Branch cuts of functions on ComplexBalls

[mmezzarobba]

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

[mmezzarobba]

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

[fredrik.johansson]

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).

[mmezzarobba]

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]

Replying to mmezzarobba:

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.

[mmezzarobba]

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.

[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]

Replying to mmezzarobba:

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.

[mmezzarobba]

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.

[vdelecroix]

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.

[chapoton]

does not apply

[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=...)

[mmezzarobba]

thanks, rebased!

[vdelecroix]

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.

[mmezzarobba]

Replying to vdelecroix:

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 :-)

[vdelecroix]

Replying to mmezzarobba:

Replying to vdelecroix:

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

On the other hand, this is the current PY_NEW documentation

    Return ``t.__new__(t)``.  This works even for types like
    :class:`Integer` where we change ``tp_new`` at runtime (Cython
    optimizations assume that ``tp_new`` doesn't change).

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

See above :-)

Oups.

[mmezzarobba]

Replying to vdelecroix:

On the other hand, this is the current PY_NEW documentation

Ok. This has nothing to do with this ticket (I'm just changing s.r.i.Integer to Integer in an existing call), but let's be safe.

[git]

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

​9305c90	#24717 support the "analytic" flag in some methods of complex balls
​f3dedd1	complex_arb: sage.rings.integer.Integer → Integer
​d8a698e	complex_arb: Integer.__new__ → PY_NEW
​d4cb5b9	#24717 implement ComplexBall.pow(expo, analytic=...)

[vbraun]

Merge conflict

[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=...)

[mmezzarobba]

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

[vbraun]

Merge conflict (wait for the next beta)

[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=...)

[mmezzarobba]

Ok, it was a trivial conflict.

[vbraun]

[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

[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=...)

[mmezzarobba]

Sorry.