#19011: Add Jones representation of braid groups and Jones polynomials of braid
closures
-------------------------------------+-------------------------------------
Reporter: fuglede | Owner:
Type: enhancement | Status: new
Priority: major | Milestone: sage-6.9
Component: algebraic | Resolution:
topology | Merged in:
Keywords: | Reviewers:
Authors: Søren Fuglede | Work issues:
Jørgensen | Commit:
Report Upstream: N/A | 6e0f181b46688c9b8ecb04a0a94583ad7c49d912
Branch: | Stopgaps:
u/fuglede/jones_rep |
Dependencies: |
-------------------------------------+-------------------------------------
Description changed by fuglede:
Old description:
> First off, this is my first ticket here, so please let me know about
> process related stuff that I missed.
>
> As per [https://groups.google.com/forum/#!topic/sage-devel/ByJURRvRgLg
> this discussion on sage-devel], these commits contain methods for Braid
> and BraidGroup_class to allow for the calculation of the Temperley--Lieb
> --Jones representations of braid groups. While interesting in their own
> right, this also allows for a straightforward implementation of the
> (uncoloured) Jones polynomial of trace closures of braids, also included,
> which for a fixed number of braid strands is polynomial in the number of
> crossings. The algorithm uses Kauffman's diagrammatic description of the
> Temperley--Lieb algebra.
>
> It should be noted that there is some overlap here with
> [http://trac.sagemath.org/ticket/17030 Ticket #17030] but as discussed on
> sage-devel, this is not necessarily a problem (although of course any
> code that is duplicated exactly should be coordinated between that ticket
> and this one).
>
> One sillily todo is to add my own name (Søren Fuglede Jørgensen) to the
> list of authors. No matter how I've tried to do this, the building
> failes; probably due to encoding issues, I would imagine (but simply
> translating the string to unicode does not solve the issue).
>
> The branch also contains a small bit of code clean-up cf.
> [https://github.com/sagemath/sage/pull/47 GH PR #47].
New description:
First off, this is my first ticket here, so please let me know about
process related stuff that I missed.
As per [https://groups.google.com/forum/#!topic/sage-devel/ByJURRvRgLg
this discussion on sage-devel], these commits contain methods for Braid
and BraidGroup_class to allow for the calculation of the Temperley--Lieb--
Jones representations of braid groups. While interesting in their own
right, this also allows for a straightforward implementation of the
(uncoloured) Jones polynomial of trace closures of braids, also included,
which for a fixed number of braid strands is polynomial in the number of
crossings. The algorithm uses Kauffman's diagrammatic description of the
Temperley--Lieb algebra.
It should be noted that there is some overlap here with #17030 but as
discussed on sage-devel, this is not necessarily a problem (although of
course any code that is duplicated exactly should be coordinated between
that ticket and this one).
One sillily todo is to add my own name (Søren Fuglede Jørgensen) to the
list of authors. No matter how I've tried to do this, the building failes;
probably due to encoding issues, I would imagine (but simply translating
the string to unicode does not solve the issue).
The branch also contains a small bit of code clean-up cf.
[https://github.com/sagemath/sage/pull/47 GH PR #47].
--
--
Ticket URL: <http://trac.sagemath.org/ticket/19011#comment:1>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica,
and MATLAB
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