#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:
Authors: Søren Fuglede | Work issues:
Jørgensen | Commit:
Report Upstream: N/A | a022f346949f96c073af54b4422a31137b88fa0f
Branch: | Stopgaps:
u/fuglede/jones_rep |
Dependencies: |
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Comment (by tscrim):
This is completely baffling to me:
{{{
sage: R.<x> = QQ[]
sage: p = R.random_element(degree=5000)
sage: %timeit p.subs(x=x^2)
1 loops, best of 3: 1.18 s per loop
sage: %timeit p(x=x^2)
1 loops, best of 3: 1.22 s per loop
sage: %timeit p(x^2)
10 loops, best of 3: 38.6 ms per loop
sage: %timeit p.subs(x^2)
10 loops, best of 3: 38.3 ms per loop
sage: %timeit p(x=x^2)
1 loops, best of 3: 1.23 s per loop
}}}
So calling `subs` or direct evaluation without parameters with way faster
for regular polynomials (and deserves a separate ticket if there isn't one
already). However nothing beats direct coercion:
{{{
sage: S.<x> = LaurentPolynomialRing(QQ)
sage: q = x^-2300 * p
sage: T.<y> = LaurentPolynomialRing(QQ)
sage: %timeit T(q)
The slowest run took 5.28 times longer than the fastest. This could mean
that an intermediate result is being cached
10000 loops, best of 3: 158 µs per loop
}}}
I will make this change as part of my review (which I am starting now).
--
Ticket URL: <http://trac.sagemath.org/ticket/19011#comment:38>
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