#17030: Knot Theory as a part of GSoC 2014.
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Reporter: amitjamadagni | Owner: amitjamadagni
Type: task | Status: needs_work
Priority: major | Milestone: sage-6.4
Component: algebraic | Resolution:
topology | Merged in:
Keywords: | Reviewers: Miguel Marco
Authors: Amit Jamadagni, | Work issues:
Miguel Marco | Commit:
Report Upstream: N/A | 29be8b00dd778425bd16cb3064dba381b8015672
Branch: | Stopgaps:
u/mmarco/ticket/17030 |
Dependencies: |
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Comment (by mmarco):
I have also checked the jones polynomial (in this case in 1064 cases).
Almost all match, with the following exceptions:
{{{
<knot:L11n307>
-q^10 + 3*q^9 - 6*q^8 + 8*q^7 - 9*q^6 + 11*q^5 - 8*q^4 + 8*q^3 - 4*q^2 +
2*q
-q^10 + 3*q^9 - 6*q^8 + 8*q^7 - 9*q^6 + 11*q^5 - 8*q^4 + 8*q^3 - 4*q^2 + 2
<knot:K11n162>
-q^10 + 3*q^9 - 5*q^8 + 7*q^7 - 9*q^6 + 9*q^5 - 8*q^4 + 7*q^3 - 4*q^2 +
2*q
-q^10 + 3*q^9 - 5*q^8 + 7*q^7 - 9*q^6 + 9*q^5 - 8*q^4 + 7*q^3 - 4*q^2 + 2
<knot:L11n271>
-q^10 + 2*q^9 - 5*q^8 + 7*q^7 - 9*q^6 + 11*q^5 - 8*q^4 + 9*q^3 - 5*q^2 +
3*q
-q^10 + 2*q^9 - 5*q^8 + 7*q^7 - 9*q^6 + 11*q^5 - 8*q^4 + 9*q^3 - 5*q^2 + 3
<knot:L10n112>
q^9 - q^8 + 6*q^7 - 5*q^6 + 11*q^5 - 5*q^4 + 10*q^3 - 5*q^2 + 4*q
q^9 - q^8 + 6*q^7 - 5*q^6 + 11*q^5 - 5*q^4 + 10*q^3 - 5*q^2 + 4
<knot:K11n63>
-q^10 + 2*q^9 - 3*q^8 + 5*q^7 - 6*q^6 + 6*q^5 - 6*q^4 + 5*q^3 - 3*q^2 +
2*q
-q^10 + 2*q^9 - 3*q^8 + 5*q^7 - 6*q^6 + 6*q^5 - 6*q^4 + 5*q^3 - 3*q^2 + 2
<knot:10_165>
q^9 - 3*q^8 + 4*q^7 - 6*q^6 + 7*q^5 - 6*q^4 + 6*q^3 - 4*q^2 + 2*q
q^9 - 3*q^8 + 4*q^7 - 6*q^6 + 7*q^5 - 6*q^4 + 6*q^3 - 4*q^2 + 2
<knot:L11n316>
q^9 - 3*q^8 + 5*q^7 - 6*q^6 + 8*q^5 - 7*q^4 + 7*q^3 - 4*q^2 + 3*q
q^9 - 3*q^8 + 5*q^7 - 6*q^6 + 8*q^5 - 7*q^4 + 7*q^3 - 4*q^2 + 3
<knot:L9n20>
-q^8 + 2*q^7 - 4*q^6 + 5*q^5 - 4*q^4 + 6*q^3 - 3*q^2 + 3*q
-q^8 + 2*q^7 - 4*q^6 + 5*q^5 - 4*q^4 + 6*q^3 - 3*q^2 + 3
}}}
In each case, the first polynomial is the one given by our implementation,
and the second the one given by the knot atlas.
Can someone confirm if the knot atlas results are correct?
--
Ticket URL: <http://trac.sagemath.org/ticket/17030#comment:29>
Sage <http://www.sagemath.org>
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