Make RealBallField useful

[mezzarobba]

After #17194, implement more comprehensive Arb bindings as part of RealBallField/RealBall.

Component: numerical

Author: Marc Mezzarobba

Branch/Commit: 37bcb77

Reviewer: Fredrik Johansson

Issue created by migration from https://trac.sagemath.org/ticket/17786

[fredrik-johansson]

comment:1

Regarding the "What is going on?!" comment: transcendental functions are not quite deterministic due to internal caches. In this case, doing something that results in an internal recomputation of log(2) to higher precision leads to a slightly more accurate value later on.

This is something that I could fix with a bit of effort.

In any case, output could also change slightly between versions due to changes in algorithms. That's an inherent drawback of doing doctests this way...

[mezzarobba]

comment:2

Replying to @fredrik-johansson:

Regarding the "What is going on?!" comment: transcendental functions are not quite deterministic due to internal caches. In this case, doing something that results in an internal recomputation of log(2) to higher precision leads to a slightly more accurate value later on.

Good to know, I wasn't aware of that.

This is something that I could fix with a bit of effort.

Unless you have other users that need it, I don't think it is worth the effort.

In any case, output could also change slightly between versions due to changes in algorithms. That's an inherent drawback of doing doctests this way...

Yes. But I thought I'd first go with a version that tested the exact output, and we could always make something more sophisticated later on if some of the outputs really changed.

Thanks for your comments!

[cheuberg]

comment:3

Two remarks:

• Shouldn't we use bint for those C functions returning an integer which is meant as a boolean? In that case, bool could be omitted in the Python methods.

• Should we really expose a function is_nonzero? We have to implement __nonzero__ anyway.

[mezzarobba]

comment:4

Replying to @cheuberg:

Two remarks:

• Shouldn't we use bint for those C functions returning an integer which is meant as a boolean? In that case, bool could be omitted in the Python methods.

Yes, indeed, thanks. I just copied the C prototypes without thinking...

• Should we really expose a function is_nonzero? We have to implement __nonzero__ anyway.

RIF intervals implement __nonzero__ with the meaning of "not exactly zero". So I think we need both if we want to stay compatible with them. But then I'm not sure doing things that way in RIF was the wisest choice in the first place...

[cheuberg]

comment:5

Replying to @mezzarobba:

Replying to @cheuberg:

• Should we really expose a function is_nonzero? We have to implement __nonzero__ anyway.

RIF intervals implement __nonzero__ with the meaning of "not exactly zero". So I think we need both if we want to stay compatible with them. But then I'm not sure doing things that way in RIF was the wisest choice in the first place...

I think we should not have methods __nonzero__ and is_nonzero with different behaviour.

[cheuberg]

Work Issues: Merge 17194, 17811 and rewrite doctest

[cheuberg]

comment:6

#17194 needs to be merged. It would be good to merge #17811 and to replace its doctest by a simpler variant using the arithmetic operations introduced here.

[sagetrac-git]

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

760e2e2	RBF: separate conversions from initialization of elements
464c601	RealBall: def accuracy
e3453ce	rst syntax fixes
624a609	RBF: more conversions
26d4130	RealBall: better error handling
ef6d130	RealBall: simple predicates
dd15270	RealBall: more comparisons
d1c6169	RealBall: contains()
b54dd6c	RealBall: sqrt and friends
2eec53a	RealBall: elementary functions

[sagetrac-git]

Changed commit from 21bee7d to 2eec53a

[sagetrac-git]

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

fae4e89	RBF: separate conversions from initialization of elements
01af6a9	RealBall: def accuracy
b1d45da	rst syntax fixes
0101f43	RBF: more conversions
cd8b230	RealBall: better error handling
6ff081a	RealBall: simple predicates
1af1a53	RealBall: more comparisons
5e00b8d	RealBall: contains()
b76df7f	RealBall: sqrt and friends
0b34a7a	RealBall: elementary functions

[sagetrac-git]

Changed commit from 2eec53a to 0b34a7a

[sagetrac-git]

Changed commit from 0b34a7a to 1c8de12

[sagetrac-git]

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

2f2e95e	RealBall: "return nonzero" → "return True" (for consistency)
d65e84e	RealBall: rename arc-trig functions
ca2f5f9	RealBall: adapt tests do deal with nondeterministic output
1c8de12	RealBall: minor changes to docstrings and comments

[fredrik-johansson]

Changed branch from u/mmezzarobba/arb to u/fredrik.johansson/arb

[mezzarobba]

Changed commit from 1c8de12 to 54340f0

[mezzarobba]

Last 10 new commits:

b518474	RealBall: contains()
d28e6c2	RealBall: sqrt and friends
8ea7a07	RealBall: elementary functions
39c7c96	RealBall: "return nonzero" → "return True" (for consistency)
17bf841	RealBall: rename arc-trig functions
f8e2db9	RealBall: adapt tests do deal with nondeterministic output
71a82e7	RealBall: minor changes to docstrings and comments
9732629	RealBall: fix comparisons involving special values
91591bf	RealBall: some special functions
54340f0	RealBallField: some ball function of non-ball arguments

[mezzarobba]

Changed branch from u/fredrik.johansson/arb to u/mmezzarobba/arb

[sagetrac-git]

Changed commit from 54340f0 to 9ab0759

[sagetrac-git]

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

9ab0759

RealBall: polylogs

[sagetrac-git]

Changed commit from 9ab0759 to 6d44ccb

[sagetrac-git]

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

6d44ccb

RealBall: more functions

[sagetrac-git]

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

5a14202

RealBall: changing my mind about nan1 == nan2 when nan1 is nan2

[sagetrac-git]

Changed commit from 6d44ccb to 5a14202

[sagetrac-git]

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

f5ed6b1	RealBallField: misc Parent stuff
5d13026	RealBall: TODO

[sagetrac-git]

Changed commit from 5a14202 to 5d13026

[sagetrac-git]

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

528fcda

RealBall: mid, rad as balls

[sagetrac-git]

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

b8036f2	real_arb: let's no longer call the bindings elementary :-)
19aee15	Fix coercion RBF → InfinityRing when arb is not installed

[sagetrac-git]

Changed commit from 28d63d8 to 19aee15

[sagetrac-git]

Changed commit from 19aee15 to 88d770d

[sagetrac-git]

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

88d770d

real_arb: rst syntax fixes

[sagetrac-git]

Changed commit from 88d770d to 0f67513

[sagetrac-git]

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

edf95ab	RealBall: mid, rad as balls
9469ce3	RealBall: fix an incorrect statement copied from the arb documentation
5183126	RealBall: remove duplicate methods introduced by mistake
8c1df6b	RealBall: comparisons with symbolic ±∞
be93dba	RealBall: floor(), ceil()
36801c6	RealBall: allow RealNumbers as radii
9e06cce	real_arb: let's no longer call the bindings elementary :-)
a6d68c6	Fix coercion RBF → InfinityRing when arb is not installed
4046200	real_arb: rst syntax fixes
0f67513	real_arb: mark all tests as optional

[sagetrac-git]

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

1c6aa0c	RealBall: improve conversion to MPFI intervals
2dd40b7	real_arb: mark all tests as optional

[sagetrac-git]

Changed commit from 0f67513 to 2dd40b7

[mezzarobba]

Changed work issues from Merge 17194, 17811 and rewrite doctest to none

[mezzarobba]

Author: Marc Mezzarobba

[sagetrac-git]

Changed commit from 2dd40b7 to 37bcb77

[sagetrac-git]

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

760c2d5	real_arb: let's no longer call the bindings rudimentary :-)
91dddf9	Fix coercion RBF → InfinityRing when arb is not installed
b4f922b	real_arb: rst syntax fixes
1134261	RealBall: improve conversion to MPFI intervals
441f1c4	RealBall: remove superfluous bool() added back by mistake
37bcb77	real_arb: mark all tests as optional

[fredrik-johansson]

comment:27

Looks good to me.

Btw, I'm unable to build the reference manual, but this is presumably some problem with my Sage install and unrelated to this ticket.

[fredrik-johansson]

Reviewer: fredrik.johansson

[mezzarobba]

comment:28

Thanks for the review!

[vbraun]

comment:29

Reviewer name is supposed to be the real name, not the trac account name

[fredrik-johansson]

Changed reviewer from fredrik.johansson to Fredrik Johansson

[vbraun]

Changed branch from u/mmezzarobba/arb to 37bcb77