about this addition to the article Prime gap, about something Reddwarf2956 calls the Ramanujan prime corollary. In addition to not understanding how their response answers my question (and so not being clear on the mathematical validity), I am worried about original research and self-promotion: the attribution at Ramanujan prime says The Ramanujan Prime Corollary is due to John Nicholson (uncited), and Reddwarf2956 signs their talkpage posts as "John W. Nicholson". I would be grateful if another editor could take a look to determine whether this content (at both Prime gap and Ramanujan prime) is meaningful, and whether it belongs in Wikipedia. (I have not tried to assess whether similar remarks have been added elsewhere.) --JBL (talk) 12:24, 14 May 2019 (UTC)

Reddwarf2956 has responded to this post by removing the cn and clarify tags at Prime gap -- more eyes would be welcome. --JBL (talk) 14:05, 14 May 2019 (UTC)

It does look like COI. But even disregarding COI, this "Ramanujan Prime Corollary" is not something mentioned anywhere except in this paper (with John W. Nicholson as co-author, plus note the email name). I haven't found anything about it anywhere else in mathematical literature so does not really belong here unless other evidence from RS can be given. I went and removed the content from both articles. — MarkH21 (talk) 02:59, 15 May 2019 (UTC)

Ok, thanks. (Maybe at some point Reddwarf2956 will discuss this so it will be easier to tell if there's any merit to inclusion.) --JBL (talk) 11:22, 15 May 2019 (UTC)

Voronoi pole

The article Voronoi pole is in dire need of attention from an expert, preferably in computational geometry.  --Lambiam 22:06, 16 May 2019 (UTC)

In particular, the illustration in that article is an atrocity. The problem resulted only from an incorrect aspect ratio. This is obviously one of those occasions when it's important to hvae the right aspect ratio. Michael Hardy (talk) 18:41, 17 May 2019 (UTC)

It should be rescaled with the horizontal scale reduced to about 42%. Since it is an svg image, that shouldn't be particularly hard. But there are other serious issues; please have a look at the talk page.  --Lambiam 20:18, 17 May 2019 (UTC)

Nested radicals

Possibly this anonymous editor is trying to say something, but obviously what was added is unsuitable for anything to be kept in its present form. Can someone who knows what Euler did with nested radicals decipher it and possibly clean it up? Michael Hardy (talk) 17:08, 13 May 2019 (UTC)

The assertion seems to be: If a and b are integers, then there exists rational numbers x and y such that ${\sqrt {a+{\sqrt {b}}}}={\sqrt {x}}+{\sqrt {y}}$ if and only if $a^{2}-b$ is a square. This is true; a proof follows. Nevertheless, I have not verified whether Euler gave a proof (in one direction my proof could certainly be given by Euler, but in the other direction, I uses Galois theory, which was unknown by him). In any case, this result is misplaced in the section about Landau's algorithm.

Proof: If x and y exist, then the left-hand side belongs to the field F generated by ${\sqrt {x}}$ and ${\sqrt {y}},$ which is a Galois extension. It follows that the conjugate ${\sqrt {a-{\sqrt {b}}}}$ belongs to the same field, and satisfies ${\sqrt {a-{\sqrt {b}}}}=\pm {\sqrt {x}}\pm {\sqrt {y}}$, since the automorphisms of F are obtained by simply changing the signs of one or two square roots. Then ${\sqrt {a+{\sqrt {b}}}}\;{\sqrt {a-{\sqrt {b}}}}={\sqrt {a^{2}-b}}=\pm (x^{2}-y^{2}).$ This shows that $a-b^{2}$ is a square. Conversely, ${\sqrt {a+{\sqrt {b}}}}$ is a root of $(x^{2}-a)^{2}-b=x^{4}-2ax^{2}+(a^{2}-b).$ If $a^{2}-b=d^{2},$ the polynomial may be rewritten $(x^{2}+d)^{2}-2x^{2}(a+d)=\left(x^{2}+d+x{\sqrt {2(a+d)}}\right)\left(x^{2}+d-x{\sqrt {2(a+d)}}\right).$ As the discriminant of both factors is $2(a-d)$ is follows that one can take ${\tfrac {a+d}{2}}$ and ${\tfrac {a-d}{2}}$ for x and y. D.Lazard (talk) 10:46, 14 May 2019 (UTC)

In fact, the easy part was already in the article, but needed also some deciphering. I have edited the article for making a specific section for the case of two nested square roots. D.Lazard (talk) 14:05, 14 May 2019 (UTC)

The assertion above and its "proof" are both wrong. Try a=0, b=1, x=0, y=1. 157.131.141.41 (talk) 14:16, 14 May 2019 (UTC)

Should be clear from context that a and b are both nonzero. This case is trivial. Reyk _YO! 14:20, 14 May 2019 (UTC)

Try a=3, b=1, x= 2(typo: should be 4), y=0. 157.131.141.41 (talk) 14:32, 14 May 2019 (UTC)

Um, that doesn't work. You mean x=4. And stop trying to pass off trivial cases where one of the numbers is zero as a counterexample. It's clear from context those aren't being considered. Reyk _YO! 14:42, 14 May 2019 (UTC)

a=3, b=1, x=1, y=1.157.131.141.41 (talk) 14:46, 14 May 2019 (UTC)

Huh, interesting. In fact, if a+sqrt(b)=4k^2 then x=y=k^2 will do. 31, 25,9,9 for instance. Or I wonder if there are counterexamples with irrational left and right hand sides. Reyk _YO! 15:26, 14 May 2019 (UTC)

It is implicit in D.Lazard’s argument that b is not a rational square (so that we really are dealing with a nested radical). —JBL (talk) 15:32, 14 May 2019 (UTC)

Euler argues (§672) that $x+y+2{\sqrt {xy}}=5+2{\sqrt {6}}\implies x+y=5$ and $2{\sqrt {xy}}=2{\sqrt {6}}$, because the rational parts must be equal and so must the irrational parts. This could probably be made rigorous but its later application relies on ${\sqrt {b}}$ to make the final terms irrational, which (as Reyk just said) fails when b is a square. Certes (talk) 16:05, 14 May 2019 (UTC)

@D.Lazard: I believe the proof is incorrect. We have that $a=7,b=2,c=6,x=6,y=1$ is a solution to ${\sqrt {a+b{\sqrt {c}}}}={\sqrt {x}}+{\sqrt {y}}$, but $5={\sqrt {a^{2}-b^{2}c}}\neq x^{2}-y^{2}=35$. Perhaps we could use an elementary proof: Assuming $c$ is not square, then $a+b{\sqrt {c}}=x+y\pm 2{\sqrt {xy}}$ implies that $a=x+y$ and $b^{2}c=4xy$, so $a^{2}-b^{2}c=(x-y)^{2}$. Pbroks13 (talk) 15:38, 17 May 2019 (UTC)

You are right, I'll fix the proof in the article. D.Lazard (talk) 16:17, 17 May 2019 (UTC)

Fixed and sourced to Euler. D.Lazard (talk) 17:17, 17 May 2019 (UTC)

I have completely rewritten the proof: no need of separate proofs for the "if" and the "only if" implications. This follows Euler's argument, although, for a rigorous proof I need some field theory, namely that 1 and ${\sqrt {c}}$ boom a basis of the $\mathbb {Q}$-vector space $\mathbb {Q} ({\sqrt {c}}).$ D.Lazard (talk) 12:24, 18 May 2019 (UTC)

Absolute number

The redirect Absolute number, which currently targets Absolute value, has been nominated for deletion at RFD. You are invited to join the discussion at Wikipedia:Redirects for discussion/Log/2019 May 19#Absolute number. Thryduulf (talk) 11:20, 19 May 2019 (UTC)

A possible Science/STEM User Group

There's a discussion about a possible User Group for STEM over at Meta:Talk:STEM_Wiki_User_Group. The idea would be to help coordinate, collaborate and network cross-subject, cross-wiki and cross-language to share experience and resources that may be valuable to the relevant wikiprojects. Current discussion includes preferred scope and structure. T.Shafee(Evo&Evo)^talk 02:55, 26 May 2019 (UTC)

Nomination of Portal:Number theory for deletion

A discussion is taking place as to whether Portal:Number theory is suitable for inclusion in Wikipedia according to Wikipedia's policies and guidelines or whether it should be deleted.

The page will be discussed at Wikipedia:Miscellany for deletion/Portal:Number theory until a consensus is reached, and anyone is welcome to contribute to the discussion. The nomination will explain the policies and guidelines which are of concern. The discussion focuses on high-quality evidence and our policies and guidelines.

Users may edit the page during the discussion, including to improve the page to address concerns raised in the discussion. However, do not remove the deletion notice from the top of the page. North America¹⁰⁰⁰ 21:11, 26 May 2019 (UTC)

Category problem

I was looking at a draft article with the {{Maths banner}} on it. I clicked on the Drafts link and was sent to Category:Draft-Class mathematics articles, which to my surprise was empty. I dug around and found the article at Category:Draft-Class mathematics pages. Is there a way that the banner can be changed? The "articles" category appears to be the standard page (for {{category class}} as well) but for some reason it gets sent to the "pages" category.--Auric talk 16:08, 26 May 2019 (UTC)

@Auric: I was excited to see a post about categories, but then became sad when I realized it was about categories. But seriously, I don't see why that would be a problem; I'm unsure what's actually going on from a technical standpoint. I can try to take a look around if you want, but I'm not really an expert with this stuff. –Deacon Vorbis (carbon • videos) 16:41, 26 May 2019 (UTC)

This sounds like a simple matter of changing |ASSESSMENT_CAT = mathematics pages to |ASSESSMENT_CAT = mathematics articles in {{Maths banner}} but I'm not sure what else that might affect. The only other page that would obviously need editing is WP:WikiProject Mathematics/List of math draft pages. Certes (talk) 16:59, 26 May 2019 (UTC)

Thanks. I don't know how I missed that.--Auric talk 22:16, 27 May 2019 (UTC)

An edit to Gamma function

I am suspicious of this edit. I cleaned up the formatting and added a "citation needed" tag. The editor is User:Lewisbrito; the alleged fact added is attributed to "Hamilton Brito", and Google finds this page belonging to "Hamilton Brito (Lewis)". Is this "OR"? And is the mathematics correct? (I haven't yet even reached the point of looking closely at what it says yet.) Michael Hardy (talk) 18:40, 28 May 2019 (UTC)

• I played around a bit with this on Wofram Alpha and as far as I can tell it is correct. I can't find a source for it though and, even though it's a pretty result, I'm not sure how important it is. Reyk _YO! 19:11, 28 May 2019 (UTC)

COI edit request 29-MAY-2019

There is currently an edit request from an editor with a conflict of interest pending in the Gray code article which requires a math background, in particular, a knowledge of the reflected binary code used in that numeral system. Any editors who might be able to review this request would be most appreciated.  Spintendo  01:04, 30 May 2019 (UTC)