On Thu, Aug 13, 2009 at 8:39 AM, Nicholas Jackson<nicholas.jack...@warwick.ac.uk> wrote: > > I'm trying to use SnapPy [1] to calculate Alexander polynomials of knot > complements. SnapPy (which interfaces nicely with Sage) will happily > give me a presentation of the fundamental group of the knot complement, > and I want to take this and calculate the free derivatives of the group's > relators by the recursive formula > > d(uv) = du + u * dv > d(u^-1) = -u^-1 * du > d(1) = 0 > > For a word w in the generators, we define the free derivative dw/dx to be > the coefficient of dx in the expression for dw - this will in general be > a polynomial in the (noncommuting) generators for the fundamental group. > > I'm having a little difficult figuring out the best way to deal with > this in Sage - I need multivariate Laurent polynomials with noncommuting > variables - and wondered if anyone has any recommendations. I've been > trying to use a FreeAlgebra or FreeAlgebraQuotient but I'm not quite > sure how to go about this. > > Any suggestions would be very welcome. > > Nicholas > > [1] http://www.math.uic.edu/~t3m/SnapPy/doc/
I'm cc'ing Nathan Dunfield since he wrote SnapPy, and I'm cc'ing the sage-combinat-devel list, since they are perhaps likely to care about functionality related to noncommutative rings. Unless they have some remarks, odds are that the structure you need isn't in Sage at all, and you'll get to implement it nearly from scratch. William --~--~---------~--~----~------------~-------~--~----~ To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to sage-support-unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-support URLs: http://www.sagemath.org -~----------~----~----~----~------~----~------~--~---
