#14496: unify the three implementations of gaussian q-binomial coefficients
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Reporter: chapoton | Owner: tbd
Type: task | Status: needs_info
Priority: major | Milestone: sage-5.10
Component: combinatorics | Resolution:
Keywords: gaussian binomial | Work issues:
Report Upstream: N/A | Reviewers:
Authors: Frédéric Chapoton | Merged in:
Dependencies: | Stopgaps:
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Comment (by fwclarke):
Replying to [comment:10 chapoton]:
> According to my own timings, it seems that for n <= ~ 78 the naive
algorithm is faster than the cyclotomic algorithm for computing the
gaussian polynomial.
I get much the same. For `gaussian_binomial(2*k, k)` I found the naive
method faster for `k < 30`, and the cyclotomic method faster for `k > 30'.
One point about the naive method:
{{{
sage: %timeit gaussian_binomial(50, 4)
1000 loops, best of 3: 287 µs per loop
sage: %timeit gaussian_binomial(50, 46)
100 loops, best of 3: 3.41 ms per loop
}}}
Since the code contains two loops of length `k`, it's obviously better to
evaluate `gaussian_binomial(n, k)` as `gaussian_binomial(n, n-k)` if `k >
n/2`.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/14496#comment:11>
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