asymptotic expansion generator for binomial(kn, n) #19510

dkrenn · 2015-11-01T18:10:01Z

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

Depends on #19306
Depends on #19521
Depends on #19528
Depends on #19957

CC: @behackl @cheuberg

Component: asymptotic expansions

Author: Daniel Krenn

Branch/Commit: c998922

Reviewer: Clemens Heuberger

Issue created by migration from https://trac.sagemath.org/ticket/19510

The text was updated successfully, but these errors were encountered:

dkrenn · 2015-11-01T18:11:01Z

Branch: u/dkrenn/asy/generators-binomial

dkrenn · 2015-11-04T16:06:41Z

Commit: 221ad4f

dkrenn · 2015-11-04T16:06:41Z

Changed dependencies from #19306 to #19306, #19521

dkrenn · 2015-11-04T16:06:41Z

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`

dkrenn · 2015-11-04T20:25:26Z

Changed dependencies from #19306, #19521 to #19306, #19521, #19528

sagetrac-git · 2015-11-05T02:37:22Z

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`

sagetrac-git · 2015-11-05T02:37:22Z

Changed commit from 221ad4f to 4a27e66

sagetrac-git · 2015-11-05T02:40:26Z

Changed commit from 4a27e66 to e59c71f

sagetrac-git · 2015-11-05T02:40:26Z

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

`e59c71f`	`toc entry (at top of file)`

sagetrac-git · 2015-11-07T00:31:24Z

Changed commit from e59c71f to ea3dd35

sagetrac-git · 2015-11-07T00:31:24Z

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

`ea3dd35`	`small bugfix`

cheuberg · 2016-01-22T05:00:54Z

Changed branch from u/dkrenn/asy/generators-binomial to u/cheuberg/asy/generators-binomial

cheuberg · 2016-01-22T05:13:18Z

Changed commit from ea3dd35 to 1529a4d

cheuberg · 2016-01-22T05:13:18Z

comment:9

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)`

sagetrac-git · 2016-01-23T18:55:36Z

Changed commit from 1529a4d to 5d9152c

sagetrac-git · 2016-01-23T18:55:36Z

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 · 2016-01-23T19:06:04Z

Reviewer: Clemens Heuberger

cheuberg · 2016-01-23T19:06:04Z

comment:11

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.
(en)(Symbolic Constants Subring) is hard to read; actually, the only exponential factor that will ever occur is (kk/(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 · 2016-01-26T19:45:40Z

Changed branch from u/cheuberg/asy/generators-binomial to u/dkrenn/asy/generators-binomial

dkrenn · 2016-01-26T19:46:53Z

comment:13

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.

(en)(Symbolic Constants Subring) is hard to read; actually, the only exponential factor that will ever occur is (kk/(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:

`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`

dkrenn · 2016-01-26T19:46:53Z

Changed commit from 5d9152c to 10cd04b

cheuberg · 2016-01-27T11:44:18Z

Changed branch from u/dkrenn/asy/generators-binomial to u/cheuberg/asy/generators-binomial

cheuberg · 2016-01-27T11:46:20Z

comment:15

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.

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`

cheuberg · 2016-01-27T11:46:20Z

Changed commit from 10cd04b to 78bdd0f

cheuberg · 2016-01-27T11:46:20Z

Changed dependencies from #19306, #19521, #19528 to #19306, #19521, #19528, #19957

vbraun · 2016-01-29T17:43:25Z

comment:17

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]

sagetrac-git · 2016-01-30T14:16:51Z

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

`2b71379`	`Trac #19510: specify relative tolerance for doctests`

sagetrac-git · 2016-01-30T14:16:51Z

Changed commit from 78bdd0f to 2b71379

cheuberg · 2016-01-30T14:17:50Z

comment:19

Added relative tolerance.

dkrenn · 2016-01-30T14:39:39Z

Changed branch from u/cheuberg/asy/generators-binomial to u/dkrenn/asy/generators-binomial

dkrenn · 2016-01-30T14:40:07Z

New commits:

`c998922`	`Trac #19510: constitent spacings`

dkrenn · 2016-01-30T14:40:07Z

Changed commit from 2b71379 to c998922

vbraun · 2016-01-31T13:31:35Z

Changed branch from u/dkrenn/asy/generators-binomial to c998922

dkrenn added this to the sage-6.10 milestone Nov 1, 2015

dkrenn added c: asymptotic expansions labels Nov 1, 2015

dkrenn added the s: needs review label Nov 5, 2015

cheuberg modified the milestones: sage-6.10, sage-7.1 Jan 22, 2016

cheuberg added s: needs work and removed s: needs review labels Jan 23, 2016

dkrenn added s: needs review and removed s: needs work labels Jan 26, 2016

dkrenn added s: positive review and removed s: needs review labels Jan 27, 2016

vbraun added s: needs work and removed s: positive review labels Jan 29, 2016

cheuberg added s: needs review and removed s: needs work labels Jan 30, 2016

dkrenn added s: positive review and removed s: needs review labels Jan 30, 2016

vbraun removed the s: positive review label Jan 31, 2016

vbraun closed this as completed in 3bf1666 Jan 31, 2016

behackl mentioned this issue Dec 29, 2022

Meta ticket: Asymptotic Expansions in SageMath #17601

Open

dkrenn mentioned this issue Feb 1, 2016

asymptotic expansion generators related to singularity analysis #19532

Closed

cheuberg mentioned this issue Jan 31, 2016

AsymptoticExpansion: Generator for expansion of harmonic number #19898

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asymptotic expansion generator for binomial(kn, n) #19510

asymptotic expansion generator for binomial(kn, n) #19510

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asymptotic expansion generator for binomial(kn, n) #19510

asymptotic expansion generator for binomial(kn, n) #19510

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