Hi Amit
Thanks for the reference; good to know that stuff is happening in that
regard.
And yes, everything here is related to the braid group. Even though this
would create some overlap, perhaps it could be of use to have both
algorithms: using braid group representations, for a fixed number of
strands, the evaluation of the Jones polynomial of the trace closures
becomes polynomial in the number of crossings (as only matrix
multiplication is involved). From a quick look at ticket #17030, that's not
the case for the existing implementation which appears to implement
Kauffman's O(2^{O(#crossings)}) algorithm (please correct me if I'm wrong).
- Søren
Den torsdag den 6. august 2015 kl. 14.28.39 UTC+2 skrev Amit Jamadagni:
>
> Hello Soren,
> Thanks for sharing the work. But we do have been working on Knot
> Theory and here is the ticket
> Ticket : http://trac.sagemath.org/ticket/17030
> <http://www.google.com/url?q=http%3A%2F%2Ftrac.sagemath.org%2Fticket%2F17030&sa=D&sntz=1&usg=AFQjCNHtremMXOZeAA7pqdSLRqPr2yNIIg>,
>
> which is currently under review. It would be helpful if you compare the
> missing features as the work on calculations of Jones polynomial has been
> included. Also from the source, as far as I understand the representations
> are mainly Braid Group, but we do have supported other representations such
> as oriented gauss code and also planar diagram. I guess you could directly
> contribute to the ticket, if something is missing.
>
> Thanks,
> Amit.
>
> On Thu, Aug 6, 2015 at 7:30 PM, <fuglede....@gmail.com <javascript:>>
> wrote:
>
>> Hey sage-devel
>>
>> In work with Egsgaard, I ended up needing an implementation of the Jones
>> representations of braid groups and figured it made sense to do it in sage.
>> While interesting in their own right, they also allow for direct
>> calculation of the Jones polynomials of the trace closures of the braids,
>> and I figured that since sage is currently rather low on quantum topology
>> (and knot theory in general), that adding this to the base could be useful
>> in general.
>>
>> The development guide suggests suggesting changes here before on trac, so
>> here you go. The source code is currently available here:
>>
>> https://github.com/fuglede/jones-representation/blob/master/curverep.sage
>>
>> - Søren
>>
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