Singularity analysis for given singular expansions #20053

cheuberg · 2016-02-14T14:49:06Z

Refactor coefficients_of_generating_function (#20056) so that the part working with one singular expansion is now a separate method of an asymptotic expansion.

This allows to perform singularity analysis also in situations where the singular expansion has been obtained by other means than the simple approach for explicit generating functions of #19944 (and follow-ups #20040 and #20056), even while #20050 is not implemented.

For now, this is a hidden method because the input will change once #20050 is done.

Once #20050 is implemented, the dual choice of output of coefficients_of_generating_function may be changed: if users want to have singular expansions (in order to show them in their paper, for instance), they could convert it into a singular expansion by using #20050 (or its dependents) and then feed it into singularity_analysis.

See #17601 for the asymptotic expansions meta ticket.

Depends on #20056
Depends on #19540

CC: @dkrenn @behackl

Component: asymptotic expansions

Keywords: singularity analysis

Author: Clemens Heuberger

Branch/Commit: b42bb05

Reviewer: Benjamin Hackl

Issue created by migration from https://trac.sagemath.org/ticket/20053

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

cheuberg · 2016-02-15T11:04:27Z

Branch: u/cheuberg/asy/allow-singular-expansion

cheuberg · 2016-02-15T11:05:38Z

comment:2

That is a bare bone implementation of what I want; I set it to needs_review because I'd like to read your opinions.

Last 10 new commits:

`9ce7b35`	`Trac #19944: exchange order of parameters var and zeta in _singularity_analysis_`
`902c182`	`Trac #20040: Merge #19944`
`866a9e3`	`Trac #20040: exchange order of parameters var and zeta in _singularity_analysis_`
`c79a6f7`	`Trac #19944: exchange zeta and var in docstrings`
`d0f5e94`	`Trac #20040: Merge #19944`
`27a8605`	`Merge branch 'u/cheuberg/asy/singularity-analysis-method-log' of git://trac.sagemath.org/sage into t/20040/asy/singularity-analysis-method-log`
`452c43b`	Trac #19944: `_singularity_analysis_` methods: more precise documentation
`4cb5934`	`Trac #20040: Merge #19944`
`8455dc2`	Trac #20040: `_singularity_analysis_` methods: more precise documentation
`8bb9046`	`Trac #20040: added myself to AUTHORS`

cheuberg · 2016-02-15T11:05:38Z

Commit: 8bb9046

cheuberg · 2016-02-15T11:05:38Z

Author: Clemens Heuberger

cheuberg · 2016-02-15T11:06:01Z

Changed dependencies from #20052, #19944, #20050 to #20052, #20040, #20050

sagetrac-git · 2016-02-15T11:07:01Z

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

`271f132`	`Trac #20053: allow singular expansions as input of singularity analysis`

sagetrac-git · 2016-02-15T11:07:01Z

Changed commit from 8bb9046 to 271f132

dkrenn · 2016-02-15T13:29:24Z

comment:5

Replying to @cheuberg:

That is a bare bone implementation of what I want; I set it to needs_review because I'd like to read your opinions.

This extensions does not work with more than one singularity as the same singular expansion is used for each singularity.

cheuberg · 2016-02-15T13:48:39Z

comment:6

Replying to @dkrenn:

Replying to @cheuberg:

That is a bare bone implementation of what I want; I set it to needs_review because I'd like to read your opinions.

This extensions does not work with more than one singularity as the same singular expansion is used for each singularity.

Option 1: forbid more than one singularity
Option 2: function could be a list of singular expansions
Option 3: function could be a dictionary, as it is the case for the output when selected.

I do not like option 3, as it is not relevant once #20050 is implemented.

cheuberg · 2016-02-15T14:09:01Z

comment:7

A completely different option would be to have singularity_analysis as a method of an AsymptoticExpansion and to call singular_expansion.singularity_analysis('n', precision=5). However, we would then have AsymptoticRing.singularity_analysis which ends up in that ring and AsymptoticExpansion.singularity_analysis which would end up somewhere else.

cheuberg · 2016-02-15T14:39:33Z

comment:8

Proposal: rename AsymptoticRing.singularity_analysis to AsymptoticRing.coefficients_of_generating_function and have AsymptoticExpansion._singularity_analysis_ and make this method public once #20050 is done.

dkrenn · 2016-02-15T14:40:36Z

comment:9

Replying to @cheuberg:

Proposal: rename AsymptoticRing.singularity_analysis to AsymptoticRing.coefficients_of_generating_function and have AsymptoticExpansion._singularity_analysis_ and make this method public once #20050 is done.

+1

sagetrac-git · 2016-02-16T14:50:02Z

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

`40b6e2e`	`Trac #20056: Rename AsymptoticRing.singularity_analysis to coefficients_generating_function`
`197fe43`	`Trac #20053: Merge #20056`
`bbbfab9`	`Trac #20053: Also rename method here`
`071a595`	`Trac #20053: Refactor: new method AsymptoticRing._singularity_analysis_`
`2b2e94d`	`Trac #20053: minor cleanup in coefficients_of_generating_function`
`7f8c745`	`Trac #20053: add warning to coefficients_of_generating_function`

sagetrac-git · 2016-02-16T14:50:02Z

Changed commit from 271f132 to 7f8c745

cheuberg · 2016-02-16T14:56:10Z

Changed dependencies from #20052, #20040, #20050 to #20056

cheuberg · 2016-02-16T14:56:10Z

comment:11

This is now a complete rewrite following yesterday's discussions and #20056.

I now think that this is basically the point that we can reach without #20050, so this now awaits your review.

sagetrac-git · 2016-02-16T16:08:12Z

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

`8a43e7e`	`Trac #19540: allow growth groups strings in TermMonoid factory`
`0384e25`	`Trac #19540: use is_one()`
`3f0f855`	`Trac #19540: variable_names for growth elements`
`eb49c65`	`Trac #19540: variable_names for terms`
`5a4adf0`	`Trac #19540: variable_names for asymptotic expansions`
`d9f2796`	Trac #19540: `_factorial_` for terms
`c801853`	`Trac #19540: rewrite factorial`
`139f7c8`	`Trac #19540: note on log(s).factorial()`
`23948e4`	`Merge branch 'u/cheuberg/asy/singularity-analysis-method' of git://trac.sagemath.org/sage into t/19540/asy/factorial`
`7acc487`	`Trac #20053: Merge branch #19540 to resolve merge conflict`

sagetrac-git · 2016-02-16T16:08:12Z

Changed commit from 7f8c745 to 7acc487

cheuberg · 2016-02-16T16:09:07Z

Changed dependencies from #20056 to #20056, #19540

behackl · 2016-03-08T18:00:30Z

comment:15

I've reviewed this implementation, and I only have one comment:

Could you revise the docstring of AsymptoticExpansion._singularity_analysis_? Because

var can also be the generator of an asymptotic ring,
zeta is the location of the singularity, and
precision is not set to the default precision of the ring if it is omitted, but has the same behavior as the SingularityAnalysis method in the generators.

Do we want that the current behavior from 3 happens, so that the asymptotic contribution has the same precision as the singular expansion by default? Would be worth considering IMHO.

Other than that, positive_review form my side.

sagetrac-git · 2016-03-09T16:08:42Z

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

`713f05f`	`Trac #20053: generator of asymptotic ring can be used`
`b42bb05`	`Trac #20053: modify behaviour of precision`

sagetrac-git · 2016-03-09T16:08:42Z

Changed commit from 7acc487 to b42bb05

cheuberg · 2016-03-09T16:16:09Z

comment:17

Replying to @behackl:

var can also be the generator of an asymptotic ring,

documented and doctested

zeta is the location of the singularity, and

done.

precision is not set to the default precision of the ring if it is omitted, but has the same behavior as the SingularityAnalysis method in the generators.

Do we want that the current behavior from 3 happens, so that the asymptotic contribution has the same precision as the singular expansion by default? Would be worth considering IMHO.

We cannot directly use the precision of this element, because we have no elegant means of defining the precision of an element (we will not introspect the group). Thus IMHO the only sensible default is the default precision of the parent of this element. Thus the behaviour is now changed.

The method coefficients_of_generating_function does not handle the precision, either, but that could be another ticket, if you want to open one. In any case, this is unrelated to this method here.

behackl · 2016-03-09T16:20:01Z

comment:18

Replying to @cheuberg:

Replying to @behackl:

var can also be the generator of an asymptotic ring,

documented and doctested

zeta is the location of the singularity, and

done.

precision is not set to the default precision of the ring if it is omitted, but has the same behavior as the SingularityAnalysis method in the generators.

Do we want that the current behavior from 3 happens, so that the asymptotic contribution has the same precision as the singular expansion by default? Would be worth considering IMHO.

We cannot directly use the precision of this element, because we have no elegant means of defining the precision of an element (we will not introspect the group). Thus IMHO the only sensible default is the default precision of the parent of this element. Thus the behaviour is now changed.

That is what I originally meant, thank you.

The method coefficients_of_generating_function does not handle the precision, either, but that could be another ticket, if you want to open one. In any case, this is unrelated to this method here.

Yes, this would certainly be a new ticket, and I think that this is definitely worth opening one.

In any case: your changes look good to me, and I'll just wait for the patchbot before I set this to positive_review. Thank you!

behackl · 2016-03-09T19:30:40Z

comment:19

The patchbot is happy, and so am I. :-)

vbraun · 2016-03-09T22:54:06Z

comment:20

Reviewer name is missing

cheuberg · 2016-03-10T05:22:41Z

Reviewer: Benjamin Hackl

vbraun · 2016-03-10T21:25:06Z

Changed branch from u/cheuberg/asy/allow-singular-expansion to b42bb05

cheuberg added this to the sage-7.1 milestone Feb 14, 2016

cheuberg added c: asymptotic expansions labels Feb 14, 2016

cheuberg added the s: needs review label Feb 15, 2016

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cheuberg changed the title ~~Singularity analysis: allow singular expansions as input~~ Singularity analysis for given singular expansions Feb 16, 2016

behackl added s: positive review and removed s: needs review labels Mar 9, 2016

vbraun added s: needs work and removed s: positive review labels Mar 9, 2016

cheuberg added s: positive review and removed s: needs work labels Mar 10, 2016

vbraun removed the s: positive review label Mar 10, 2016

vbraun closed this as completed in 85b26cd Mar 10, 2016

behackl mentioned this issue Dec 29, 2022

Meta ticket: Asymptotic Expansions in SageMath #17601

Open

cheuberg mentioned this issue Feb 16, 2016

Rename AsymptoticRing.singularity_analysis to coefficients_of_generating_function #20056

Closed

behackl mentioned this issue Dec 29, 2022

coefficients_of_generating_function fails for log-singularity with zeta != 1 #20076

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Singularity analysis for given singular expansions #20053

Singularity analysis for given singular expansions #20053

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