#13798: q-Bernoulli numbers of Carlitz
---------------------------------+------------------------------------------
Reporter: chapoton | Owner: sage-combinat
Type: enhancement | Status: needs_work
Priority: minor | Milestone: sage-5.6
Component: combinatorics | Resolution:
Keywords: bernoulli | Work issues:
Report Upstream: N/A | Reviewers: Francis Clarke
Authors: | Merged in:
Dependencies: | Stopgaps:
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Changes (by fwclarke):
* status: needs_review => needs_work
* reviewer: => Francis Clarke
Comment:
I believe the code implements Carlitz's definition accurately. It's
difficult to see how it could easily be speeded up.
Just a few improvements are needed, I think.
* As in the code for classical Bernoulli numbers, the definition ought to
start with the lines
{{{
from sage.rings.all import Integer
m = Integer(m)
}}}
This allows the argument to be an `int`, which is compatible with
`gaussian_binomial`, letting users write things like
{{{
[q_bernoulli(i) for i in range(13)]
}}}
and gives a less confusing error message for
{{{
q_bernoulli(1/2)
}}}
* To make `q_bernoulli` even more compatible with `gaussian_binomial` it
would be worth having a second argument, defaulting to a the polynomial
generator `q`. [Actually `q_binomial(4, 2, 1)` raises a
`ZeroDivisionError` at present. I'll raise a ticket for this.]
* It would be worth citing Carlitz's 1948 paper in the docstring.
* I would write "q-analogue of the Bernoulli numbers" (one analogue, many
numbers).
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/13798#comment:3>
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