#19011: Add Jones representation of braid groups and Jones polynomials of braid
closures
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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 | 8202cf5754bcecd608e1dfb2c189eb7846febb6c
Branch: | Stopgaps:
u/fuglede/jones_rep |
Dependencies: |
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Comment (by mmarco):
Some timings for conversion between univariate laurent polynomial rings:
{{{
sage: R.<t> = LaurentPolynomialRing(ZZ)
sage: f = (t^-2+t^2) ^2 + 5*t -1
sage: f
t^-4 + 1 + 5*t + t^4
sage: S.<a> = LaurentPolynomialRing(IntegerModRing(7))
sage: d = f.dict()
sage: d
{-4: 1, 0: 1, 1: 5, 4: 1}
sage: %time f.subs(t=a)
CPU times: user 9 ms, sys: 1 ms, total: 10 ms
Wall time: 9.29 ms
a^-4 + 1 + 5*a + a^4
sage: %time S(f)
CPU times: user 1 ms, sys: 0 ns, total: 1 ms
Wall time: 1.31 ms
a^-4 + 1 + 5*a + a^4
sage: %time S(d)
CPU times: user 1 ms, sys: 0 ns, total: 1 ms
Wall time: 1.02 ms
a^-4 + 1 + 5*a + a^4
sage: %time S(d)
CPU times: user 1 ms, sys: 0 ns, total: 1 ms
Wall time: 293 µs
a^-4 + 1 + 5*a + a^4
sage: d1 = (f+1).dict()
sage: %time S(d1)
CPU times: user 0 ns, sys: 0 ns, total: 0 ns
Wall time: 211 µs
a^-4 + 2 + 5*a + a^4
sage: f1 = f+1
sage: %time S(f1)
CPU times: user 0 ns, sys: 0 ns, total: 0 ns
Wall time: 147 µs
a^-4 + 2 + 5*a + a^4
}}}
Definitely .subs is not a good idea. Direct conversion or construction
from the underlying dictionary are much faster.
Of course, this might deppend a lot on the rings involved, and the
dictionart approach might not work if we talk about fraction fields or
multivariate polynomial rings.
--
Ticket URL: <http://trac.sagemath.org/ticket/19011#comment:20>
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