#17030: Knot Theory as a part of GSoC 2014.
-------------------------------------+-------------------------------------
Reporter: amitjamadagni | Owner: amitjamadagni
Type: enhancement | Status: needs_work
Priority: major | Milestone: sage-6.9
Component: algebraic | Resolution:
topology | Merged in:
Keywords: | Reviewers: Miguel Marco, Karl-
Authors: Amit Jamadagni, | Dieter Crisman, Frédéric Chapoton
Miguel Marco | Work issues:
Report Upstream: N/A | Commit:
Branch: | 06aad784cdd03604d77f9f9c7e6c9332a4982fc6
public/ticket/17030 | Stopgaps:
Dependencies: |
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Comment (by mmarco):
I will look at it more carefully tomorrow.
In the meantime, the failing doctest is indeed a typo. The knot should be
defined as
{{{
sage: L = Link([[1, 2, 3, 3], [2, 4, 5, 5], [7, 4, 1, 7]])
}}}
> I made a lot of minor to micro optimizations and code cleanup. I created
a `Knot` class as Miguel suggested (and was what I had in mind initially).
I created an equality check by looking at the braids (is that a link
invariant?) and put a warning message about false negatives (but if it is
a link invariant, then we should be able to remove the warning message).
The braid is not a link invariant. Actually we should be careful about
what equality means. If it means equality of diagrams (that is, the planar
diagrams are actually the same, although maybe the elements are enumerated
in a different order), we could write some method to check if there exists
a different choice of labels that makes the presentations identical. If by
equality we mean isotopy invariants, then we are definitely out of luck,
since as far as a i know there is no effective method for that.
>
> There shouldn't be any more large refactoring of the code after this
point I think.
>
> I think for the catalog, we should open up a followup ticket rather than
put an explicit todo in the file. However a big +1 on doing this.
--
Ticket URL: <http://trac.sagemath.org/ticket/17030#comment:123>
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