Hi Pat! On 27 Jun., 05:54, Pat LeSmithe <qed...@gmail.com> wrote: ... > Unfortunately, the source code is not available. However, the author > mentioned that the program is written in Delphi. Perhaps the literature > contains a computational recipe we can adapt for Sage.
The existence proof for Seifert surfaces is constructive: Given a knot diagram (i.e., a generic orthogonal projection with over/ undercrossings marked), it is straight forward to construct a Seifert surface. Much more complicated would it be to construct a Seifert surface of *minimal* genus. It is possible, though, based on the theory of normal surfaces that goes back to Wolfgang Haken. In a nutshell (hope I remember things correctly): - Given a knot diagram, construct a triangulation of the knot complement. - The triangulation gives rise to a system of linear equations with integer coefficients, whose non-negative integral solutions with some extra-condition are in one-one correspondence to Normal Surfaces (i.e., surfaces in the knot complement that are 'nice' with respect to the triangulation). - The cone of non-negative integral solutions is finitely generated, and it is possible to construct a generating set. As much as I remember, the size of the generating set is bounded from above by 2 to the power of (10 times number of tetrahedra). There is a series of examples of triangulations for which there is now sub-exponential lower bound for the coefficients occuring in the generating set. Ugly, but that's life. - Based on these generators, one can read off minimal Seifert surfaces. Note that a while ago I had started a "topology" Wiki: http://wiki.sagemath.org/topology Perhaps it could be revived? In the Wiki, I mention a package t3m, that, as much as I know, could do the above computation. I don't know about visualisation, though. Best regards, Simon --~--~---------~--~----~------------~-------~--~----~ 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 For more options, visit this group at http://groups.google.com/group/sage-devel URLs: http://www.sagemath.org -~----------~----~----~----~------~----~------~--~---
