Note: I copied these remarks to the trac ticket
<http://trac.sagemath.org/ticket/17030#comment:124>.
Den torsdag den 6. august 2015 kl. 17.01.55 UTC+2 skrev
fuglede....@gmail.com:
>
> 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> 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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