Talk:Modular group

message: I can add a lot to this...although I think the article title should just be "Modular group" rather than "Modular group Gamma", the standard notation can just be mentioned in the article itself.  Also, technically, the modular group is PSL(2,Z), not SL(2,Z), although the distinction is usually glossed over in practice.  There are a lot of applications of this to number theory and geometry.  Revolver
Please do - I see you are working on Fuchsian groups. Eventually someone will redirect modular group here. We could have a page for Gamma-zero-of-N for all small N! (Just kidding.)
Charles Matthews 19:38, 5 Nov 2003 (UTC)
thread_title:  Title 

message: Thanks for catching that mistake with S, Gandalf. Revolver 01:09, 9 Apr 2004 (UTC)
thread_title:  Thanks 

message: This section doesn't seem to be correct.  
* The dyadic monoid seems to be a term for the monoid generated by all finite strings of symbols A and B with A2 = B2 = 1: this happens to be the free product of groups C_2 \star C_2.  So the definition isn't correct.  The modular group, on the other hand, contains the free product C_2 \star C_3, which isn't the same thing as either of the above.  
: (Later, not quite right, see below)
* I don't understand what it means to say "This monoid occurs naturally in the study of fractal curves, and describes the self-similarity symmetries of the Cantor function, Minkowski's question mark function, and the Koch curve, each being a special case of the general de Rham curve."  Firstly, how does it "describe" anything?  Secondly, the Cantor function is not a curve.  Should that read "the graph of the Cantor function"?
* "The monoid also has higher-dimensional linear representations".  Does this mean a map into a general linear group?
* "the N=3 representation can be understood ..." not by me I'm afraid, since this is the first mention of N in the section.  Is it a reference back to the previous on congruence subgroups?
I propose this section be deleted pending a complete revision.  Richard Pinch (talk) 22:22, 15 July 2008 (UTC)
replies: text: Sorry, got that first point a bit wrong.  The dyadic monoid is the free monoid on 2 generators, ie all finite strings of the form XXX...YYY...XXX...YYY... .  What's described in the article is the monoid on generators S and T subject to the relation S2 = something, possibly 1.  The modular group contains the free product of cyclic groups C_2 \star C_3, which isn't the same thing as either of those two.  However, because that free product contains free groups of all finite rank, in particular it contains, but is not equal to, the free group on two generators, which in turn contains but is not equal to, the free monoid on two generators.  Richard Pinch (talk) 23:01, 15 July 2008 (UTC)
replies: text: I think this section would be a lot saner if S and T were specified.  There are countably many copies of the free monoid on two generators in PSL(2,Z), and if any copy will do, then I don't see why it is described here, rather than simply linking to the Tits alternative.  I suspect that its relation to the fractals is somewhat interesting, perhaps being generators of the set of endomorphisms of the fractal?  Do we know who wrote this section?  It might be polite to drop them a note. WP:V suggests taking a look at the index of the only reference given.  If "dyadic monoid" is in there, then we should try to fix the section. JackSchmidt (talk) 01:55, 16 July 2008 (UTC)
replies: text: Looks like the section was rewritten several times.  It might be WP:OR by User:Linas.  Here is the [ introduction] of the section.  Here is the [ removal] of a WP:COI/WP:EL problem, but the only reference for that section.  Here is the section [ rename]. JackSchmidt (talk) 02:04, 16 July 2008 (UTC)
replies: text: According to the version of the reference I found here neither "dyadic" nor "monoid" appears in the index.  I'll look up some more references (including a physical copy of Apostol) in slower time.  Richard Pinch (talk) 06:03, 16 July 2008 (UTC)

text: That last diff was interesting, as it explains the origin of the stray N=3 that I didn't understand.  Just to record that text here: "The modular group also has pairs of representations in GL(N,R). The N=3 representation can be understood to describe the self-symmetry of the blancmange curve, and higher N 's as the symmetries of similar curves."  I'm not sure it's correct but it certainly makes more sense.   However, it seems to be in essence about the monoid and perhaps should go to Free monoid if anywhere.  Richard Pinch (talk) 06:08, 16 July 2008 (UTC)
thread_title:  Dyadic monoid 

message: I have reverted a series of experimental markup and formatting changes that were made (and then partly reversed) in a series of edits by User:Yecril. I feel strongly that significant and non-standard markup changes like this should only be made after consensus has been sought and gained and after obvious bugs in the new markup have been ironed out, so I am reverting these changes pending a wider discussion within the Wikipedia community. I have suggested to Yecril that he should initiate a discussion of his ideas at Wikipedia talk:WikiProject Mathematics, but so far he seems to be reluctant to do this - see thread at User talk:Yecril. Gandalf61 (talk) 08:37, 4 September 2008 (UTC)
replies: text: I am not reluctant; progress is blocked by Bug 9119.  --Yecril (talk) 06:56, 15 September 2008 (UTC)
thread_title:  Revert experimental markup changes 

message: Hey, I made a visualization showing how Klein's j-invariant is invariant under action of SL(2,R). 
<a href="http://www.youtube.com/watch?v=kvQ7e2AiE2g">Klein's j-Invariant j(τ) under τ→-1/τ in SL(2,R)</a>
If anyone wants to turn this into an animation for this page, I would be happy to supply them with the movie file for it.
tryptographer (talk) 18:27, 7 July 2013 (UTC)
thread_title:  visualization 

message: A recently added reference to my diploma thesis has been removed by Wcherowi with the comment "Duplicate reference; COI; not a secondary source". I just wanted to point out that the proof given in my thesis is in fact different than that of Roger C. Alperin. As I understand it, the reference therefore is not a duplicate. To my best knowledge, it is also not secondary, since I did not find my proof in a comparable form anywhere else by now.
Tponweiser (talk) 09:11, 11 July 2014 (UTC)
replies: text: The point being made by Wcherowi is that sources for Wikipedia articles should, in general, be secondary sources - primary sources must be used with care - see WP:PRIMARY. Also, the referencce to COI is short-hand to say that you have a conflict of interest when citing your own work, and this is also discouraged - see WP:CITESELF. Gandalf61 (talk) 14:52, 11 July 2014 (UTC)
replies: text: @ I apologize for the terseness of my edit summary, I was in a bit of a hurry at the time.  has nicely explained two of the points I made. My statement of "Duplicate reference" was not meant to cast any aspersions upon your work, I only meant to say that the statement already had a reference and you had just added a second reference to the same statement, that, because of other concerns was not adding to the article. Had someone else published a statement saying that your proof had certain good qualities, then a second citation to that would have been an addition to the article that I would have supported. Bill Cherowitzo  (talk) 23:42, 11 July 2014 (UTC)

text: Dear  and , thank you for taking the time to clarifying this to me! Obviously I should have read the guidlines more carefully before editing - sorry for that! Nevertheless, I would like to share some of my work and to contribute to this article. For example I could provide some nice graphics and animations related to the action of the modular group on the upper half-plane. Could you give a Wikipedia newbie some advice on the preferred way to proceed? Should I create addition/change proposals on a sandbox page or edit the article directly? Are there restrictive guidlines for self-created animations and graphics too? Thank you for your help! Thomas (talk) 10:36, 13 July 2014 (UTC)
replies: text: I think that you will find that the "guidelines" for images are quite a bit looser than they are for the written word. My impression has been that there is not quite as much concern about WP:OR, but more concern about copyright violation when it comes to images. Of course, if you have created an image yourself, you own the copyright and when you upload it you are asked to give permissions by signing a license (the initial one essentially gives away the farm ... anyone can copy and use your image, but there are other choices which are a bit more selective about which rights you are giving up.) An image is more likely to be criticized on aesthetic grounds (how does the graphic look with respect to the rest of the article?, is it legible?, does it make its point clearly?, and so on) than it is to be considered an editor's interpretation of some content. I played around in my sandbox with the first image I uploaded, just to get a feel for some of the parameters that need to be set and how that translates into what you see on a page. After that, I worked directly with the articles (not that I couldn't have used a bit more sandbox time, but I learn faster by trial and error and hitting the Show preview button a zillion times when I'm under some pressure to get it right.) Good luck with the graphics, I'll be looking forward to seeing them. Bill Cherowitzo  (talk) 05:09, 14 July 2014 (UTC)
thread_title:  Reference to diploma thesis 

message: In the section Number-theoretic properties there are two instances of the notation S*L(2,Z).
Nowhere in this article is that notation defined.  Nowhere in the article on SL(2,R) is it defined, either.
I have never come across this notation before. It needs to either be defined in the article — before it is used — or removed in favor of understandable notation. (And it is irrelevant that someone has defined it on this Talk page.)Daqu (talk) 15:52, 8 March 2016 (UTC)
thread_title:  S*L(2,Z) is left undefined 

message: I have made some visualizations of the action of generators of the modular group. I have added them under "Group presentation". Can someone please make the pictures appear correctly? Currently they look too out of order with the text.
I'm sorry for my inexperience. Nihargargava (talk) 14:54, 5 December 2017 (UTC)
thread_title:  Visualization of generators