Branch cuts of functions on ComplexBalls

[mezzarobba]

Add support for the analytic flag required by the rigorous integration code in some methods of complex balls.

Depends on #24627
Depends on #24686

CC: @fredrik-johansson @videlec @cheuberg

Component: numerical

Author: Marc Mezzarobba

Branch/Commit: c827491

Reviewer: Vincent Delecroix

Issue created by migration from https://trac.sagemath.org/ticket/24717

[mezzarobba]

Commit: 39c78d1

[mezzarobba]

Author: Marc Mezzarobba

[mezzarobba]

comment:1

Let's hope I didn't get too many branch cuts wrong...

---

Last 10 new commits:

374a942	#24686 robustify, clean up, document rigorous integration using arb
376811d	doc markup fixes
0902f14	another doc fix
1d6ca9c	add a few more doctest examples
120bcb4	#24686 minor fixes
16962e5	real_arb: use arb 2.6+ comparison functions
ac4ba37	complex_arb: use arb 2.6+ comparison functions
b55e3c2	stop considering inexact balls equal to themselves
09f788c	Merge branch 'arb_cmp' into cuts
39c78d1	#24717 support the "analytic" flag in some methods of complex balls

[mezzarobba]

Branch: u/mmezzarobba/acb_cuts

[fredrik-johansson]

comment:2

This looks great. I would just suggest adding a pow method with this flag as well, and perhaps documenting some examples for .integral() where these are used (examples with .integral() could also be used as doctests for the individual methods).

[mezzarobba]

comment:3

Replying to @fredrik-johansson:

This looks great. I would just suggest adding a pow method with this flag as well,

Yes, and there are several other methods that could implement analytic=True--but I thought it would be better to have some easy ones now rather than all later. (Though, thinking of it, pow wouldn't be that hard to support.)

and perhaps documenting some examples for .integral() where these are used (examples with .integral() could also be used as doctests for the individual methods).

Either I don't understand what you mean, or there are already one or two such examples.

[fredrik-johansson]

comment:4

Replying to @mezzarobba:

Replying to @fredrik-johansson:

This looks great. I would just suggest adding a pow method with this flag as well,

Yes, and there are several other methods that could implement analytic=True--but I thought it would be better to have some easy ones now rather than all later. (Though, thinking of it, pow wouldn't be that hard to support.)

Indeed, but pow is perhaps the most important of them all...

and perhaps documenting some examples for .integral() where these are used (examples with .integral() could also be used as doctests for the individual methods).

Either I don't understand what you mean, or there are already one or two such examples.

Thanks, I missed that.

[mezzarobba]

comment:5

Replying to @fredrik-johansson:

Indeed, but pow is perhaps the most important of them all...

Yes, but it is also a bit harder to implement due to the need to share code with the __pow__, which participates in the coercion system... but ok, I'll try to see what I can do.

[sagetrac-git]

Changed commit from 39c78d1 to c97bfcf

[sagetrac-git]

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

c566ca7	complex_arb: sage.rings.integer.Integer -> Integer
c97bfcf	#24717 implement ComplexBall.pow(expo, analytic=...)

[tscrim]

comment:7

Replying to @mezzarobba:

Replying to @fredrik-johansson:

Indeed, but pow is perhaps the most important of them all...

Yes, but it is also a bit harder to implement due to the need to share code with the __pow__, which participates in the coercion system... but ok, I'll try to see what I can do.

If you implement __pow__, you bypass the coercion system altogether (similar to if you implement __mul__). ADDENDUM - Unless of course you call the coercion framework yourself.

[mezzarobba]

comment:8

Replying to @tscrim:

ADDENDUM - Unless of course you call the coercion framework yourself.

Yes, that's what both the previous code and my patch are doing.

[videlec]

comment:10

I agree with comment:2 that this would better be tested in conjunction with numerical integration.

Moreover, does it work correctly with function compositions? Could I integrate cos(exp(x)) using

lambda z,f: z.exp(f).cos(f)

If so, we shoud add examples in CBF.integral.

[fchapoton]

comment:11

does not apply

[sagetrac-git]

Changed commit from c97bfcf to 08cd02d

[sagetrac-git]

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

3b26420	#24717 support the "analytic" flag in some methods of complex balls
aad5a45	complex_arb: sage.rings.integer.Integer -> Integer
08cd02d	#24717 implement ComplexBall.pow(expo, analytic=...)

[mezzarobba]

comment:13

thanks, rebased!

[videlec]

comment:14

You should be using PY_NEW(Integer) and not Integer.__new__(Integer) (unless something changed around Cython about tp_new).

It would be nice to have usage example in the integral docstring.

[mezzarobba]

comment:15

Replying to @videlec:

You should be using PY_NEW(Integer) and not Integer.__new__(Integer) (unless something changed around Cython about tp_new).

Can you explain the difference? I thought Integer.__new__(Integer) had been working already for a long time, and

$ git grep 'Integer.__new__' | wc -l
95

It would be nice to have usage example in the integral docstring.

See above :-)

[videlec]

Reviewer: Vincent Delecroix

[vbraun]

comment:20

Merge conflict

[sagetrac-git]

Changed commit from d4cb5b9 to 93679c5

[sagetrac-git]

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

7023769	#24717 support the "analytic" flag in some methods of complex balls
8164105	complex_arb: sage.rings.integer.Integer → Integer
aa833ee	complex_arb: Integer.__new__ → PY_NEW
93679c5	#24717 implement ComplexBall.pow(expo, analytic=...)

[mezzarobba]

comment:22

Rebased (but without conflict for me: are you seeing a merge conflict with develop, or was that with additional changes?).

[vbraun]

comment:23

Merge conflict (wait for the next beta)

[sagetrac-git]

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

c921c89	#24717 support the "analytic" flag in some methods of complex balls
cb84329	complex_arb: sage.rings.integer.Integer → Integer
4b8df54	complex_arb: Integer.__new__ → PY_NEW
e174e59	#24717 implement ComplexBall.pow(expo, analytic=...)

[sagetrac-git]

Changed commit from 93679c5 to e174e59

[mezzarobba]

comment:25

Ok, it was a trivial conflict.

[vbraun]

comment:26

[sagelib-8.3.beta0] Error compiling Cython file:
[sagelib-8.3.beta0] ------------------------------------------------------------
[sagelib-8.3.beta0] ...
[sagelib-8.3.beta0]             sage: ZZ(CBF(i))
[sagelib-8.3.beta0]             Traceback (most recent call last):
[sagelib-8.3.beta0]             ...
[sagelib-8.3.beta0]             ValueError: 1.000000000000000*I does not contain a unique integer
[sagelib-8.3.beta0]         """
[sagelib-8.3.beta0]         cdef Integer res
[sagelib-8.3.beta0]             ^
[sagelib-8.3.beta0] ------------------------------------------------------------
[sagelib-8.3.beta0] 
[sagelib-8.3.beta0] sage/rings/complex_arb.pyx:1512:13: 'Integer' is not a type identifier

[sagetrac-git]

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

9395581	complex_arb: sage.rings.integer.Integer → Integer
19005f5	complex_arb: Integer.__new__ → PY_NEW
c827491	#24717 implement ComplexBall.pow(expo, analytic=...)

[sagetrac-git]

Changed commit from e174e59 to c827491

[mezzarobba]

comment:28

Sorry.

[vbraun]

Changed branch from u/mmezzarobba/acb_cuts to c827491