asymptotic expansion generator for binomial(kn, n)

[dkrenn]

Implement a generator for binomial(k*n, n).

[dkrenn]

Last 10 new commits:

​f0c7440	use symbolic constants subring (instead of SR)
​0d6cce3	remove automatic parenthesing in parent_to_repr_short
​3f5e1b1	fix bug in split_str_by_op
​6e366a5	binomial_kn_n: change to symbolic constants subring (WIP)
​ae1877c	rename binomial* --> Binomial*
​f0ab41a	delete code of binomial* since it was
​559d1c4	Merge branch 't/19306/asy/generators' into asy/generators-binomial
​fd35046	change base class to SageObject
​532c41c	write docstrings of Stirling generators
​221ad4f	Merge branch 't/19306/asy/generators' into asy/generators-binomial

[git]

Branch pushed to git repo; I updated commit sha1. Last 10 new commits:

​a2b744d	Merge branch 'coerce/inverse-action' into asy/generators-binomial
​1bd2223	make Binomial_kn_n really working
​421e377	mutable poset map: remove elements ``None``
​1d28240	term monoid: write change_parameter
​2c37889	correct a bug in change_parameter
​bdcb72b	write map_coefficients
​2a0815d	Merge branch 'asy/map_coefficients' into asy/generators-binomial
​e93ce46	simplify coefficients automatically and use the faster algorithm per default
​f468de6	docu
​4a27e66	result over QQ if skip-parameter given

[git]

Branch pushed to git repo; I updated commit sha1. New commits:

​e59c71f

toc entry (at top of file)

[git]

Branch pushed to git repo; I updated commit sha1. New commits:

​ea3dd35

small bugfix

[cheuberg]

Merged latest version of #19306 to avoid doctest failure.

---

New commits:

​cc256c8	Trac #19306: remove old code
​31e4dc4	Trac #19306: other variables than n
​a3fad56	Trac #19306: fix error terms for low precision
​a4c3f9d	Trac #19306: Fix low precision for Stirling
​eac4977	Trac #19306: minor changes (cross-review and incorporate reviewer comments)
​946a828	Trac #19306: change % to .format
​809d653	Trac #19306: Merge tag '7.0' due to #19879
​4d80eb3	Trac #19306: sage.rings.arith -> sage.arith.all (after #19879)
​1529a4d	Trac #19510: Merge #19306 (due to #19879)

[git]

Branch pushed to git repo; I updated commit sha1. New commits:

​3e30659	Trac #19510: modify constant factor: factor sqrt(k-1) is removed, too.
​5d9152c	Trac #19510: state constant factors/summands in Stirling and binomial

[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.

[dkrenn]

Replying to 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.

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Last 10 new commits:

​1b62954	Trac #19946: add doctests to document behavior
​24c153c	Trac #19946: reviewer commit: ReSt error
​7918417	Trac #19946: additional doctest
​1471336	Trac #19946: rewrite and improve explaination of 1b62954
​9f9a23f	Trac #19961: document rpow
​101e4de	Merge branch 'u/dkrenn/t/19961' of trac.sagemath.org:sage into t/19946
​7179c78	Trac #19946: link from general doc to detailed explaination
​1259201	Trac #19946: fix typo
​37caf25	Merge branch 'u/cheuberg/t/19946' of trac.sagemath.org:sage into t/19510/asy/generators-binomial
​10cd04b	Trac #19510: major rewrite of binomial kn over n

[cheuberg]

I reviewed this version.

I merged #19957 and added doctests using compare_with_values. Please cross-review and set to positive if you are satisfied.

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Last 10 new commits:

​7337e61	Trac 19957 review: restructure part of the code and remove inner list to make it better readable
​0632fd3	Trac 19957 review: minor changes in doc
​4a8ea9a	Trac #19957: move see also blocks to position given in developer guide
​9ea47b9	Trac #19957: fix dead link
​3d51289	Trac #19957: Merge #19946 to avoid work-around
​b606fdf	Trac #19957: remove work-around for #19946
​4346994	Trac #19957: rename e to expansion in doctests
​5d6e9b2	Trac #19957: Introduce parameter relative tolerance
​00eae5d	Merge branch 't/19957/asy/compare-with-values' into t/19510/asy/generators-binomial
​78bdd0f	Trac #19510: additional doctests using compare_with_values

[vbraun]

​http://build.sagedev.org/release/builders/%20%20fast%20Oxford%20arando%20%28Ubuntu%2013.04%20i686%29%20incremental/builds/797/steps/shell_4/logs/stdio

sage -t --long src/sage/rings/asymptotic/asymptotic_expansion_generators.py
**********************************************************************
File "src/sage/rings/asymptotic/asymptotic_expansion_generators.py", line 141, in sage.rings.asymptotic.asymptotic_expansion_generators.AsymptoticExpansionGenerators.Stirling
Failed example:
    expansion.compare_with_values(n, lambda x: x.factorial(), [5, 10, 20])
Expected:
    [(5, 0.00675841118?), (10, 0.0067589306?), (20, 0.006744925?)]
Got:
    [(5, 0.006758411181?), (10, 0.0067589306?), (20, 0.006744925?)]
**********************************************************************
1 item had failures:
   1 of  11 in sage.rings.asymptotic.asymptotic_expansion_generators.AsymptoticExpansionGenerators.Stirling
    [45 tests, 1 failure, 8.78 s]

[git]

Branch pushed to git repo; I updated commit sha1. New commits:

​2b71379

Trac #19510: specify relative tolerance for doctests

[cheuberg]

Added relative tolerance.

[dkrenn]

New commits:

​c998922

Trac #19510: constitent spacings