#19510: asymptotic expansion generator for binomial(kn, n)
-------------------------------------+-------------------------------------
Reporter: dkrenn | Owner:
Type: enhancement | Status: needs_work
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 | 5d9152ce307eafd280374cce90ff05c7fa2937c2
/generators-binomial | Stopgaps:
Dependencies: #19306, #19521, |
#19528 |
-------------------------------------+-------------------------------------
Changes (by cheuberg):
* status: needs_review => needs_work
* reviewer: => Clemens Heuberger
Comment:
Reviewed the code (without its dependency #19521) and the documentation,
but did not yet verify the final output of the doctests. I had to modify
the "constant factor" in order to get rational coefficients when `k-1` is
not a square.
I am not happy with the growth group of the output:
- `(e^(n*log(n)))^(Symbolic Constants Subring)` will never occur.
- `log(n)^(Symbolic Constants Subring)` will never occur.
- `(e^n)^(Symbolic Constants Subring)` is hard to read; actually, the only
exponential factor that will ever occur is `(k^k/(k-1)^(k-1))^n`, so
`FractionField(k.parent())^n` would be enough (so `QQ^n` in all examples).
However, it is not clear to me how to implement this without pain.
--
Ticket URL: <http://trac.sagemath.org/ticket/19510#comment:11>
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