Hello Sage developers! Some time ago I made an animation of the Hopf fibration using Sage. Recently, a graduate of the African Institute for Mathematical Sciences has finished animating a different map from S^3 to S^2. Ihechukwu Chinyere worked with Bruce Bartlett there and made an animation visualizing what he calls the modular fibration. This is a map related to the j-invariant of elliptic curves and to the SO(2) action on SL_2(R) / SL_2(Z). The generic fibers are trefoils, and there are two singular fibers which are unknotted circles.
I'll leave the rest of the explanation to people who understand it better than me -- here are links to Ihechukwu's essay and a relevant question / answer on Mathoverflow: https://sites.google.com/a/aims.ac.za/ihechukwu/links http://mathoverflow.net/questions/93942/why-s3-k-and-sl2-r-sl2-z-are-diffeomorphic-here-k-is-a-trefoil-in-s3 And here's a link to the video: http://www.youtube.com/watch?v=eqeqbjec97w Lastly, there's a heartwarming example of the benefits of open development here: I made all of the Sage code for my animation public, and I deliberately tried to use open-source software for the entire project so that someone else could easily use the code I wrote. I had never met Ihechukwu or Bruce when they started working on this, nor did I know anything about this modular fibration. But I'm thrilled with their work! I certainly couldn't predict this, and this outcome makes me even happier that I decided to make the source public :) enjoy, Niles -- You received this message because you are subscribed to the Google Groups "sage-devel" group. To post to this group, send email to sage-devel@googlegroups.com. To unsubscribe from this group, send email to sage-devel+unsubscr...@googlegroups.com. Visit this group at http://groups.google.com/group/sage-devel?hl=en.
