#19969: asymptotic expansion generator: singularity analysis (log-type)
-------------------------------------+-------------------------------------
Reporter: behackl | Owner:
Type: enhancement | Status: needs_review
Priority: major | Milestone: sage-7.1
Component: asymptotic | Resolution:
expansions | Merged in:
Keywords: | Reviewers: Clemens Heuberger,
Authors: Benjamin Hackl | Daniel Krenn
Report Upstream: N/A | Work issues:
Branch: u/dkrenn/asy/SA- | Commit:
generator-log | 456d8c383b55ab6ebbbd473370278180177326be
Dependencies: #19532, #19993, | Stopgaps:
#20043 |
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Comment (by cheuberg):
Replying to [comment:13 dkrenn]:
> I'm in the middle of the review.
>
> I didn't investigate further, but the (correct) result of
> {{{
> sage: asymptotic_expansions.SingularityAnalysis('n',
> ....: alpha=0, beta=2, precision=23).subs(n=n-2)
> }}}
> does not seem to depend on the precision anymore for values at least 13.
What is `n`? Could it be that it is the generator of an asymptotic ring
with lower default precision?
I cannot reproduce the problem:
{{{
result = {}
for p in range(1, 20):
a = asymptotic_expansions.SingularityAnalysis('n', alpha=0, beta=2,
precision=p)
n = a.parent().gen()
result[p] = a.subs(n=n-2)
error = result[p] - result[p].exact_part()
if p >= 2:
print p, error, result[p] - result[p-1]
}}}
yields
{{{
2 O(n^(-1)) O(n^(-1)*log(n))
3 O(n^(-2)*log(n)^2) O(n^(-1))
4 O(n^(-2)*log(n)) O(n^(-2)*log(n)^2)
5 O(n^(-2)) O(n^(-2)*log(n))
6 O(n^(-3)*log(n)^2) O(n^(-2))
7 O(n^(-3)*log(n)) O(n^(-3)*log(n)^2)
8 O(n^(-3)) O(n^(-3)*log(n))
9 O(n^(-4)*log(n)^2) O(n^(-3))
10 O(n^(-4)*log(n)) O(n^(-4)*log(n)^2)
11 O(n^(-4)) O(n^(-4)*log(n))
12 O(n^(-5)*log(n)^2) O(n^(-4))
13 O(n^(-5)*log(n)) O(n^(-5)*log(n)^2)
14 O(n^(-5)) O(n^(-5)*log(n))
15 O(n^(-6)*log(n)^2) O(n^(-5))
16 O(n^(-6)*log(n)) O(n^(-6)*log(n)^2)
17 O(n^(-6)) O(n^(-6)*log(n))
18 O(n^(-7)*log(n)^2) O(n^(-6))
19 O(n^(-7)*log(n)) O(n^(-7)*log(n)^2)
}}}
so the result gets better in every iteration. Due to cancellations, some
of the coefficients are not present ...
--
Ticket URL: <http://trac.sagemath.org/ticket/19969#comment:16>
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