asymptotic expansions: singularity analysis #19944

behackl · 2016-01-23T02:05:28Z

This ticket aims to implement singularity analysis as a callable method of asymptotic rings.

Depends on #19532
Depends on #19969
Depends on #19981

CC: @dkrenn @cheuberg

Component: asymptotic expansions

Author: Benjamin Hackl, Clemens Heuberger

Branch/Commit: 452c43b

Reviewer: Daniel Krenn

Issue created by migration from https://trac.sagemath.org/ticket/19944

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

behackl · 2016-01-23T02:07:52Z

Author: Benjamin Hackl, Clemens Heuberger

behackl · 2016-01-23T02:07:52Z

Last 10 new commits:

`267718d`	`Trac #19532: Additional tests`
`0860173`	`Trac #19532: List log log factors, document missing implementations`
`a3a6dfd`	`Trac #19532: Add references`
`3e23a35`	`Merge branch 't/19532/asy/singularity-analysis' into t/17601/public/asy/trunk`
`bedd23a`	`Trac #19898: rename harmonic_number to HarmonicNumber`
`e107b79`	`Merge branch 't/19898/asy/harmonic-number' into t/17601/public/asy/trunk`
`e750dde`	`add code for singularity analysis`
`af7c73b`	`add example`
`f212dee`	`fix: .summand --> .summands`
`25a5dd5`	`add precision keyword`

behackl · 2016-01-23T02:07:52Z

Dependencies: #19532

behackl · 2016-01-23T02:07:52Z

Commit: 25a5dd5

behackl · 2016-01-23T02:07:52Z

Branch: u/behackl/asy/singularity-analysis

cheuberg · 2016-01-23T05:40:34Z

comment:2

Rebased on top of #19532 instead of #17601.

New commits:

`1529a4d`	`Trac #19510: Merge #19306 (due to #19879)`
`b30388b`	`Trac #19532: Merge #19510 to fix doctest`
`7f74b31`	`Trac #19532: Implement zeta != 1`
`0c600cf`	`add code for singularity analysis`
`b8a52c6`	`add example`
`e3588b6`	`fix: .summand --> .summands`
`f6a233d`	`add precision keyword`

cheuberg · 2016-01-23T05:40:34Z

Changed branch from u/behackl/asy/singularity-analysis to u/cheuberg/asy/singularity-analysis-method

cheuberg · 2016-01-23T05:40:34Z

Changed commit from 25a5dd5 to f6a233d

sagetrac-git · 2016-01-23T06:49:47Z

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

`f38cdfc`	`Trac #19532: fix more issues with location of singularities`
`042849a`	`Trac #19944: merge #19532`
`a7aec7c`	`Trac #19944: use generating function (as function) instead of singular expansion`

sagetrac-git · 2016-01-23T06:49:47Z

Changed commit from f6a233d to a7aec7c

sagetrac-git · 2016-01-23T07:28:02Z

Changed commit from a7aec7c to a832ebd

sagetrac-git · 2016-01-23T07:28:02Z

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

`5d87b05`	`Trac #19944: use precision for singular expansion`
`a832ebd`	`Trac #19944: return singular expansions on request`

cheuberg · 2016-01-23T08:55:49Z

comment:5

Once #19947 is done, input could also be as a symbolic expression plus a variable, which would probably be friendlier.

cheuberg · 2016-01-25T20:26:25Z

comment:6

Adapt to new version of #19532 and doctest OZero condition.

behackl · 2016-01-26T20:56:44Z

comment:7

Replying to @cheuberg:

Adapt to new version of #19532 and doctest OZero condition.

Done.

Last 10 new commits:

`24c153c`	`Trac #19946: reviewer commit: ReSt error`
`7918417`	`Trac #19946: additional doctest`
`bfb72dc`	`Trac #19532: Merge #19946`
`21054cb`	`Trac #19532: get rid of work-around for #19946`
`53a35cf`	`Merge branch 'u/cheuberg/asy/singularity-analysis-generator' of git://trac.sagemath.org/sage into asy/singularity-analysis-method`
`9f650b0`	`handle OZeroException in singularity_analysis`
`8aa55e2`	`implement exact_part`
`7276172`	`delete terms from copy instead of building new poset`
`742ce5b`	`Merge branch 'asy/exact_part' into asy/singularity-analysis-method`
`a2e430e`	`add doctest for NotImplementedOZero`

behackl · 2016-01-26T20:56:44Z

Changed branch from u/cheuberg/asy/singularity-analysis-method to u/behackl/asy/singularity-analysis-method

behackl · 2016-01-26T20:56:44Z

Changed commit from a832ebd to a2e430e

dkrenn · 2016-01-27T12:32:19Z

Changed branch from u/behackl/asy/singularity-analysis-method to u/dkrenn/asy/singularity-analysis-method

dkrenn · 2016-01-27T12:46:26Z

Changed commit from a2e430e to 3743f9d

dkrenn · 2016-01-27T12:46:26Z

comment:9

I've reviewed the patch and have the following comments:

result.exact_part() == result: Maybe create a follow up ticket implementing is_exact.
The code

            if isinstance(summand, ExactTerm):
                expansion = asymptotic_expansions.\
                    SingularityAnalysis('Z', alpha=alpha, zeta=singularity,
                                        precision=precision).subs(Z=self.gen())
                return summand.coefficient * expansion
            elif isinstance(summand, OTerm):
                return (self.gen() ** (alpha - 1)).O()

is not ideal. It looks like the singularity analysis should be done by the terms themselves and eventually by the growth groups (since they know what they are).

(self.gen() ** (alpha - 1)).O() should depend on the singularity.
In some sense the transfer term (self.gen() ** (alpha - 1)).O() has the same status as the expansion asymptotic_expansions.SingularityAnalysis. So a generation in the generations would be an option. However, I understand, that it is much simpler, so I do not have a strong preference for this.
Parameter description function: mentioned the word "callable"(?) Say that it is a function in one variable.
Parameter return_singular_expansions: in an ideal world, there would not be a different kind of output (asymptotic expansions vs. named tuple). However, I understand it is as it is; it seems that there is no other satisfying solution to this. Am I right?

New commits:

`3743f9d`	`Trac #19944 minor changes during review`

dkrenn · 2016-01-27T12:46:26Z

Reviewer: Daniel Krenn

cheuberg · 2016-02-14T12:35:48Z

comment:22

Replying to @dkrenn:

There is an inconsistency in the order of the parameters: in the generators we have var, zeta=1, ..., but in all the _singularity_analysis_ we have zeta, var.

OK, I'll change the _singularity_analysis_ routines.

Once we have #20050, the parameter zeta will be removed.

cheuberg · 2016-02-14T12:36:28Z

comment:23

Replying to @dkrenn:

...and maybe (but really, maybe): name argument precision in the doctests to make them better readable; e.g. `singularity_analysis('n', 1/2, precision=5)'.

I will do that.

cheuberg · 2016-02-14T12:46:57Z

Changed branch from u/dkrenn/asy/singularity-analysis-method to u/cheuberg/asy/singularity-analysis-method

cheuberg · 2016-02-14T12:47:41Z

Changed commit from ad62c31 to 9ce7b35

cheuberg · 2016-02-14T12:47:41Z

comment:25

Replying to @cheuberg:

Replying to @dkrenn:

There is an inconsistency in the order of the parameters: in the generators we have var, zeta=1, ..., but in all the _singularity_analysis_ we have zeta, var.

OK, I'll change the _singularity_analysis_ routines.

Done.

New commits:

`9ce7b35`	`Trac #19944: exchange order of parameters var and zeta in _singularity_analysis_`

cheuberg · 2016-02-14T12:47:59Z

comment:26

Replying to @cheuberg:

Replying to @dkrenn:

...and maybe (but really, maybe): name argument precision in the doctests to make them better readable; e.g. `singularity_analysis('n', 1/2, precision=5)'.

I will do that.

done.

cheuberg · 2016-02-14T13:00:53Z

comment:27

Replying to @cheuberg:

Done.

New commits:

`9ce7b35`	`Trac #19944: exchange order of parameters var and zeta in _singularity_analysis_`

I forgot to change the docstrings. I will do so now.

sagetrac-git · 2016-02-14T13:04:30Z

Changed commit from 9ce7b35 to c79a6f7

sagetrac-git · 2016-02-14T13:04:30Z

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

`c79a6f7`	`Trac #19944: exchange zeta and var in docstrings`

cheuberg · 2016-02-14T13:06:40Z

comment:29

Replying to @sagetrac-git:

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


c79a6f7	`Trac #19944: exchange zeta and var in docstrings`
Done.

dkrenn · 2016-02-14T13:23:06Z

comment:30

Replying to @cheuberg:

Replying to @dkrenn:

Is (1-z\zeta) \to 0 correct or should it be (1-z/\zeta) \to 0? Maybe using z\to\zeta instead of (1-z/\zeta) \to 0? (I don't have a strong preference for changing, but from an outside view, this would be easier to understand.

I prefer (1-z/\zeta) \to 0 or perhaps T = 1/(1-z/\zeta) \to \infty.

Should it be mentioned that (in terms and growth groups) a variable (_var_ of the parent) represents/equals 1 / (1-z/\zeta) ?

This should change once asymptotics z->z_0 are implemented.

What about "T = 1/(1-z/\zeta) \to \infty where this element is a growth element (resp. monomial) in T"?

I'm happy with this formulation.

All the other changes are positivly reviewed form my side.

sagetrac-git · 2016-02-14T14:11:17Z

Changed commit from c79a6f7 to 452c43b

sagetrac-git · 2016-02-14T14:11:17Z

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

`452c43b`	Trac #19944: `_singularity_analysis_` methods: more precise documentation

cheuberg · 2016-02-14T14:12:06Z

comment:32

Replying to @dkrenn:

What about "T = 1/(1-z/\zeta) \to \infty where this element is a growth element (resp. monomial) in T"?

I'm happy with this formulation.

done. needs review.

dkrenn · 2016-02-14T15:17:41Z

comment:33

Replying to @cheuberg:

Replying to @dkrenn:

What about "T = 1/(1-z/\zeta) \to \infty where this element is a growth element (resp. monomial) in T"?

I'm happy with this formulation.

done. needs review.

Fine.

vbraun · 2016-02-16T17:05:56Z

Changed branch from u/cheuberg/asy/singularity-analysis-method to 452c43b

behackl added this to the sage-7.1 milestone Jan 23, 2016

behackl added c: asymptotic expansions labels Jan 23, 2016

cheuberg added the s: needs review label Jan 23, 2016

cheuberg added s: needs work and removed s: needs review labels Jan 25, 2016

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

cheuberg added s: needs work and removed s: needs review labels Feb 14, 2016

cheuberg added s: needs review and removed s: needs work labels Feb 14, 2016

dkrenn added s: positive review and removed s: needs review labels Feb 14, 2016

vbraun removed the s: positive review label Feb 16, 2016

vbraun closed this as completed in 0f5b09e Feb 16, 2016

behackl mentioned this issue Dec 29, 2022

Meta ticket: Asymptotic Expansions in SageMath #17601

Open

dkrenn mentioned this issue Feb 18, 2016

AsymptoticExpansion.factorial #19540

Closed

asymptotic expansions: singularity analysis #19944

asymptotic expansions: singularity analysis #19944

Comments

behackl commented Jan 23, 2016

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