#14496: unify the three implementations of gaussian q-binomial coefficients
-------------------------------------+--------------------------------------
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:
-------------------------------------+--------------------------------------
Changes (by chapoton):
* status: needs_work => needs_info
Comment:
Here is a new patch.
Point 1 is indeed a problem. I do not understand either what is computed
in the weight function. The procedure q_bin was returning 1 for any
negative values of n and any k. This is not a very natural behaviour.
Point 4 : I have chosen that the name to be kept would be q_binomial.
There is another problem remaining. The existing algorithm in
sage.combinat.q_analogues uses cyclotomic polynomials and become faster
than the naive one when the arguments are big (and of similar size ?), but
is much slower in some cases (when n is small or k is small ?).
{{{
sage: timeit("sage.combinat.q_analogues.q_binomial(85,3)")
625 loops, best of 3: 246 µs per loop
sage: timeit("sage.combinat.q_analogues.q_binomial_via_cyclotomic(85,3)")
125 loops, best of 3: 2.78 ms per loop
sage: timeit("sage.combinat.q_analogues.q_binomial(85,43)")
25 loops, best of 3: 9.21 ms per loop
sage: timeit("sage.combinat.q_analogues.q_binomial_via_cyclotomic(85,43)")
25 loops, best of 3: 8.18 ms per loop
}}}
So one needs to keep both and find a strategy of choice..
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/14496#comment:7>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica,
and MATLAB
--
You received this message because you are subscribed to the Google Groups
"sage-trac" group.
To unsubscribe from this group and stop receiving emails from it, send an email
to [email protected].
To post to this group, send email to [email protected].
Visit this group at http://groups.google.com/group/sage-trac?hl=en.
For more options, visit https://groups.google.com/groups/opt_out.
