Hello Soren,
Yeah, we have used the Kauffman's bracket decomposition for the
construction of Jones polynomial. I am not sure (may also be not the right
person to comment) on whether we could include this in the current ticket.
I guess may be we could have it in the groups/braid.py as we have an
implementation of Alexander polynomial which is also implemented in the
ticket #17030.
Thanks,
Amit.
On Thu, Aug 6, 2015 at 9:20 PM, <fuglede.sagem...@gmail.com> wrote:
> 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> 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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