Implement symbolic confluent hypergeometric functions #14896

eviatarbach · 2013-07-16T05:23:21Z

This patch implements the Kummer confluent hypergeometric functions hypergeometric_M and hypergeometric_U (superseding the previous numerical-only version), complete with numeric evaluation, simplification, and transformation to generalized hypergeometric functions.

Depends on #2516
Depends on #16697

CC: @kcrisman @benjaminfjones

Component: symbolics

Keywords: hypergeometric, kummer

Author: Eviatar Bach, Ralf Stephan

Branch/Commit: 23a5c65

Reviewer: Jan Keitel, Ralf Stephan, Nils Bruin, Paul Masson

Issue created by migration from https://trac.sagemath.org/ticket/14896

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

eviatarbach · 2013-07-16T05:27:11Z

comment:1

Attachment: trac_14896.patch.gz

Whittaker functions can be easily implemented similarly; the reason I didn't include them in this patch is because the Maxima conversion is a bit more complicated.

eviatarbach · 2013-07-17T00:07:13Z

Attachment: trac_14896_2.patch.gz

eviatarbach · 2013-07-17T00:08:17Z

comment:2

Last patch, to be applied independently, adds LaTeX names which I forgot in the original.

fchapoton · 2014-03-06T17:08:10Z

Changed keywords from none to hypergeometric

KPanComputes · 2014-05-07T20:43:23Z

comment:8

This one does not have a valid git branch attached to it... So, I have set it to "needs work". I am willing to review this ticket once there is a valid git branch.

nbruin · 2014-05-08T07:25:16Z

comment:9

is this a dupe of #2516?

eviatarbach · 2014-05-08T07:30:56Z

comment:10

No. Confluent hypergeometric functions are a specific type of hypergeometric function, which are solutions to Kummer's differential equation.

Thanks for offering to review, Kannappan! I'm new to the Git workflow, but I'll try to create the branch as soon as possible.

sagetrac-jkeitel · 2014-05-21T07:32:00Z

Commit: 3b32a6c

sagetrac-jkeitel · 2014-05-21T07:32:00Z

comment:11

I've created a git branch and fixed a few failing doctests. There are still many functions that do not have docstrings.

Last 10 new commits:

`4b4ed75`	`Merge branch 'develop' into t/2516/ticket/2516`
`0dbbacd`	`2516: fix last doctests`
`934d057`	`2516: remove hack`
`0f5a4ff`	`2516: fix doctest`
`eeb273e`	`Merge branch 'develop' into t/2516/ticket/2516`
`62f7faa`	`Merge branch 'master' into t/2516/ticket/2516`
`9c6749d`	`doctest coverage`
`051edff`	`Merge branch 'develop' into t/2516/ticket/2516`
`9d6eea1`	`# Branch hyper`
`3b32a6c`	`Remove trailing whitespace and fix a few doctests by adding algorithm argument.`

sagetrac-jkeitel · 2014-05-21T07:32:00Z

Branch: u/jkeitel/ticket/14896

rwst · 2014-07-16T13:40:45Z

Changed branch from u/jkeitel/ticket/14896 to u/rws/ticket/14896

rwst · 2014-07-16T13:47:15Z

Changed commit from 3b32a6c to b87c57b

rwst · 2014-07-16T13:47:15Z

comment:13

Documentation as is looks good. I fixed a newly appearing doctest fail.

Last 10 new commits:

`e5a5343`	`6882: do word search/replace for symtable keys`
`4c1b0eb`	`6882: correction to previous commit`
`518de3e`	`6882: add symable rules for e,i,I; fix maxima_var; add doctests`
`7a6696b`	`Merge branch 'u/rws/bugs_in_conversion_of_variable_names_from_maxima_to_sage' of trac.sagemath.org:sage into t/8734/ticket/8734-1`
`a8df107`	`Merge branch 't/8734/ticket/8734-1' into t/16007/ticket/16007`
`9e66d16`	`Merge commit 'a8df107e76527d83a87456520395ab85dbc44050' of trac.sagemath.org:sage into t/2516/public/hypergeometric`
`5ac8224`	`2516: fix doctests affected by 16007 merge`
`b2f8dc5`	`2516: this 16007-related doctest fail seems to be uncovered only by 2516, so fix it here`
`c2b74cb`	`Merge branch 't/2516/b2f8dc5a1c82312271f2e2361b142358a66d0965' into t/14896/ticket/14896`
`b87c57b`	`14896: fix doctest failing due to changes by 16007`

rwst · 2014-07-16T14:04:57Z

comment:14

Seems I found a Maxima interface problem with hypergeometric:

sage: hypergeometric_M(1,b,x).simplify_hypergeometric()
(b - 1)*x^(-b + 1)*e^x*gamma_greek(b - 1, x)
sage: hypergeometric([1],[b],x).simplify_hypergeometric()
(b - 1)*x^(-b + 1)*e^x*gamma_greek(b - 1, x)

Of course that should be gamma.

nbruin · 2014-07-16T15:31:09Z

comment:15

Replying to @rwst:

(b - 1)*x^(-b + 1)*e^x*gamma_greek(b - 1, x)
Of course that should be gamma.

I'm not so sure: according to the maxima documentation:

gamma - gamma function (complete)
gamma_greek - lower incomplete gamma function
gamma_incomplete - upper incomplete gamma function

in sage, gamma(a,z) is documented to be the upper gamma function, which gets translated appropriately. We might not have a lower gamma function yet.

kcrisman · 2014-07-17T02:51:40Z

comment:16

(b - 1)*x^(-b + 1)*e^x*gamma_greek(b - 1, x)
Of course that should be gamma.
I'm not so sure: according to the maxima documentation:

gamma - gamma function (complete)

gamma_greek - lower incomplete gamma function

gamma_incomplete - upper incomplete gamma function

Good catch.

in sage, gamma(a,z) is documented to be the upper gamma function, which gets translated appropriately. We might not have a lower gamma function yet.

Maybe we can make it by gamma - upper incomplete?

rwst · 2014-07-17T08:48:34Z

comment:17

Replying to @kcrisman:

Maybe we can make it by gamma - upper incomplete?

Maybe define it in special.py both as maxima and Sage-evaluated (gamma-gamma_inc) function. Objections?

nbruin · 2014-07-17T16:14:00Z

comment:18

If maxima can produce gamma_greek spontaneously, then we should be able to make sense of it. The most straightforward way is by having a transliteration, gamma_incomplete_lower or gamma_lower perhaps. Adding new symbolic functions isn't that laborious, is it? Simplification methods can be grown later.

FYI: Mathematica seems to have Gamma[a,z] for upper and Gamma[a,0,z] for lower; Maple seems to have upper Gamma. So it does seem packages have been gravitating to the upper one more than the lower one. However, if that means our confluent hypergeometric functions always end up being translated into a more convoluted expression than a straight gamma_lower would give, we're not doing ourselves favours

(e.g., for numerical work: do you really want to evaluate gamma_lower(a,z) as gamma(z)-gamma_upper(a,z) ?)

Without strong indications in either direction, I'd be hesitant to make a choice and rather follow the lead of our main underlying engine: implement gamma_lower.

rwst · 2015-03-17T07:51:40Z

comment:35

Also needs merge in of updated #16697 and a squash.

rwst · 2015-03-17T16:32:37Z

comment:36

Pending because #16697 is pending.

rwst · 2016-05-21T13:10:10Z

Changed branch from u/rws/ticket/14896 to u/rws/14896

rwst · 2016-05-21T13:12:34Z

comment:38

Updated with newest #16697, squashed into three tickets, removed pending. Please review.

New commits:

`0e19f0b`	`Merge branch 'develop' into u/jkeitel/ticket/14896`
`da3a146`	`14896: fix documentation, doctests, coverage; use mpmath, other`

rwst · 2016-05-21T13:12:34Z

Changed commit from a628fcb to da3a146

rwst · 2016-05-21T13:16:08Z

comment:39

Please review/merge #16697 first (its commit metadata is missing here).

paulmasson · 2016-06-28T21:36:24Z

comment:40

Ralf, I'm trying to merge existing commits to a branch that already includes #16697 but I'm getting errors:

    STDOUT: Auto-merging src/sage/symbolic/expression_conversions.py
    STDOUT: CONFLICT (content): Merge conflict in src/sage/symbolic/expression_conversions.py
    STDOUT: Auto-merging src/sage/symbolic/expression.pyx
    STDOUT: Auto-merging src/sage/functions/special.py
    STDOUT: Auto-merging src/sage/functions/other.py
    STDOUT: CONFLICT (content): Merge conflict in src/sage/functions/other.py
    STDOUT: Auto-merging src/sage/functions/hypergeometric.py
    STDOUT: Auto-merging src/sage/functions/all.py
    STDOUT: CONFLICT (content): Merge conflict in src/sage/functions/all.py
    STDOUT: Automatic merge failed; fix conflicts and then commit the result.

Am I doing something wrong or do these commits need updating after all this time? Would like to get this one reviewed.

sagetrac-git · 2016-06-29T05:53:31Z

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

`58f6a12`	`Merge branch 'develop' into t/14896/14896`

sagetrac-git · 2016-06-29T05:53:31Z

Changed commit from da3a146 to 58f6a12

paulmasson · 2016-06-29T20:21:22Z

comment:42

Still getting an error:

    STDOUT: Auto-merging src/sage/symbolic/expression_conversions.py
    STDOUT: CONFLICT (content): Merge conflict in src/sage/symbolic/expression_conversions.py
    STDOUT: Auto-merging src/sage/functions/all.py
    STDOUT: Automatic merge failed; fix conflicts and then commit the result.

rwst · 2016-06-30T05:34:37Z

comment:43

As you can see at the top of the ticket the branch cleanly merges with beta5. So you seem to want to merge it with a different version? And why merge at all? Just git trac checkout 14896 and compile.

paulmasson · 2016-06-30T20:52:34Z

comment:44

I assumed I needed keep track of changes from#16697 manually, but clearly Trac does that automatically.

Running a doctest on symbolic/expression_conversions.py gives an error:

ValueError: line 93 of the docstring for sage.symbolic.expression_conversions.InterfaceInit.derivative has inconsistent leading whitespace: '======='

This is the same file that had a merge conflict.

sagetrac-git · 2016-07-01T05:41:11Z

Changed commit from 58f6a12 to 23a5c65

sagetrac-git · 2016-07-01T05:41:11Z

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

`23a5c65`	`Merge branch 'develop' into t/14896/14896`

rwst · 2016-07-01T05:42:33Z

comment:46

I updated to beta6 and had a merge conflict there too which should be resolved now. Let's try again, please.

paulmasson · 2016-07-01T20:07:41Z

Changed reviewer from Jan Keitel, Ralf Stephan, Nils Bruin to Jan Keitel, Ralf Stephan, Nils Bruin, Paul Masson

paulmasson · 2016-07-01T20:07:41Z

comment:47

Doctests all pass. Documentation builds. Random numeric testing accurate and both functions plot. Symbolic behavior as expected.

Looks good to me.

rwst · 2016-07-02T04:46:24Z

comment:48

Thanks for the review.

vbraun · 2016-07-02T12:07:33Z

Changed branch from u/rws/14896 to 23a5c65

eviatarbach added this to the sage-6.1 milestone Jul 16, 2013

eviatarbach added c: symbolics labels Jul 16, 2013

eviatarbach assigned burcin Jul 16, 2013

eviatarbach added the s: needs review label Jul 17, 2013

sagetrac-vbraun-spam mannequin modified the milestones: sage-6.1, sage-6.2 Jan 30, 2014

sagetrac-vbraun-spam mannequin modified the milestones: sage-6.2, sage-6.3 May 6, 2014

KPanComputes added s: needs work and removed s: needs review labels May 7, 2014

rwst removed this from the sage-6.4 milestone Mar 17, 2015

rwst added the pending label Mar 17, 2015

rwst added this to the sage-7.3 milestone May 21, 2016

rwst added s: needs review and removed pending s: needs work labels May 21, 2016

paulmasson mannequin added s: positive review and removed s: needs review labels Jul 1, 2016

vbraun removed the s: positive review label Jul 2, 2016

vbraun closed this as completed in 606dd27 Jul 2, 2016

rwst mentioned this issue Dec 29, 2022

Metaticket: priority symbolic functions implementations #17454

Open

Implement symbolic confluent hypergeometric functions #14896

Implement symbolic confluent hypergeometric functions #14896

Comments

eviatarbach commented Jul 16, 2013

eviatarbach commented Jul 16, 2013

eviatarbach commented Jul 17, 2013

eviatarbach commented Jul 17, 2013

fchapoton commented Mar 6, 2014

KPanComputes commented May 7, 2014

nbruin commented May 8, 2014

eviatarbach commented May 8, 2014

sagetrac-jkeitel mannequin commented May 21, 2014

sagetrac-jkeitel mannequin commented May 21, 2014

sagetrac-jkeitel mannequin commented May 21, 2014

rwst commented Jul 16, 2014

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nbruin commented Jul 16, 2014

kcrisman commented Jul 17, 2014

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