#19011: Add Jones representation of braid groups and Jones polynomials of braid
closures
-------------------------------------+-------------------------------------
Reporter: fuglede | Owner:
Type: enhancement | Status: needs_review
Priority: major | Milestone: sage-6.9
Component: algebraic | Resolution:
topology | Merged in:
Keywords: | Reviewers: Travis Scrimshaw
Authors: Søren Fuglede | Work issues:
Jørgensen | Commit:
Report Upstream: N/A | 3f2973241fd68c2885fd2ecd107efd9e5d081da0
Branch: | Stopgaps:
u/tscrim/jones_rep-19011 |
Dependencies: |
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Comment (by fuglede):
Thanks for the detailed review!
Since most of the changes were related to internals in
{{{TL_representation}}} and {{{jones_polynomial}}}, I ran some tests on
those methods. Each test was performed three times, alternating between
the old branch and the one that includes your fixes.
'''Test 1:''' Calculation of a huge {{{TL_representation}}} (34
13260x13260 matrices):
My branch:
{{{
sage: B = BraidGroup(18)
sage: %time B.TL_representation(4)
CPU times: user 1min 23s, sys: 104 ms, total: 1min 23s
CPU times: user 1min 23s, sys: 104 ms, total: 1min 23s
CPU times: user 1min 22s, sys: 92 ms, total: 1min 22s
}}}
Your branch:
{{{
sage: B = BraidGroup(18)
sage: %time B.TL_representation(4)
CPU times: user 1min 12s, sys: 84 ms, total: 1min 12s
CPU times: user 1min 12s, sys: 80 ms, total: 1min 12s
CPU times: user 1min 13s, sys: 116 ms, total: 1min 13s
}}}
Conclusion: Considerable speed gain.
**Test 2**: Calculation of the Jones polynomials of 2961 knots obtained as
closures of braids on at most 7 strands. The test does not use
{{{skein_normalisation}}} so that in particular, any speed gain obtained
through the removal of {{{subs}}} should be visible here. The (somewhat ad
hoc) test is [https://gist.github.com/fuglede/13016f20c16dd2830756
available here].
My branch:
{{{
sage: load("jonesdata.py")
sage: test_against_dictionary()
2961 matches and 0 mismatches found in 36.658627 seconds
2961 matches and 0 mismatches found in 35.956593 seconds
2961 matches and 0 mismatches found in 36.534720 seconds
}}}
Your branch:
{{{
sage: load("jonesdata.py")
sage: test_against_dictionary()
2961 matches and 0 mismatches found in 34.822386 seconds
2961 matches and 0 mismatches found in 34.758321 seconds
2961 matches and 0 mismatches found in 36.320710 seconds
}}}
Conclusion: Speed gain appears to be less significant here.
--
Ticket URL: <http://trac.sagemath.org/ticket/19011#comment:40>
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