2022-08-30 11:38:54 +0100 | received badge | ● Popular Question (source) |

2020-07-26 16:15:12 +0100 | received badge | ● Supporter (source) |

2020-07-13 22:15:33 +0100 | received badge | ● Student (source) |

2020-07-12 01:48:31 +0100 | asked a question | Defining $S^1$ with four charts Hello, I am trying to implement the construction of the manifold $S^1$ using the four charts, as described at en.wikipedia.org/wiki/Manifold#Circle . It's not clear to me how to define the charts in terms of the projection operators within SageMath. I'm also not sure how to isolate open sets that I would like to define the charts over. The circle is parameterized using polar coordinates, and the four charts have the form: $
\begin{align $
\begin{align $
\begin{align $
\begin{align Once we have these charts, how would I define the four transition functions to complete the description? Thank you for your help! |

Copyright Sage, 2010. Some rights reserved under creative commons license. Content on this site is licensed under a Creative Commons Attribution Share Alike 3.0 license.