#19969: asymptotic expansion generator: singularity analysis (log-type)
-------------------------------------+-------------------------------------
Reporter: behackl | Owner:
Type: enhancement | Status: needs_work
Priority: major | Milestone: sage-7.1
Component: asymptotic | Resolution:
expansions | Merged in:
Keywords: | Reviewers: Clemens Heuberger
Authors: Benjamin Hackl | Work issues:
Report Upstream: N/A | Commit:
Branch: u/behackl/asy/SA- | c83baa89cb1f86815d85fd4cf9aa579ecc117d2a
generator-log | Stopgaps:
Dependencies: #19532 |
-------------------------------------+-------------------------------------
Changes (by {'newvalue': u'Benjamin Hackl', 'oldvalue': ''}):
* status: needs_review => needs_work
* reviewer: => Clemens Heuberger
* author: => Benjamin Hackl
Comment:
I had a first look at this implementation.
1. I am not sure that three different implementations (beta=0, beta in ZZ
and beta>0, otherwise) are needed: the only difference is the range over
with `k`, `l`, `r` iterate and possibly the growth groups. But the basic
coefficients stay the same. Perhaps we should even abolish the function
`_sa_coefficients_e_` because collecting for a single `Gamma(alpha)` is
not really worthwhile. That would mean removing the parameter
`skip_constant_factor` which seems to be less important here.
2. the error term in the case of beta not in NN is not good, it should
depend on beta (I very much prefer the strategy for beta in ZZ).
3. summation index `k` should be replaced by `r` in case beta not in ZZ in
order to have consistent naming of summation indices.
4. Could you please post values for `compare_with_values` for `alpha=2`
and `beta=1/2`? With `precision=10`, I get
{{{
[(5, -140.014037108338),
(10, -432.585380667007),
(20, -1894.51971835043),
(40, -5905.52939497361),
(80, -13574.5908343596)]
}}}
which I do not find convincing. Of course, convergence will be bad due
to slow growth of logarithms, so larger values might be of interest, but I
do currently lack computer power to test it myself. But that might be a
consequence of 2.
--
Ticket URL: <http://trac.sagemath.org/ticket/19969#comment:4>
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