I have been going through the implementation Knot Atlas, as per my understanding they have stored the knots in a table and have inputted it to get various results, I would like to know whether we will be using tables to input or any other way to input. I have seen through Vogel's algorithm which takes in the oriented gauss code and ends up giving out the braid word [1] from which we can construct the knot(as it is closed braid) and from the braid word we can calculate the Alexander polynomial from the Burau's representation(which is currently implemented in braid in Sage) (I have heard is not true for strings greater than 5). I have been reading through [2] which mentions how to calculate Seifert matrix from a braid representation which can be again used to represent knots. I have been searching for algorithms which would relate the Seifert matrix and various invariants. It would be really helpful if I could get more reference to the algorithms that could be implemented. I have just started the implementation details mentioned in [3].
[1] http://magma.maths.usyd.edu.au/~danr/site/talks/20070531.pdf [2] http://www.maths.ed.ac.uk/~jcollins/SeifertMatrix/SeifertMatrix.pdf [3] http://www.layer8.co.uk/maths/braids/braid-user-documentation.html On Tue, Feb 25, 2014 at 7:16 PM, kcrisman <kcris...@gmail.com> wrote: > >> >> [2] http://legacy.earlham.edu/~peters/knotlink.htm#software >> >> > *"June 2, 2004*. Unfortunately I no longer have time to update *Knots on > the Web*. I know it conntains many dead links and omits many good, new > sites. " > > And my understanding is that the Knot Atlas > http://katlas.math.toronto.edu/wiki/Main_Page and the Mathematica package > creating it is the state of the art. Does SnapPy now really have all that > combinatorial stuff? I think that at the very least a good wrapper > allowing for use of *any* robust backend for knots would be a great > contribution to Sage. mmarco seems to have a good sense of what would > actually be needed to do this. It's definitely a significant hole in Sage. > - one might even wonder whether the authors of the Mma package would be > willing to license their package in such a way that the algorithms for > computing various invariants etc. could be used/{P,C}ythonized in Sage, if > some people know them http://katlas.math.toronto.edu/wiki/Acknowledgement > > -- > 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. > -- 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.
