User talk:Fropuff/Archive 2

Vector flow
Hi,

While copying (the awful) article flow (mathematics) from planetmath, I stumbled upon your marvelous User:Fropuff/Notes, noted that it had a solid overview of flows, better than anything else that we have on WP, and thus I mangled it into a stand-alone article, titled vector flow. linas 16:37, 5 September 2005 (UTC)


 * Well, at some point in time I wanted to write an article on vector flows in geometry, so I started those notes to sort out (at least in my head) the various ideas involved. As usual, I got sidetracked with other things. The notes were/are in a extremely rudimentary form; hardy article quality. However, if you or someone else would like to expand those notes into an actual article or set of articles I have no objection.


 * At first glance, I'm not sure why you have flow (mathematics) and vector flow as two separate articles; they seem to have considerable overlap. Also, I prefered the name flow (geometry) to flow (mathematics) as there is another meaning of flow in mathematics: namely network flow. -- Fropuff 17:01, 7 September 2005 (UTC)

Binary tetrahedral group
Hi, i was looking through your page and saw you were interested in writing up something on the binary tetrahedral group. Do you know any good references on the subject? -- User:147.10.133.92 19:07, 6 September 2005


 * Part of the reason I wanted to write something up on the binary tetrahedral group (and the other binary polyhedral groups) is that I do not have any good references on the subject. My knowledge has been pasted together from a variety of places, mostly online notes and scattered references in miscellaneous books (e.g. the book by Conway and Smith, On Quaternions and Octonions, has some minimal information). Hopefully, I can find the time to put these notes together into an actual article. -- Fropuff 17:01, 7 September 2005 (UTC)

Science pearls
Hello,

Since you contributed in the past to the publications’ lists, I thought that you might be interested in this new project. I’ll be glad if you will continue contributing. Thanks,APH 11:06, 11 September 2005 (UTC)

Discrete groups
Noticed that the paragraph about examples of discrete subgroups of Lie groups was axed. While recognizing the inadequacies of the paragraph, I want there to be a further explanation of discrete subgroups of Lie groups, that being the primary way the terminology of "discrete groups" is used today, for example: G. A. Margulis "Discrete subgroups of semisimple Lie groups"; Farkas-Kra "Riemann surfaces"; etc. The closest I can find to this topic is a brief paragraph in Lattice (group). Any suggestions? --Mosher 03:51, 5 October 2005 (UTC)


 * I'm a little confused. I axed the statement because I thought it was a repetition of what was stated in the first paragraph: A discrete subgroup H of a topological group G is a subgroup whose relative topology is the discrete one. Clearly, a discrete subgroup of a topological group is a discrete group. This covers the Lie group case as well. Were you trying to say something more than this? -- Fropuff 04:18, 5 October 2005 (UTC)

Yes, it was repetetive, sorry about that. I was trying to emphasize the naturality of discrete subgroups of Lie groups: many familiar groups are naturally described as discrete subgroups of Lie groups. Perhaps one way to get this emphasis across  would be to organize the list of examples according to the Lie group that they live in. For example the reorganized list could start out like this:


 * Frieze groups and wallpaper groups are discrete subgroups of the isometry group of the Euclidean plane
 * Space groups are discrete in the isometry group of Euclidean space of arbitrary dimension.
 * Fuchsian groups are, by definition, discrete subgroups the isometry group of the hyperbolic plane.
 * Kleinian groups are, by definition, discrete subgroups of the isometry group of three-dimensional hyperbolic space. These include quasi-Fuchsian groups.

and so on, perhaps including examples for which there are as yet no links. --Mosher 11:35, 5 October 2005 (UTC)


 * I think organizing the examples like that would be a great idea. -- Fropuff 16:30, 5 October 2005 (UTC)

Coxeter groups
The intro is still incorrect.

Perhaps the issue is the question of what is meant by a reflection. The naive notion is an isometric reflection across a hyperplane in Euclidean space, but that is wrong for Coxeter groups. For example, the 3-generator Coxeter group
 * $$G_{2,3,7} = \{a,b,c | a^2 = b^2 = c^2 = (ab)^2 = (ac)^3 = (bc)^7\}$$

is a cocompact triangle group in the isometries of the hyperbolic plane, generated by isometric reflections in the sides of the hyperbolic triangle with angles $$\pi/2, \pi/3, \pi/7$$. On the other hand, it is not isomorphic to any discrete group of isometric reflections in a Euclidean space (an application of the Bieberbach theorems).

There is a more general notion of an affine reflection in Euclidean space, alluded to very briefly in the article Reflection (mathematics). For example the map $$(x,y) \to (-x,y+x)$$ is a non-isometric but affine reflection in the Euclidean plane.

It is accurate to say that every Coxeter group is generated by certain affine reflections in some Euclidean space. But not every group generated by affine reflections in a Euclidean space is a Coxeter group. In fact, not even every group generated by isometric reflections in Euclidean space is a Coxeter group. Describing the exact manner in which a Coxeter group acts by affine or isometric reflections is a little complicated, although it could be done in a Wikipedia article.

So the question is, how best to give the kind of brief "definition" that one expects in the first paragraph of a Wikipedia article. To say "reflections" but not "affine reflections" is misleadingly vague, I would say incorrect, because of the naive understanding as referring to "isometric reflections". To say "affine reflections" without further qualifying the restrictions on the group is misleadingly precise.

I chose instead a slightly vague formulation by analogy, which avoids being misleading in either of the above manners. The locution "abstract reflection group" is commonly used, and the real point, as far as the definition is concerned, is that the form of the presentation is analogous to the form of certain well known examples of finite or Euclidean Coxeter groups (which may be what led Coxeter to his definition in the first place).

I'm also planning to add more to the article, along the lines proposed in Talk:Coxeter group. --Mosher 11:10, 8 October 2005 (UTC)


 * Okay, I see your point. I guess we'll have to sacrifice some concreteness in the introduction in order to avoid misleading readers. Feel free to edit it as you see fit. It would be very helpful to highlight the exact relationship between Euclidean reflection groups and Coexter groups somewhere article (I see this is on your list of things to do). -- Fropuff 23:46, 11 October 2005 (UTC)

Draft subpages
I like how you have drafts in subfolders on your user page. How do you do that? --Mosher 01:10, 18 October 2005 (UTC)


 * Yeah, I find them useful. Just make a red link on your user page like this:
 * /Draft 1
 * (make sure there is a foward-slash in front). Then click and edit like a normal page. -- Fropuff 01:19, 18 October 2005 (UTC)

Thanks, but no
To anonymous user 151.204.6.171: Thanks for your contributions here and welcome to Wikipedia. I would strongly suggest creating a user account. It is much easier to interact with a name than an IP address; it doesn't have to be your real name. Again, welcome. -- Fropuff 01:32, 4 November 2005 (UTC)


 * Thank you for your vote of confidence. But I have little interest in being identified either by a handle or by my own actual IP address.  Even under a successful subpoena to the ISP of my currently spoofed address, it is even then highly unlikely you would discover my true identity.  I'm sorry for the indirection, but I have come to value my online privacy.  Regards, 151.204.6.171

As you wish. Although I don't think anyone here is out to discover your true identity. Even if they were, I think you can maintain your anonymity just as well with a fake name. It just makes it easier for us to interact. At any rate, I hope you enjoy Wikipedia. -- Fropuff 15:19, 4 November 2005 (UTC)
 * I do plan to disover this anon's identity, use it, make huge credit card debt in Vegas strip bars, and as a final touch, publish it on the web under the GFDL. Oleg Alexandrov (talk) 19:39, 4 November 2005 (UTC)

Join (topology)
Thank you very much for correcting my horrible error on join (topology). -- Jitse Niesen (talk) 20:21, 3 December 2005 (UTC)

Tangent half-angle formula
Regarding your request for diagram for the Tangent half-angle formula article, is it something like this you had in mind? --Gustavb 00:21, 11 December 2005 (UTC)


 * That looks great, thanks! The only other thing to add would be a &phi;/2 angle marker where the straight line crosses the x-axis. If it's not too cluttered you could also have a little triangle connecting the points (cos &phi;, sin &phi;), (cos &phi;, 0), and (1,0) with the appropriate &phi;/2 angle marker. This way people can easily see the relationships
 * $$t = \tan\left(\frac{\varphi}{2}\right) = \frac{\sin(\varphi)}{1 + \cos(\varphi)} = \frac{1-\cos(\varphi)}{\sin(\varphi)}.$$
 * -- Fropuff 00:29, 11 December 2005 (UTC)


 * Note however, that when it shows up as a thumb, the text is too tiny and lines too thin. I would suggest making the circle bigger, the font larger, the lines thicker, and the arrows bigger too. Wonder what you think. Oleg Alexandrov (talk) 00:37, 11 December 2005 (UTC)
 * You wouldn't to make it so small though. This looks good:


 * It might be nice to crop some of the white space at the bottom. -- Fropuff 00:45, 11 December 2005 (UTC)
 * Okey, I've tried to make it clearer. How about this? (and yes, it was not intended to be used as a thumbnail) --Gustavb 02:24, 11 December 2005 (UTC)
 * Looks better, thanks! Oleg Alexandrov (talk) 05:23, 11 December 2005 (UTC)
 * Looks good! Although I noticed someone else has loaded a competing pic on the page. I think I like this one a little better. -- Fropuff 03:35, 12 December 2005 (UTC)
 * I like this one more too. Oleg Alexandrov (talk) 04:47, 12 December 2005 (UTC)

Wanted Images
Hi Fropuff - I note that you've requested a cone image as well as others. I'm happy to render such images using povray (a math-accurate raytracer), but, not being a mathematician, I'm not sure what specific features you require. Also, if you want any other topology images, I'd be happy to oblige.

Anyway, drop me an email or update my talk page. ttfn.

(email wiki@tomandlu.co.uk)

Tomandlu 16:09, 12 December 2005 (UTC)


 * Well these images are all really simple. They should probably just be simple line diagrams (no need for raytracing). For the cone diagram it might be nice to show a cylinder (X &times; I) with an arrow pointing to the cone which is the cylinder with one end collapsed to a point. The base space X can just be a circle (or a deformed circle if you are more creative). I don't know if this is making any sense or not. -- Fropuff 17:06, 12 December 2005 (UTC)



Is this okay? Or OTT? Tomandlu 10:17, 13 December 2005 (UTC)


 * These are very nice images of cones, but not suitable for the article on topological cones. It is difficult to see the construction of a topological cone from these pictures. As I said above, I think a simple line diagram would work best. -- Fropuff 16:45, 13 December 2005 (UTC)


 * Make one then. :) Come on Fropuff, it is really easy. There is Xfig on Linux (on Windows they have winfig). Any vector drawing package would work just fine too, like inkscape. All you need to draw is several lines and maybe circle arcs. Easy. Matlab or maple would work too, if you know how to use them (otherwise I can help you with matlab) Easy. :) Oleg Alexandrov (talk) 19:26, 13 December 2005 (UTC)


 * My problem is that I don't have any good vector drawing program, otherwise I would. Do you have any recommendations. My criteria are:
 * It must run on Windows (preferably native)
 * It must be free (as in beer)
 * It must be able to export to EPS (and preferably to SVG)
 * It must be easy for a non graphics artist to use.
 * Ideally, it should be compatible with LaTeX so that I can include typeset equations in the diagram. Also it should use the same standard fonts as LaTeX.
 * I've spent some time in the past looking for good programs and never found anything I like. Maybe I've missed some stuff. -- Fropuff 19:41, 13 December 2005 (UTC)
 * As Oleg said, have you tried Inkscape? It's open source, available for windows, uses SVG natively and can export simple illustrations (without transparencies and gradients) to EPS. Unfortunately it does not support TeX commands, but you should be able to simulate it using a True Type version of Computer Modern (TeX's default font). –Gustavb 21:09, 13 December 2005 (UTC)
 * Yes, I used inkscape too. Very nice and easy to use, free as in beer, and easy to install. I really love the way it draws splines. You can draw a shape, then it is very easy to fine-tune it. And it does export to eps as far as I know. Oleg Alexandrov (talk) 21:33, 13 December 2005 (UTC)


 * Thanks, I'll give it a try -- Fropuff 21:45, 13 December 2005 (UTC)

this more what you are after?



BTW pov-ray is a pretty good program if you need to produce complex shapes - it has an iso-surface capability, which means it can pretty much any shape based on an equation threshold. --Tomandlu 21:36, 13 December 2005 (UTC)


 * This is getting closer. One also has to label the base space X and the interval I. I might try my own version with Inkscape to see if I can get something nice. I do have a copy of pov-ray on my computer, although I've never figured out how to use it. -- Fropuff 21:45, 13 December 2005 (UTC)

Re:red links
I replied on my talk page. Oleg Alexandrov (talk) 04:50, 13 December 2005 (UTC)

Two replies
About redlinks, see User:Mathbot/List of mathematical redlinks (the files are being uploaded as I write). I myself doubt how useful that is going to be, but it may. :)


 * I've already found the list useful. If nothing else people can scan through it and create redirects/fix broken links as needed. It's also useful to see what redirects need to be made when creating a new article. We should mention this page at WP:WPM to see if anyone else finds it useful. -- Fropuff 05:29, 14 December 2005 (UTC)

About your remark that you would like a image editor which also plays very well with LaTeX, well, that's too much to ask. But there is hope. :) Usually people generate eps figures with very simple text labels, and then manipulate those from within the LaTeX document (so from the TeX article you are writing you can control everything about the text in the eps figures it includes, like what formulas to have, what font, what size, etc.) The package with helps with that is called psfrag. See here, towards the middle of the page. There is a learning curve, but no harder than learning one more LaTeX command. Cheers, Oleg Alexandrov (talk) 04:00, 14 December 2005 (UTC)


 * Pictures in LaTeX are an eternal pain in the a**. I think every time I've looked for a vector drawing program I've given up, because I can never make anything work right. I've always wondered why I need 14 seperate programs/packages to make one simple picture. And even then it'll only typeset on one machine. Send the source to your buddy and it all comes crashing down. Someday (long into the future) someone is going to fix all this.


 * I'm playing with Inkscape. But it runs awfully slow on Windows. If I can ever make a cone I'll upload it (don't hold your breath). Thanks for the psfrag tip. -- Fropuff 05:29, 14 December 2005 (UTC)
 * If you don't want to use 14 separate programs, and if you don't want to use that bloated inkscape, you can just use LaTeX's drawing facilities (draw points, draw lines, draw curves). Doable, but that's the real pain in the ass. :) Oleg Alexandrov (talk) 08:10, 14 December 2005 (UTC)

Coffee cup to donut in Topology
The handle switches sides in the middle picture. This would be confusing for people who have never seen it before. --C S (Talk) 08:52, 16 December 2005 (UTC)


 * Yeah, I know. I didn't make this picture myself, I just found it on Wikimedia Commons. I'd welcome a better version. -- Fropuff 08:56, 16 December 2005 (UTC)


 * Oh, ok. I'll add it to my to-do list.  --C S (Talk) 09:00, 16 December 2005 (UTC)

Yes, I put the portals back in their own space
I did it on my own initiative. I am started from Wikipedia:Browse and I am assessing what the user will find most irritating about the lack of uniformity. The portals in most of the Top 8 cats was out-of-place with the rest of the categories. I am forcing a larger decision to be made. Enough uniformity now exits where if some serious, thought-out consesus decision is made to move the portals to the cats, it will be easy to do so for the Top 8 (and then maybe serveral dozen others). My point is that all remaining Portals should then follow the example set by the Top 8 (or 10 or 12, depending on who you talk to). -- Fplay 19:25, 21 December 2005 (UTC)

More on red links
Hi Fropuff. I updated the redlinks pages (actually, it is doing it now). This time I wrote a real, useable script instead of a hack, so the process is fully automated. I can restart it at anytime with no work. Bug me again when you want those links refreshed (maybe a couple of weeks could be a good interval, I don't know). Oleg Alexandrov (talk) 03:35, 7 January 2006 (UTC)


 * Thanks Oleg. I think updating every couple of weeks or so would be more than sufficient. -- Fropuff 03:47, 8 January 2006 (UTC)

Admin ambitions?
Do you have any ambitions to be a sysop round here? If so, I'd gladly nominate you. Charles Matthews 15:10, 8 January 2006 (UTC)


 * Thanks for your vote of confidence. Although perhaps my editcount won't merit a sysop promotion. But I'd gladly accept a nomination if you were so inclined. -- Fropuff 17:22, 9 January 2006 (UTC)

Please indicate acceptance (Requests for adminship/Fropuff). Charles Matthews 10:04, 10 January 2006 (UTC)

General linear group
Do you have a reference on GLn(F) being a semidirect product of F&times; with SLn(F)? In particular, how is the homomorphism
 * &phi;: F&times; &rarr; Aut(SLn(F))

defined? - Gauge 00:43, 10 January 2006 (UTC)


 * Reference is Rotman, 4th ed. Theorem 8.8. You can embed F&times; in GLn(F) by
 * $$x\mapsto\mbox{diag}(1,1,\cdots,1,x)$$
 * The automorphism &phi;(x) is then conjugation by this element. -- Fropuff 00:52, 10 January 2006 (UTC)

Deleted image
Hi Fropuff. When the image was originally uploaded in Nov 2004, no licencing details were included. The image was then tagged by another editor in December 2004 as having no licence, and any images which do not have source and copyright details are speedy deletable seven days after being tagged as such. So if you do re-upload the image, please be sure to include details of the source and the copyright status to prevent it from being deleted again. Regards, CLW 16:50, 14 January 2006 (UTC)

Congratulations
Hi,, Congratulations on Becoming a Sysop Hey there. Congratulations, you've just been made a sysop! You've volunteered to do housekeeping duties that normal users sadly cannot participate in. Sysops can't do a lot of stuff: They can't delete pages just like that (except junk like "aojt9085yu8;3ou BOB IS GAY"), and they can't protect pages in an edit war they are involved in. But they can delete random junk, ban anonymous vandals, delete pages listed on Votes for deletion (provided there's a consensus) for more than one week, protect pages when asked to, and keep the few protected pages that exist on Wikipedia up to date.

Almost anything you can do can be undone, but please take a look at The Administrators' how-to guide and the Administrators' reading list before you get started (although you should have read that during your candidacy ;). Take a look before experimenting with your powers. Also, please add Administrators' noticeboard to your watchlist, as there are always discussions/requests for admins there. If you have any questions drop me a message at My talk page. Have fun! &mdash; Ilyan  e  p  (Talk)  05:26, 17 January 2006 (UTC)


 * Congrats! Oleg Alexandrov (talk) 05:41, 17 January 2006 (UTC)

Thanks! I feel honored. (First, I'm a white sysop on a black background, and then an orange sysop on a blue background. All I want to know is: When do I get my Wikipedia black belt?) -- Fropuff 06:29, 17 January 2006 (UTC)


 * Also congratulations from me. I'm glad you came through the sometimes vitriolic process of RfA without too many bruises. I do hope though that your work on the maths articles won't suffer too much. -- Jitse Niesen (talk) 13:46, 17 January 2006 (UTC)

Thanks!!
Hi Fropuff,

Thanks for the advice -  it's good to know someone's looking over my shoulder whilst I'm learning. Dmaher 10:42, 19 January 2006 (UTC)

Tangent bundle
Any particular reason why you removed this statement from the tangent bundle article?


 * When this happens the tangent bundle is said to be trivial. Just as manifolds are locally modelled on Euclidean space, tangent bundles are locally modelled on M &times; Rn.

-- Fropuff 15:31, 18 January 2006 (UTC)


 * Yes. 1) "when this happens" is misleading/ambiguous. 2) TM does NOT locally look like M x R^n. --MarSch 12:19, 19 January 2006 (UTC)

I've moved this discussion to Talk:Tangent bundle and replied. -- Fropuff 20:20, 19 January 2006 (UTC)

unicode
resp on my talk page --Trovatore 05:23, 20 January 2006 (UTC)

Hjelmslev transformation
Hi, congrats on your admin nom. Anyway, I got sucked back very temporarily from a wikibreak to respond to a comment on the talk page of hyperbolic geometry. Basically, if you haven't been following, SJCStudent has created Hjelmslev transformation, which appears to me to be the same as the Klein model. S/he added a description of it to hyperbolic geometry, which I removed with a comment on the talk page; I have now added a lengthier response. Our discussion is pretty friendly; unfortunately s/he doesn't seem to know enough about hyperbolic geometry to respond to my concerns. Anyway, I don't think I'll have time to check back on it for a while, so I would appreciate if you could take over the discussion. You seem to have more than enough experience with the subject to handle it. It will probably be necessary to move most of Hjelmslev transformation to a new article on Klein model, but I'm not sure what should be done with the info on Hjelmslev. --C S (Talk) 22:48, 23 January 2006 (UTC)

I've just added a new entry for hyperboloid model and plan to do one on Klein model, but I wonder what I should do with Hjemslev.Gene Ward Smith 16:51, 16 April 2006 (UTC)


 * I'll try and follow up. I've never heard of a Hjelmslev transformation either, although the article is clearly describing something related to the Klein model. -- Fropuff 06:34, 24 January 2006 (UTC)

blahtex bug report
thanks.... and remember, he (or she) who finds the most bugs wins! Keep them coming. Dmharvey 03:59, 30 January 2006 (UTC)

Supermatrices
Hi Fropuf,

I know that you want to write an article on supermatrices as used in super linear algebra (see supervector space, supertrace, and superdeterminant) and I do not want to be unreasonable. Go ahead and write the article and at the end append a section, introduced perhaps as... supermatrices are also conceptualized in other disciplines, e.g., in statistics, as... and add mine material to that section. Best Wishes, David Cruise 08:19, 7 February 2006 (UTC).


 * Thanks, I appreciate your willingness to work with me. I hope to get around to writing that article sometime soon. -- Fropuff 22:52, 7 February 2006 (UTC)

Joke's RfA
Hi Fropuff, thanks for your comments and support in my (successful) RfA! –Joke 16:24, 7 February 2006 (UTC)

commutative diagrams
Hi Fropuff. I've recently made some commutative diagrams (Image:Welldefined.png, Image:Rangediagram-01.png, Image:Rangediagram-02.png). It is my opinion that they don't look nearly as nice as most of the diagrams around these parts, which I guess are all due to you. Can you give me some pointers? I'm using xypic with Equation service and Preview.app for conversion. Do you think these can do the job? What do you use? -lethe talk [ +] 09:30, 25 March 2006 (UTC)


 * You might try a better conversion program. I recommend textogif. It's a Perl script for converting TeX source directly to a GIF or PNG. I believe the script makes use of the Netpbm library for doing the graphics conversions. I usually run it with the options . I guess the only other factor is the package you use to do the diagrams themselves. I've been using Paul Taylor's diagrams package. Whether or not it produces nicer results than XY-pic is a matter of opinion of course. -- Fropuff 17:33, 25 March 2006 (UTC)