#19510: asymptotic expansion generator for binomial(kn, n)
-------------------------------------+-------------------------------------
Reporter: dkrenn | Owner:
Type: enhancement | Status: needs_review
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/dkrenn/asy | 10cd04bde3be402ea4c3550793475135096f27fb
/generators-binomial | Stopgaps:
Dependencies: #19306, #19521, |
#19528 |
-------------------------------------+-------------------------------------
Changes (by dkrenn):
* status: needs_work => needs_review
* commit: 5d9152ce307eafd280374cce90ff05c7fa2937c2 =>
10cd04bde3be402ea4c3550793475135096f27fb
Comment:
Replying to [comment:11 cheuberg]:
> 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.
More or less complete rewrite of function.
----
Last 10 new commits:
||[http://git.sagemath.org/sage.git/commit/?id=1b62954467b74292e349a1631f9837dbe8ff9c3b
1b62954]||{{{Trac #19946: add doctests to document behavior}}}||
||[http://git.sagemath.org/sage.git/commit/?id=24c153cd49a1857b06ff2779e4442bace4a24c65
24c153c]||{{{Trac #19946: reviewer commit: ReSt error}}}||
||[http://git.sagemath.org/sage.git/commit/?id=7918417adce86770e782d2f7607f8be6f80c258d
7918417]||{{{Trac #19946: additional doctest}}}||
||[http://git.sagemath.org/sage.git/commit/?id=1471336d55af25f699c0e09ae5689197bdb8e232
1471336]||{{{Trac #19946: rewrite and improve explaination of 1b62954}}}||
||[http://git.sagemath.org/sage.git/commit/?id=9f9a23f9807fa2ffe914516daa8b43f3a486d8d7
9f9a23f]||{{{Trac #19961: document rpow}}}||
||[http://git.sagemath.org/sage.git/commit/?id=101e4dee74ef436884d2fe93bb4258b28fad4c80
101e4de]||{{{Merge branch 'u/dkrenn/t/19961' of trac.sagemath.org:sage
into t/19946}}}||
||[http://git.sagemath.org/sage.git/commit/?id=7179c784bbd69881e7505053ff5bfb50ecdb1371
7179c78]||{{{Trac #19946: link from general doc to detailed
explaination}}}||
||[http://git.sagemath.org/sage.git/commit/?id=1259201fe2a01fd64adf0b21489ecb8f321a987f
1259201]||{{{Trac #19946: fix typo}}}||
||[http://git.sagemath.org/sage.git/commit/?id=37caf2577b8606d04ff5caaf0f1b0b716056a401
37caf25]||{{{Merge branch 'u/cheuberg/t/19946' of trac.sagemath.org:sage
into t/19510/asy/generators-binomial}}}||
||[http://git.sagemath.org/sage.git/commit/?id=10cd04bde3be402ea4c3550793475135096f27fb
10cd04b]||{{{Trac #19510: major rewrite of binomial kn over n}}}||
--
Ticket URL: <http://trac.sagemath.org/ticket/19510#comment:13>
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