Elementary and special functions for complex balls

[mezzarobba]

Wrap the elementary and special functions on complex balls provided by arb (as of arb 2.6; a few more functions were added since then). We typically wrap only the high-level versions with automatic algorithm choice, and provide no Python access to implementations variants.

Depends on #19063
Depends on #19152

Component: numerical

Keywords: arb

Work Issues: rebase over 7.0, doc. CBF

Author: Marc Mezzarobba

Branch/Commit: 3873da1

Reviewer: Dima Pasechnik

Issue created by migration from https://trac.sagemath.org/ticket/19082

[mezzarobba]

Commit: cdede7e

[mezzarobba]

Branch: u/mmezzarobba/19082-acb-funs

[mezzarobba]

Last 10 new commits:

b4e82aa	{Real,Complex}Ball: implement conversions to QQ
5e1cbda	ComplexBall: containment and overlapping predicates
d44c1b1	ComplexBall: abs(), arg()
62af563	RealBall: implement abs()
448bf24	{Real,Complex}Ball: implement {above,below}_abs()
11f545b	ComplexBall: elementary functions
91f95f7	ComplexBall: optimized powering methods
8e30743	ComplexBall: rising_factorial()
1d98780	ComplexBall: special functions
cdede7e	ComplexBall: additional special functions, from acb_hypgeom

[fredrik-johansson]

comment:3

In hypergeometric(), you could check if one of the upper parameters (typo: "paramaters") is equal to 1, and remove it. I guess you could also wrap hypgeom_m for 1F1 in this function. On the other hand, maybe it's best to wait until I put a function for pFq in Arb that takes care of all such special cases...

If you upgrade to Arb 2.7.0, you can add Bessel Y, Bessel I, polygamma, barnes_g, log_barnes_g, and some more hyperbolic functions of complex arguments.

[sagetrac-git]

Changed commit from cdede7e to c203cfb

[sagetrac-git]

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

c203cfb

ComplexBall: unify & improve hypergeometric functions

[sagetrac-git]

Changed commit from c203cfb to a64cde3

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1. This was a forced push. Last 10 new commits:

a872274	Trac #19063: Merge #18546 in preparation of doctest fix for 32 bit
8479dd2	Trac #19063: fix doctests on 32 bit
c022236	Merge branch 'acb-arith' into 6.9
0c0a630	ComplexBall: elementary functions
22adfbb	ComplexBall: optimized powering methods
ac54861	ComplexBall: rising_factorial()
cd8e074	ComplexBall: special functions
78a06c5	ComplexBall: additional special functions, from acb_hypgeom
3474911	ComplexBall: unify & improve hypergeometric functions
a64cde3	{Real,Complex}Ball: extend log() to accept a base

[mezzarobba]

comment:6

Rebased, added one commit.

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1. This was a forced push. Last 10 new commits:

91f9282	Trac #19063: Replace interval by ball in title
08d3d29	#19063 Implement reviewer's comments
d13e70f	Trac #19063: fix doctests on 32 bit
dd32bbd	ComplexBall: elementary functions
738240e	ComplexBall: optimized powering methods
3c0e32b	ComplexBall: rising_factorial()
8ee7c27	ComplexBall: special functions
df6f04e	ComplexBall: additional special functions, from acb_hypgeom
c1651ee	ComplexBall: unify & improve hypergeometric functions
74b5751	{Real,Complex}Ball: extend log() to accept a base

[sagetrac-git]

Changed commit from a64cde3 to 74b5751

[sagetrac-git]

Changed commit from 74b5751 to 7f456bd

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1. This was a forced push. Last 10 new commits:

a50fde3	Trac #19063: Replace interval by ball in title
e3233c5	#19063 Implement reviewer's comments
fa41787	Trac #19063: fix doctests on 32 bit
767ea82	ComplexBall: elementary functions
e7463cc	ComplexBall: optimized powering methods
fa17f51	ComplexBall: rising_factorial()
8cb73bd	ComplexBall: special functions
ca4b436	ComplexBall: additional special functions, from acb_hypgeom
07a8e06	ComplexBall: unify & improve hypergeometric functions
7f456bd	{Real,Complex}Ball: extend log() to accept a base

[sagetrac-git]

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

cc74b61	Trac #19152: fix one link and add SEEALSO
f51cd86	{Real,Complex}Ball: better document add_error()
49a2e9b	{Real,Complex}Ball: improve doc of is_nonzero()
154b65d	{real,complex}_arb: rm AUTHORS blocks
dfccd23	e22f4074539b1833befb7f24bd700a7fe11589a
73a928a	real_ball: one more instance of [non]zero -> True/False
3749cbb	{real,complex}_arb: clarify that b == b in arb too
660075f	Merge branch 'arb-misc' into arb-all
5038f5a	Merge in arb-misc (and 6.10.beta4) to fix minor conflict
9b147a9	real_arb: rst syntax

[sagetrac-git]

Changed commit from 7f456bd to 9b147a9

[mezzarobba]

Changed dependencies from #19063 to #19063, #19152

[sagetrac-git]

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

8d55755

complex_arb: remove unneeded imports from doctests

[sagetrac-git]

Changed commit from 9b147a9 to 8d55755

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1. This was a forced push. New commits:

a6db0a6

complex_arb: remove unneeded imports from doctests

[sagetrac-git]

Changed commit from 8d55755 to a6db0a6

[mezzarobba]

comment:14

Note that the branch appears to merge cleanly despite the red link, and to pass the testsuite despite the patchbot's report.

[cheuberg]

comment:15

I get the same doctest errors as the patchbot under 6.10.beta7, perhaps the upgrade to arb 2.7 induced the problem. (No problems under 6.10.beta4 where this patch is based).

Do the tests really pass for you when merging with 6.10.beta7?

[dimpase]

comment:20

it has to be rebased over 7.0, and I also don't see any explanation of what CBF is in the docs.

Note that CBF occurs earlier on in the doc, and it's not mentioned that it's the same thing as ComplexBallField. It would be good to mention in the top part of the doc, I think.

[dimpase]

Work Issues: rebase over 7.0, doc. CBF

[dimpase]

comment:21

you might just use public/19082 branch where I merged 7.0 into your branch, but docs I ask for are still for you to write.

[sagetrac-git]

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

3873da1

Document the shortcut CBF for ComplexBallField()

[sagetrac-git]

Changed commit from 235696d to 3873da1

[mezzarobba]

comment:23

Thanks for your comments!

Replying to @dimpase:

it has to be rebased over 7.0,

What do you mean? Unless I made a mistake while checking, the branch merges without conflict into 7.0.

and I also don't see any explanation of what CBF is in the docs.

Note that CBF occurs earlier on in the doc, and it's not mentioned that it's the same thing as ComplexBallField. It would be good to mention in the top part of the doc, I think.

Yes, that's similar to the situation with RR, CC, RIF... that aren't documented in the corresponding modules either. So I'm not convinced that this ticket is the right place to make the change. But I added a commit with a bit of documentation about CBF; please tell me if that's what you had in mind.

---

New commits:

3873da1

Document the shortcut CBF for ComplexBallField()

[dimpase]

comment:25

Replying to @mezzarobba:

Replying to @dimpase:

it has to be rebased over 7.0,

What do you mean? Unless I made a mistake while checking, the branch merges without conflict into 7.0.

I meant that I checked it out, instead of merging it into 7.0, and had to wait for 10 minutes for the re-builds to finish :-)

and I also don't see any explanation of what CBF is in the docs.

Note that CBF occurs earlier on in the doc, and it's not mentioned that it's the same thing as ComplexBallField. It would be good to mention in the top part of the doc, I think.

Yes, that's similar to the situation with RR, CC, RIF... that aren't documented in the corresponding modules either. So I'm not convinced that this ticket is the right place to make the change. But I added a commit with a bit of documentation about CBF; please tell me if that's what you had in mind.

That's exactly what I meant, thanks!

[vbraun]

comment:26

Reviewer name missing

[dimpase]

Reviewer: Dima Pasechnik

[mezzarobba]

comment:28

Thanks for the review!

[vbraun]

Changed branch from u/mmezzarobba/19082-acb-funs to 3873da1