Wikipedia talk:WikiProject Mathematics

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Mathematician categories

As I was adding some Category:Women mathematicians into non-gendered parts of the tree, I noticed that Category:American mathematicians, and several others, have by-century trees, but that are sparsely populated. What would think about making those century trees (like Category:20th-century American mathematicians diffusing on the head category, and move all mathematicians into those trees, by century, out of the head cat? Something similar was done recently at Category:American novelists (though there is still some controversy about it). What about here? If not, I might suggest otherwise to delete those cats, as having them as non-diffusing is a bit non-standard (by-century cats are usually diffusing elsewhere in the tree). Best --Obi-Wan Kenobi (talk) 23:24, 21 May 2013 (UTC)

Any thoughts? --Obi-Wan Kenobi (talk) 16:33, 3 June 2013 (UTC)

Yurii Reshetnyak

The new article Yurii Reshetnyak has been proposed for deletion under WP:BLPPROD. Reshetnyak is a very influential figure in geometric analysis and mathematical elasticity. We should have an article about him, even if it's only a stub. Unfortunately most biographical sources appear to be in Russian. Please help to improve the article! Sławomir Biały (talk) 23:02, 2 June 2013 (UTC)

Disambiguation help needed.

Greetings! Expert mathematical help is needed in determining the correct targets for links to the following disambiguation pages:

1. Facet (mathematics) and Facet (geometry) both redirect to Facet (disambiguation), for a total of 138 links. Y Done D.Lazard (talk) 16:31, 3 June 2013 (UTC)
2. Normed algebra: 24 links
3. Sum of squares: 18 links
4. Lie bracket: 17 links
5. Primitive polynomial: 17 links Y Done D.Lazard (talk) 09:41, 3 June 2013 (UTC)
6. Simple root: 17 links Y Done Mark M (talk) 12:55, 3 June 2013 (UTC)

Please also double check to make sure that these terms are indeed ambiguous, and are not susceptible to being presented in a substantive article as a topic an and of themselves. Cheers! bd2412 T 00:18, 3 June 2013 (UTC)

I got to ask: why is Lie bracket a disambig page? Not just a redirect to Lie algebra. (maybe I don't have a good perspective.) -- Taku (talk) 00:54, 3 June 2013 (UTC)

"Lie bracket" by itself is often used to refer to the Lie bracket of vector fields. Although a disambiguation doesn't seem to be necessary. We can do that with a hat note or, even better, mention the algebra of vector fields in the lead of the Lie algebra article, with a link to the relevant notion of Lie bracket. Sławomir Biały (talk) 03:04, 3 June 2013 (UTC)

I agree, per WP:TWODAB; so I redirected Lie bracket to Lie algebra, and put a hatnote. Though the Lie bracket of vector fields is also mentioned later in the article, so I'm not sure if a hatnote is even necessary. Mark M (talk) 08:27, 3 June 2013 (UTC)

Thanks, I appreciate the solution. bd2412 T 12:04, 3 June 2013 (UTC)

For Simple root, there is a strange situation: All articles linking to this dab page are intended for the meaning in group theory (root system), while, IMO, for most people the main topic refers to a root of a polynomial. Both links of the dab page are redirects to sections. Thus I suggest to redirect Simple root to Polynomial#Solving polynomial equations (the target of Simple root (polynomial)) and to add a hatnote to the target section. I believe that it will be more useful for the readers than the symmetric action, which would need less editing work. D.Lazard (talk) 09:41, 3 June 2013 (UTC)

Incoming links can be a tricky indicator, since editors may link to an article merely because it is the existing target, rather than being a primary topic. If "real world" sources on the internet and in print indicate that Polynomial#Solving polynomial equations is the primary target, then this can be redirected per WP:TWODABS. Ideally, a disambiguation page should only exist if there are too many meanings of a term to fit neatly into a hatnote, or if the few meanings that do exist are in equipoise. Cheers! bd2412 T 12:08, 3 June 2013 (UTC)

Okay, I've fixed all of the incoming links to Simple root, and sent all but one to Simple root (root system) (which is a redirect). Only one incoming link was actually intended for Polynomial#Solving polynomial equations, which is where Simple root is now redirected. Mark M (talk) 12:55, 3 June 2013 (UTC)

I have moved the geometric content of Facet (disambiguation) to Facet (geometry), which is now a stub, and redirected Facet (mathematics) to Facet (geometry). There is no reason to tag Facet (geometry) as a dab page, because the different meanings are strongly connected, and a part of the content does not appear elsewhere. D.Lazard (talk) 16:31, 3 June 2013 (UTC)

Fantastic! That leaves only Normed algebra and Sum of squares in the top 500 disambiguation pages. bd2412 T 17:25, 3 June 2013 (UTC)

BTW, I did not find [1] a good move. Unfortunately there are some users who say: if this is a dab page with inbound links, then let us… to disguise a dab page as an article, and disambiguators become happy. I do not think it improves an encyclopedia. Moreover, Bubka42’s edit actually concealed the Normed associative algebra red link which, unlike the current piece of crap, could be a valid encyclopedic topic. May I revert this? Incnis Mrsi (talk) 09:59, 6 June 2013 (UTC)

The over-riding question is whether there is a topic here that is capable of being discussed as an article, or whether there are merely a collection of unrelated terms that happen to share the same name. So far as I can tell from the previous version of the page, there are no title matches at all. It is not as though there is an album titled "Normed Algebra" and bird called the "Normed Algebra" and a person named "Normed Algebra" in the mix. "Normed associative algebra" and "Normed division algebra" are partial title matches, and are therefore not ambiguous to one another. What is left, then, but a single mathematical concept which is merely applied in different ways? bd2412 T 13:24, 6 June 2013 (UTC)

I don't think that your original dab page was truly a disambiguation page either. A normed algebra after all is an algebra with a norm. So the links there were all topics related to this. So I'd suggest reverting the edit if you like, but removing the disambiguation template. Sławomir Biały (talk) 13:51, 6 June 2013 (UTC)

A dab or a stub, but “normed associative algebra” is a more concrete structure which the (ambiguous) wording “normed algebra” usually, but not always, denotes. Recent edits plays this circumstance down. And in any case… fix what occurred at Normed division algebra (|talk|history|links|watch|logs), please. I hoped to fuse two dabs into one, but if there is no support for it, then it would be better to restore its original tiny dab page or do something else but redirecting to a strange stub. Incnis Mrsi (talk) 15:23, 6 June 2013 (UTC)

I note that neither Gelfand–Mazur theorem nor Hurwitz's theorem (composition algebras) mention the term "Normed division algebra", which means that they can not be included on any disambiguation page for the unmentioned term (see WP:DABMENTION). To the extent that the phrase "Normed division algebra" is used with respect to either article, it must be discussed in that article before it can be included on a disambiguation page, because disambiguation pages only disambiguate content that is already in the encyclopedia. Without that restriction, we could not be sure that the disambiguation page itself is strictly reporting notable uses. However, since those are the only two links claimed to be associated with the exact phrase, "Normed division algebra", WP:TWODABS also applies. Why not redirect Normed division algebra to whichever of those two links is more likely the primary topic of the term, with a hatnote pointing to the other link? (I take it no one would look for Banach algebra or Composition algebra under the name "Normed division algebra"). bd2412 T 15:40, 6 June 2013 (UTC)

This is because you are preoccupied with a formal (link-structural, mention rules, etc.) well-being of Wikipedia, not semantic one, and push forward your “WP:TWODABS” on any pretext or even without one. If there is no clear WP:PRIMARYTOPIC, then do not enforce your dreams that there should be a primary topic. Let experts to decide it, please. There will be numerous links to a dab and you will be slightly unhappy, but eventually it would be better for readers, believe me. Incnis Mrsi (talk) 17:01, 6 June 2013 (UTC)

If there are distinct and different topics, then it should be no problem to fix the links themselves, so that they point to the intended article, and not to a disambiguation page. Remember, disambiguation pages are a means to an end, not an end in and of themselves. They exist to clear up confusion where a term can mean different things, and should not exist if this confusion can be cleared up without creating an extra page to do it. bd2412 T 17:05, 6 June 2013 (UTC)

Long-time requests

Looking at the dates embedded in Wikipedia:Requested articles/Mathematics, I see there are some 40 requests dating back to 2005 and one to 2004. Perhaps we should try to clear the backlog? For reference, they are listed below. Spectral sequence (talk) 17:15, 3 June 2013 (UTC)

IMHO, this list is obsolete and the best is to destroy it. There are many topics of much larger importance which are not, or badly, described in WP and which deserve to have a much higher priority, like Multivariate resultant or D-finite function. D.Lazard (talk) 17:59, 3 June 2013 (UTC)

The traditional approach would be to archive very old entries. Charles Matthews (talk) 15:17, 9 June 2013 (UTC)

Calculus of variations

• Deformation theorem

Category theory

• Atomic topos
• Coquasitriangular Hopf algebra
• Ribbon category
• Semi-abelian category (with redirect from Semiabelian category)

Coding theory

• Coding lemma -

Convex analysis / Optimization

• Constrained conjugate gradient / Conjugate gradient with barriers (how does the barrier effects the conjugate gradient solution) -
• Waterfilling theorem -

Cryptography

• Multilinear modular hashing

Differential geometry and topology

• Natural bilinear concomitant -

Dynamical systems

• Zeeman catastrophe machine -

Functional analysis

• Codistribution -
• Convenient analysis -
• Nonlinear operator theory -

Geometry

• Diametral circle
• Diametral lens

Graph theory

• Intrinsically linked graph
• Restriction scaffold problem

Group theory

• Recoupling theory

History of mathematics and other cultural aspects

• Etymology of mathematical notation —

Lie groups, Algebraic groups / Lie algebras

• Primitive invariant -

Mathematical analysis

• Percent recovery

Algebraic number theory

• Brandt module -

Numerical analysis

• Model order reduction -
• Nested dissection algorithm -

Order theory

• Continuous poset -
• Ideal completion -

Probability theory

• Bayesian mapping -
• Luders rule -
• Marked point process -
• Threshold function and their relation to combinatorics/graph theory, number theory, etc. -

Real analysis

• Maharam theorem -

Statistics

• Burstiness -
• Gap statistic -
• Ryan Einot Gabriel Welsch method -
• Tukey B method -

Topology

Algebraic topology

• Witt space -

General topology

• Contiguity space -
• Double fibration -

Uncategorized

• Dynamic subtraction -
• Eigenfilter -

Six operators

The new article titled Six operators definitely needs work! Including links, context, and some explanation of the role and importance of the concept. Michael Hardy (talk) 21:38, 4 June 2013 (UTC)

L. E. J. Brouwer

Someone moved Luitzen Egbertus Jan Brouwer to Bertus Brouwer. I've always heard him called L. E. J. Brouwer, and I'd never heard Bertus Brouwer before. I've moved it to L. E. J. Brouwer. Michael Hardy (talk) 21:59, 4 June 2013 (UTC)

Ambox-throwing to sections

Jarble (talk · contribs) (notified) was already well-known to me thanks to his “interesting” work with redirects. Recently he turned attention to mathematics, where can see:

1. Placing {{unreferenced section}} to Real number #Properties section, which unlikely contains anything beyond textbooks on mathematical analysis;
2. Cluttering Quotient ring #Examples with {{unreferenced section}} and {{original research}}(!)

Of course, there may be original researches in mathematical articles, but unlikely a reasonable person could claim that a section consisting of disjoint examples, most of which can be found in textbooks, is an WP:original research. Does anybody think that these edits actually helps to improve 10 affected articles? Incnis Mrsi (talk) 06:14, 6 June 2013 (UTC)

These unreferenced sections should be verified by external sources, if possible. I found several lengthy unreferenced sections, and decided to tag them as needing additional references. Adding additional references to these sections would be helpful to readers, since it would enable them to confirm the validity of the statements that are made. Jarble (talk) 06:26, 6 June 2013 (UTC)

How this makes the list of examples an original research? And how do you imagine an intended “externally verifiable” Real number #Properties where most statements are backed by hundreds of textbooks? A dozen of <ref>s on each statement? With page numbers for each instance, or only a chapter name/number? Incnis Mrsi (talk) 06:39, 6 June 2013 (UTC)

I noted a similar phenomenon at Transcendental number#Sketch of a proof that e is transcendental. The section begins We will now follow the strategy of David Hilbert and ends For detailed information concerning the proofs of the transcendence of π and e see the references and external links. In the references, the first item is David Hilbert, "Über die Transcendenz der Zahlen e und $\pi$", Mathematische Annalen 43:216–219 (1893), which is precisely to the point. It seems clear that the section is adequately supported by a reliable source and that any reader would be able to identify the source being relied on. Spectral sequence (talk) 06:42, 6 June 2013 (UTC)

In that case, an inline citation to that particular article should be added to the section, using the <ref> tag. Jarble (talk) 06:55, 6 June 2013 (UTC)

Pointing out what is hopefully obvious: inconsistent citation style and lack of references are two different things. In this case, there was a reference and a citation to that reference contained in the text. If you don't find the citation adequate, then WP:SOFIXIT becomes an issue. Sławomir Biały (talk) 13:20, 6 June 2013 (UTC)

It is not necessary to give citations for each individual statement in an article provided the material is uncontroversial and widely available in general sources. For such kinds of information, general sources are sufficient. WP:SCICITE has more details about this. The "original research" tag pointed out above is obviously ridiculous. Very likely all of these examples will appear in either the textbook referenced by Lang or the textbook by Dummit and Foote. It seems to me that the onus is on the person placing the template to check the references, and I think there is little likelihood that this happened here. I don't really think that these kind of templates in general improve articles. It's more likely that a {{fact}} tag here or there, preferably accompanied by an explanation on the discussion page, will lead to a reference. The placement of large and disruptive templates to articles seems to have more to do with social psychology than with encyclopedia building. Sławomir Biały (talk) 13:44, 6 June 2013 (UTC)

Those tag-tacking edits should be undone. Mct mht (talk) 16:04, 6 June 2013 (UTC)

For a section with uncontroversial knowledge, WP:SCICITE#Uncontroversial knowledge recommends a citation or two for the entire section, often placed in or after the first sentence. So if a section is completely unreferenced, is it within policy guidelines to ask for a citation for the section, but it is also easy to fix this problem. Such a citation can show a reader where to find more information about a section topic; doing so is in my opinion an important part of encyclopedia building. --Mark viking (talk) 10:46, 8 June 2013 (UTC)

Actually it's sufficient to provide a general reference for an entire article. It isn't strictly necessary to have footnotes to the general references in each section. Most (all?) of the articles under discussion include such references already. I do think that citations generally improve the overall quality of the articles, but I disagree very strongly with the application of templates to enforce what is actually just a style issue (especially templates placed without any discussion on the talk page). Sławomir Biały (talk) 12:55, 8 June 2013 (UTC)

Where is the policy that it is sufficient to provide a general reference for an entire article? Again, WP:SCICITE says this is fine for articles of a few sentences, but longer articles should have citations. I agree with you about the drive-by tagging; when I see uncited sections where the material seems fine and I want to know more, I usually either contact the dominant editor, if there is one, or I post a query on the talk page. --Mark viking (talk) 19:21, 8 June 2013 (UTC)

WP:SCICITE specifically says that general references are adequate when most of the content of an article appears in multiple general sources (e.g., textbooks on the subject), regardless of article length. It may be appropriate in some cases to include a citation in the section, the lead of the article, or in a list of references at the bottom. This has all been standard practice in mathematics articles for a long time. Sławomir Biały (talk) 20:39, 8 June 2013 (UTC)

In general examples should not have original research tags stuck on them because they are counted as illustrations and come under WP:PERTINENCE. They may be made up by an editor and don't need citations however if so they must not bring in any new ideas but simply be an obvious demonstration of what has been said around them. Any new idea in them would of course be subject to the verification policy. For instance if in the addition article we say 5+7 is an addition giving the result 12 that does not need a citation showing an example of 5 and 7 being added. Citations can be good if people want to follow up but that is not the purpose of an example. If someone thinks an example is not straightforward from what has been said then a citation can be called for but sticking in block tags is not the way to get clarification of an example. After all one can always say an illustration doesn't seem right but you don't put in tags saying all the images in an article need citations. Dmcq (talk) 13:38, 8 June 2013 (UTC) +WP:IUP we must not copy peoples examples straight as they are copyright even if they involve mathematics. Dmcq (talk) 13:53, 8 June 2013 (UTC)

Equality, identity and equation

I have recently rewritten the leads of equality, identity and equation. Before my edits, none of these articles contained any understandable definition of their topic. Instead, either they were too technical (introduction of Peano and extensionality axioms in the first line of the lead) or they contained silly assertions like "An identity is a relation which is tautologically true" or "An equation, in a mathematical context, is generally understood to mean a mathematical statement that asserts the equality of two expressions". Editing these leads, I was faced with the problem of lacking of sources providing general definitions of these basic concepts. In fact, they are too difficult to be accurately defined in elementary textbooks. And more advanced studies, such as in mathematical logic, usually deal with only one aspect of these questions.

Therefore I have tried to write down what I believe to be commonly meant by these words. But I may have omitted some important aspect. More important, the lack of convenient sources makes that a consensus is needed on these fundamental questions. Also, I have not edited the bodies of these articles which need also some attention. D.Lazard (talk) 10:15, 8 June 2013 (UTC)

Your edits were partially wrong. An equation does not differ from an equality, it uses the equality binary relation but has a sense different from that of an identity. An (equality-based) identity is a statement of the form ∀⋯: F(⋯) = G(⋯), where F and G are terms, which must be a theorem in certain theory. An equation is a predicate expression of the form F(⋯) = G(⋯) on one or more variables with the equality as the upper (outer) logical relation, and is not a theorem. Incnis Mrsi (talk) 10:44, 8 June 2013 (UTC)

While "equality" may merely mean that two expressions happen to have the same value (extensionally), "identity" is usually taken to mean that they have the same meaning (intentionality). That is, two things are identical if they are necessarily equal, not merely contingently equal.

Equality is characterized by reflexivity and the substitution property of equality. The substitution property implies symmetry and transitivity among other things. However, the article on equality (mathematics) misstates the substitution property as "For any quantities a and b and any expression F(x), if a=b, then F(a)=F(b).". The correct statement would be "For any quantities a and b and any predicate P(x), if a=b and P(a), then P(b).". JRSpriggs (talk) 12:18, 8 June 2013 (UTC)

This explanation is quite enlightening. Sławomir Biały (talk) 12:43, 8 June 2013 (UTC)

Intention and contingency have their own hard to pin down philosophical definitions. From the point of view of mathematical logic, are you saying that identity is like logical equivalence, something that holds in all models, and that equality is more like material equivalence, which is model-dependent? Thanks, --Mark viking (talk) 18:59, 8 June 2013 (UTC)

First of all, I think the desired word is intension, not intention.

I don't really agree with either JR or Incnis here. Two objects are identical just in case they are the same object; necessity or contingency doesn't enter into it, and axiomatic theories still less (Incnis's claims seem to assume a formalist POV). There is an older usage whereby two expressions are said to be "identically equal" if their values are equal for all values of the free variables, whereas just saying they're "equal" may leave open the possibility that you have a particular set of values in mind for the free variables, and the values are equal for that particular assignment. But this is mostly a convenience in exposition, and shouldn't be overinterpreted. --Trovatore (talk) 19:46, 9 June 2013 (UTC)

As a non-expert in these things, I found your version of the leads to be clear and easy to read. Leads are necessarily summaries and approximations of main articles; I don't think one can address all the mathematical and philosophical subtleties of these concepts in a lead, keep a lead short enough for MOS, and keep a lead understandable for non-experts. Equivalence may be a related concept to deal with. --Mark viking (talk) 19:12, 8 June 2013 (UTC)

I have some concerns about them, frankly.

The first point is cosmetic: The changes use boldface repeatedly, which is contrary to Wikipedia style. The article title, and synonyms redirected to it, should be bolded at first occurrence, but not thereafter. Similarly, be careful of WP:OVERLINK.

More substantively, I doubt that some of the proposed distinctions are really standard, specifically the supposed distinction between equation and equality. The distinction I would make is rather that an equation is a syntactic object, something you can write down, whereas equality is a property or relation. --Trovatore (talk) 21:33, 9 June 2013 (UTC)

I agree with Trovatore. I'm not convinced there is a widely held distinction between "equation" and "equality" (in the same way that "inequality" and "inequation" should probably be merged). I understand there are two uses of two similar words, but I'm not convinced mathematicians (or anyone else) actually use these words in the way described. Mark M (talk) 12:34, 10 June 2013 (UTC)

The difference between equation and equality in the leads seems reasonable to me, at least in common usage. We solve for unknown variables in quadratic or differential equations, and the solutions make both sides satisfy an equality or make both sides equal. Also in computer languages, we test variables or objects for equality, which comes down to determining the truth value of a predicate expression whose variables are already determined or bound at the time of testing. --Mark viking (talk) 15:54, 10 June 2013 (UTC)

Several posts are about the difference, if any, between equation and equality. I agree that opposing them, as in equation is too strong. I am thinking to a better formulation. I agree also that, from a formal point of view there is no syntactic difference between the two notions. But this does not means that they have the same semantic. If the notions would have the same semantic, the two words would be synonymous, and one could find sources talking of the equation $(x+1)^2=x^2-x+1$, presenting $x^2+y^2=1$ as the equality of the unit circle or $ax^2+bx+c=0$ as the quadratic equality. As these articles are not intended for specialists of formal logic, not even for experimented mathematicians, it is essential to explain the distinction between these two notions that the mathematicians (not the logicians) make in their common usage . And this explanation must not involve high level notions. I have tried to solve this difficult equation :-), but this may certainly be improved. D.Lazard (talk) 18:20, 10 June 2013 (UTC)

I don't think this use of equality as a count noun is very usual. Equality is generally a property; one ordinarily does not speak of an equality at all, and there is certainly no bar against talking about the "equation describing the unit circle". Is it possible that you are being overly influenced by French usage here? --Trovatore (talk) 18:31, 10 June 2013 (UTC)

I think it may be helpful to some readers to draw a distinction between the two concepts.. but I don't see the point in having two separate articles, equation and equality (mathematics). I think this gives the impression that the concepts are more different than they actually are (and the false impression that it is a really important distinction). It think it would be better to explain terminology in a single article. Mark M (talk) 22:17, 10 June 2013 (UTC)

I continue to find this situation problematic. I simply do not believe the purported distinction between "an equality" and "an equation" is standard in English-language mathematics (or, indeed, that it is usual to speak of "an equality" at all). D.Lazard, Mark viking, anyone else who makes this distinction, can you back this up? --Trovatore (talk) 18:23, 12 June 2013 (UTC)

I personally am quite comfortable with the phrase "an equality" as a partial synonym for "an equation", and I am more comfortable with "an inequality" than I am with "an inequation". It seems to me that in good encyclopedic fashion the appropriate thing to do here would be to find one or two reliable sources that either do or do not draw distinctions between these terms, and report on what they have to say, rather than trying to formulate the rules ourselves from scratch. --JBL (talk) 21:43, 12 June 2013 (UTC)

I can believe some sources will use the terms in such a way, but I think the main thrust of the articles should follow common scholarly usage, which I think uses equality primarily as a mass noun rather than a count noun. I agree with you about inequation, a very ugly word that is probably attested somewhere but is definitely not standard. --Trovatore (talk) 21:45, 12 June 2013 (UTC)

You are free to dislike "inequation", but, please, remember that in the context of system of equations solving and real algebraic geometry, both inequation and inequality are commonly used with different standard meanings: $A\ne B$ is an inequation, while $A>B$ and $A\ge B$ are inequalities. D.Lazard (talk) 11:40, 13 June 2013 (UTC)

Can you source that? I do not think the term inequation is really standard at all, in any field. But I don't know all fields of mathematics, so I could be wrong. Oh, MathWorld doesn't count, of course, especially in this sort of case, as it frequently seems to borderline make stuff up in regards to terminology, or at least pull it from idiosyncratic sources. --Trovatore (talk) 16:27, 13 June 2013 (UTC)

Not exactly in reply, but syntactically "inequality" much more resembles "identity" than "equality" or "equation". Sławomir Biały (talk) 18:25, 13 June 2013 (UTC)

In common practice in English-based reliable sources like scholarly articles and books, these terms are in no way interchangeable. In Google scholar, "differential equation" nets 1,810,000 results but "differential equality" nets 593 results. In the other direction, "test for equality" nets 31,300 results but "test for equation" nets get 454 results and most of the first page results are bogus. "Equality predicate" gets 4200 results and "equation predicate" gets 24. --Mark viking (talk) 22:52, 12 June 2013 (UTC)

None of that surprises me. As I said, in my usage, "equality" is a property (or predicate), so it's used as a mass noun. I don't have a problem with treating the property of equality separate from the syntactic object of an equation (or the semantic object of the proposition intended by the equation).

What I don't find convincing is talking about an equality, and distinguishing that from "an equation". It's not implausible that such a distinction could be made, and some authors probably do, but I don't believe it's standard. --Trovatore (talk) 23:52, 12 June 2013 (UTC)

Parity of zero is up for peer review

Wikipedia:Peer review/Parity of zero/archive1

That's right, folks, I'm getting back on this horse. Please feel free to chime in! Cheers, Melchoir (talk) 22:17, 8 June 2013 (UTC)

Transformed redirect Cartesian tensor into an article

This should be an article. Cartesian tensors are the first approach to tensors and index notation (at least in my experience).

I wrote this from the perspective of someone with a firm grip on basic vector algebra, and some possible exposure to linear algebra and tensor index notation, but not lots, so there is some preamble on notation and terminology.

It is hoped to bridge the gap between basic (Gibbsian, as it were) vector algebra and tensor analysis.

Feel free to complain about the potentially trillions of typos, or anything, on the talk page and we can improve the article.

There is room for more sections and expansion also. M∧Ŝc²ħεИ_τlk 23:56, 8 June 2013 (UTC)

Could you explain better what does it mean: a tensor in an Euclidean space? There is no such thing as a “tensor which exists in Cartesian coordinates” because a tensor must have a representation in any basis, by its very virtue to be a tensor. Incnis Mrsi (talk) 09:43, 9 June 2013 (UTC)

Fixed, any more specific inaccuracies please take it to the talk page. M∧Ŝc²ħεИ_τlk 09:56, 9 June 2013 (UTC)

3x12 = ?

I have a different opinion about what (or who) was silly in Hexadecimal. Incnis Mrsi (talk) 04:09, 9 June 2013 (UTC)

Perhaps you could explain what you think the purpose of the link is? --JBL (talk) 15:52, 9 June 2013 (UTC)

Perhaps, an inhabitant of Unicodified worlds needs a hint to understand the “humour” invented by ASCII-based tribes in prehistoric times before the advent of HTML? Incnis Mrsi (talk) 16:13, 9 June 2013 (UTC)

This is why the "joke" is followed immediately by an explanation, is it not? --JBL (talk) 17:51, 9 June 2013 (UTC)

<hit with="bone"><monolith/></hit> Sławomir Biały (talk) 19:38, 9 June 2013 (UTC)

Is there a reliable source which supports anything at all in the section Hexadecimal#Common_patterns_and_humor? Spectral sequence (talk) 20:54, 10 June 2013 (UTC)

There are a lot of sources (but of dubious reliability) in the main article on this topic, hexspeak. Apparently the original source for this is Kernighan and Pike The Practice of Programming (1999) but I don't have a copy to check. —David Eppstein (talk) 20:54, 12 June 2013 (UTC)

As far as I can see, hexspeak is a random collection of mildly amusing jokes that can be or have been made using hexadecimal notation, sourced only to primary sources, and with no single reliable secondary source to suggest that the list is complete, or representative, or significant. The section Hexadecimal#Common_patterns_and_humor mentions a few of those jokes and recounts some others, all without any sources at all. It seems completely undue. Spectral sequence (talk) 21:17, 12 June 2013 (UTC)

Links to fractional-order system

Fractional-order system is a new article. No other articles link to it. Creating some links to it from other articles, and other work, should get done. Michael Hardy (talk) 18:15, 9 June 2013 (UTC)

Sorry if it is a dumb question, Chaos in fractional order system is another new article. Should they not be merged? Solomon7968 18:24, 9 June 2013 (UTC)

Perhaps. Michael Hardy (talk) 19:05, 9 June 2013 (UTC)

Merged. No significance to the example, so I removed it. It might be required to determine whether the statement makes any sense, even if there is insufficient information in the reference to locate it. — Arthur Rubin (talk) 19:49, 9 June 2013 (UTC)

Proposing a merge into fractional dynamics; same subject, that's almost an orphan, as well, but it's better-connected. — Arthur Rubin (talk) 20:59, 9 June 2013 (UTC)

Anatolii Alexeevitch Karatsuba

There is a request for further input at Talk:Anatolii Alexeevitch Karatsuba. Spectral sequence (talk) 21:25, 10 June 2013 (UTC)

New article: Spherical basis

I started it for now. It is incomplete and probably full of typos/inaccuracies, and I intend to finish it soon, but it's been sitting in my userspace for a very long time so for now it's been moved into mainspace allowing others the freedom to edit it, if inclined. M∧Ŝc²ħεИ_τlk 08:30, 12 June 2013 (UTC)

I also redirected spherical tensor, spherical tensor operator, and tensor operator to spherical basis for now. Do people think they should have their own articles? Spherical tensor and Spherical tensor operator makes sense to redirect since the literature seems to explain spherical basis and spherical tensors and spherical tensor operators together. So tensor operator should have its own article? M∧Ŝc²ħεИ_τlk 14:16, 12 June 2013 (UTC)

Would some slightly more concrete examples and material, presumably relating the abstract content you develop to the concrete set of spherical harmonics as perhaps the simplest and well-known such basis, be appropriate? (And then perhaps discussing other possible such concretely-realised basis sets?) Or have I missed the point? Jheald (talk) 18:01, 12 June 2013 (UTC)

Yes, as said, more work is needed, including examples and other applications will be added as I learn them in time. M∧Ŝc²ħεИ_τlk 18:08, 12 June 2013 (UTC)

While tensor operator seems to be used by physicists mostly in the context of tensors under rotation in quantum mechanics, the concept is used in other ways, too. For instance, in image processing, there is the concept of tensor operators for energy tensors, e.g., Energy Tensors: Quadratic, Phase Invariant Image Operators and also in the more general concept of structure tensor. Neither of these necessarily involve 3D rotational invariance/covariance. Tensor operator algebras have also been created for other groups, e.g., Tensor Operator Algebra for Point Groups. I don't think the redirect from tensor operator to spherical basis is a bad move, but if an editor wanted to do so, creating a standalone tensor operator article seems reasonable. --Mark viking (talk) 20:24, 12 June 2013 (UTC)

Yes, I suspected tensor operator would potentially have it's own article for the reasons you mention. It's easy to overwrite a redirect. Thanks, M∧Ŝc²ħεИ_τlk 20:34, 12 June 2013 (UTC)

In the end I split the tensor operator stuff from spherical basis to overwrite tensor operator, for reasons explained here and at Talk:Spherical basis, Talk:Tensor operator. The redirects are changed as stated on these articles. M∧Ŝc²ħεИ_τlk 08:56, 13 June 2013 (UTC)

An instance of erroneous eponymy

I have created this new section, explaining that the so-called Weierstrass substitution was used by Euler long before Weierstrass was born. I don't know how this came to be called the Weierstrass substitution by respectable authors, but Google Books confirms that it is. Maybe the answer to that last question should be included in the article if it can be found. Did Weierstrass even used this substitution? Where, specifically, is it found in Weierstrass' work. If it isn't there, what source could be cited to confirm that it isn't there? Would this warrant renaming the article? How best should the topic of erroneous nomenclature be treated in Wikipedia? Michael Hardy (talk) 13:06, 17 June 2013 (UTC)

I have never heard of this name for the tangent half-angle substitution and I would never find this article by myself. I have created the redirect Tangent half-angle substitution, and I support to move Weierstrass_substitution to this new page. Also it could be worth to merge this page with Tangent half-angle formula. D.Lazard (talk) 13:58, 17 June 2013 (UTC)

Is there an independent reliable source stating that this substitution was used by Euler? So far, all we have is a reference to Euler E342.V.261 where a substitution equivalent to this appears for one specific case. Michael Hardy may be correct about Euler, and in deed I personally think he is, but we go by what the sources say. It seems to be at best original research by way of synthesis to suggest from this reference alone that Euler was aware of the substitution for general rational functions. It is also unwarranted to assert that the assignment to Weiesrstrass is "erroneous". There may be a good historical reason for it -- we just do not know, because there are no sources cited to support the assertion either way. Whereof one cannot speak, thereof one must be silent. Spectral sequence (talk) 17:03, 17 June 2013 (UTC)

Euler knew that

$\begin{align} \text{if }y & = \tan\frac\theta2 \\[8pt] \text{then }\frac{2y}{1+y^2} & = \sin\theta \\[8pt] \text{and }\frac{1-y^2}{1+y^2} & = \cos\theta \\[8pt] \text{and }\frac{2\,dy}{1+y^2} & = d\theta. \end{align}$

Certainly he was aware of that substitution. Whether he knew it could be applied to all or to only some rational functions of sin θ and cos θ, I can't say for sure. Whether Weierstrass knew that, or ever wrote anything about this substitution, I don't know. What we can say is erroneously attributed to Weierstrass is the first use of this substitution. Michael Hardy (talk) 22:51, 17 June 2013 (UTC)

. . . . and I should add: Secondary sources are needed to establish notability, and we certainly have those secondary sources for this substitution. But primary sources are what is needed to establish that a particular author used this substituion. Michael Hardy (talk) 22:52, 17 June 2013 (UTC)

"I don't know". That's exactly my point. Wikipedia reports what reliable sources say, not our personal guesses. Is there a reliable source that says that the name "Weierstrass" is erroneous? The primary source indicates that Euler was aware of one particular use of this substitution. Does any source state that Weierstrass was the first person to use this substitution, which would indeed be an error if so? Perhaps it was named after Weierstrass because he rediscovered it, generalised it, popularised it, used it heavily, or whatever -- I don't know and it seems that you don't either. Saying that the attribution to Weiestrass is "erroneous" appears to be synthesis at best. Spectral sequence (talk) 06:15, 18 June 2013 (UTC)

Additional: I see that you have removed the word "erroneous" anyway so this part of the discussion is perhaps moot. In any event it seems to belong at Talk:Weierstrass substitution, not here. Spectral sequence (talk) 06:23, 18 June 2013 (UTC)

┌────────────────────────────────────────────────────────────────────────────────────────────────────┘ The general points raised do seem worth continuing to discuss here. I prefer the term "unhistorical" to "erroneous". It seems to me that we should use the terminology most commonly used in the current literature, whether or not that happens to be historically accurate. That is what readers expect and will think it odd not to find. We are here to follow, not lead, the scientific literature. We are not here as advocates or to right great wrongs. Spectral sequence (talk) 06:32, 18 June 2013 (UTC)