#19532: asymptotic expansion generators related to singularity analysis
-------------------------------------+-------------------------------------
Reporter: dkrenn | Owner:
Type: enhancement | Status: needs_info
Priority: major | Milestone: sage-7.1
Component: asymptotic | Resolution:
expansions | Merged in:
Keywords: | Reviewers: Clemens Heuberger
Authors: Daniel Krenn | Work issues:
Report Upstream: N/A | Commit:
Branch: u/cheuberg/asy | f38cdfc7f03ff9c88d299080debd4700b9805538
/singularity-analysis-generator | Stopgaps:
Dependencies: #19437, #19510, |
#19576 |
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Comment (by cheuberg):
Replying to [comment:19 dkrenn]:
> Replying to [comment:18 cheuberg]:
> > What would `O(0)` mean?
>
> `f(n)` is in `O(0)` if there is an `N` such that `f(n)=0` for `n >= N`.
Thus the coefficients of polynomials (seen as power series) would be in
`O(0)`.
so `O(0)` would be smaller than any other element in the poset and be
absorbed by any other error term? Would it live in some kind of `n^ZZbar`
with `ZZbar = {- infinity} \cup ZZ`?
>
> > How would that affect #19944?
>
> E.g. inserting the generating function `(1-z)^alpha` for non-negative
integers `alpha` would result in a `O(0)`, but this behavior comes from
this ticket here. I am not sure if #19944 would need adaptions.
ok, may be.
The question is whether it is worth the effort. After working on #19944 I
doubt that this generator here will frequently be called outside of
#19944. After all, calling #19944 with a polynomial as an argument is
erroneous anyway, because polynomials do not have singularities. Thus we
should never have to return `O(0)` so we might as well go for a warning
box here and be done with the problem.
--
Ticket URL: <http://trac.sagemath.org/ticket/19532#comment:20>
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