Wikipedia talk:WikiProject Mathematics/Archive/2012/Apr

Persistent vandalism/self-promotion of Angle trisection
Some user is repeatedly vandalizing angle trisection in an attempt to insert links to his own webpage. (He has successfully managed to get such links included on a variety of other, non-math, pages; this appears to be the only purpose of the account.) If someone with appropriate powers could do something to prevent this, it would be wonderful. --Joel B. Lewis (talk) 18:04, 29 March 2012 (UTC)


 * Now accompanied with legal threats: http://en.wikipedia.org/w/index.php?title=Angle_trisection&curid=91111&diff=484576133&oldid=484575649 (btw, the claim of copyright violation is obviously absurd.) --Joel B. Lewis (talk) 18:38, 29 March 2012 (UTC)
 * Now discussed at Administrators' noticeboard/Incidents, both editors blocked for a day. Could be a page to watch for further trouble,--Salix (talk): 23:02, 29 March 2012 (UTC)
 * Yes, please keep an eye on it -- I've agreed to leave it alone for a bit, but it seems extremely likely to me that the other user will continue to self-promote (as e.g. he continues to assert that he has a 1995 copyright on the idea of using repeated bisection to trisect an angle -- https://en.wikipedia.org/w/index.php?title=User_talk:WIKI-1-PIDEA&diff=484617642&oldid=484606285 ). --Joel B. Lewis (talk) 01:51, 30 March 2012 (UTC)
 * There's always someone wrong on the internet ;-) I wouldn't worry, there's enough people watch that article. Dmcq (talk) 11:51, 30 March 2012 (UTC)

The concerned editor has been indefinitely blocked, see User talk:WIKI-1-PIDEA. — D.Lazard (talk) 10:03, 1 April 2012 (UTC)

Robin Williams (in character): "I want to bisect her angle"
The project members may be interested in the article about Robin Williams and Steve Martin at the USA's Mathematical Sciences Research Institute (MSRI), which features e.g. William's ad-libbing about a math geek wishing "I want to bisect her angle". Or not.

Kiefer .Wolfowitz 10:25, 1 April 2012 (UTC)

John Rainwater April Fools DYK: Peter Orno delayed
The pseudonymous mathematicians John Rainwater and Peter Orno were approved for the 2012 April Fools DYK in April 2011. John Rainwater's DYK should appear in a few hours. Peter Orno's DYK has been delayed. Kiefer .Wolfowitz 10:30, 1 April 2012 (UTC)

Merge help needed - Ordered ring
I need help with math merging. There is consensus at Talk:Partially ordered ring to merge in the page Ordered ring, but I don't know the math and have no idea how to do it. I was hoping that one of your math whizzes here could do that for Wiki. Thanks, D O N D E groovily   Talk to me  02:26, 4 April 2012 (UTC)

Featured picture candidate
This picture has been nominated as a featured picture it has been pointed out that the picture has little or no encyclopaedic value in describing symmetry to the reader. I am wondering is that correct ? Some editors in the discussion don't think so. Penyulap  ☏  04:52, 4 April 2012 (UTC)

Terminology of inflexion points
In the page inflexion point it is said (in other words) that it is a point where a curve has a contact of odd order with its tangent. The name of a contact of even order higher than two is not given. In French, it is "méplat", but the article Meplat does not give this meaning. What is the correct English word?.

By the way, "flex" is frequently used instead of "inflexion point" and this is not mentioned in the article.

D.Lazard (talk) 16:22, 7 April 2012 (UTC)

Matrix multiplication
Given the importance of this article, and it hasn't really improved since last posted my own suggestions for improvement on the talk page (to which no one has responded to, or even at all since then, recently archived by myself), I intend to just re-write most of the first half of the article.

There is plenty of repetition and it just dribbles on and on. All that's really needed it the general definition and a couple of concrete examples, followed by the properties. By no means will remove anything referenced or the image already included, though the first half only has one reference, I (and surley many others) have access to loads (and if ordinary multiplication is such a trivial concept, why aren’t there more anyway??).

The "too technical" banner has been there a long time also... about time this was sorted out. F = q(E+v×B) ⇄ ∑ici 23:17, 7 April 2012 (UTC)

Coons surface
Coons surface is a really messy new article. Work on it. Michael Hardy (talk) 19:55, 7 April 2012 (UTC)


 * I'm not knowledgable on that specific topic to re-write, but still cleaned it up and removed the clean up banner. F = q(E+v×B) ⇄ ∑ici 09:23, 8 April 2012 (UTC)

Combinatorial game theory
I don't want to edit the article as it is completely outside my area of expertise, but the recently added section on Fraser Stewart's PhD thesis reads to me like a shameless (self?-)promotion of a topic of marginal importance for this introductory article. Can someone knowledgeable have a look at it?—Emil J. 17:45, 8 April 2012 (UTC)


 * Judging from the way it is written, it is fully dependent on ideas from the dissertation. It might well be self-promotion, as there is a Fraser Stewart on google with email ending in computing.dundee.ac.uk, and geolocate puts the IP in the UK. I'll remove the section for now on the grounds that this dissertation is not notable. Rschwieb (talk) 19:55, 8 April 2012 (UTC)

Help needed with pi article
I'm planning on nominating the pi article soon for Featured Article status. I'm looking for math-knowledgable editors to review the article for accuracy & prose quality .... just post any comments or ideas for improvement on the article's Talk page. The criteria for FA are at Featured_article_criteria. Thanks in advance for any help. --Noleander (talk) 14:04, 9 April 2012 (UTC)

Group theory templates
Hi, I noticed at least two group theory templates. There is the one at Abelian group and the one at group theory. They both have their strong points. The one without the picture is easier to navigate, and I like the last two items. On the other hand, the one with the picture is pretty neat, and pretty much subsumes the one without the picture. Should we think about merging or do we just use them haphazardly? Rschwieb (talk) 18:58, 9 April 2012 (UTC)
 * Probably should be merged. --Noleander (talk) 19:46, 9 April 2012 (UTC)
 * I merged them into the template with the picture: Groups.   I put the misc groups at the bottom, into a new region called "Other" ... so an editor who is an expert in groups should probably review those articles and see if they are better off in another region in the template. --Noleander (talk) 20:11, 9 April 2012 (UTC)

saccheri quadrilateral: obtuse angle
Looking for help here about Saccheri quadrilateral. :)--Nickanc (talk) 22:12, 9 April 2012 (UTC)

New WPM guideline
Recent discussions at Talk:twice pi suggest that it may be helpful to have an explicit guideline to the effect that youtube videos and yellow media reports are not considered to be reliable sources for math-related articles. Tkuvho (talk) 14:52, 2 April 2012 (UTC)
 * Bogus mathematical theories that nevertheless receive significant popular attention should be considered notable. Yellow media should not be considered reliable in terms of their mathematical content but should certainly be considered sufficient to establish notability, and at least somewhat reliable when it comes to statements about cultural impact. 69.195.54.191 (talk) 18:58, 8 April 2012 (UTC)


 * This seems misguided since the article topic in question is more notable for its cultural impact than anything else. It's like Time Cube. Fringe/minority viewpoint, popular in spurts among the media, but not insane like Time3, instead just frivolous. --Cyber cobra (talk) 16:11, 2 April 2012 (UTC)
 * Cybercobra, you must be coherent with yourself: Half a month ago you have requested (and obtained) to revert the move of this article to "Tau against pi debate" with the reason "Significantly altering an article's topic". And now you say that the notable part of this article is the report by the news of this supposed debate. If the article topic is not about a mathematical constant but about its notability in popular culture, the article title and the two first sentences should be changed, for not mislead the reader: Presently, both asserts that the topic is a mathematical constant. D.Lazard (talk) 17:07, 2 April 2012 (UTC)

Obvious target candidate: 2&pi; in popular culture. Sławomir Biały (talk) 21:34, 2 April 2012 (UTC)
 * Come on, guys, how many times are we going to keep spinning around the same issues? We need to stop conflating 2&pi; and Tau for the sake of argument. The former is a well-sourced (mathematically speaking) concept regarding the usage of a different circle constant, and the latter is a recent proposal that received considerable adoption especially (but not exclusively) in non-mathematical circles. They are indeed inseparable as far as article content is concerned (both should be present in an article about this whole issue) but we can't discuss about the article by arguing for or against only one part of it. "2&pi; in popular culture" would make sense if we decided to keep only the tau part (and then again wouldn't, for inexplicably keeping Tau out of the title), but again, omitting the background to the current surge of interest in 2&pi; is just misleading and a disservice to readers. This would only make sense if the content grew so large that it would make reading the article cumbersome (case in point: Pi Day).
 * Regarding this proposal, I am entirely against more rule creep that attempts to define rigid boundaries and automatize the editorial process. We have enough policies and guidelines, we just need to use our common sense and be willing to consider compromise solutions. This is how Wikipedia works. Besides, Wikipedia is a general reference work, not a mathematical compendium. Nothing prevents a math-related article to include relevant non-mathematical content (see Pi for instance), which should naturally follow the appropriate proportion as agreed by editors. --Waldir talk 05:10, 3 April 2012 (UTC)
 * I agree that guidelines should not be created for the sake of having more guidelines. However, in this case we have encountered persistent misconceptions on the part of editors who think, for example, that youtube videos have weight in notability discussions.  If not a guideline, perhaps we could have an extra question in the FAQ at the top of this page. Tkuvho (talk) 11:56, 3 April 2012 (UTC)
 * We already have the needed guidelines: WP:YOUTUBE and WP:ELNO. Nageh (talk) 12:29, 3 April 2012 (UTC)
 * Thanks, I did't see this. The clause about "case-by-case basis" could be clarified in the context of math pages.  I think there is room for stronger opposition in the context of scientific pages.  Again, having such a guideline may help us to orient well-meaning but misguided editors and save everybody time.  Tkuvho (talk) 12:37, 3 April 2012 (UTC)
 * The other link you provided does not seem to say anything about media, tabloid or otherwise. Tkuvho (talk) 12:39, 3 April 2012 (UTC)
 * WP:ELPOV is also worth to be considered. D.Lazard (talk) 12:44, 3 April 2012 (UTC)

It would be nice if there were some concrete way to address the issue of "yellow media". This is not the first time this issue has arisen in science-related articles of the media running some story of dubious scientific merit, simply because some scientist somewhere had said something. My favorite example is Articles for deletion/Jacob Barnett, which was picked up as a viral news story because upon posting his idiotic ramblings to YouTube, Jacob Barnett's mother contacted an MIT physicist who encouraged Barnett to continue studying math and physics. The media spun this as "Boy genius challenges all of modern physics" or other such ridiculousness. The point is, as a rule news media should not be allowed as a reliable source for this sort of thing. The news is a reliable source for news (e.g., what Russia is doing at the moment), less so for all the other stuff presented as a sideshow to the news. Sławomir Biały (talk) 12:47, 3 April 2012 (UTC)
 * I agree with the thrust of your comment but would like to limit it somewhat. Every now and then there are legimitate pieces on science that appear in the popular media.  I would formulate an objection in terms of "tabloids" to avoid making them too sweeping.  Sensationalism may be in the eye of the beholder, but when a number of WPM members behold an item of science "news that's fit to sell" and eye it with suspicion, this should be enough to block it systematically. Tkuvho (talk) 13:02, 3 April 2012 (UTC)
 * Note that twice pi currently has 13 (!) references to make the point that B. Palais proposed a new symbol for 2 pi, one of them a "Life of pi over" piece from the friendly Times of India. I have no previous experience with this best-selling journal but if anyone has additional evidence of it engaging in tabloid tactics to reach its best-selling status, they are invited to step forward with the information.  Tkuvho (talk) 13:15, 3 April 2012 (UTC)
 * I propose the following addition to the FAQ at the top of this page: Question. Why don't math pages rely more on helpful YouTube videos and media coverage of mathematical issues? Answer.  Mathematical content of YouTube videos is often unreliable, whereas media reports are typically sensationalistic.  This is why they are generally avoided. Tkuvho (talk) 14:11, 4 April 2012 (UTC)
 * The change proposed above was without any consensus in this discussion. I reverted it for now. --Waldir talk 09:15, 10 April 2012 (UTC)

Stacks project dump
I don't have any particular plan, but what does anyone think of dumping materials from Stacks project ? (Apparently, there is no Wikipedia article on the project.) On the one hand, this is the quickest way to increase our coverage of scheme theory, and even more reliable (more reliable than some random graduate student.) On the other hand, ah..., there might be an issue like quality for instance. (The project is licensed under GFDL, which is compatible with Wikipedia. I know some people like/enjoy actual writing. But I'm more interested in the ends than the means. -- Taku (talk) 12:48, 10 April 2012 (UTC)

Oh, the materials I have in mind are statements of theorems and examples. -- Taku (talk) 12:51, 10 April 2012 (UTC)

Index notation
There are several articles which explain the meaning and use of this notation:


 * 1) Index notation
 * 2) Tensor
 * 3) Antisymmetric tensor
 * 4) Einstein notation
 * 5) Raising and lowering indices
 * 6) Abstract index notation
 * 7) Covariance and contravariance of vectors

yet the specialized notations of commas, semicolons, sqaure/round brackets (e.x. $$A^{\alpha}{}_{,\beta},A_{\alpha;\beta}, \,A_{[\alpha\beta]},\,A^{(\alpha\beta)}$$) seem to be dispersed, so readers will have to search them out (even if linked) which is not much help. It would be convenient to add a list of all the attributes just as a summary in one place  (in an obviously titled article - like abstract index notation so people will look there and its easier for editors to remember that link), then linking to all of the main articles from there.


 * {| class="toccolours collapsible collapsed" width="80%" style="text-align:left"

!proposed summary:  Covariant tensor

Indices are lowered (subscript): $$A_{\alpha\beta\gamma \cdots}$$

Contravariant tensor

Indices are raised (superscript): $$A^{\alpha\beta\gamma \cdots}$$

Mixed tensor

Indices are raised and lowered: $$A_{\alpha}{}^{\beta}{}_{\gamma}{}^{\delta\cdots}$$ 

Indices can be raised and lowered using the metric tensor.

Partial derivative

Comma before the index of spatial variable: $$A_{\alpha\beta\cdots,\gamma} = \partial_\gamma A_{\alpha\beta\cdots} = \dfrac{\partial A_{\alpha\beta\cdots}}{\partial x^\gamma} $$

Covariant derivative

Semicolon before the index of the tangent vector: $$A_{\alpha\beta\delta\cdots;\gamma}$$

Symmetric part of tensor

Round brackets around the number of symmetrized indices, then permutations, divided by the factorial of the number of indices in round brackets:

two symmetrized indices
 * $$A_{(\alpha\beta)\gamma\cdots} = \dfrac{1}{2!} \left(A_{\alpha\beta\gamma\cdots} + A_{\beta\alpha\gamma\cdots} \right)$$

example:
 * $$A_{(\alpha}B_{\beta)\gamma} = \dfrac{1}{2!} \left(A_{\alpha}B_{\beta\gamma} + A_{\beta}B_{\alpha\gamma} \right)$$

three symmetrized indices
 * $$A_{(\alpha\beta\gamma)\delta\cdots} = \dfrac{1}{3!} \left(A_{\alpha\beta\gamma\delta\cdots}

+ A_{\gamma\alpha\beta\delta\cdots} + A_{\beta\gamma\alpha\delta\cdots} + A_{\alpha\gamma\beta\delta\cdots} + A_{\gamma\beta\alpha\delta\cdots} + A_{\beta\alpha\gamma\delta\cdots} \right)$$ p symmetrized indices, sum over all permutations: $$A_{(\alpha_1\alpha_2\cdots\alpha_p)\alpha_{p+1}\cdots\alpha_q} = \dfrac{1}{p!} \sum_{\alpha_1\alpha_2\cdots\alpha_p}A_{\alpha_1\alpha_2\alpha_3\cdots\alpha_p\cdots\alpha_q} $$

Antisymmetric part of tensor

Square [ ] brackets around the number of antisymmetrized indices, simalarly

two antisymmetrized indices
 * $$A_{[\alpha\beta]\gamma\cdots} = \dfrac{1}{2!} \left(A_{\alpha\beta\gamma\cdots} - A_{\beta\alpha\gamma\cdots} \right)$$

three antisymmetrized indices
 * $$A_{[\alpha\beta\gamma]\delta\cdots} = \dfrac{1}{3!} \left(A_{\alpha\beta\gamma\delta\cdots}

+ A_{\gamma\alpha\beta\delta\cdots} + A_{\beta\gamma\alpha\delta\cdots} - A_{\alpha\gamma\beta\delta\cdots} - A_{\gamma\beta\alpha\delta\cdots} - A_{\beta\alpha\gamma\delta\cdots} \right)$$ example:
 * $$F_{[\alpha\beta,\gamma]} = \dfrac{1}{3!} \left(\partial_\gamma F_{\alpha\beta}

+ \partial_\beta F_{\gamma\alpha} + \partial_\alpha F_{\beta\gamma} - \partial_\gamma F_{\beta\alpha} - \partial_\beta F_{\alpha\gamma} - \partial_\alpha F_{\gamma\beta} \right)$$

p antisymmetrized indices, sum over cyclic permutations: $$A_{[\alpha_1\alpha_2\cdots\alpha_p]\alpha_{p+1}\cdots\alpha_q} = \dfrac{1}{p!} \epsilon_{\alpha_1\alpha_2\cdots\alpha_p}A_{\alpha_1\alpha_2\cdots\alpha_p\cdots\alpha_q} $$</li> </ol>
 * }

Reference which includes all of these: Gravitation, MTW, 1972, p.85-86, §3.5 . If no-one objects I'll add it to the end of abstract index notation (an alternative place would be tensor but there is a section which links to abstract index notation anyway...). F = q(E+v×B) ⇄ ∑ici 09:28, 10 April 2012 (UTC)


 * The point that such a collected summary would be useful is well-made. I would however argue against such a central summary being placed under abstract index notation, since that is a side-branch and does not cover all uses of the notation).  I would suggest that such a summary should rather be placed under tensor as the more central article.  — Quondum☏ 11:32, 10 April 2012 (UTC)


 * I had that in another mind, so you think in tensor under the subsection Abstract index notation? F = q(E+v×B) ⇄ ∑ici 11:45, 10 April 2012 (UTC)


 * The title of the article abstract index notation may be misleading. It is not about the index notation which uses numbers as indices. It is about a system which merely indicates which aspects of a tensor are equivalent or may be contracted with which other aspects. As such, I would avoid that article like the plague that it is. JRSpriggs (talk) 12:27, 10 April 2012 (UTC)


 * Well, in its own subsection titled as "summary of notation" under notation in the tensor article, or whatever. Thanks both of you for clarifying this in the right direction, I thought they were the same somehow... F = q(E+v×B) ⇄ ∑ici 12:40, 10 April 2012 (UTC)


 * (@JRSpriggs) I don't follow you. How exactly is abstract index notation a plague?  This is standard terminology in physics and differential geometry, not a misleadingly titled article.   Sławomir Biały  (talk) 12:41, 10 April 2012 (UTC)


 * I think the point has been made and agreed that abstract index notation (or even such a section heading) is unsuitable for the purpose suggested by F = q(E+v×B) ⇄ ∑ici. Speaking of this, an alternative to tensor for such a summary may be the article Einstein notation.  So my suggested candidates are these two articles, and I would welcome comments.  — Quondum☏ 14:18, 10 April 2012 (UTC)


 * The article Einstein notation is about the summation convention (as Einstein himself introduced) and pretty much every application of it in linear algebra. The link summation convention itself redirects to there. When people read tensor equations which happen to include commas/semicolons/brackets etc, the first place they will think of is tensor and hope to find the notation there. So I'd be inclined for the previous suggestion: in the article tensor, under the section notation, and start a new subsection called "summary of index notation for tensors" (or words to that effect) and simply paste the contents of that box under the heading. =) F = q(E+v×B) ⇄ ∑ici 15:43, 10 April 2012 (UTC)

Btw., the historical name is Ricci calculus, see Schouten (1924) Der Ricci-Kalkül.--LutzL (talk) 16:49, 10 April 2012 (UTC)

(ec) The article does create the impression that the phrase Einstein notation is synonymous with Einstein summation convention, but it also seems possible that it is a broader term to describe the use of superscripts, subscripts etc. to index coefficients, plus potentially all the twiddles in your proposed summary; if this is the case, the Einstein summation convention would be merely one facet thereof. I would not be surprised if this article focuses primarily on the summation convention as a result of a misconception amongst WP editors. I am having difficulty googling references that authoritatively support either view. I would appreciate input from people with experience on this point. — Quondum☏ 16:54, 10 April 2012 (UTC)


 * I would like to ask a math historian about the origins of the summation convention and index convention. Tensor calculus was around before Einstein, and it wouldn't be surprising if these conventions were already in use before Einstein. Rschwieb (talk) 17:37, 10 April 2012 (UTC)


 * Fourier, I believe. --Matt Westwood 17:42, 10 April 2012 (UTC)


 * Its perfectly fine add a historical note about the notations when the time comes, but shall we add the box or not? If so where? Einstein notation would be unsuitable since that article does, and should, concentrate on the summation convention which is just one part of the index notation (and Einstien's contribution to the notation). It’s also trivial to get used to, and is without fail explicitly stated and linked "we are using the summation convention in this equation/what follows". What isn't trivial is knowing what the "punctuation" in the indices read. (Even a couple of tensor analysis books I have do not even include the index "punctuation": the theoretical physics book sourced above does, but do typical readers have access to degree-level books?).


 * By the way, there is another convention not included for spinors (since presumably not used for tensors): dotted indices for right-chiral spinors (no implication to include though)... F = q(E+v×B) ⇄ ∑ici 18:10, 10 April 2012 (UTC)


 * Let us assume that the article Einstein notation is about the summation convention, and that if there is conflict with actual usage, then it is a matter of renaming that article. Then IMO the answer is simple: the summary should be in Tensor, I propose under a subsection of its own in the section Notation.  The ues of each notation can later be elaborated under the following section, Operations.  — Quondum☏ 18:46, 10 April 2012 (UTC)


 * I said identically above... F = q(E+v×B) ⇄ ∑ici 19:54, 10 April 2012 (UTC)


 * (Again you're repeating youself). Anyway the summary is really good, and by the look of it no one opposes the main article on tensors, so why don't you just add it? Maschen (talk) 20:05, 10 April 2012 (UTC)


 * The point of coming to this Wikiproject page is to discuss things for improving maths articles. Just as well I did, since everyone above has provided careful guidance (else would have just pasted it to abstract index notation by my own sore misunderstanding of that name, but waiting a little was worth it). You're right though - it'll be done now... and take discussion to the talk page there... F = q(E+v×B) ⇄ ∑ici 20:15, 10 April 2012 (UTC)


 * Done, see here. Thanks, F = q(E+v×B) ⇄ ∑ici 20:26, 10 April 2012 (UTC)


 * Nice work! Maschen (talk) 20:44, 10 April 2012 (UTC)


 * Actually, that is quite terrible (And I'm not just talking about the MOS rape going on there). It doesn't make much sense to talk about notation conventions for (covariant) derivatives in an article that is just about normal tensors, not tensor fields. (Not to mention that it suggests that this notation is universalm while it is my experience that the comma/semicolon notation is slowly going extinct, and rightly so I might add.) I will revert for now.TR 07:00, 11 April 2012 (UTC)


 * Thank you fantastically!! - do what the hell you like!!... For one thing: it wasn't just for covariant tensors either, and in the cited source it happens that those comma/semicolon derivatives are in those index positions, which is why it was written that way. Anyway its on you now... I tried... F = q(E+v×B) ⇄ ∑ici 07:45, 11 April 2012 (UTC)

To Sławomir Biały: So called 'abstract index notation' is for people who want to use index notation (because it is by far the most convenient way to express the ideas) while still pretending that they are not using index notation to manipulate arrays of numbers but instead some abstract notion of tensors which requires the use of "$$\otimes$$" and such. So it allows people to do algebraic manipulations with indices, but if you dare to try to figure out what it means by substituting actual numbers, then you are violating the arbitrary rules of 'abstract index notation'. What a load of s--t. JRSpriggs (talk) 03:21, 11 April 2012 (UTC)


 * I'm actually not a huge fan of indices, abstract or otherwise, but your rather imperious viewpoint seems to betray a lack of basic familiarity with the notation. I'm sorry that you have this issue, but please don't try to impose it on the rest of us.   Sławomir Biały  (talk) 12:05, 11 April 2012 (UTC)


 * Potential alternative: Create an entire article dedicated to "index notation for tensors/tensor fields", and merge all notation content from


 * 1) Index notation (leave the computer science stuff and re-direct the maths section - for an introduction)
 * 2) Einstein notation (explain summation convention + applications)
 * 3) Raising and lowering indices (explain + applications)
 * 4) Symmetric tensor (explain the symmetrization notation)
 * 5) Antisymmetric tensor (explain the antisymmetrization notation)
 * 6) the summary above [can be expanded and integrated into new article (assuming no reverts of course)]


 * into it (if articles become empty, they will clearly be redirects to the new main article). For articles 4 and 5, rather than "merge" I mean "copy and paste", but give a couple of examples in more detailed explanation.


 * That way, when it comes to explaining a tensor equation (in physics, maths or anything else) - we just link to that one article every time and everything will be in one place for convenient reference (the article which uses whatever metric and signature is a separate link with explanation):


 * "For details on the summation convention and how to raise and lower indices etc.. see the article tensor notation."


 * and of course it will not have to be re-explained in any other article because it can be linked?... The reason for kicking up such a fuss on this particular concept is becuase it's hoped to make life easier for the typical reader is all...


 * On the other hand... what are the chances of people agreeing with this thought? None. (Really - no offense taken, if you have a genuinely good reason to disagree please tell). F = q(E+v×B) ⇄ ∑ici 08:51, 11 April 2012 (UTC)


 * There is Tensor notation that could be used as a central summary (currently a redirect to Glossary of tensor theory). The name is probably too broad for the purpose, though.  There is also Tensor index notation, which might be quite suitable (currently a redirect to Einstein notation, which I feel should be renamed to Einstein convention).  How about using Tensor index notation for your proposal?  On a side note, until an article is found for this, I feel it should remain in Tensor.  — Quondum☏ 09:15, 11 April 2012 (UTC)
 * I think having a separate article on tensor index notation is probably a good idea. Having a place to link to for explaining notation is good, and having all the notation gathered in one place is good as well. I would not actually merge any of the notational content from the articles mentioned above though. Having the notation explained along side the concept it is supposed to express is very useful as well. There is no reason why we shouldn't have both.TR 09:22, 11 April 2012 (UTC)


 * As said this is only a potential alternative which may not happen, but thanks for pointing out the better link and title. For now (in principle) the summary above in the tensor article is plenty, but user:TimothyRias has reverted twice already... F = q(E+v×B) ⇄ ∑ici 09:20, 11 April 2012 (UTC)


 * The section is very much misplaced in the tensor article, because it discusses notation that is specific to tensor fields, which are not discussed in that article. This is why I reverted the addition there. The idea of adding this section to the tensor article is a red herring.TR 09:27, 11 April 2012 (UTC)

I do not see any major problem with such articles, as the topic itself is quite confusing and (some time ago) even controversial. But I see a minor problem, that the tensor article does not explain the hierarchy of notations, i.e. which notation is related to which and how exactly. I think, WP ought to explain the following points: Incnis Mrsi (talk) 09:29, 11 April 2012 (UTC)
 * "Abstract index notation" and "Penrose graphical notation" are two inherently invariant notations suitable for tensors of arbitrary ranks;
 * "Einstein notation" is essentially the same as "abstract index notation" with the metric tensor, although there may be some minor differences and application semantics in Einstein notation;
 * The simple "index notation" may be considered as a low-level translation of the abstract index notation for finite-dimensional spaces, but it is not inherently invariant;
 * Covariance and contravariance of vectors is a matter of semantics, not of notation;
 * $dx_{k}$ (also written as $dx^{k}$ for compatibility with EN/AIN) and $∂ ∕ ∂x_{k}$ is yet another notation suitable for tensor fields, its semantics relies on differential geometry, but it is syntactically compatible with EN/AIN and index notation;
 * Differential forms are antisymmetric $(0, k)$-tensors;
 * The common algebraic notation of vectors and operators (as well as quite similar bra-ket notation) is virtually another tensor notation, but restricted to $(1, 0)$, $(1, 1)$ and possibly $(0, 1)$-tensors. It is inherently invariant, like AIN and PGN.


 * Well, I didn't imply symmetric and antisymmetric tensor should be merged and pulled into new articles fully, but if we didn't merge Index notation, Einstein notation, Raising and lowering indices they would then be redundant. Also - the Einstein notation article really should be trimmed down, its too long for what it actually is ("set two indices equal - then sum over these components?" too much repetition of vector representations). The main statement and a few examples (like vector calculus operations given in less prose) would be plenty.


 * Given that Quondum suggested to rename as Einstein convention, why not:
 * just shorten the content there (at least slightly), then with out merging anything for now:
 * copy and paste Raising and lowering indices and the summary into it
 * amalgamate everything into one article,
 * rename as tensor index notation (removing double redirects).


 * Then we can decide on whether to leave alone or blank + redirect the pasted articles. F = q(E+v×B) ⇄ ∑ici 09:44, 11 April 2012 (UTC)
 * Note that there are many links bound to "raising and lowering indices" and probably it should exist even more such links, because this is a concrete operation: contraction with the metric tensor. I do not think that the article should be merged to another article. But I see a problem with index notation: IMHO a dab page should exist there, not an article. What now constitutes "index notation" may be moved to tensor index notation (I could eliminate that redirect) and rewritten, to preserve the edit history. Incnis Mrsi (talk) 10:15, 11 April 2012 (UTC)


 * Forgot to mention, by all means we can include Incnis Mrsi's suggestion. For now I'll begin reducing bits of Einstein notation. F = q(E+v×B) ⇄ ∑ici 10:14, 11 April 2012 (UTC)


 * Also, it has been suggested that content from articles like antisymmetric tensor and symmetric tensor be merged out somewhere else. I think this is a bad idea as well.  I think things should basically be kept where they are (modulo Incnis Mrsi's suggestion).  If someone wants to add something to an article like index notation, that sounds fine, but not at the expense of other articles.   Sławomir Biały  (talk) 10:28, 11 April 2012 (UTC)
 * (ec)I am not sure about renaming Einstein notation to tensor index notation. The Einstein summation convention is just that the convention to leave out the summation symbol for repeated indices. By itself this convention is quite notable, and warrants its own article. (I agree however that the current article may be a bit long.)
 * I am also not entirely convinced that merging Raising and lowering indices into a general article about notation is the best idea. "Raising (or lowering) an index" is more than just notation, it is an operation that changes the type of a tensor. Again I agree that the current Raising and lowering indices article is not very good, and I see why you would want to do something with it. But I think that merging it into the notation article may lead to the misleading suggestion that Raising an index is just a notational thing, rather than a mathematically meaning full operation (this is a form of duality). TR 10:31, 11 April 2012 (UTC)
 * I think the suggestion is (optionally) renaming to Einstein notation to Einstein convention which seems not to be contradicted by what you (T) are saying, and to replace the link at Tensor index notation with a short article including the notation summary under contention. I agree that Raising and lowering indices should remain its own article (as you say, it is not a notation), though mention thereof is appropriate in the notation article for understanding the notation with differing index positions for the same symbol.  — Quondum☏ 10:52, 11 April 2012 (UTC)
 * I may have misunderstood. But which article is F=q(E+v^B) talking about then when he suggests "rename as tensor index notation (removing double redirects)"? Since tensor index notation currently redirects to Einstein notation, I assumed he was suggesting to rework the Einstein notation article and rename it tensor index notation. TR 11:31, 11 April 2012 (UTC)


 * About double redirects, I don't know. Just in case any appear is what I must have been thinking.


 * Approx 6000 bytes of repetition has been cut from Einstein notation. Still tweaking now, but is everyone OK with the new state of the article? Will anyone revert back? Anything you think was good that I removed and should be added back? etc... (as said above, I'll not move/merge at this stage, or ever actually...)


 * If no-one would like to merge, then is there going to be a new article just on tensor index notation or not? I can't tell from above. Can understand that you would rename Einstein notation, and not merge anything leaving the articles where they are, but there seems to be nothing against (or a descision for) copying and amalgamating into a new article... F = q(E+v×B) ⇄ ∑ici 11:32, 11 April 2012 (UTC)

I really don't understand what is being proposed at all. Here is what I suggest: Best, Sławomir Biały  (talk) 12:05, 11 April 2012 (UTC)
 * 1) Leave Einstein notation alone.  This is about the Einstein summation convention, which is a separate topic for an article, distinct from "tensor index notation".  If that is unclear from the article title, then move it to Einstein summation convention over the redirect.
 * 2) Leave all of the articles Index notation, Tensor, Antisymmetric tensor, Raising and lowering indices, Abstract index notation, Covariance and contravariance of vectors alone (as well as possibly any others I might have missed)
 * 3) Create a new article Ricci calculus (or tensor index notation, although the former is preferable) which covers the basic rules for the tensor indices (symmetrization, skew symmetrization, covariance and contravariance, and covariant differentiation).  This article can be linked from the various related articles as needed.


 * I didn't know what exactly was being proposed either. Thank you for suggesting a new article where we can write about this. If you were to revert my edits on Einstein notation, I'll not be offended, but there really was too much dribble for nothing so removed as much as possible... F = q(E+v×B) ⇄ ∑ici 12:20, 11 April 2012 (UTC)


 * Those edits were probably ok. I haven't looked at them in detail, but I doubt it's necessary.   Sławomir Biały  (talk) 12:33, 11 April 2012 (UTC)


 * Thats fine. Thanks again Sławomir Biały for the clear-cut suggestion - Ricci calculus has been created. =) F = q(E+v×B) ⇄ ∑ici 12:38, 11 April 2012 (UTC)


 * Yes, I agree this is a nice name Sławomir, and I would suggest redirecting tensor index notation from its current target to Ricci calculus. As per F=q(E+v^B)'s comments, the bulk of the current article on Einstein notation really belongs in Ricci calculus, as it is irrelevant to the Einstein summation convention; that it is there attests to the confusion surrounding the name Einstein notation.  — Quondum☏ 13:47, 11 April 2012 (UTC)


 * I thought I would just do it, instead of debating over things. Tensor index notation now redirects to Ricci calculus. Now is the time to add historical sources for fluency with Ricci's work and the contents of the article. =) F = q(E+v×B) ⇄ ∑ici 13:54, 11 April 2012 (UTC)


 * This seems a most satisfactory solution. May suggest that any further discussion continues on talk:Ricci calculus?TR 14:37, 11 April 2012 (UTC)
 * Yes. One last thing: shall we move this section Coefficients on tensors and related from Einstein notation to a new section in Ricci calculus? By no means merge/rename or move anything else, since Einstein notation is pretty much fine now, but that section doesn't help understand the summation convention at all. They're just formulae, but where to put them? (Quondum - sorry, this is what you meant all this time, havn't you?) F = q(E+v×B) ⇄ ∑ici 15:21, 11 April 2012 (UTC)
 * I agree that section is out of place where it is now. By all means move it, rewrite it to make sense, etc. Sławomir Biały  (talk) 18:50, 11 April 2012 (UTC)


 * It will be cut and pasted to Ricci calculus. F = q(E+v×B) ⇄ ∑ici 18:53, 11 April 2012 (UTC)

To Sławomir Biały: With what aspect of "the notation" do you think my allegedly imperious viewpoint betrays a lack of basic familiarity? And I am not trying to impose my view on anyone; just stating the facts as I see them. JRSpriggs (talk) 10:06, 12 April 2012 (UTC)


 * First of all, it is entirely in your mind that numerical indices need to be introduced to understand anything, no more so than they need to be introduced to understand expressions written without any indices at all. (But you probably wouldn't understand these expressions either, given that your antipathy to abstract indices seems to extend to expressions involving the symbol "$$\otimes$$" as well.) People I know who use the notation do not mentally substitute numbers in for the indices.  Indeed, they do not do this any more than algebraists writing down a polynomial in an indeterminate cannot understand what it represents without substituting values in for the indeterminate.  Secondly, it's wrong to say that the notation does not permit the use of numerical indices.  To do this, you just need to introduce a basis and contract the free abstract indices against the elements of the basis.  (There are even different conventions to distinguish numerical indices from abstract indices, as well as indices in different vector bundles such as spinors.)   Sometimes it is useful to do this, since in practice there are often anisotropies that can be exploited in a frame (not necessarily a coordinate frame, e.g., PNDs for the Weyl tensor may not be integrable).  Finally, the advantages of such a notation are clear to anyone who has used it:  expressions are invariant when written in this notation, unlike in classical numerical index notation.  With classical index notation, one often sees horrors like $$\partial v^i/\partial x^j$$, for instance, but a more subtle point is things like $$dv^i$$.  In classical index notation, there is ambiguity in this expression: it could be the exterior derivative applied to the components $$v^i$$ or it could be the covariant exterior derivative applied to the vector.  One of these is invariant and the other isn't.  In abstract indices, you have no choice but to interpret $$dv^i$$ as a covariant exterior derivative.  The idea that the "rules" are somehow "arbitrary" (your words) is ludicrous.   Sławomir Biały  (talk) 12:45, 12 April 2012 (UTC)

Reasonable numbers of published works
Can someone inform me on policies delineating how many publications it is reasonable to list in an article on a living person? David Hestenes currently has 47. That seems kind of gratuitous to me, but again, I have no idea what the policies suggest. Rschwieb (talk) 18:31, 11 April 2012 (UTC)
 * My rule of thumb would be: each one needs to have something to distinguish it. Books (but maybe not edited volumes) and papers that have won awards can always be listed. Papers about which there is a separate review article (not just a MathSciNet entry). Papers that are in the top five for citations by that author. Beyond that, as in the case you mention, it starts to look too indiscriminate to me. —David Eppstein (talk) 18:50, 11 April 2012 (UTC)


 * You might see Notability (people) and Biographies of living persons. F = q(E+v×B) ⇄ ∑ici 18:58, 11 April 2012 (UTC)


 * There were (may still be) numerous WP:POV problems with the article, which I recently took a whack at. At the end of March, User:Xtr rossi began massive edits, and appears to be editing only that article. It appears this is the editor responsible for the bevy citations and less-than-neutral descriptions. You can see the claims of success and popularity were uncited, but nary a Hestenes publication was forgotten :(
 * I haven't altered the citations yet, I'm not sure what to do. If I find time, I will try to apply the "most cited" criterion you mentioned, David Eppstein. Thank you both for the advice. Rschwieb (talk) 19:38, 11 April 2012 (UTC)


 * I tried to add inline citations, but it breaks down since there is no [1] or [19] inline with the article text, yet they are there in the list... I’ll tell him off at user page for this... Why should others have to clean these things (an easily preventable mess...). =/


 * Good job for raising this problem Rschwieb, its pretty bad... F = q(E+v×B) ⇄ ∑ici 20:24, 11 April 2012 (UTC)
 * Those two citations might have been lost when I was cleaning up the POV. There might be a COI here too... a diagram uploaded by the user as "own work" (now visible at geometric calculus is very similiar to this one at Hestenes website. Rschwieb (talk) 21:52, 11 April 2012 (UTC)
 * No worries, not suprised you lost the citations (if so) the way he did it. Yes that image does appear to be copied and claimed for his own. Yet why did you add it ? Do anyone know if that's his website? F = q(E+v×B) ⇄ ∑ici
 * I like the graphic, but it was just out of place in a biography... is there a reason it shouldn't be used at all? Rschwieb (talk) 23:00, 11 April 2012 (UTC)
 * I had no implication against using it - you suggested there might be a COI but then added the image to Geometric calculus, which seemed contradictory. Nevermind I guess... =) F = q(E+v×B) ⇄ ∑ici 23:20, 11 April 2012 (UTC)

My opinion is that all of the geometric algebra stuff is a bit on the fringes (WP:FRINGE), and the GA viewpoint is often pushed in articles where it is not really helpful, nor does it typically conform to WP:WEIGHT. Hestenes is certainly one who has made quite a cult industry out of appropriating the works of others and rebranding them under the rubric of "geometric algebra", and for that he is certainly notable. But his notability as a legitimate physics researcher is dubious at best. I think the lack of secondary sources definitely bears this out. Indeed, as do the (exclusively primary) sources referenced in the article: for instance, the "long series of papers" referenced in the article includes many papers of dubious scientific merit (for instance those published in the American Journal of Physics, which is apparently not a research journal). I would suggest removing everything in that article that cannot be attributed to reliable secondary sources, including the long publication list of debatable worth. The most relevant policies here are WP:PSTS and WP:BLP, although if push comes to shove other policies are also relevant. Sławomir Biały (talk) 00:05, 12 April 2012 (UTC)
 * I think I could handle math papers but I never learned the proper tools to check numbers of citations for papers in other fields. What's the best tool? Thanks Rschwieb (talk) 00:17, 13 April 2012 (UTC)
 * It varies a lot by field. For many of them, ISI/Web of Science is good, but for computer science it's not, and I generally use Google Scholar instead. For math I'm not sure; MathSciNet is very good at finding all published math papers but much less good at counting citations. —David Eppstein (talk) 02:00, 13 April 2012 (UTC)

I think generally, a bio should contain no list of published papers. In almost all cases it is better to provide an external link to either: 1)a Bibliography by the author himself. 2)A search of any appropriate indexing service providing a list of all published works. The only reason to really deviate from this, is if the published work is in itself notable (but possibly not notable enough for its own article) or if the published work is important for establishing the notability of the subject.TR 11:07, 13 April 2012 (UTC)
 * Hm, now I've got conflicting advice: "use top cited works" and "none, use external links if possible". Is either of these in print somewhere so that I can decide? Rschwieb (talk) 13:46, 13 April 2012 (UTC)

π peer reviewer needed
The pi article is in need of a peer reviewer at Peer review/Pi/archive2. The reviewer should be someone familiar with FA criteria. Thanks. --Noleander (talk) 17:01, 13 April 2012 (UTC)

new article about mesh-free method of computational fluid dynamics needing initial review
Viscous vortex domains method is a very new, quite short, article that needs might benefit from expansion after a quick look-over by someone vaguely familiar with mathematics & mechanics (or your local variant of such concepts...) and then the "new unreviewed article" template removing. I'm informed that it's half physics and half mathematics (don't they overlap still?) so I'll post at the Physics project as well if I get time. Many thanks! --Demiurge1000 (talk) 21:09, 13 April 2012 (UTC)

777sms's crusade for Planet Math
User has been going through all our articles systematically changing the "planetmath" template to the "PlanetMath attribution" template. This introduces an implication that we have actually borrowed material in those articles from Planet Math where no such implication was previously present. While that may be appropriate in some cases, I suspect that there are many other cases where we have not borrowed from them, but merely wanted to make another source available to the user. What, if anything, should we do about this? JRSpriggs (talk) 06:42, 14 April 2012 (UTC)
 * Has anyone tried talking to this user? He or she may be doing it out of ignorance, not realizing the difference in meaning between these two templates. —David Eppstein (talk) 06:46, 14 April 2012 (UTC)


 * I only just became aware of this problem. Since you mentioned it, I have left a message for him/her to see this thread and respond here. JRSpriggs (talk) 06:56, 14 April 2012 (UTC)

Note. This probably explains most of the edits, and is a good idea. (But this editor really has to use edit summaries to avoid this kind of misunderstanding. But he positively refuses to do so.)   Sławomir Biały  (talk) 10:43, 14 April 2012 (UTC)


 * The editor's "explanation" for this refusal is https://en.wikipedia.org/w/index.php?title=User_talk:777sms&diff=next&oldid=413744431 --Joel B. Lewis (talk) 13:03, 14 April 2012 (UTC)
 * There was an ANI in January 2012 on 777sms' refusal to provide edit summaries. The ANI is here.  The consensus in that ANI was that edit summaries are optional. and refusing to supply them is not grounds for sanctions; unless the editor is doing something else wrong.  In that ANI, there was no additional problem with their edits (beyond the absence of edit summaries), so no action was taken. --Noleander (talk) 13:16, 14 April 2012 (UTC)
 * Two users being of that opinion isn't consensus, if I may say so. ;) Nageh (talk) 13:36, 14 April 2012 (UTC)
 * Citing from WP:Editing policy: "...the more radical or controversial the change, the greater the need to explain it. Be sure to leave a comment about why you made the change." It seems that this is being a controversial change that needs to be explained. Nageh (talk) 13:42, 14 April 2012 (UTC)
 * I agree that edit summaries should be provided; and I concur that the ANI was rather brief and not very conclusive. I'm just pointing out the ANI so other editors can gather the background. --Noleander (talk) 17:14, 14 April 2012 (UTC)

Just to make sure I've understood correctly: the old "Planetmath" template has been renamed to PlanetMath attribution, and the other edits consist of pointing things to the renamed template? Jowa fan (talk) 13:27, 14 April 2012 (UTC)
 * We now have three different templates a simple link,  a full citation,  for pages which incorporates material from PlanetMath. There is also  which is only used, on one talk page and should probably be deleted. I think in most cases   is incorrect and should be changed to one of the other two.--Salix (talk): 17:49, 14 April 2012 (UTC)

Bulk nomination of some polygons with a large number of sides
Please comment on Articles for deletion/Chiliagon and give your opinions. Double sharp (talk) 03:16, 15 April 2012 (UTC)
 * I, for one, disagree that these 10 polygons are non-notable, and the purpose of the AfD is to decide whether they are. WP:Canvassing notes that notifications of this kind should be "neutrally worded with a neutral title." -- 202.124.73.129 (talk) 15:45, 15 April 2012 (UTC)
 * Deciding whether an article is notable isn't the only purpose of AfD, but I've changed the wording of the heading anyway. Double sharp (talk) 13:09, 16 April 2012 (UTC)

Physicist uses math to beat traffic ticket
This incident might be notable enough for a Wikipedia article. —Wavelength (talk) 20:24, 15 April 2012 (UTC)
 * Buzz Blog: Physicist Uses Math to Beat Traffic Ticket


 * Please do not make an article on it. I think it's a rather old joke. In college, I heard a physicist use it in a word problem on the speed of a snail being observed by some graduate students. Rschwieb (talk) 13:39, 16 April 2012 (UTC)


 * In a word - no. In more words - you added this to wikiproject physics, with no success of agreement. F = q(E+v×B) ⇄ ∑ici 14:54, 16 April 2012 (UTC)

Complete Elliptic integrals
Could someone check out what I've said at Talk:Elliptic integral that I'm not making a complete something else thanks. It has long been a bit confused and it would be nice to fix it all up properly. Dmcq (talk) 09:53, 17 April 2012 (UTC)

HighBeam

 * HighBeam details an opportunity for experienced Wikipedia editors to have free access to HighBeam Research, an invaluable resource for locating reliable sources for articles and content related to politics as well as other subjects.

The notice above is being circulated to various WikiProjects, but AFAIK hasn't appeared here yet. What do people think of this? Michael Hardy (talk) 01:18, 22 April 2012 (UTC)
 * I got one of the first-round accounts. So far I've found it quite useful for finding fairly recent US newspaper stories (say within the last 30 years); this might be helpful in sourcing some of our mathematical biographies and has definitely been helpful to me in some non-mathematical articles. I haven't tried to use it to find mathematics journal articles, though, because I get access to many of those through my employer. —David Eppstein (talk) 02:29, 22 April 2012 (UTC)

I went to the HighBeam web site, where I have no account, and I was able to do some searches, but the difference between having and not having an account was that I could read only the beginnings of the articles I found. I entered "Karlis Kaufmanis" and found a few things, but not much beyond what I'd already found elsewhere. (I created the article about him recently and have found a dearth of information to expand the article.) Michael Hardy (talk) 02:59, 22 April 2012 (UTC)

I got an account as well. It's overall use for math is somewhat limited but still it can be useful in particular for those who do not have access to journal archives like JSTOR or others. Afaik there are still account available since not all 1000 accounts were used up in the original application period.--Kmhkmh (talk) 05:42, 22 April 2012 (UTC)

Edit war at vector space
There is an edit war with some IPs at vector space regarding the example of complex numbers. I have started a discussion at the talk page. Please comment there. Sławomir Biały (talk) 13:58, 22 April 2012 (UTC)

Input needed at pi regarding alternate tau = 2*pi
Input would be helpful in the pi Talk page regarding how much mention, if any, should be made in the pi article about the proposed alternate constant   tau = 2*pi. The discussion is at Talk:Pi. --Noleander (talk) 16:06, 22 April 2012 (UTC)

D.Lazard's edits in Sturm's theorem and Root-finding algorithm
Hello,

I started editing these articles because of "orphaned article" message on the article "Budan's theorem" that my students and I have worked on for the past month. My function was to fine-tune the article at the end.

I am astonished that the author of the Sturm article claims that Sturm's method is available "in every computer algebra system". That is simply not true; he admits as much by claiming, in his other article on root finding algorithms, that maple uses the Vincent-Collins-Akritas method as the default method! Add to this Mathematica, which always had the VAS algorithm, (S works for Mathematica), Sage also, etc etc ... and you get the degree of accuracy of his statement.

Besides, Sturm's method is to be compared with other methods, like VCA and VAS; why does he not want this comparison? I believe that Lazard (whom I have never met or interacted with in the past) is the one who tries to impose HIS limited point of view on the readers. Besides, (assuming good intentions) his knowledge of English did not allow him to differentiate (in the article on root finding algorithms) between "Uspensky's method" and "modified Uspensky's method" and he used the first thinking the two expressions are interchangeable.

Also, on Sturm's theorem he talks about bounds and the only one that came to his mind was what he calls Cauchy's bound; Cauchy gave a bound ONLY on the positive roots and NOT on the absolute value of the roots. The mathematicians of the 19th century knew better. See Bourdon's algebra.

In summary, I have only ADDED material to the above mentioned articles and DID NOT ERASE anything Lazard wrote. I expect the same courtesy from him as well. He got his point of view and I have mine and I think both need to be taken into consideration. But we both have to write accuracies. So, I expect Sturm's method to be reverted to the previous version where I was saying that Sturm's method was used by "everybody until about 1980 --- when it was replaced by methods derived from Vincent's theorem", along with the supporting references.

And I close with the following: If Lazard does not like anything on the Budan article he should say so and explain the reason he does not like it. Saying that the article is "... entirely devoted to the personal views of Akritas on the history of mathematics" proves nothing; he should tell us his own views -- if he has any. My views have already been judged by peers.

Alkis Akritas2 (talk) 12:17, 19 April 2012 (UTC)


 * With regards to this article, editors will need to remain alert and judge the appropriateness of possible self-citation in the references. Rschwieb (talk) 13:31, 19 April 2012 (UTC)


 * For most Akritas assertions, my answer is simply "Look on the history of these articles and on the reasons given in the edit summaries". However, for wikipedians who are not familiar with this subject, I have to give some technical information.
 * For counting and locating the real roots of a polynomial, there are two main algorithmic methods, Sturm's theorem, and a method based on Descartes' rule of signs and Vincent theorem. The first true algorithm based on the latter method was called "Uspensky algorithm" by its authors (Collins and Akritas himself). As this algorithm implies a change of variable at each step of a recursion, it has been improved by several authors mainly by a better way of changing of variable or, I believe, by replacing this change of variable by a continuous fraction expansion. This leads to several variants of "Uspensky algorithm", that most authors (except Akritas) continue to call "Uspensky algorithm".
 * As explicitly stated in Collins-Akritas paper, Uspensky algorithm is not due to Uspensky.
 * When Uspensky algorithm was widely known under this name by the computer algebra community, Akritas decided to rename it. As far as I know, he has not been followed. He decided also to try to attribute it to an earlier author, which seems an historical mistake, as "Uspensky algorithm" was new as an algorithm, even it is based on a series of previous theorems (Descartes rule of signs, Budan's and Vincent's theorem): As usual, a new result uses previous knowledge.
 * For the comparison of the various algorithms, the existing knowledge is that they have all the same worst case time complexity. However the variants of Uspensky algorithm are, in practice, faster than Sturm's algorithm, mainly because the worst case complexity is always reached with Sturm's algorithm while it is rarely reached with the other algorithms. As far as I know, there is no reliable comparison between the variants of Uspensky algorithm. This the reason while Akritas edit in root-finding algorithm may not been kept. However, if the default root-finding algorithm of Mathematica uses a variant of Uspensky algorithm, this has to be said.
 * Sturm's theorem is not a well written article. In particular, a section on complexity is lacking.
 * D.Lazard (talk) 14:08, 19 April 2012 (UTC)
 * The root finding article also still has content which should be examined by more editors for WP:COI and WP:POV problems. Rschwieb (talk) 19:50, 19 April 2012 (UTC)


 * Just a comment on the history: Vincent wrote his "theorem", in fact an algorithm to derive the continued fraction expansion of each (positive) root of a polynomial, in 1834, the available publication in Compte Rendu (vol. 1) is from 1836. There he cited the extension of Decartes rule by Budan and Fourier. Uspensky wrote an article (or book section) on his interpretation of Vincents algorithm, eliminating the continued fraction part for an easier complexity result. Akritas added the Cauchy bound and step sizes greater than one to the original Vincent algorithm and provided a complexity result for the modified algorithm.--LutzL (talk) 09:19, 20 April 2012 (UTC)
 * And a comment on contents: I would really like to see the Budan article split into two or three with a separate Vincent method article. The Akritas extentions and results could be a second part of that article or even another separate article. And no, at the moment I will not insert myself between the "clash of giants".--LutzL (talk) 09:19, 20 April 2012 (UTC)
 * First, there is no clash whatsoever. I believe Lazard has made constructive criticism on various points and will eventually accept the fact that there cannot be a Uspensky's method, because otherwise everybody would be taking somebody else's method, double its computing time and present it as his/her own. This is precisely what Uspensky did to Vincent's (exponential) method, as is shown in the diagrams of Budan's thorem, and therefore one can talk only about Vincent's (exponential) method. I am sure Lazard will be persuaded when I show him the printed evidence. And instead of looking at the "... the history of these articles and on the reasons given in the edit summaries", as Lazard suggests, I suggest that we look at the articles THEMSELVES; they can be found on my webpage at the University of Thessaly.
 * Second, Lazard should read the Collins-Akritas paper to the end; he seems to stop in the middle where we describe what we erroneously called "Uspensky's algorithm" (the process seen in Budan's theorem) and it seems that he never reached the end of the paper where we talk about "modified Uspensky's method". It is the latter that has been renamed the Vincent-Collins-Akritas (VCA) method. More on the topic in a forthcoming article in Wikipedia.
 * Third, after I published the "There is no "Uspensky's method" the computer algebra community realized the fallacy and started calling it "Collins-Akritas" (partly right) or "Descartes' method" (totally wrong). It was a Frenchman who called it the "Vincent-Collins-Akritas" (VCA) method.
 * Fourth, even a great supporter (German) of calling the VCA method "Descartes' method" recently changed tack and calls it the Vincent-Collins-Akritas method.
 * Finally, with my students, we do plan to write a separate article about Vincent's theorem and the methods derived from it. We just came back from Easter recess, and are ready to go. Then Lazard will be persuaded by the historical evidence. Till then,
 * Akritas2 (talk) 11:16, 23 April 2012 (UTC)

Response to LutzL: Uspensky did not eliminate the "... continued fraction part for an easier complexity result". Both Vincent's method AND Uspensky's implementation of Vincent's theorem use continued fractions and are BOTH exponential in nature; in fact, Uspensky's is twice more exponential because he doubles the work done by Vincent. See Budan's thorem and Vincent's figure right above it to get a clear picture. What I did was to make Vincent's exponential method polynomial in time. To prove it, back in 1978, I had made some plausible assumption, but in 2008 Sharma proved it without any assumptions whatsoever. Akritas2 (talk) 11:55, 23 April 2012 (UTC)

Category:Theorems in Galois theory
Category:Theorems in Galois theory, which is within the scope of this WikiProject, has been nominated for deletion. If you would like to participate in the discussion, you are invited to add your comments at the category's entry on the Categories for discussion page. Thank you.. -- Brown HairedGirl (talk) • (contribs) 15:17, 23 April 2012 (UTC)

User:Akritas2's edits in Sturm's theorem and Root-finding algorithm
User:Akritas2 has recently edited Sturm's theorem and Root-finding algorithm in order to add references to his publications and introduce his personal point of view on the subject. I have reverted his edits per wp:COI, wp: NPOV wp:OR and lacking of secondary sources. He has reverted my reverts. I may not revert again, because, knowing personally the guy, I am sure this will lead immediately to an edit war. For the same reason, I cannot discuss constructively with him. Could someone look at this problem?

He has also created Budan's theorem, a page which deserve some attention.

D.Lazard (talk) 15:11, 14 April 2012 (UTC)


 * Hello,


 * I started editing these articles because of "orphaned article" message on the article "Budan's theorem" that my students and I have worked on for the past month. My function was to fine-tune the article at the end.


 * I am astonished that the author of the Sturm article claims that Sturm's method is available "in every computer algebra system". That is simply not true; he admits as much by claiming, in his other article on root finding algorithms, that maple uses the Vincent-Collins-Akritas method as the default method! Add to this Mathematica, which always had the VAS algorithm, (S works for Mathematica), Sage also, etc etc ... and you get the degree of accuracy of his statement.


 * Besides, Sturm's method is to be compared with other methods, like VCA and VAS; why does he not want this comparison? I believe that Lazard (whom I have never met or interacted with in the past) is the one who tries to impose HIS limited point of view on the readers. Besides, (assuming good intentions) his knowledge of English did not allow him to differentiate (in the article on root finding algorithms) between "Uspensky's method" and "modified Uspensky's method" and he used the first thinking the two expressions are interchangeable.


 * Also, on Sturm's theorem he talks about bounds and the only one that came to his mind was what he calls Cauchy's bound; Cauchy gave a bound ONLY on the positive roots and NOT on the absolute value of the roots. The mathematicians of the 19th century knew better. See Bourdon's algebra.


 * In summary, I have only ADDED material to the above mentioned articles and DID NOT ERASE anything Lazard wrote. I expect the same courtesy from him as well. He got his point of view and I have mine and I think both need to be taken into consideration. But we both have to write accuracies. So, I expect Sturm's method to be reverted to the previous version where I was saying that Sturm's method was used by "everybody until about 1980 --- when it was replaced by methods derived from Vincent's theorem", along with the supporting references.


 * And I close with the following: If Lazard does not like anything on the Budan article he should say so and explain the reason he does not like it. Saying that the article is "... entirely devoted to the personal views of Akritas on the history of mathematics" proves nothing; he should tell us his own views -- if he has any. My views have already been judged by peers.


 * Alkis (talk) 12:29, 19 April 2012 (UTC)


 * Observations of an outsider: To help reduce the backlog, I patrol a few new pages each time I log into WP.  I approved the Budan's theorem article but marked it as needing improvement.  Improvement by several interested editors is notable.  From my browsing related articles, it appears that both of you are well known and highly respected in your field.  Wikipedia is richer with contributions from both of you.


 * Alkis, within Wikipedia, Lazard's observations are correct. Nine of the 17 citations in the Budan's theorem article refer to your papers.  Even though your work was peer reviewed and correct, it is still your work expressing your point of view which is a potential conflict of interest.  I judge that the solution is simple.  You wrote that "my students and I have worked on" the article.  Now it the time to back away and challenge your students to take over, to edit the Budan article and related articles.  Your students' styles may express the material in a way that seems more relevant to their peers (who are more likely to read the article than your or my peers).  When your students write or edit an article, your papers become valid second or third party rather than primary sources.  Don't just use student accounts to avoid these objections; challenge your students to think and write for themselves.  Everyone will benefit.  Take care, DocTree (talk) 23:12, 19 April 2012 (UTC)


 * Indeed Doctree, I felt uneasy myself about this fact and have solicited the help of two professors of the history of mathematics. One told me this is ok, as nobody else has dealt with this subject. I am waiting for the other one as well (to come back from a conference where she went) and I will ask them to write a report. Moreover, as you can see from the the talk page of Sturm's theorem (17:16, 22 April 2012 (UTC)) I have even invited Lazard to evaluate our page.
 * Akritas2 (talk) 11:41, 23 April 2012 (UTC)


 * For the quick access of readers, the following contributed sections are relevant: Budan%27s_theorem, Sturm%27s_theorem, and Root-finding_algorithm. The issue is that it appears there are little to no independent citations which argue the same thing. While the material may be true, I'm worried that the current level of citation does not meet WP's level of verifiability. Rschwieb (talk) 13:39, 24 April 2012 (UTC)


 * To the above list of sections I would add Sturm%27s_theorem
 * Akritas2 (talk) 14:46, 25 April 2012 (UTC)

PlanetMath as source?
Any opinions on this? Please comment here. Sławomir Biały (talk) 11:57, 15 April 2012 (UTC)
 * This set the problem of sources for the result of a mathematical computation. The present rule for such a sourcing is to provide a text containing the result. IMO, this is archaic, as most of the time, such a result is the result of built-in a function of most computer algebra systems. Thus, in this case, a source could be "result of Laplace function of Maple (software) applied to the first column of the table". This is, not only, more reliable than a text source, as typos are avoided, but also more useful for the reader, as giving him a way to obtain the result for similar inputs, not appearing in the table. Is there some guideline for this kind of sources? D.Lazard (talk) 12:30, 15 April 2012 (UTC)


 * Perhaps some like Wolfram Mathworld are good for external links in the last resort, but not so much PlanetMath (it’s not that brilliant anyway). In any case, it’s better to just use books obviously. I have many so if people use websites like this as sources, I (or anyone) will try to replace them as and when. (Perhaps that was obvious anyway...) F = q(E+v×B) ⇄ ∑ici 14:12, 15 April 2012 (UTC)


 * Aside from any quality concerns, it also does not look very durable. The front page at Planetmath says they recently lost all changes since last October in a crash after "many months of instability". Rschwieb (talk) 14:24, 15 April 2012 (UTC)

Well planet math is community wiki without any read editorial by noted experts but just by the community at large (like WP), hence it is normally not suited as a source. However it is still sometimes or even often well suited to listed under external links.--Kmhkmh (talk) 08:41, 25 April 2012 (UTC)

Double exponential function
We have a persistent single-purpose account active on Double exponential function who has been adding material which is somewhat relevant but in (what I feel is) an unencyclopedic style that unbalances the article, and has shown no attempt to engage other editors on the subject. More eyes on it would be helpful. —David Eppstein (talk) 20:58, 25 April 2012 (UTC)

MediaWiki 1.20wmf1 deployed and broken
This is just to inform you that MediaWiki version 1.20wmf1 has just been deployed, but its TeX output is broken, unfortunately. In particular, this means that you will see a lot of "Misplaced &" errors or spurious "&amp;"s in MathJax. Nageh (talk) 20:23, 23 April 2012 (UTC)
 * Ok, I have implemented a work-around. Bypass or clear your cache to reload the script. Nageh (talk) 23:57, 23 April 2012 (UTC)
 * Not sure if this is related but the font is no longer working at golden ratio and probably many other pages. Tkuvho (talk) 20:02, 26 April 2012 (UTC)
 * Hmm, it just came back. Tkuvho (talk) 20:03, 26 April 2012 (UTC)
 * Probably it took too long loading one of the scripts. Nageh (talk) 20:15, 26 April 2012 (UTC)

Definitions of operator symbols
When trying to get a quick overview of a topic in mathematics, a reader sometimes encounters a barrier with the inability to quickly determine what an operator symbol means. As a (maybe too easy) example, consider the following extracts from the article Chain rule:
 * 1) "...the chain rule expresses the derivative of the composite function f ∘ g in terms of the derivatives of f and g..."
 * 2) "The rule is sometimes abbreviated as $$(f\circ g)' = (f'\circ g) \cdot g'.\, $$"

Please note, I am not alleging that anything is wrong with the chain rule article. However, for someone who is not familiar with the use of $$\circ$$ to denote function composition, there might be three reasons for initial confusion:


 * 1) The reader may not immediately be able to figure out what the symbol means.
 * 2) The symbol for function composition is present in two very different sizes, which might not be seen as the same symbol.
 * 3) The small instance of the symbol could be mistaken for the raised-dot symbol used for multiplication.

If $$\circ$$ had been a word instead of a symbol, its initial use would have carried a link to an article about the symbol. But we do not (as far as I know) have a way to turn a symbol into a link, as in $\circ$, which does not work.

What is the best practice for an article-writer (or editor) to use when an operator definition is needed? Is there a nice way to add a footnote-style link to an operator?

Incidentally, the problem usually arises for symbols less familiar than $$\circ$$. For example, what is the definition of $$\vDash \!\,$$. . . and how would I best make that definition available to a reader? Dratman (talk) 22:37, 26 April 2012 (UTC)


 * In the instance you mention, one could simply insert the words "where $\circ$ denotes composition of functions" in an appropriate place. I would think something like this is possible in almost every instance.  (By the way, I agree that the size difference in this case is really atrocious.  Is there a better HTML (or whatever) symbol, or is that really it?) --Joel B. Lewis (talk) 23:35, 26 April 2012 (UTC)
 * There seems to be a difference between the "correct" unicode symbol U+2218 RING OPERATOR (&#x2218;) and Latex's \circ ($$\circ$$). The unicode U+25CB WHITE CIRCLE (&#x25CB;) might actually be a better fit. Perhaps \circ and  U+25CB are typographically the same but both semantically wrong.--Salix (talk): 08:35, 27 April 2012 (UTC)
 * White circle is used on the Function composition page and I've now changed Chain rule to use it as well.--Salix (talk): 08:41, 27 April 2012 (UTC)


 * To me (in Firefox with the Verdana font size 16), the unicode U+25CB does not appear to be a circle. Rather it is flattened with the vertical diameter smaller than the horizontal diameter. The other two are true circles. JRSpriggs (talk) 08:49, 27 April 2012 (UTC)

AFC input needed
Please could a knowledgeable member of this project take a look at Wikipedia talk:Articles for creation/Carlitz exponential and let us know weather it is notable and accurate? I'm a mathematical dunce and would appreciate some expert input into this submission's suitability. Pol430 talk to me 13:21, 27 April 2012 (UTC)


 * It seems perfectly acceptable to me, so I created the article at Carlitz exponential. -- Jitse Niesen (talk) 15:48, 27 April 2012 (UTC)


 * I tagged it an orphan. Then I created one link from another article, but probably there should be more.  (I also did some edits to bring it closer to the norms of WP:MOSMATH and WP:MOS. Michael Hardy (talk) 21:56, 27 April 2012 (UTC)


 * Thanks to both of you for the assistance :) Pol430  talk to me 23:06, 29 April 2012 (UTC)

Antarctica Journal of Mathematics at AfD
See Articles for deletion/Antarctica Journal of Mathematics. -- 202.124.74.240 (talk) 11:24, 30 April 2012 (UTC)