Talk:Main Page

Way to synchronize equation numbering in Transcluded text?
I have had to fix up equation numbering problems on several pages (i.e., Definition:Sturm-Liouville Equation, Sturm-Liouville Theory and Orthogonality of Solutions to the Sturm-Liouville Equation with Distinct Eigenvalues) as material was moved from the main article into a Definition. This raises a pertinent question. Are there templates for equation numbering that would solve these kinds of problems? I imagine this synchronization requirement is not limited to the pages I work on. Dan Nessett 16:48, 29 March 2012 (EDT)


 * No there's not, but it hasn't been seen as a problem before. It is rare that a train of thought is so long as to stretch over multiple pages (transcluded or not), as (has been explained before) the nature of this site is more as a dictionary (short pithy entries) than as an encyclopedia (longer discursive entries).


 * TL;DR - If equation numbering breaks under the influence of refactoring, it's just one of those things that will need fixing. --prime mover 16:57, 29 March 2012 (EDT)


 * Maybe this is something that can be fixed; some ideas drip in that may allow for the extension being developed to cover this (but I imagine that it will be hard to cover things like $(3')$ and $(1a)$ which occur now and then. Should I put some more thought into it? --Lord_Farin 17:21, 29 March 2012 (EDT)


 * If you think you have a strategy, then it's worth exploring. For one, I'd suggest a template "eqno" or something equally pithy, which might also contain a means of directly linking back to the original equation in the same / similar way that "eqref" etc. works in a conventional $\LaTeX$ work.


 * But the question is bigger. Pure maths is one thing, where the expositions are short, and there is no need for lengthy pages. However, applied maths and mathematical physics may require that the descriptions are considerably longer (thinking ahead to the delights of the analysis of the behaviour of waves and ripples on the surface of a body of liquid is filling me with anticipation as I type) and so, as with S-L Theory, a new approach will need to evolve.


 * The challenge will be in the crafting of short, self-contained but transcludable, pages like Definition:Sturm-Liouville Equation such that any page referencing it will be able to either link to it or, as necessary, transclude it, without the need to copy-paste or any otherwise repeating material.


 * Another challenge: if several pages are so transcluded, what if the equation numbers clash? --prime mover 17:32, 29 March 2012 (EDT)

Good point, and nice elaboration on the challenges we are coming to face with the advent of more applied systems and research fields. The only possible ways I see to solve this problem are by using eg. an optional unique identifier (like 'eqnaboutblabla') or allowing only for a possible subscript to be added to a number (eg. where 'a' yields $(na)$, and "'" gives $(n')$ with $n$ as appropriate). But these are bound to be fiddly and will put up a wall of syntax for new aspiring editors. Maybe this last point isn't really big because the convention could be applied in a 'only-when-required' fashion. In any case, the amount of documentation I would deem necessary will demand a lot of time, time I seem not to have in the coming few months.

But then, I haven't even spoken about what to do with things like 'Axiom $(2)$' or 'Equation $(3)$ on "somepage"' as references; I haven't got a solution for that yet (maybe we needn't look, as this is of relatively small impact, on crystallised pages). --Lord_Farin 17:45, 29 March 2012 (EDT)


 * I thought about this problem a bit and I now think it will be difficult (but perhaps not imposssible) to provide the requisite functionality even with an extension. What I think is needed is a way for equations transcluded from a page to be tagged with a number based on their context on the referencing (not the transcluded) page. For example, an equation labeled (1) on a source page might require labeling as equation (3) on the referencing page.


 * Achieving this would seem to require global state on the referencing page that figures out where the first reference to the equation occurs and then assigns it a number. That number would then be assigned for each reference to the equation. This is a bit like citations implemented by the Cite extension, but with dynamic numbering.


 * It wouldn't be hard to uniquely identify equations based on a page name and a number on that page, but then to map that into a dynamically allocated number on the referencing page would require MW parser functionality that doesn't exist. In the past I wanted to write templates that did arithmetic on citation numbers for a similar purpose, but discovered that the parser simply doesn't support this. The MW parser is a big mess, but not particularly sophisticated from a computer language point of view. So, achieving the goals of dynamically allocated equation numbering is probably a bridge too far.


 * By the way. In regards to transcluding individual equations from other pages, it might be useful to install the Labeled_Section_Transclusion extension. Just a thought. Dan Nessett 18:46, 29 March 2012 (EDT)


 * Sounds like a good idea to me. This may be particularly useful when we might want to transclude more than one section of a given page - at the moment (or when I last tried it) when you have more than one "onlyinclude" section in a page it doesn't work properly. --prime mover 02:00, 30 March 2012 (EDT)


 * Labeled section transclusion is superseded by the (PW-tailored) extension in development, which will allow for customisation of the header levels under transclusion. To achieve this I am already working with global states; I think it's possible, albeit with a special, to-be-written parser function that outputs $(3)$ (because it's possible that one would like to write $(3)(4)$ to indicate multiplication (though this is disallowed by house style, I think that the distinction should be made clear) and thus simply fetching the occurrences of $(n)$ (and then, which one of the occurrences labels the equation itself? 'see equation $(n)$ below' would cause problems) would be too simple an approach). --Lord_Farin 03:12, 30 March 2012 (EDT)

Laugh and a half
Here's a wally who thinks you can copyright $\frac 1 3 = \frac 1 2 - \frac 1 4 + \frac 1 8 - \frac 1 {16} + \cdots$

http://en.wikipedia.org/wiki/User_talk:WIKI-1-PIDEA#Angle_trisection

How we laughed! --prime mover 15:20, 30 March 2012 (EDT)

Category:Disproofs
Just today, Restriction of Non-Reflexive Relation is Not Necessarily Non-Reflexive was posted. I would argue it belongs in the category Category:Disproofs and maybe some more specialised category linking to Proof by Counterexample. The title could then maybe even be:


 * Disproof:Restriction of Non-Reflexive Relation is Non-Reflexive

I'm bringing this up as the 'not necessarily' in the title shows that it isn't really a 'proof' in some intuitive, emotional sense. What do you think? I haven't bothered practical objections like the linking structure on the site. --Lord_Farin 10:56, 1 April 2012 (EDT)


 * Possibly ... but then there are going to be some borderline cases (can't think of any) which are perhaps proofs of a negative result, etc. Proofs by counterexample may already exist as a category (like "direct proofs" and "proofs by induction") but I've never been a fan of such categorisation strategies so I haven't kept them up to date. --prime mover 14:39, 1 April 2012 (EDT)


 * That's what redirects are for. I noticed that the categories expressing kinds of proofs aren't very popular, and I don't care enough to change that. --Lord_Farin 18:25, 1 April 2012 (EDT)

Source works
Before I just delete the offending line, what's the thoughts of others on a discussion in a maths forum as an appropriate "source work" for a given page? I expect you may be able to guess which page(s) I'm talking about. The forum consists of the contributor raising hypotheses which other contributors to that forum are either disproving immediately or expressing scepticism about. --prime mover 17:58, 4 April 2012 (EDT)


 * I'd rather have no source. --Lord_Farin 18:06, 4 April 2012 (EDT)

Axiom of Countable Choice
As concern had been expressed about the inability to adequately discuss results depending upon the Axiom:Axiom of Countable Choice, I have put together Template:ACC which can be included, in a similar way to Template:AoC, at the bottom of any result which requires the ACC for its validity.

However, I am unfamiliar with the philosophical implications of ACC (they're nowhere near as widely discussed as those of AoC) so can't do justice to the wording.

Is there anyone out there who knows (and is philosophically liberal) enough about this to be able to make a better job of wording it? --prime mover 03:47, 5 April 2012 (EDT)

Editing suggestion
Apparently, nobody noted my suggestion over at Help talk:Editing, but I would like to know your opinions; consider this a gentle push. --Lord_Farin 13:26, 14 April 2012 (EDT)


 * Hadn't noticed it. Have now commented. Have amended the page you talked about it on. Would like to alert users to experiment with nuances of formatting (adding spaces here and there as needed) as MathJax has some shortcomings. --prime mover 15:34, 14 April 2012 (EDT)

Relicensing under CC-By-SA
(This post has been copied into here from my own chat user page. I endorse what this guy is saying.)

Hi prime mover: As we discussed at the MathWikis workshop, I'd like to work with you on getting some or all of ProofWiki relicensed under CC-By-SA. If we're talking about your own entries, all you really have to do is say someplace "I agree to license my contributions to ProofWiki under CC-By-SA", then me (or someone else) can go ahead and find them and download them, and use them under those terms. However, if we're talking about shifting the license on the entire wiki, that means tracking down all existing contributors, and getting them to agree to the same terms.

Basically, CC-By-SA and the GNU FDL are almost equivalent, so in principle there should not be much of a problem. The primary benefit (outside of ProofWiki) to releasing the material under CC-By-SA is that it can then be re-used on sites like PlanetMath and Wikipedia. I'm guessing that broader re-use of the ProofWiki materials would have some benefits here, including more links back to this site (due to the attribution clause of CC-By-SA), and general access to a healthier mathematics ecosystem around the topics discussed here.

For me personally, I'm interested in looking at the proofs you've developed here as a collection of "Worked Examples" for my thesis (http://metameso.org/~joe/thesis-outline.html). That is more or less independent of licensing issues, but a CC-By-SA license would give me the most leverage, I think.

Please let me know how I might be of further assistance in this matter! Arided 17:24, 14 April 2012 (EDT)


 * Everyone: feel free to comment on this - technically we need the agreement of all contributors to allow this change to the copyright licensing, but we can settle with "active contributors", I guess. --prime mover 18:22, 14 April 2012 (EDT)


 * What is not apparent from the 'human-readable' statement but is in fact included in the formal juridical language in which it is cast, is that anything released under the CC-By-SA license is irrevocably released (i.e., I cannot, eg. for the purpose of removing some ludicrous stuff I could have put on PW, demand that such content be removed from PW, and is not to be bound by CC-By-SA any longer (such is specifically prohibited by point 7b (and thereof the part after the last semicolon))) which I consider a possible problem (although unlikely to occur) of adopting this license. I would rather have a license allowing me (or any other editor) to remove certain parts of the made contributions if so desired. However, as long as anything in the 'talk' and 'user' namespace will be amended to have such a possibility (since I do feel that such an irrevocability condition is desirable for bona fide PW entries) of legally allowed removal, I think it is a good idea to implement this licence. But then, GNU-FDL may have already got me there; in any case, such a clause will calm my paranoid mind. Otherwise, I endorse the suggestion.
 * In summary, I think that the actual pages (viz. the main and defn namespaces) are suitable for this licence, while the user-specified pages are only under the condition that it is legally allowed to completely remove them. --Lord_Farin 19:33, 14 April 2012 (EDT)
 * I'm for the CC-SA license - but perhaps the non-commercial license (CC By-NC-SA) would be better? --GFauxPas 21:34, 14 April 2012 (EDT)
 * I also am totally fine with a move to some flavor of CC license - I've never really cared about the subtle distinctions that may or may not exist between CC and GNU/GFDL. I'd pass on the NC addition I think, just cause I don't really see why it would matter (although as I said, I've never bothered to research licenses, I typically release whatever content I put online as un-restrictively as possible). --Alec  (talk) 23:43, 14 April 2012 (EDT)
 * I'm totally against NC because then it means you can't use ProofWiki in the context of commercial writing to contract. That would be silly because this is mathematical proofs and therefore is out there in the real world. It may result in the death of textbooks. --prime mover 01:10, 15 April 2012 (EDT)
 * Okay, I'm pretty neutral on the matter, just thought the issue was worth mentioning. --GFauxPas 08:37, 15 April 2012 (EDT)


 * Hi all, bolded text about CC-By-SA being compatible with PlanetMath and Wikipedia. CC-By-SA-NC would not be compatible w/ those sites.  @Lord_Farin, I don't think it is possible to "revoke" an FDL license on material that has been copied and distributed downstream.  AFAIK the only way would be to delete the "ludicrous stuff" from the upstream site (ProofWiki in this case) and hope that it hasn't spread on to other users!  Cheers, Arided 20:20, 15 April 2012 (EDT)
 * I understand that part; the idea is that I would like to prevent possibly ludicrous stuff on the talk pages from falling under a Licence; rather I would like to see that no implicit approval for citation is given when one puts up stuff on talk pages. Simply deleting the parts which in hindsight aren't desirable will not really work, due to the history-viewing capabilities MediaWiki has implemented. My concern, as I apparently didn't express clear enough, is that users are bound by the Licence, and thence are not allowed to request an administrator to permanently delete a page (for such would be a violation of said Licence), also from the history functionality, when they feel that, in hindsight, a particular contribution is deemed very foolish and undesirable. I deem it undesirable that users are not allowed (whether or not this has been the case in the past) to delete any information they put up on the internet section called ProofWiki (be it under a pseudonym or not). I am not sure how such a thing can be put into effect but I think it is good that users will not be eternally bound by stuff they put up on some discussion page. If this isn't the case already, please point out why. Hopefully I have now more clearly expressed my point. --Lord_Farin 05:41, 16 April 2012 (EDT)
 * What he said - talk pages are (or should be) considered ephemeral and not part of the "canonical" content of ProofWiki. Exactly how to treat the legal aspects of such pages would need to be discussed, but I would suggest: what one says on a chat page should be "owned" by the person saying it at least to the extent that they should be allowed to decide whether it is to be deleted irrevocably. Having said that, this is of course not foolproof because somebody might already have copied what you said into a different place which is outside of your legal control. --prime mover 08:15, 16 April 2012 (EDT)

I am glad at least one person caught on to my points, having spent all those thousands of characters explaining them. I wonder if it would be enough to add a clause to the (now likely soon-to-be-written) Copyrights page stating something like 'ProofWiki and/or its users (maybe: Licensor) prohibits the right to permanently/irrevocably delete any attributed/user-specific content without any further notice.'. --Lord_Farin 10:39, 16 April 2012 (EDT)

Database dump?
While we're at it (see licensing discussion above), a snapshot ("dump") of the current set of articles would make it much easier for me to work with the articles offline. Is there a standard way to request that? Arided 20:32, 15 April 2012 (EDT)
 * Would XML format be okay? I understand that a MediaWiki database (of which this is an instance) can be output in that format - but I've never tried it myself and I am not 100% sure it would do the $\LaTeX$ properly (although this would be hoped). I expect this may be a job for Joe (talk) as he's the one who has been responsible so far for performing admin / maintenance / under-the-hood work. --prime mover 02:39, 16 April 2012 (EDT)
 * Database dump located here . I can set it to dump daily if anyone is interested. --Joe (talk) 07:28, 16 April 2012 (EDT)
 * You're a star.
 * Daily might be too often (I understand it might compromise the ability to edit stuff? please confirm). I suspect that once a week would be plenty enough. --prime mover 08:08, 16 April 2012 (EDT)
 * It will temporarily disable database access for a few minutes. I can just do it at the same time I do a database backup every night, no should even notice (Unless you never sleep). Though in the future I'll probably move them to a better folder (subdomain? Suggestions welcome).--Joe (talk) 08:24, 16 April 2012 (EDT)
 * Good call, there. Usually I'm online by 06:00 UK time, which would be anytime between 10pm and 1am US time wherever you are ... --prime mover 10:33, 16 April 2012 (EDT)
 * I'm UTC−3:30 --Joe (talk) 12:13, 16 April 2012 (EDT)
 * Oh of course, the wonderful Newfoundland. (Or is it Labrador?) Rock on. --prime mover 14:47, 16 April 2012 (EDT)

You're not doing (ahem) a dump now, are you? It's been crashing on me all evening. "Technical difficulties", it sez. --prime mover 15:39, 16 April 2012 (EDT)
 * Well, I was, actually; I am sorry for any problems that have occurred. I will try again at a more suitable time. --Lord_Farin 15:43, 16 April 2012 (EDT)
 * Ah, okay, that explains it. Thx. --prime mover 16:17, 16 April 2012 (EDT)

Can't upload file
On trying to upload a file, I got:
 * "The upload directory (public) is not writable by the webserver."

Can this be sorted? kthxbai. --prime mover 12:42, 17 April 2012 (EDT)
 * On it. --Joe (talk) 12:42, 17 April 2012 (EDT)
 * Try now. --Joe (talk) 12:45, 17 April 2012 (EDT)
 * Gotcha. Thx. --prime mover 12:51, 17 April 2012 (EDT)

Search PW via Google
After a tedious trial and error procedure I have finally found how to simply search PW through Google (thus, without having to type the tedious 'site:proofwiki.org' every time).

Let me point out how to do this in three commonly used browsers.

Chrome:
 * Go to chrome://settings/searchEngines
 * Add a new search engine: name is up to you, as is the keyword (I use pw), the URL is http://www.google.com/search?hl=en&as_sitesearch=proofwiki.org&q=%s

Firefox:
 * Go to Main > Bookmarks > Show all bookmarks
 * Make a new bookmark: name up to you, as is the keyword (I use pw), URL is again http://www.google.com/search?hl=en&as_sitesearch=proofwiki.org&q=%s

Opera:
 * Go to Main > Bookmarks > Manage bookmarks
 * Make a new bookmark: name and nickname (i.e., keyword) as above, URL again http://www.google.com/search?hl=en&as_sitesearch=proofwiki.org&q=%s

In all three browsers, typing eg. pw surjective will let Google search for occurrences of surjective on PW; IMO this is a better (more accurate) search feature than ProofWiki's own (except for brand new pages, which may not have been indexed yet). Hopefully, this helps y'all to find stuff on PW faster. --Lord_Farin 18:23, 19 April 2012 (EDT)
 * Very nice. --GFauxPas 20:03, 19 April 2012 (EDT)


 * Wow - that's pretty good. And more to the point: I have now learned another useful computer technique. Good man. --prime mover 01:25, 20 April 2012 (EDT)

Attack of the spambots
Looks like we're under attack again from spammers. No worries, got it covered. But we might want to review our captcha system. --prime mover 16:21, 24 April 2012 (EDT)


 * ... and we've just had our 1000th user join up. Shame he was a pimping spam-merchant. --prime mover 15:38, 26 April 2012 (EDT)


 * ... and I'm willing to bet a considerable value that the latest 4 users who have just joined are not here to contribute towards the dissemination of mathematical knowledge. --prime mover 02:31, 2 May 2012 (EDT)


 * ... and the latest one just tried to replace this talk page with a spamvert to its website. You can't exactly admire the intelligence of something like that. If it was truly a bot then it needs to be deleted. If it's human then euthanasia (or perhaps extermination of vermin) would be 100% appropriate. --prime mover 02:06, 8 May 2012 (EDT)

I've modified the security question when making an account. Let's see if that makes a difference. --Joe (talk) 12:42, 10 May 2012 (EDT)

Linear Transformations and Matrices
There's a lot of places where a result is proved on the space of linear transformations, and then exactly the same result is being added again but for matrices. As the two are equivalent (i.e. matrices are a tool via which linear transformations are manipulated), this seems to me like a level of redundancy which is not needed. I would argue that this is a different situation from separating out results for $\R$ and $\C$, in that the latter type of result is a genuinely different set of result as they are on a different domain - but as matrices and linear transformations are the same thing, it looks like a lot of duplication. Argue me out of this one, somebody? --prime mover 16:34, 9 May 2012 (EDT)


 * Typically, matrices constitute a special case of linear transformations (namely, they are essentially (up to choices of bases) the finite dimensional linear transformations) and the finite dimensional case is usually where everything will hold trivially (these all being Hilbert spaces, the nicest kind of vector space I know (except for finite dimensional vector spaces...)). As Conway states it: 'Upon introducing a new concept, it is always good to check how it behaves in the finite dimensional case' (IIRC). There is a case for these results as most of the applications work in the matrix setting; it is often convenient to have the result already phrased in this setting. No reason to incorporate such stuff as more than merely a corollary, though; some results get tedious and often very hard to prove when taken out of the abstract functional analytic setting. --Lord_Farin 17:05, 9 May 2012 (EDT)


 * I've been corollarying null spaces under kernels, matrix-vector products under linear transformations, things like that. I have been arbitrarily deciding that some of the theorems "feel different" for matrices and LTs, though. Can you put a mergeto on the pages I made that you think are unnecessary, and I'll work on corollarying some theorems? --GFauxPas 17:28, 9 May 2012 (EDT)


 * I'll get to it. I'm a few chapters away from it in my project to plough through Warner. It won't be for a few weeks yet. --prime mover 17:42, 9 May 2012 (EDT)

Pointwise operations
Taking up this project again, I needed some distraction from building up measure theory. It appears that there are already two strategies cropping up in defining pointwise operations. They are adequately described on Definition:Pointwise Scalar Multiplication of Mappings and Definition:Pointwise Scalar Multiplication of Real-Valued Functions (where the latter approach may also be found on Definition:Pointwise Maximum of Mappings).

Before continuing to streamline (and expand upon) the host of definitions in this range, I want to determine which approach we desire. I have been doing a lot of the second type lately, but I feel that rigour and insight are more served by the first, although I encourage one to look at Definition:Pointwise Supremum which would be hard to convert to the first approach.

So my final suggestion is, that we use the set of all mappings $S^X$ as long as possible, while when only a subset of these mappings applies, we take the more indirect, 'point-by-point' (in this case, 'function-by-function') approach (i.e., the second approach). What do you think? --Lord_Farin 04:42, 31 May 2012 (EDT)
 * What you are doing looks good. I'd suggest: if it makes sense and fits into the strategy you have planned, then go for it. If something does not work too well, then we can restructure it at a later time when the subject has been filled out a bit. In short: I agree with your final suggestion. --prime mover 05:22, 31 May 2012 (EDT)
 * Having thought about it some more, I wonder whether Definition:Pointwise Scalar Multiplication, rather than being a redirect, could be a page in whcih the various instances of pointwise multiplications could appear as transclusions? See (for example)Definition:Rank for the sort of approach I mean. The various definitions are dissimilar enough to need their own pages, but are not so dissimilar as to need a fullscale disambiguation. --prime mover 05:32, 31 May 2012 (EDT)
 * I have reworked Definition:Pointwise Scalar Multiplication of Real-Valued Functions, it is now quite similar to Definition:Pointwise Scalar Multiplication of Mappings. Has this (en passant) resolved the need for the Definition:Rank-analog? --Lord_Farin 03:33, 8 June 2012 (EDT)

I've never liked the tendency in some text books to refer to "addition" and "multiplication" in the context of abstract algebraic structures. If it's an abstract construct, then so is the operation. "Addition" and "multiplication" should IMO be used in the context of numbers only (with the exception that in a ring, the distributand is conventionally called "ring addition"). Separating out the definitions for nothing more (effectively) than a different notation (using "+" sign and juxtaposition) seems a bit "grade school" to me.

What you also see in some books is something like: "If the operation is 'like' addition (or multiplication), then ..." What does it mean for an operation to be "like" addition?

Equally, building two definitions, one for commutative operations and one for not-necessarily-commutative is also overdoing it a bit as well. --prime mover 04:14, 8 June 2012 (EDT)
 * I see your point, and to some extent you are right. But it would IMO be rather awkward to refuse to speak about 'module addition' which by definition behaves like an extension of ring addition. I would rather suggest to restrict 'addition' to numbers, and '(ring-ish) addition' to suitable R-algebraic structures (probably modules). This covers most or even all of the cases in which we are used to talking about addition (like the 'sum' of two vectors); for remaining cases, addition would indeed, as you rightfully state, be a misnomer and will lead readers to tacitly apply certain (possibly false) familiar principles. As for multiplication, it would, continuing this vision on the (non-)use of common names, probably be best to restrict it to numbers only. One generally speaks about 'ring product'. So finally my proposal is as follows:
 * Pointwise Addition of Mappings: transclusion of:
 * Pointwise Number Addition of Mappings (codomain of numbers)
 * Pointwise Addition of Extended Real-Valued Functions
 * Pointwise Ring Addition of Mappings (codomain a ring)
 * Pointwise Multiplication of Mappings (only numbers and $\overline \R$)
 * Pointwise Scalar Multiplication of Mappings: as-is


 * I deem it useful to have a separate page for multiplication because of the explicit setting we put it in - in general it will suffice to consider Definition:Operation Induced on Set of Mappings. It may be best to generalise the current pages for $\R$-valued functions to number-valued functions, while maintaining the $\overline \R$ versions (as $\overline \R$ tends to behave a bit odd). Whilst putting myself vulnerable to critiques on changing my mind so often, I think the abstract-algebraic and number viewpoint are sufficient to cover all cases one would like to consider (at some point we will have to assume the reader has some working knowledge and can instantiate the general induced mapping to any particular case, since the overview is already lost). We can always ad hoc put up particular nonstandard instances (eg. pointwise limit of bounded linear transformations) as we deem fit. Is this strategy acceptable? --Lord_Farin 05:12, 8 June 2012 (EDT)


 * My view is that Definition:Operation Induced on Set of Mappings (possibly renamed) should be the master page here, with various subpages as appropriate, e.g. Pointwise Addition of Mappings. Pointwise scalar multiplication could be a separate page, taking the concept of modules as its basis. If you must have separate pages discussing numbers, then link to the existing pages in (Real) Analysis where the concept is already in place. --prime mover 15:47, 8 June 2012 (EDT)


 * Agreed on which ought to be the master page. It isn't from a personal point of view that I would like instances for numbers, merely from considering the viewpoint of people without knowledge of abstract algebra (GFP is/was an example; where is he, in any case?). A more complete analysis on what is already covered where is likely necessary to get an overview, and develop a more concrete strategy from there. We don't want to keep reinventing the wheel over and over again. Also I sense we are having a bit of a bi-monologue instead of a discussion, which is not very productive. Putting it on the shelf for now. --Lord_Farin 17:27, 8 June 2012 (EDT)

Concerning Categorisation
I'm having questions about the use of displaying the Category:Disambiguated and Category:Disambiguations categories at the bottom of pages. I would consider putting __HIDDENCAT__ on these respective category pages to suppress their display, yet retain their functionality. Similarly I plead for a category for every book (eg. by ISBN reference) so that every page containing a reference to it will automatically appear in that category. For clarity of categorisation these categories will need the same 'hidden' attribute, yet be accessible via the PW:Books page for it. This will allow an easier search through certain books, which sometimes may be desirable. Another possiblity for naming the category would simply be replacing ProofWiki: in the book's title page with Category: which will probably make it easier to refer to stuff. What do you think? --Lord_Farin 12:17, 5 June 2012 (EDT)
 * If it makes it easier to find stuff, then I'm all for it. As we already have a template for the placement of a citation on a page (several such templates, in fact, borne of my own inexperience with MediaWiki when I put them together, I'd do it differently now) this should not be an impossible maintenance burden. So yes, this all sounds good to me. --prime mover 12:46, 5 June 2012 (EDT)
 * ... all very well, but now look at a disambiguated page, it says: "Hidden category: Disambiguated" at the bottom now. That's no good at all ... --prime mover 12:49, 5 June 2012 (EDT)

One can turn display of hidden categories on or off at one's preferences page. I believe it is default not to see hidden categories; so while you may see it, others (like me) won't. If you so desire, you can of course change the setting. My idea was to put the category link inside the Template:BookReference which is the most common reference method if I'm correct. --Lord_Farin 15:12, 5 June 2012 (EDT)
 * Disambiguation categories have now been HIDDENCATed. As for the book categories, you will have to provide an example so I can see what you mean. Amend the BookReference template if you need to, we can always change it back if it all goes wrong. --prime mover 15:27, 5 June 2012 (EDT)
 * For an (as of now imperfect) example, see Characterization of Integrable Functions. IIRC, there is a way to force that the book ref cat comes after the measure theory category; I will probably think of a neater way to name the category, but that is a concern for later. --Lord_Farin 15:47, 5 June 2012 (EDT)
 * Adjusting the order of display appears impossible; this is a possible downside of the idea. Of course, we could make the categories hidden (eg. only linking from the book page to the category (by for example 'Pages incorporating material from this source can be found in "catname"')). --Lord_Farin 15:58, 5 June 2012 (EDT)
 * We might need to rethink that idea. I'm not dismissing it completely, I just wonder whether there's another way to do it ...--prime mover 16:31, 5 June 2012 (EDT)
 * Same here. But I still think we should make it easier to find pages referring to a particular source work. It makes sense to do such a thing. --Lord_Farin 17:21, 5 June 2012 (EDT)
 * Can't we already see what pages referr to a source work through the "What links here" link on the book page? --Alec (talk) 20:17, 5 June 2012 (EDT)

Entirely correct, thanks for pointing that out.

Definition categories - sorting of entries
We have been adding to the sort field of Definition category entries, so as to make sure that the entries in their category are sorted and entered on the entry name rather than on the D of Definition. Now I notice that some entries recently added have not had the tag added - but they still sort as though they did.

Has there been an amendment to the MediaWiki software that we hadn't noticed that automatically ignores the namespace of an entry when sorting? If so, then that makes our lives considerably easier. --prime mover 16:12, 18 June 2012 (EDT)


 * It has been for a while, and has been the reason for me not including the tedious stuff any longer. Of course, it is still needed when dealing with actual subpages (so that 'Page/Subpage' is sorted under S, not P, if that is desired). --Lord_Farin 17:12, 18 June 2012 (EDT)


 * IMO generally you need to sort on Page rather than Subpage - or that's how I read it. --prime mover 17:15, 18 June 2012 (EDT)

Internal Error
We have a bug in our system. Every so often when I save a page I get:

Internal error (as a page heading)

Set  $wgShowExceptionDetails = true; </tt> at the bottom of LocalSettings.php</tt> to show detailed debugging information.

I have not as yet followed the above advice.

It does not affect the page saved, that is, if I then click on the page to reload it, it comes up fine. --prime mover 22:00, 22 June 2012 (UTC)

... and it just did it again then when I saved the above. --prime mover 22:01, 22 June 2012 (UTC)

This should be fixed now. I switched servers and the package for sending mail wasn't installed. When a page was being saved, it was throwing this error because it couldn't send a message. --Joe (talk) 16:16, 23 June 2012 (UTC)


 * Nice one. Thx. --prime mover 18:23, 23 June 2012 (UTC)

Can't upload file again
Can't create a thumbnail or something.

Include this file and it works adequately:


 * [[File:Finish-work.jpg]]

... but try to do something fancy line and you get:


 * Finish-work.jpg

Bleah.

Click on the file itself to see what its settings look like in the raw. --prime mover 21:45, 28 June 2012 (UTC)


 * Fixed. --Joe (talk) 11:56, 29 June 2012 (UTC)

NUM bot
The new user message appears not to be working. A new user registered overnight (and who has already started making useful contributions) didn't get one. --prime mover 06:37, 5 July 2012 (UTC)
 * Will be fixed shortly. --Joe (talk) 13:11, 6 July 2012 (UTC)
 * Good stuff - it's back. --prime mover 21:03, 6 July 2012 (UTC)

Cookie trouble
Further problems have risen; there appears to be an issue with the reading of the cookies for login. --Lord_Farin 13:07, 7 July 2012 (UTC)
 * Looks like this was caused by a shortage of disk space... should be working fine now. --Joe (talk) 21:37, 8 July 2012 (UTC)
 * It's been a bit of a long weekend, but we're back again now. I'm once more editing. Good job. --prime mover 22:18, 8 July 2012 (UTC)

Incorrect proofs and nonsense definitions
We had an email sent to the ProofWiki admins informing us of inaccuracies (defined as "nonsense" by the person sending it, who also emphasised his ire by WRITING IN CAPITALS!).

He then added the comment:
 * "When I see this kind of stuff in ProofWiki, I realize that I can't depend on it."

The question is: if someone, as a result of using an incorrect definition or proof on ProofWiki, fails to achieve a particular objective, and as a result loses out on a potentially lucrative opportunity, how liable can we be held? Can the person who wrote the original pile of rubbish be extradited from their country of domicile and forced by the courts to pay substantial damages to the plaintiff? --prime mover 22:45, 13 July 2012 (UTC)


 * The 'general disclaimer' (accessible through 'Disclaimers' at the bottom of any page) ensures that, to the extent admissible by law, we are not liable. Now I'm not sure under what jurisdiction we are, but I suspect that this does not pose a problem. --Lord_Farin 07:29, 14 July 2012 (UTC)


 * Good to know - I will carry on posting up nonsense with impunity. --prime mover 07:56, 14 July 2012 (UTC)

SSL fun
Using the new HTTPS channel on Chrome for the first time. Chrome says: "This page has insecure content.". Following the steps Google advises, I detect the source of these insecurities. Apparently, they stem from 'pageads.googlesyndication.com/page_ads.js' (interesting how Google warns on their site for JavaScript that is poorly written as a possible cause for such warnings). +1 on the fail counter for Google :). --Lord_Farin 08:09, 14 July 2012 (UTC)

Yeah, I noticed that yesterday which is why I decided to not force HTTPS. Also, any pages which have external link which don't start with HTTPS will show as insecure. --Joe (talk) 10:56, 14 July 2012 (UTC)


 * ... what I've found is that pages load far quicker and work smoother without the ads on them (i.e when pressing "don't allow insecure content"). No problems encountered apart from the aforementioned. --prime mover 11:10, 14 July 2012 (UTC)

Logical Flow Chart
It would be nice for proofwiki to have a way to see the logical interdependence--which proofs are referenced where, and what theorems/axioms do these pages depend on, etc. I have two particular motivations in mind: this could also help to avoid circular reasoning, and it would make the site more ordered and straightforward. Is there a way of doing this? Andrew Salmon 05:24, 19 July 2012 (UTC)


 * Certainly an interesting thought; I suspect that it will necessarily be manual work. Recently we were pointed to an attempt at such a logical flow chart, cf. Brubeck which is currently covering only topological spaces and their properties. There is not a surge of creativity in me seeing how to extrapolate this to the whole PW structure, but it could be given some thought. I imagine it to be a hard and daunting task at the least; but it could be worthwhile in the aspects you mention. --Lord_Farin 07:07, 19 July 2012 (UTC)


 * I've moved this discussion into here because I believe this is a matter which requires wider circulation than my talk page.
 * My initial plan, going back as far as 2003, was to experiment with just such a concept. I got round to designing the logical data model, and started designing the page structure, but got bogged down on representing the mathematical symbols (at the time MathML was in its infancy and browser LaTeX support was minimal if it existed at all. Then I discovered this site and started filling it. It was always an aim to construct a graph (which would by necessity be a directed acyclic graph) but my intellectual pursuits have not gone in that direction.
 * If anyone wants to take it on board, let them be welcome. It seems to me that all it would take would be a parser for the pages, to specifically take "definition" and "proof" sections and extract the links into graph nodes. Elementary graph operations (easy to program, I did a similar job for a former employer) will then determine whether the graph has cycles, and it will take a mere snip of code to present any given page in its place in the tree.
 * As for making the site "more ordered and straightforward", I admit that it's not perfect yet (I'm currently involved in an exercise to refactor imperfect page structures), but I would challenge (as in: to a duel, sirrah) anyone who claims its general structure and philosophy could be more ordered and straightforward than it already is. --prime mover 08:16, 19 July 2012 (UTC)

Wikipedia article
''This section has been moved from the Help:Questions page as the purpose of the latter is for "How do I..." advice.''

Why does ProofWiki not have its own article on Wikipedia?--Jshflynn 02:20, 19 July 2012 (UTC)


 * Because they don't consider it as worthy. I have had communication with one or two people on that site and they generally dismiss this site as "trivial", and not worth even sneering at. --prime mover 08:19, 19 July 2012 (UTC)


 * Unbelievable. This site is a jewel among rocks. A model of rigor and a sanctuary of consistency. I suppose though, Wikipedia isn't in the business of recognising excellence. --Jshflynn 10:35, 19 July 2012 (UTC)


 * Well, I wouldn't put it quite that strongly - there are considerable gaps ... --prime mover 13:37, 19 July 2012 (UTC)


 * True, I am a little bit in love with the mechanics of the site and sometimes forget how many stubs there are. I have a lot of questions about the site so that I may make worthwhile contributions. Answer any you wish:
 * 1) How does the physics category work? Would it be good to perhaps provide a physical law and then have links to experimental verifications of the law?
 * 2)If my proof requires definitions used in a single paper can I make it explicit that I have only seen them in that paper and then provide the proof (I have always wanted to contribute a few proofs concerning parastrophes).
 * 3)When should definitions require examples?
 * 4)Should everything be interconnected (obviously not if the article uses the word more than once)? For example on Definition: Inner product it is clear that anyone looking up that knows what a mapping is but is it okay to just make the link anyway?
 * 5)Proof vs no proof. I could quite easily create or copy a few proofs written in the usual (less readable) essay like style and just put a "Does not meet standards" banner above it. Is this better than no proof of the proposition at all. The idea being not everyone knows the site inside out (nor how to format elegantly). Note: I despise stubs and am referring to poor proofs as opposed to half finished proofs. --Jshflynn 15:37, 19 July 2012 (UTC)


 * 2) We can always move stuff if necessary (or if we so please), so putting up defs (not colliding with stuff already up) is something I'd do as well. A quick web search on the term may provide additional insights. Compare with 5.
 * 3) The examples section is not yet fully developed. I encourage examples, as long as they are worked out thoroughly.
 * 4) Assume nothing; link everything (for all we know a random click session took a user there), this avoids grey areas, and having an unnecessary link is better than not having a necessary one.
 * 5) A 'tidy' call is definitely better than a 'stub' call; if half-finished proofs are presented, best create a separate section to encourage multiple proofs (we'll handle the formatting, compare Cantor-Bernstein-Schroeder Theorem (which needs a rename with the diaeresis instead of the 'oe' btw) for an excellent example). --Lord_Farin 16:00, 19 July 2012 (UTC)
 * "Schroeder": Titles with non-standard characters and modified letters are more difficult to find. --prime mover 09:20, 20 July 2012 (UTC)

Here is the relevant log, citing reason A7. If someone wanted to redo the page and make us sound important then they might not delete it. We have grown considerably. --Joe (talk) 13:48, 19 July 2012 (UTC)

Here is an exchange:

"...to drift away from Wikipedia and start or join our own wikis which have a more welcoming attitude towards inclusion..." — Hmmm, do you mean something like [http://knowino.org/wiki/Knowino:Welcome! this]? Boris Tsirelson (talk) 13:01, 2 October 2011 (UTC)


 * Looks good! I endorse it. The more wikis in the world, the better the world is. But I was particularly thinking of this, as it reflects my particular interests. --Matt Westwood 13:04, 2 October 2011 (UTC)


 * Proofwiki could be good, but here is what I wrote about it: "Trying their site I got discouraged. A lot of proofs of ridiculously trivial statements. And proofs of more interesting statements are often unfinished (and even stubby)." Or is it getting better? Boris Tsirelson (talk) 13:17, 2 October 2011 (UTC)
 * Fair comment. It might be getting better. OTOH since you wrote your comment only in March, probably not.
 * In its defence, that's what its intention is - everything gets documented. THere are some bigger proofs in there (check out Named Theorems) but the ratio of trivial to profound is larger than it might be. --Matt Westwood 13:30, 2 October 2011 (UTC)

...to which there was no response.--prime mover 13:53, 19 July 2012 (UTC)


 * We could take this as a sign to cut down on the 690 pages with a stub template, not mentioning the considerable amount of redlinks. But while our pool of editors is rather small, we can't really expect fundamental change any time soon, or so I fear. --Lord_Farin 15:06, 19 July 2012 (UTC)


 * Getting it into Wikipedia will be a challenge because they only allow articles which can be referenced to an outside source. As far as I can tell, Proofwiki is not widely (if anywhere) discussed. --prime mover 09:20, 20 July 2012 (UTC)

"Hence the result"
What's the primary role of this often appended sentence in comparison to the QED block. Could you point to examples of where it is necessary and where it should be omitted so I can get a better feeling of when to include it. Thanks. --Jshflynn 20:40, 20 July 2012 (UTC)


 * If I understand its use correctly, it is intended mostly to patch results together, some kind of finishing line. In the spirit of: "It suffices to prove 1 and 2. [proof of 1], [proof of 2]. Hence the result.", an explication that serves to indicate that only the most trivial of reasoning steps could be needed to achieve the desired conclusion.


 * Other possible variants are 'Hence the result, by definition of ...' and 'Hence the result, by theorem blabla'. --Lord_Farin 21:21, 20 July 2012 (UTC)


 * "Hence the result" is what I've been using, as it's a formal way of ending the proof process which is better (in my mind) to the kindergarten "and we're done". It seems to be necessary to end with some concluding words in addition to the "qed" box and "hence the result" (or whatever is appropriate given the nature of the proof) works for me. --prime mover 14:33, 21 July 2012 (UTC)

Presentation of Contents Lists
I have noticed that entries in contents lists seem to be spreading over into two lines (i.e line breaks being thrown in them), even for modest length titles. It has only just started doing this. This makes it look silly.

Does anyone know of any setting that might have been adjusted to make this happen - or anything silly I might have done in my browser? (Google Chrome).

Its also inconsistent, because I can't make it do it now. --prime mover 20:03, 3 August 2012 (UTC)


 * I recall that happening yesterday, also in Chrome. I've got no clue as to what may be the cause. --Lord_Farin 20:09, 3 August 2012 (UTC)


 * It's not only contents list. Look what's happened to the category list:


 * Subgroups of Group of Prime Order Power.jpg


 * Click on it to expand it. --prime mover 10:30, 4 August 2012 (UTC)

Interesting, I have no idea why it's doing this :s --Joe (talk) 12:52, 4 August 2012 (UTC)


 * For that matter, this stuff has been bothering me for a while now:


 * DisplayError.png


 * I suspect it is some MediaWiki issue but it is very strange in any case. The first screenshot originates from the standard page, the second when previewing before an edit. --Lord_Farin 14:36, 4 August 2012 (UTC)

Axiom template
Not entirely without enthusiasm I present the new Template:Axiom. It provides for a less ad hoc option to structure certain lists of statements that can't be handled by the eqn template (without hacking one's way into it, exploiting internal structure and leaving no hope for the uninitiated to understand what is happening). Hopefully, it will grow in use over time. --Lord_Farin 19:26, 7 August 2012 (UTC)


 * Looks useful ... immediate use: Definition:Group Axioms and so on? --prime mover 20:03, 7 August 2012 (UTC)


 * Indeed, specifically designed for that (although I discovered that Characterization of Measurable Functions could benefit from it as well). --Lord_Farin 20:05, 7 August 2012 (UTC)


 * What a useful construction. Thanks Lord_Farin. Should current definitions be edited accordingly or do you go by "if it ain't broke, don't fix it". I would probably start with something as harmless as the definition for $B$-Algebra. --Jshflynn 22:42, 7 August 2012 (UTC)


 * I've started putting it up here and there, as there is not much else I can crank out mentally at this hour before I go to bed (no intensive discussion this night). Feel free to go ahead, I hope the documentation is adequate. --Lord_Farin 22:45, 7 August 2012 (UTC)


 * Don't know about you guys, but the B in Jshflynn's post was messing up the formatting on this page, so I un-TeX'd it and added a link instead. --Alec (talk) 23:28, 7 August 2012 (UTC)

Caused by an un-escaped dollar sign earlier on the page; regexp matching is relentless. Fixed now. --Lord_Farin 23:32, 7 August 2012 (UTC)

6000'th Proof
We're up to 5999. Do we bother or are we going for steps of 2500 already? --Lord_Farin 09:46, 8 August 2012 (UTC)


 * I wasn't going to say anything. But this is pretty exciting for us base 10 using humans. I'm not going to take the honour. Make it something special guys. --Jshflynn 10:42, 8 August 2012 (UTC)


 * I've picked the Abel-Ruffini Theorem since its statement is relatively easy, and most of the prerequisites for stating it were already present. Add the landmark mark if you wish. --Lord_Farin 11:21, 8 August 2012 (UTC)


 * Wheee! --prime mover 12:44, 8 August 2012 (UTC)

I think we can be proud to note that it only took four months and a bit to add one thousand proof pages (so not counting definitions c.s.). Let us keep up the good work. --Lord_Farin 12:48, 8 August 2012 (UTC)


 * A considerable amount of that was due to refactoring. Every time a page was split up into two separate proof pages that turned 1 page into 3, thus artificially boosting the count. The upshot is that the count is always going to be artificially high, because of that two-proofs-live-on-three-pages effect. --prime mover 12:53, 8 August 2012 (UTC)

Bookreference template
I just broke the BookReference template. All I wanted to do was add a "ref" parameter so as to be able to add the internal reference of the book being referenced. But when I added it, it threw a new line at the end of the existing line, and so the reference appeared on the next line. So I reverted, after a few tries, and now it insists on throwing a new line after EVERY invocation of this template. Who writes this shitty software? They need their arses kicked. --prime mover 06:21, 9 August 2012 (UTC)
 * Now it's behaving itself. But the software is still shit. --prime mover 06:27, 9 August 2012 (UTC)

Independent Reinvention
It might be an interesting topic of conversation (brought on by Jshflynn's work on e.g. B-Algebras) ...

Who has invented a mathematical concept and been really, really pleased with it - only in order to find it's already been analysed to death?

I remember as a child (approx. 7) discovering that you can get 1/3 by successive adding and subtracting 1/2 of what's left, i.e. 1/3 = 1/2 - 1/4 + 1/8 - 1/16 ....

I also invented the Stern-Brocot tree while passing the time calculating what fraction of my time I had left to do on a daily basis at one time when I had been restricted of my liberty. When I showed it years later to my number-theory tutor during my MMath I was well pleased to find she'd never heard of it - I was sure it was original. Then my father-in-law got me Knuth etc's Concrete Mathematics and I was gutted to find it in there. --prime mover 12:02, 10 August 2012 (UTC)


 * Many times. I have personally discovered this (with no clue as to how it really works) and the Ulam spiral (although no one knows how that works).


 * This is why the world needs sites like ProofWiki though. Everythings documented, linked and accessible worldwide. I have met a maths professor before who said that many brilliant maths papers languish in obscurity (his original language was Hungarian) and that many are churned out year after year with (for want of a better word), isomorphic ideas. IMHO, I think a degree of redundancy is inevitable and necessary. But how much so is anyone's guess.


 * I am very thankful I have discovered user pages on here though. So I put up any harebrained idea I might have without ruining the work of others :) --Jshflynn 13:39, 10 August 2012 (UTC)

Cannot see latest version of proof unless I am logged in.
I was horrified to find two errors in Logarithmic Derivative of Riemann Zeta Function, so I joined up so I could correct them.

I thought I had successfully done this, but I have now noticed that I only see the latest version when I am logged in. When not logged in I see the old version with the stupid errors again. Why is this happening?

--nojameson 02:05, 13 August 2012 (UTC)


 * Possibly a caching issue. Have you tried clearing your cache? --Joe (talk) 02:12, 13 August 2012 (UTC)


 * I noticed that too. Caching issue or no, this seems wrong to me. Just one of a number of weirditudes seen recently. I wonder whether Google have released a dodgy version of Chrime (typo appropriate) or something? --prime mover 05:19, 13 August 2012 (UTC)


 * Both Firefox and Chrome state that there are 5813 proofs on the main page unless I'm logged in. --Jshflynn 07:54, 13 August 2012 (UTC)

How about now? --Joe (talk) 12:49, 13 August 2012 (UTC)


 * I had tried clearing my browser's cache but it didn't help. However, the problems seems to have resolved itself now - I see the latest version when logged out. --nojameson 15:09, 13 August 2012 (UTC)
 * I disable the file caching system on the server. Looks like there must be a bug in it. --Joe (talk) 15:24, 13 August 2012 (UTC)

Was I thinking about concatenation naïvely?
Please excuse me if I am posting this in the wrong place but I'm quite desperate for a second opinion. Please see the my user page: Concatenation issue --Jshflynn 17:44, 15 August 2012 (UTC)


 * It would be interesting to see where it's going, but it just seems like sequences in which the elements of the sequence are themselves sequences. Replace the angle brackets with round ones and it looks no different from operations on ordered tuples. --prime mover 18:01, 15 August 2012 (UTC)


 * Also nested sequences to me seem very similar to labelled trees. I can't think of any useful questions about them other than brain teasers. --Jshflynn 15:27, 16 August 2012 (UTC)

xymatrix (moved from User talk:Lord_Farin)
I see your link about xymatrix, but from what I can tell this has not yet been included into MathJax. If you know different, and have a technique by which we can exploit this package, please let us know. --prime mover 22:15, 7 August 2012 (UTC)


 * Some reading on the MathJax site suggests that the inferior amscd</tt> package is available, but xymatrix</tt> is a long way off. I have volunteered to help implement it just a few seconds ago. --Lord_Farin 22:18, 7 August 2012 (UTC)
 * We can always make our own branch of MathJax. --Joe (talk) 22:59, 7 August 2012 (UTC)


 * Yes, and why not make rainbow coloured unicorns spawn from one's monitor upon visiting the site as well... The xymatrix</tt> project is going to be huge and difficult enough without trying to build it with just us two. --Lord_Farin 23:02, 7 August 2012 (UTC)


 * " ...rainbow coloured unicorns spawn from one's monitor..." I can sort that one out for you if you like, one of the websites I follow has a "cornify" tool which vomits these vile pictures all over the screen when you hover over certain links. --prime mover 05:25, 8 August 2012 (UTC)

The developer of https://github.com/sonoisa/XyJax has just released a new version compatible with MathJax v2.0 as a simple extension file (like amsmath</tt>. It will hopefully provide us with quick availability of xymatrix</tt> or at least the low-level xypic</tt> core package (the former is an interface for the latter). I've asked Joe to enable the stuff for testing. I'll keep you posted, and when it becomes available, I will move this topic to Main talk. --Lord_Farin 13:48, 12 August 2012 (UTC)


 * It is not without pride or excitement that I present:


 * $\begin{xy}

<0em,0em>*+{X \times Y}="xy", <5em,0em>*+{X}="x", <0em,-5em>*+{Y}="y", <5em,-5em>*+{Z}="z", <-4em,4em>*+={U}="u", "xy";"x" **@{-} ?>*@{>} ?<>(.5)*!/^0.5em/{\scriptstyle p}, "xy";"y" **@{-} ?>*@{>} ?<>(.5)*!/_0.5em/{\scriptstyle q}, "x";"z" **@{-} ?>*@{>} ?<>(.5)*!/^0.5em/{\scriptstyle f}, "y";"z" **@{-} ?>*@{>} ?<>(.5)*!/_0.5em/{\scriptstyle g}, "u";"xy" **@{--} ?>*@{>}, "u";"y" **\crv{<-3em,-2em>} ?>*@{>} ?<>(.5)*!/^.5em/{y}, "u";"x" **\crv{<2em,3em>} ?>*@{>} ?<>(.5)*!/_.5em/{x} \end{xy}$


 * the XyJax extension of MathJax, enabling us to draw commutative diagrams. It does not support the xymatrix</tt> environment yet, but at least a start can be made with developing commutative diagrams in TeX style. Documentation is sparse at this point, but please see this web page for an introduction and samples to tinker with. --Lord_Farin 18:50, 15 August 2012 (UTC)


 * I take my hat off to you: that is pretty impressive. I expect you want me to do the unicorn thingy now. :-) --prime mover 20:33, 15 August 2012 (UTC)


 * I have crafted some nice examples at Definition:Morphism Category. Soon, there will be curved arrows involved. Oh, and 'page.cornify' :). --Lord_Farin 08:41, 16 August 2012 (UTC)


 * Curved arrows at Definition:Composition Functor. I am seriously starting to like this package. --Lord_Farin 11:13, 16 August 2012 (UTC)