Here’s an implementation of SO3 Lie Group and Lie Algebra as a manifold using Sage Math 6.6 and Sagemanifolds 0.7.
<a href=”https://github.com/ernestyalumni/diffgeo-by-sagemnfd/blob/master/SO3.sage”>SO3.sage on GitHub</a>
Michał Bejger and Eric Gourgoulhon’s Sagemanifolds 0.7 package is a delight to use and is excellent in that it is architected EXACTLY how differentiable manifolds behave.
I follow Darryl D. Holm, Tanya Schmah, Cristina Stoica. Geometric mechanics and symmetry: From finite to infinite dimensions 2009 as a reference and liberally implement from there.
I’m going to put this same file and updates on here, ernestyalumni.wordpress.com, and on my Patreon ernestyalumni (please go donate if you can to help support me!) because I want to be able to simply download the file as is and someone doesn’t need to install github app or go through a command line prompt.
Just go to my Patreon page, go to my “Creations” subpage, and click on the icon and it downloads. This is how I’d like github to function sometimes: point, click, download, computer code/script is there.
<a href=”https://www.patreon.com/ernestyalumni?ty=c”>Patreon ernestyalumni profile page</a>
<a href=”https://www.patreon.com/creation?hid=2213880&u=645287&alert=3″>If you click correctly on my Patreon ernestyalumni profile page and click on the Creations subpage, you get here</a>
<a href=”https://www.patreon.com/creation?hid=2213880″>You click on this link and you download SO3.sage immediately: this is how I wish github could word sometimes for code snippets</a>