#17030: Knot Theory as a part of GSoC 2014.
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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: | cb84cec88f012844ac65d102296644a77f89818c
public/ticket/17030 | Stopgaps:
Dependencies: |
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Comment (by mmarco):
> Please go ahead with a full review. I think a new `Knot` class would be
good. For future work, it would also be nice to have a catalog of links
and knots (e.g., `knots.Trefoil()`) and also ways of producing new links
from old. Could you add a `.. todo` list?
>
I am working on a package that would provide a knot/link database taken
from the knot atlas (http://katlas.org).
Once done that, i would also like to have an "identify" method that, given
a knot/link, computes its invariants and compares them with the ones in
the database, giving then a list of possibilities from the database for
the given knot/link.
> I agree that more documentation would be great, with definitions,
references, and (for `plot` at least) algorithms.
>
Agree on all. I defintely need to document better the plot method. That
was one of the reasons for my proposal of splitting: right now the plot
code is specially hard to review.
> How is equality determined? How should it be? Should the oriented Gauss
code be good enough?
> {{{
> sage: trefoil = Link([[1, 5, 2, 4], [5, 3, 6, 2], [3, 1, 4, 6]])
> sage: trefoil == Link([[1, 5, 2, 4], [5, 3, 6, 2], [3, 1, 4, 6]])
> False
> }}}
>
We can't realistically determine equality. Even determining if a given
diagram corresponds to the unknot is a really hard problem. Oriented Gauss
code is not even a knot invariant.
Now that you mention it, i think that equality checking should raise "not
implemented error".
Thanks for the suggestions. I will work on them.
--
Ticket URL: <http://trac.sagemath.org/ticket/17030#comment:119>
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