In fact, when matching the return values of Link.jones_polynomial() with
the one I posted, I ran into some problems for sufficiently trivial links:
sage: B = BraidGroup(2)
sage: b = B([])
sage: L = Link(b)
sage: L.jones_polynomial()
...
IndexError: list index out of range
Likewise, it does not appear to give the expected results when it does give
results:
sage: B = BraidGroup(8)
sage: b = B([1])
sage: L = Link(b)
sage: L.jones_polynomial()
1
sage: b.jones_polynomial()
A^12 + 6*A^8 + 15*A^4 + 15/A^4 + 6/A^8 + 1/A^12 + 20
This was obtained using the version of link.py in 04facf8.
- Søren
Den torsdag den 6. august 2015 kl. 15.58.42 UTC+2 skrev Amit Jamadagni:
>
> 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....@gmail.com <javascript:>>
> 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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>>>
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