I would be happy to mentor a student in a knot theory related project in sage. I had mainly two ideas:
First idea is to write a class for knots/links. This class should be able to translate between the different possible representations of links (Gauss codes, 3d curves, braid closure...) and compute some of their invariants (the usual polynomials, Seifert forms, fundamental groups...). It should also produce pictures of knot diagrams and 3d representations of the knot/link. Some (or most) of this features can be either written from scratch, or just wrap external code (like the mentioned SnapPy). Another idea, closely related to the previous one, is to write a javascript editor for knots and links, following what knotplot [1] does. This can be part of the same project or a separated one, if someone else writes the backend (although i think that it should be possible to write the editor and a simple backend in a single gsoc project, but that can be discussed). An important part of this editor would be the algorithm for dynamically relaxing the link. In particular, such an algorithm is explained in chapter 7 of Scharein's thesis [1]. [1] http://www.knotplot.com/thesis/thesis.html -- You received this message because you are subscribed to the Google Groups "sage-devel" group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-devel+unsubscr...@googlegroups.com. To post to this group, send email to sage-devel@googlegroups.com. Visit this group at http://groups.google.com/group/sage-devel. For more options, visit https://groups.google.com/groups/opt_out.
