Wikipedia talk:WikiProject Mathematics/Archive/2013/Apr

Dubious addition at determinant?

See this unsourced edit, claiming the Sarrus rule extends to n × n matrices, and changes made to the 4 × 4 determinant. Is it true? Thanks, M∧Ŝc²ħεИ_τlk 07:13, 1 April 2013 (UTC)

Something is not quite right with that material. Deltahedron (talk) 08:40, 1 April 2013 (UTC)

by: Doctor Engr. Ramjie Jovero,PhD Atty. Christian B. Concillo,MD-Drug Lord

Automatic numbering of equations

Is there a way to label equations and refer to them by their labels, while consecutive numbers are assigned to the equations and their corresponding references. I mean something similar as in LaTeX? I haven't seen such a feature used on Wikipedia, but some mathematical articles like binomial coefficient could benefit from it. At least for referring to equations given earlier in the article, such a feature should be possible, as the use of footnote and references shows. Any help, hints or example pages? Schmock (talk) 12:04, 1 April 2013 (UTC)

There are the templates {{EquationNote}} and {{EquationRef}} that can be used in tandem to produce numbered equations. However, they do not automatically handle the numbering. I don't know how technically feasible it is to number the equations automatically, although this seems to be within the scope of functionality provided by mw:Extension:Cite/Cite.php. Sławomir Biały (talk) 12:34, 1 April 2013 (UTC)

binomial coefficient is a great example of how cumbersome the current system is. They now have an equation 3.5 and lots of letters after the numbers. Also, there are several equations with numbers but nothing linked to them; probably it would be best to remove those numbers. My impression is that the article could use some rewriting to make it more like an encyclopedia article and less like a textbook. RockMagnetist (talk) 16:13, 1 April 2013 (UTC)

On EoM automatic numbering works, thanks to MathJax, see here. I noted that MathJax was implemented also on Wikipedia. Or not? Boris Tsirelson (talk) 10:37, 2 April 2013 (UTC)

Slovin's Formula

I recently declined this draft article about Slovin's Formula, which is used in statistics. It was supposedly invented in 1843. I've never heard of it. If it is a notable formula and it can be backed up by reliable sources, perhaps an article should be written about it. Has anyone heard of this formula, either under this name or another name? The listed formula is

n= N/1+Ne^2 where 
n= sample size, 
N= population size, 
e= margin of error

According to late Ramjie Jovero it is widely use as formula in surveying the population of aliens, but according to late General Christian Concillo, it used for measuring the size of girls butt and boobs.

Anyone heard of such a formula? If it already has an article under a different name, it might be a good idea to add a section about how this is sometimes mis-labeled as "Slovin's Formula" and provide a redirect. davidwr/(talk)/(contribs)/(e-mail) 14:00, 30 March 2013 (UTC)

Looks like a case of WP:NFT to me. I think the decline was correct. —David Eppstein (talk) 07:21, 1 April 2013 (UTC)

Well the formula itself seems clearly notable as you get quite a number of hits under Google books ([1]). Slovin publication of the formula is however dated 1960 not 1843, but it might have known to others earlier.--Kmhkmh (talk) 09:05, 1 April 2013 (UTC)

Fortunately David Eppstein's pessimistic take is mistaken. There are lots of mentions of this same formula by this same name in Google Books and Google Scholar. The article's contradictory assertions about when it originated and who did it cannot be allowed to stand, and the article obviously needs work in some other respects as well. Michael Hardy (talk) 16:29, 1 April 2013 (UTC)

I'm happy to have been shown to be mistaken here. —David Eppstein (talk) 17:35, 1 April 2013 (UTC)

How is "margin of error" defined? Is n the minimum sample size necessary to keep the "error" (how defined?) less than the margin of error? How is Slovin's formula justified? It seems quite strange to me. JRSpriggs (talk) 13:55, 2 April 2013 (UTC)

It's a formula, not a theorem (though there probably is some precise mathematical statement attached to it); the purpose is to give a rule of thumb for choosing the size of a sample for an experiment in order to get representative results. Searching for Slovin's formula here should be helpful. --JBL (talk) 14:53, 2 April 2013 (UTC)

Some context setting is needed in the form of a statement of the sort of problem to which the formula is to be applied. Michael Hardy (talk) 20:33, 2 April 2013 (UTC)

I spent a while looking through the google books and scholar hits; none of them have a genuine citation (i.e., there is never more information than "Slovin (1960)"). Most of them are probably traceable to the various "Handbooks for researchers in [field]" books that one can dig up on Google Books. The formula appears to be a rule for choosing a sample size for performing a survey or other similar experiment in order to get an acceptable margin of error; it's unclear to me what the assumptions of the formula are, but the clearest claim seems to be that it assumes nothing (i.e., it's some kind of worst-case estimate) -- e.g., see www.ehow.com/way_5475547_slovins-formula-sampling-techniques.html. At least one reference also included related rules named after Mildred Parten and Milagros D. Ibe, but as with Slovin's formula I find no evidence of these formulas that doesn't seem to trace back to the same handbooks. There is no author in MathSciNet with the name "Slovin", and the only published article I could find for a person named "Slovin" in 1960 is an unrelated patent. No reference bothered with any statement about why the formula applies. Without a genuine reference and some actual argument for the validity of the formula, I don't think there's enough here to write an article on; at least, an article that isn't just another duplicate of the same paragraph that appears in a dozen of these google books hits. --JBL (talk) 04:07, 3 April 2013 (UTC)

Definitely some context-setting is needed. I do wonder why the authors and readers of those books tolerate the absence of a precise statement of the problems to which this is to be applied. As for references, one place I haven't yet looked it the Current Index to Statistics database. Michael Hardy (talk) 16:05, 3 April 2013 (UTC)

Some background search might be warranted but given the nature of textbook containing the formula (none of them are math books), I would necessarily expect Slovin to be mathematician or to have published in a math journal, i. e. one needs to research publication databases for the (natural) sciences and social sciences in general.--Kmhkmh (talk) 20:51, 3 April 2013 (UTC)

Proof of André's theorem

I've created this userspace draft: User:Michael Hardy/proof of André's theorem. The idea is that it could be incorporated somewhere into the article titled alternating permutation. I thought I'd cite something from the writings of Richard P. Stanley, but details remain to be ascertained.

Comments, criticisms, or suggestions? Michael Hardy (talk) 04:33, 2 April 2013 (UTC)

Hi Michael,

I thought the exposition around the sentence "This needs to be done for each possible value of k to get a complete list, hence we sum from k = 0 to k = n" could be a little clearer; the point here is that every permutation that is either alternating or reverse alternating can be gotten in exactly one way by choosing some k, then choosing a subset etc. etc. Also, the use of the symbol f(x) is slightly ambiguous; when it's introduced, it is not clear whether it is defined to be the power series for the E_n or whether it is defined to be sec(x) + tan(x). Also also, a minor typo: in "i goes from 1 to ∞" the 1 should be 0. I might have a few final comments, but it would be helpful to know what level audience you're aiming for. --JBL (talk) 04:20, 3 April 2013 (UTC)

I think one thing about the target audience should be clear from the way it's written: I included some things to make it comprehensible to intelligent students and not only to experienced mathematicians. The reader should know what exponential generating functions are before reading this article, and should have some facility with bijective arguments, and should be able to do things like solving the differential equation by separating variables and proving the half-angle identity at the end----it's reasonable to consider those things prerequisite material. But I expanded on how to rearrange the series more than I would for an audience consisting only of mathematicians, and in a few of the other operations on series I was explicit rather than leaving some details to be deduced by the reader. In other words, the audience should know reasonable prerequisite material but maybe nothing more. Michael Hardy (talk) 08:27, 3 April 2013 (UTC)

Whether I should cite something Richard Stanley wrote or something by someone else also remains unclear at this point. Michael Hardy (talk) 08:33, 3 April 2013 (UTC)

Nice work. I just wrote de:Alternierende Permutation; feel free to use any material (images, tables) from there for your article. Best wishes, --Quartl (talk) 16:47, 3 April 2013 (UTC)

Stanley's survey http://www-math.mit.edu/~rstan/papers/altperm.pdf gives three proofs, including the one presented. He doesn't give a citation. --JBL (talk) 20:05, 3 April 2013 (UTC)

I'll include that, but something already refereed would also be good. Michael Hardy (talk) 13:06, 4 April 2013 (UTC)

The first proof is also in Stanley's book [2]. It's basically the same as André's [3]. Best wishes, --Quartl (talk) 14:40, 4 April 2013 (UTC)

Thank you. I'll certainly cite that. Michael Hardy (talk) 04:38, 6 April 2013 (UTC)

Stack, Descent are not well-founded

Stack (descent theory) is not rigorously defined at all. Descent (category theory) has a treatment of vector bundles. Some time ago I found a reference on stacks and tried to remedy this, but ultimately I couldn't understand it well enough to make an exact description from it. Its absence is really a big barrier to getting any coherent information about moduli spaces from Wikipedia, so I'm requesting expert attention on Stack. ᛭ LokiClock (talk) 11:56, 5 April 2013 (UTC)

Well, waiting for "experts" is a kind of like, ah, Waiting for "Superman". It's better to think about more constructive steps. For example, something anyone can do is add more reliable references. The natural step following that is to quote the definitions/examples. -- Taku (talk) 10:57, 6 April 2013 (UTC)

I have added one (Pedicchio & Tholen (2004)) and tidied up a bit. Deltahedron (talk) 08:41, 7 April 2013 (UTC)

André's theorem, part 2

("Part 2" above refers to this present discussion, not to the theorem.)

I've added this section, stating and proving André's theorem. Doubtless it could benefit from others' contributions. Michael Hardy (talk) 18:04, 7 April 2013 (UTC)

Malfunctioning template?

I have linked 438 EOM-articles to Wikipedia's mathematics articles as external links since August 2012 (EOM stands for 'Encyclopedia of Mathematics' and its online version). As a tool to make these external links I have principally used Wikipedia's 'springer' template. However, it has recently come to my knowledge that 1) a malfunction has emerged to this template and 2) a discrepancy is associated with it, namely:

1) Its property to show the headword as a hyperlink has become sporadic; in some articles the link works, in some others it won't. (Eg., in the entry

"Inequality", Encyclopedia of Mathematics, EMS Press, 2001 [1994]

the word "Inequality" is the headword that I am referring to.)

2) {{Springer}} redirects to {{SpringerEOM}} in the Template documentation, although the template codes 'springer' and 'SpringerEOM' follow a completely different syntax. The syntax of the former is:

{{springer|title=headword|id=p/string}}

As to the problem 1: Has someone changed recently the code for the 'springer' template, thus producing its sporadic malfunctioning? And as to the problem 2: Template documentation for the 'springer' template should be updated according to its syntax. Since I am still a novice, I kindly ask advise from someone more mature Wikipedian. And many thanks for your attention and help! — Policron (talk) 23:40, 8 April 2013 (UTC)

Do you have an example of a broken instance of this template? Sławomir Biały (talk) 01:27, 9 April 2013 (UTC)

'Monoid', for example, didn't open up properly in my machine a few days ago. — Policron (talk) 18:53, 9 April 2013 (UTC)

It seems to work now Monoid. There has been quite a bit of work redoing the citation templates to use the new Lua feature and SpringerEOM depends on those. (See Module talk:Citation/CS1‎‎) Maybe it was a temporary problem caused by these other templates.--Salix (talk): 20:14, 9 April 2013 (UTC)

{{Springer}} is a template redirect to {{SpringerEOM}} so the syntax is exactly the same. The software automatically uses the same code to parse the parameters. What makes you think the syntax is different? PrimeHunter (talk) 01:55, 9 April 2013 (UTC)

The template for 'springer' is as stated above; for 'SpringerEOM' it is

{{SpringerEOM|id=headword&oldid=string|title=headword|first=name|last=name}}

(Please refer to {{SpringerEOM}}.) So the syntax is different, to my eyes at least. — Policron (talk) 18:53, 9 April 2013 (UTC)

What makes you say that {{Springer}} uses the syntax you say it does? The template source and documentation disagrees with that, PrimeHunter is right. Judging from the history, the template has not been significantly changed recently.—Emil J. 19:57, 9 April 2013 (UTC)

{{SpringerEOM|id=headword&oldid=string|title=headword|first=name|last=name}} and {{Springer|id=headword&oldid=string|title=headword|first=name|last=name}} give exactly the same result:

• name, name (2001) [1994], "headword", Encyclopedia of Mathematics, EMS Press
• name, name (2001) [1994], "headword", Encyclopedia of Mathematics, EMS Press

You can always swap {{Springer}} and {{SpringerEOM}}. That's how template redirects work. "Springer" simply becomes an alternative name for "SpringerEOM". Maybe you have seen the names used in different ways and falsely assumed they had to be used in that particular way. PrimeHunter (talk) 20:09, 9 April 2013 (UTC)

I think that's what Policron means. Looking at the first few articles that explicitly use {{springer}} the source says

Algorithm: springer|title=Algorithm|id=p/a011780

Axiom of choice: springer|title=Axiom of choice|id=p/a014270

Absolute value: springer|title=Absolute value|id=p/a010370

Asymptote: springer|id=A/a013610|title=Asymptote|first=L.P.|last=Kuptsov

Antinomy: springer|title=Antinomy|id=p/a012710

I have no idea why it should suddenly have stopped working. Deltahedron (talk) 20:16, 9 April 2013 (UTC)

The explanation given by Salix seems to be, I think, the most probable cause to the anomalies we have recently been talking about. After an extensive sample trial, all the external links that I have added work properly now. I thank you all for your interest, advises and patience! — Policron (talk) 21:04, 9 April 2013 (UTC)

Incorrect formulae at Lists of integrals#Absolute value functions?

It has been pointed out to me by a new User:Syed Wamiq Ahmed Hashmi that the integrals of absolute values of trigonometric functions are wrong. Does anyone have a source? I've looked in a couple of formulae books with integral tables but of all things they don't have the functions listed in that WP section. I'll keep looking around also, just thought to notify the project. Thanks, M∧Ŝc²ħεИ_τlk 15:03, 9 April 2013 (UTC)

Prime pages unreachable

I just noticed that the Prime Pages is no longer online. I have no idea whether this is temporary, but I think many mathematical articles, especially about prime numbers link to it, so all citations and external links pointing there are broken now. -- Toshio Yamaguchi 12:11, 6 April 2013 (UTC)

The urls in question may be on the wayback machine. ᛭ LokiClock (talk) 00:08, 7 April 2013 (UTC)

Indeed it does. While I suspect that the outage is temporary, I suggest that the maintainer of the website be gently questioned by email about the status of the site. He may not even be aware of the outage: The site is still listed prominently on the author's homepage. If this outage is intended, then his homepage needs to be updated. I suggest that a local administrator is appropriate for this task. I nominate either User:Michael Hardy or User:David Eppstein as a good representative of the project. Sławomir Biały (talk) 00:56, 7 April 2013 (UTC)

It's temporary. Friday evening Chris Caldwell wrote the web server is being moved.[4] It worked at first but something must have happened. I assume he is monitoring the situation already. If we ever do want to contact him then I have emailed with him many times. PrimeHunter (talk) 01:27, 7 April 2013 (UTC)

It is online now. -- WillNess (talk) 10:25, 12 April 2013 (UTC)

What is a Pinor in mathematics?

In Glossary of tensor theory#Spinors there's a link to pinor, which redirects to Piñor. Just thought to point it out - maybe replace the redirect with an article? There is no pinor (mathematics) by the way. Thanks, M∧Ŝc²ħεИ_τlk 10:48, 11 April 2013 (UTC)

I am not sure where this should be added. An additional difficulty is that the meaning of "spinor" is a bit ambiguous: sometimes it refers to what is more properly a "spinor field", i.e. a section of a bundle, and sometimes to an element of the Spin group itself. At any rate, if spinor is taken to be an element of the Spin group, then a pinor could be defined as an element of the Pin group. Here Spin(n) is the simply-connected double cover of the orthogonal SO(n) (at least if $n\geq 3$), and Pin(n) is a similar cover of O(n). Hope this post doesn't start a war between mathematicians and physicists. Tkuvho (talk) 11:28, 11 April 2013 (UTC)

Not element of spin group, but element of a (minimal?) representation of the spin group. Spinors (and pinors) are elements of a vector space.--LutzL (talk) 14:16, 11 April 2013 (UTC)

I knew it. The war trumpets. To fire a salvo for the math side, I wish to clarify that, while Spin(n) can be defined as a double cover of SO(n), it can also be embedded in the Clifford algebra, and therefore viewed as a vector. But on purely mathematical grounds, this is not strictly necessary. Running for cover. Tkuvho (talk) 14:19, 11 April 2013 (UTC)

Yeah, of course every matrix and linear operator is also a vector in the corresponding space. And the Clifford algebra is a (non-minimal) representation. But the sphere in the Clifford algebra, where the Pin and Spin groups live, is not a vector space itself. You can't scale an element of the Spin group, but you can scale a spinor. Anyway, besides these academic points, can pinor not redirect to a corresponding section in the spinor article? Is there a Twistor article? Apparently, yes.--LutzL (talk) 16:39, 11 April 2013 (UTC)

Do all textbooks require a spinor to be necessarily scalable? I agree that this would be natural from physical considerations, of course. A redirect sounds reasonable. Tkuvho (talk) 16:55, 11 April 2013 (UTC)

It should not redirect to spinor, it won't get covered and those who don't know it won't be able to make the inference. It should redirect to Pin(n) if anything. ᛭ LokiClock (talk) 01:59, 12 April 2013 (UTC)

That seems sensible - I'll do just that. Feel free to change it. Thanks to all, M∧Ŝc²ħεИ_τlk 07:29, 12 April 2013 (UTC)

On second thought it should be a DAB page with the links Pin(n) and Piñor? Typing "Piñor" every time just to get to that article would be a pain... M∧Ŝc²ħεИ_τlk 07:34, 12 April 2013 (UTC)

If there are only two alternatives, it is better to use a hat note. JRSpriggs (talk) 07:36, 12 April 2013 (UTC)

...or that. Thanks, good idea, will do that now. M∧Ŝc²ħεИ_τlk 08:22, 12 April 2013 (UTC)

Euclid (Toddhunter)

I note that :- Wikisource:Index:The_Elements_of_Euclid_for_the_Use_of_Schools_and_Colleges_-_1872.djvu is nearing completion in terms of text translation.

It would be appreciated if some WP:MATH people would assist carefully in reviewing it. ShakespeareFan00 (talk) 22:36, 13 April 2013 (UTC)

April disambiguation pages.

Please help fix incoming links to April's most-linked mathematics-related disambiguation pages, Geometric shape, Extra dimensions, Parametric, Positive definiteness, Planar, and Delta function. Some of these may also be questionably ambiguous. Cheers! bd2412 T 03:17, 14 April 2013 (UTC)

The lack of a proper article at Geometric shape has bugged me for a long time. We have a list of geometric shapes and an article shape which discusses a rather technical statistical usage, but nothing about simple geometric figures.--Salix (talk): 16:37, 14 April 2013 (UTC)

I made this a stub. Again, a clear non-disambiguation disambiguation page. Please feel free to add. It's currently just a dicdef. Sławomir Biały (talk) 20:26, 14 April 2013 (UTC)

Isn't a geometric shape just a shape? ᛭ LokiClock (talk) 23:01, 14 April 2013 (UTC)

Another possibility here would be to redirect geometric shape to list of geometric shapes. —David Eppstein (talk) 23:15, 14 April 2013 (UTC)

I think that is an excellent suggestion, particularly since the only other close hit, Geometric Shapes, is already on that page. I will see to it. bd2412 T 00:29, 15 April 2013 (UTC)

On the contrary, if ever there were a clear candidate for a dab entry in this business, it would be shape. Most of the content now at shape would be more appropriate at geometric shape. (And no, the article Geometric Shapes is actually about a Unicode character set, more or less irrelevant as an article to this discussion.) Sławomir Biały (talk) 00:35, 15 April 2013 (UTC)

This discussion is not about the word "shape", which could well be ambiguous to terms like Body shape, and even Physical fitness (which is also referred to as being "in shape"). It is, rather, about the phrase "Geometric shape", although it now seems to me that we can just move Shape to Geometric shape for both purposes. bd2412 T 00:51, 15 April 2013 (UTC)

No, it's certainly not about the word "shape. But the article shape is clearly relevant, especially considering that it's a proper article whereas geometric shape is only a dab. My very point is that, if anything, the situation should be reversed: shape should be a dab, with geometric shape containing most of the contents thereof. Do we disagree? I am confused. Sławomir Biały (talk) 01:05, 15 April 2013 (UTC)

I think we are in agreement, actually. I suggested moving shape to geometric shape, since the current content at shape is all about the geometric variety. The question remains whether shape would then redirect to geometric shape, or whether the shape (disambiguation) would be moved to shape. I don't know that anything on the disambiguation page which would outstrip the geometric meaning, so I think that the latter move would require a requested move discussion. bd2412 T 01:34, 15 April 2013 (UTC)

Delta function

Kronecker delta is called delta function by anyone in last 80 years, really? Incnis Mrsi (talk) 18:48, 14 April 2013 (UTC)

Try Google for "Kronecker delta function". It appears to be standard usage in MATLAB. Deltahedron (talk) 19:12, 14 April 2013 (UTC)

I think probably the issue is not whether the phrase "Kronecker delta function" has been used recently, but rather whether the exact phrase "delta function" has actually been used to refer to the Kronecker delta. It's hopefully clear that the Dirac delta function is by far the more common use of "delta function" (with no additional qualifications) so I think a disambiguation page (as opposed to a hatnote) is not terribly helpful here. Sławomir Biały (talk) 20:03, 14 April 2013 (UTC)

Since there are only two articles for "delta function", and the Dirac one is arguably primary, I converted it to a redirect with a hatnote rather than having a separate dab. —David Eppstein (talk) 20:34, 14 April 2013 (UTC)

I forgot to note here that I disambiguated all the delta function links in article space except the redirects. Thanks for finishing it off. Most of the ambiguous links were in fact referring to Dirac delta functions. --Mark viking (talk) 21:03, 14 April 2013 (UTC)

And now Delta function is back to being a dab, or will be after the history rearrangement is complete. Are the modular discriminant and Ramanujan delta functions considered the same thing? They're almost the same but the discriminant has a factor of (2π)¹² that doesn't seem to be present when talking about the corresponding cusp form. This is far from my area, though, so maybe I'm just confused. —David Eppstein (talk) 06:53, 16 April 2013 (UTC)

Could someone please explain what is going on with all the page moves here -- two lots today? Deltahedron (talk) 17:28, 16 April 2013 (UTC)

There appears to be some disagreement over whether delta function should go to Dirac delta function or to delta function (disambiguation). But if it goes to the disambiguation page, it should be the main title of the page rather than redirecting to it. The page moves are trying to keep the edit history synchronized with the titles. —David Eppstein (talk) 17:38, 16 April 2013 (UTC)

I'm concerned that all these moves, counter-moves, deletions, undeletions and so forth, are taking place before any kind of consensus has been achieved. Deltahedron (talk) 18:14, 16 April 2013 (UTC)

And now it's been moved again — Steel1943 seems to be doubting that Dirac should be primary. See Wikipedia:Requested moves/Technical requests. —David Eppstein (talk) 23:24, 16 April 2013 (UTC)

Yes, yes. Let's just drop it for now. Anyone can comment on the appropriate discussion pages about the ultimate outcome. An RfC might be appropriate, with this project notified along with all affected discussion pages, although at present it seems likely that this can be handled amicably without appealing to a wider consensus. Sławomir Biały (talk) 00:24, 17 April 2013 (UTC)

This should be resolved just like any other primary topic discussion. Generally, a primary topic is determined by page views and extrinsic evidence of the proportion of real-world uses (on Google and the like) wherein the term is used to refer to proposed primary topic as opposed to other topics. bd2412 T 00:29, 17 April 2013 (UTC)

If the problem is considered to be settled by Googliomancy, then David Eppstein's solution is obviously the correct one. I challenge anyone to a Google competition on this point. Sławomir Biały (talk) 00:36, 17 April 2013 (UTC)

I agree completely. A quick Google search yields 320,000 results for Dirac AND "Delta function", compared to 78,800 results for Kronecker AND "Delta function"; Google Books results yield 109,000 results for Dirac AND "Delta function", compared to 20,100 results for Kronecker AND "Delta function". In terms of Wikipedia primacy, last month Dirac delta function got 26741 hits, compared to Kronecker delta getting 6870 hits, and (just for the heck of it) Modular discriminant getting 115 hits. bd2412 T 00:43, 17 April 2013 (UTC)

To me, Mark viking's anecdotal evidence that most of the ambiguous links that he fixed were to the Dirac delta is more convincing, since what we want to know is not how popular the different deltas are but rather how often each is the intended meaning for the unqualified phrase "delta function". But the distinction doesn't matter much, since all the evidence points the same way. —David Eppstein (talk) 01:00, 17 April 2013 (UTC)

Positive definiteness

Positive definiteness should me a multiple cross index page rather than a dab. I know that concept is supposedly deprecated, but you should seriously wonder why it is that every few months it comes to the top of your blacklist. I have gone ahead and changed it to a multiple-cross-reference page. Presumably the onus is now on those who oppose this idea to write an article instead, since it was clearly not a dab page. Perhaps User:BD2412 would obligingly write such an article? Sławomir Biały (talk) 20:20, 14 April 2013 (UTC)

I would not presume the expertise to begin such an enterprise (which is, of course, why I have come here to seek the help of experts in the field). Cheers! bd2412 T 00:33, 15 April 2013 (UTC)

Very well, and good luck with that. Unfortunately, no one to my knowledge has so far been willing to write an article on "positive definiteness" in general, despite half a decade of prodding. Although most of us know what positive-definiteness means (precisely in some cases, roughly in others), there is apparently no adequate secondary source that links the various cases. So therefore under our WP:PILLARS, no proper article can be written. Yet equally clearly, this should not be a dab page: the uses of the term are each a hair's breadth from each other. I honestly don't know what this means procedurally, but my suggestion is either: (1) leave it as an unsanctioned {{Multiple-cross-reference page}}, or (2) nominate the page for deletion via the standard process. If neither of these options is tasteful to you, then I should remind you that there is no deadline. Eventually the ultimate expert on positive definiteness in mathematics may come along and write an article that adheres to our WP:PILLARS. Until that time, if you notify this Wikiproject (as you have several times in the past about this very issue) you'll have to be satisfied with the responses offered by the idiotic schlubs that occupy it. Sławomir Biały (talk) 01:27, 15 April 2013 (UTC)

Of course, if there is no real meaning to "positive definiteness", it raises the question, why do so many articles link to it? As a disambiguator, I only bring here the disambiguation pages that regularly come up as having the most incoming links requiring repair, in the course of dealing with recurring errors. If the concept is ambiguous, the incoming links need to be fixed. If it is unambiguous, then the appropriate page should be there. If some other solution is appropriate, I will be glad to see it implemented. We are all working together here to correct mistakes such as ambiguous links. bd2412 T 02:05, 15 April 2013 (UTC)

They link to it because they are more interested in the general concept than in specific variations of it. But the rules prevent us from having things that look like disambiguation pages but are allowed to have links. Perhaps that indicates a problem with the rules. Perhaps calling it list of positive definite topics would help; after all, the dsiambiguation rules enthusiasts haven't yet succeeded in ruling that lists are too similar to disambiguation pages to be allowed to exist. —David Eppstein (talk) 02:23, 15 April 2013 (UTC)

An article on a list of positive definite topics sounds like a good idea. There exist surveys of what positive definiteness means in different mathematical contexts that could be used to provide the intro needed for such an article, for example, Positive definite functions and generalizations, an historical survey and Positive Definite Kernels: Past, Present and Future. --Mark viking (talk) 02:38, 15 April 2013 (UTC)

I know of no effort on the part of disambiguators to rule that lists are too similar to disambiguation pages to be allowed to exist. In fact, quite the opposite, we have converted many pages into lists that were incorrectly tagged as disambiguation pages, but did not contain ambiguous topics. We have also set up {{SIA}} pages for lists of things that share a common name, but for which examples are unlikely to individually notable (for example, Iasus) or for which references are likely to be for the entire class of members rather than any individual member (like NO2). bd2412 T 02:49, 15 April 2013 (UTC)

The context is Wikipedia talk:Policies and guidelines/Archive 13#Accepting "WP:Multiple-cross-reference page" as a guideline. —David Eppstein (talk) 02:58, 15 April 2013 (UTC)

I agree with Einstein's proposition: "Everything should be as simple as it can be, but not simpler". I would say that to the greatest extent possible, we should have articles if an article can be written on a topic, no matter how abstract or nebulous the topic; or, if there is not enough material to justify an article, then a section in whatever article encompasses the topic. However, I am all for innovative solutions, so long as we do not end up having disambiguation pages for topics that are not truly ambiguous to one another. In that vein of thought, what should be done with Extra dimensions, which has been tagged as WP:DABCONCEPT? bd2412 T 13:02, 15 April 2013 (UTC)

IMO, Extra dimensions must be merged as a new section in Dimension (mathematics and physics). For Positive definiteness, I suggest to add at the beginning ot the article the sentence: "Positive definiteness is a property of any mathematical object to which a bilinear form or a sesquilinear form may be naturally associated, which is positive definite. See, in particular:". As such, the article would become a WP:DABCONCEPT stub. The remaining problem is that I do not know any tag warning the editors to not add the tag {{dab}} to a WP:DABCONCEPT article. D.Lazard (talk) 14:22, 15 April 2013 (UTC)

A hidden note would probably suffice. bd2412 T 15:30, 15 April 2013 (UTC)

Defining "positive definite" only in terms of bilinear or quadratic forms fails to capture the definition relating to dynamical systems (currently at Positive-definite function) or that of Positive-definite function on a group. Deltahedron (talk) 17:21, 15 April 2013 (UTC)

I do not agree: I do not well understand the definition given in Positive-definite function on a group, but a bilinear function appears clearly in it (bracket notation). On the other hand, a Positive-definite function is a function whose gradient is zero and the Hessian matrix of second derivatives is definite positive. The fact that some articles are incomplete does not implies that the definition I have given is wrong. D.Lazard (talk) 18:01, 15 April 2013 (UTC)

I did not say that they were completely unconnected, just that it fails to capture the notion. The characterisation of a positive definite function in terms of positive definiteness of the Hessian is a theorem about positive definite functions that happen to be twice continuously differentiable. Other functions exist. Deltahedron (talk) 18:18, 15 April 2013 (UTC)

In terms of fashioning an article on this topic, my first question would be whether these dynamic and group functions can be explained under the same heading as the bilinear or quadratic forms. My second question would be, if they are too distinct for such a description, is there a primary topic between them that would be the thing people most likely expect to find when searching for or linking to "positive definiteness". bd2412 T 18:31, 15 April 2013 (UTC)

The definition in Positive-definite function on a group (usually a locally compact group) is not quite right; the added B(H) coefficients are unneeded and irrelevant generality. The standard definition from times of yore (say in Dixmier's book on C* algebras, Gelfand-Naimark or Mackey's Chicago notes) is for scalar functions on a group with some mild measurabilty or continuity properties (the usual theorem, from Banach's book and Calvin Moore's papers on Borel cohomology, that a Borel homomorphism on a Polish group is continuous). Certainly for the two articles I wrote on representation theory (zonal spherical functions and Plancherel theorem for spherical functions) the wikipedia definition is not helpful, in fact useless, and misses the point entirely (the Gelfand-Naimark-Segal or the Gelfand-Naimark construction). I don't know how that happened. I am not at all surprised. Mathsci (talk) 20:49, 15 April 2013 (UTC)

You are, of course, our resident expert on operator theory, so you're undoubtedly correct and this problem should be fixed (by someone...) Sławomir Biały (talk) 00:31, 17 April 2013 (UTC)

Euler's Doodle

I think I can follow most of the allusions in http://www.google.com/doodles/leonhard-eulers-306th-birthday but I am not sure which of Euler's contributions the animated "O" is supposed to illustrate. Any ideas? Tkuvho (talk) 09:38, 17 April 2013 (UTC)

Euler angles--Salix (talk): 10:04, 17 April 2013 (UTC)

Yep. Such an animation would be a nice addition to the WP article. --Mark viking (talk) 14:21, 17 April 2013 (UTC)

That would be nice, but it is not entirely clear whether this is in the public domain. I just looked through their "store" without conclusive results. Tkuvho (talk) 14:35, 17 April 2013 (UTC)

Google's specific rendition is definitely not in the public domain, but anyone with the ability to make a similar animation is free to do so. bd2412 T 15:24, 17 April 2013 (UTC)

Lucas primality test

Bob Baillie wrote me, asking for help with the article Lucas primality test. In particular:

this wikipedia page
http://en.wiki.x.io/wiki/Lucas_primality_test
does not describe any kind of lucas test at all.
instead, it describes pocklington's theorem.  the whole article needs to be renamed to something else, and the {{number theoretic algorithms}}  template needs to be corrected.

We have Pocklington primality test, LL, and LLR; I'm not sure what should be where and what the best names are. Any thoughts?

CRGreathouse (t | c) 15:13, 17 April 2013 (UTC)

The Lucas test described in

Baillie, R. (1980-10). "Lucas Pseudoprimes" (PDF). Math. Comp. 35 (152): 1391–1417. {{cite journal}}: Check date values in: |date= (help); Unknown parameter |coauthors= ignored (|author= suggested) (help)

seems to be rather different to what the article Lucas primality test claims it to be. The test described in Lucas primality test appears to be an extension of the Fermat primality test (I don't know whether that extension has a specific name). -- Toshio Yamaguchi 16:40, 17 April 2013 (UTC)

The subject is discussed at length in Hugh Williams (1998). Édouard Lucas and primality testing. Wiley. ISBN 0-471-14852-0. Deltahedron (talk) 06:43, 18 April 2013 (UTC)

Equation formatting disagreement

There's a discussion going on at Talk:Sexagesimal on how to format some equations. Please contribute. —David Eppstein (talk) 15:35, 18 April 2013 (UTC)

Polynomial recurrence AfD

The article polynomial recurrence is being considered for deletion. Please add your thoughts here. This article has been discussed at least once before on this page; see this past discussion. Thanks. --JBL (talk) 18:50, 18 April 2013 (UTC)

Idèle vs idele

Is there a consensus on this? It is under discussion at Talk:Adele ring#Idèle vs idele. Deltahedron (talk) 06:32, 18 April 2013 (UTC)

Good question. More generally, do we keep or omit accents? In the place or people names, we keep them. What about mathematical terms? -- Taku (talk) 13:46, 18 April 2013 (UTC)

It would certainly be nice not to have to type them :/ As long as the search function can fuzzily match the two, and that there is no danger of confusion between a word with accented and unaccented characters, I'm not sure there is much to stress about. (Of course, forthcoming examples could prove me wrong.) Rschwieb (talk) 13:44, 19 April 2013 (UTC)

Marilyn's Cross: a hoax or not?

Someone tagged Marilyn's Cross as a possible hoax. Is it? Michael Hardy (talk) 17:36, 19 April 2013 (UTC)

I don't know about hoax, but it seems to be original research. GScholar generated no hits and a general Google search turned up little that was not related to the Wikipedia article and nothing that could be considered independent. There seems to be a conflict of interest, as editor LMcCormick created the knot and created the article. The history of the editor's talk page suggests that there was controversy about this page. In particular, it was claimed that the editor simply renamed a well-known knot (e.g., Borromean Ring) and substituted their own diagram for an already existing illustration at File:Brunnian-3-not-Borromean.png. It does look fishy. --Mark viking (talk) 18:11, 19 April 2013 (UTC)

"Marilyn's Cross" is not found in ZMATH. Deltahedron (talk) 19:18, 19 April 2013 (UTC)

None of the above makes it a hoax, but maybe it makes it a mistake. Michael Hardy (talk) 22:32, 19 April 2013 (UTC)

Proposal to delete our article on an axiom of set theory

Please see Wikipedia:Articles for deletion/Axiom of global choice. Eozhik (talk · contribs) believes that Axiom of global choice is a hoax. Obviously, I disagree. If you have an opinion on this, I urge you to express it on the AfD page. JRSpriggs (talk) 09:28, 21 April 2013 (UTC)

The nomination for deletion was withdrawn after considerable discussion. JRSpriggs (talk) 21:38, 22 April 2013 (UTC)

Domain (mathematics): fixes to ∼ 150 inbound links? Or back to domain of a function with a hatnote?

I do not know what to do with these consequences of those clumsy changes in 2009 (and earlier). And the proposal about deprecation of redirects, which could avoid this kind of situation in the future, also did not attract any support. Incnis Mrsi (talk) 09:26, 23 April 2013 (UTC)

IMO, the easiest solution is to redirect Domain (mathematics) to Domain of a function, and to add to the latter a hat note For other use of "domain" in mathematics, see Domain#Mathematics D.Lazard (talk) 10:03, 23 April 2013 (UTC)

"Namesakes"

This edit was done by a user whose most recent edit history does not mention the following:

• List of things named after Archimedes
• List of things named after Thomas Bayes
• List of things named after Augustin-Louis Cauchy
• List of things named after Arthur Cayley
• List of things named after Richard Dedekind
• List of things named after Gustav Lejeune Dirichlet
• List of things named after Albert Einstein
• List of things named after Euclid
• List of things named after Leonhard Euler
• List of things named after Paul Erdős
• List of things named after Fibonacci
• List of things named after Carl Friedrich Gauss
• List of things named after Charles Hermite
• List of things named after Joseph Louis Lagrange
• List of things named after Adrien-Marie Legendre
• List of things named after Gottfried Leibniz
• List of things named after Pythagoras
• List of things named after Srinivasa Ramanujan
• List of things named after Bernhard Riemann
• List of things named after James Joseph Sylvester
• List of things named after Alfred Tarski
• List of things named after Karl Weierstrass
• List of things named after Hermann Weyl

Michael Hardy (talk) 02:46, 26 April 2013 (UTC)

The new version is neither clearer nor less vague, and also reads awkwardly. I recommend reversion. --JBL (talk) 03:07, 26 April 2013 (UTC)

I've complained there that it is much more vague, to many people namesake means anything or anyone with a name like Leonhard Euler, and not necessarily named after the mathematician. Dmcq (talk) 03:28, 26 April 2013 (UTC)

I've changed the article's title back to List of things named after Leonhard Euler and commented on the article's talk page about my reasons for this. Michael Hardy (talk) 13:49, 26 April 2013 (UTC)

Good job. -AndrewDressel (talk) 21:53, 26 April 2013 (UTC)

Organization of the List of things named after Archimedes

I've just organized the List of things named after Archimedes into sections. Further work could probably be done, possibly including alphabetizing, creating subsections of the "Mathematical concepts" section, further refining the organization, and other things. Some of our lists of (pardon the expression) "namesakes" are organized this way, and I think some are not. Some of those that are not might benefit from such work. Michael Hardy (talk) 14:28, 26 April 2013 (UTC)

Help needed on Tessellation

This is a request for assistance on Tessellation, which has been in a scrappy state for some years. There are clearly several aspects of the mathematics of the subject (such as in higher dimensions, and of non-Euclidean surfaces) that need proper treatment with decent visual examples, citations and intelligible explanation. I have done some work on the basics and on the artistic and historical side, but a mathematician's hand is now required. I'm happy to lend a hand where I can. Chiswick Chap (talk) 15:48, 26 April 2013 (UTC)

Reference spam at Pursuit-evasion

An editor at Pursuit-evasion is adding references that are not used in the text and appear likely to be a conflict of interest. Are they sufficiently significant in the history of this topic to keep in the article? If not, could I have some help keeping them out, please? —David Eppstein (talk) 17:30, 26 April 2013 (UTC)

Ha, and of course one of the references added would be a paper in Chaos, Solitons & Fractals, wouldn't it? --JBL (talk) 22:14, 26 April 2013 (UTC)

I skimmed the two papers that Chiswick Chap reverted. Both concern differential games with a particular dynamics and constraints and the conditions for successful pursuit. My best guess (I know a little about the field, but am far from an expert) is that these are nice little problems, but are not of fundamental significance to different games theory. The papers themselves don't seem to have any bearing on the article. GScholar shows that each paper has 2 citations, and one was published in 1999. I have to agree, this looks like COI and refspam. --Mark viking (talk) 23:00, 26 April 2013 (UTC)