sqrt(n) conversion/comparison

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Ralf Stephan

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Feb 26, 2015, 3:41:24 AM2/26/15
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Hi,

with current Sage,
sage: bool(sqrt(2)==CC(sqrt(2)))
False

You would expect that this leads to
sage: sqrt(2) in CC
False
but due to a bug I'm fixing atm in #12967 this returns True.
However, now that it's fixed I'm faced with the question if
answer to both really should be False. If one doctest in parent.py
is right both should be True. But how could Sage see that equation
holds if
sage: CC(sqrt(2))
1.41421356237309
sage
: sqrt(2).n()
1.41421356237310
so either there is a bug in SR+CC or the abovementioned doctest
is wromg.

What do you think?

Regards,

Vincent Delecroix

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Feb 26, 2015, 3:50:40 AM2/26/15
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Hello,

There is something wrong

sage: bool(RR(pi) == pi)
True
sage: bool(RR(golden_ratio) == golden_ratio)
True

which is fine to me. You coerce to the field with less precision. But

sage: bool(RR(sqrt(2)) == sqrt(2))
False
sage: sqrt(2).n() == RR(sqrt(2))
True
sage: RR(sqrt(2)) == CC(sqrt(2))
False

which is very wrong.

Vincent

2015-02-26 9:41 UTC+01:00, Ralf Stephan <gtr...@gmail.com>:
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Ralf Stephan

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Feb 26, 2015, 4:02:08 AM2/26/15
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On Thursday, February 26, 2015 at 9:50:40 AM UTC+1, vdelecroix wrote:
sage: bool(RR(sqrt(2)) == sqrt(2))
False
sage: sqrt(2).n() == RR(sqrt(2))
True
These two come from bool(sqrt(2)==sqrt(2).n()) being False I think
(because Maxima is involved here) but this is different than 

sage: bool(sqrt(2).n()==CC(sqrt(2)))
False

Vincent Delecroix

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Feb 26, 2015, 4:10:03 AM2/26/15
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We also have

sage: RR(tan(pi/20)) == CC(tan(pi/20))
False

But it seems right for cos, sin, exp, atan, cosh, sinh. Is there a way
to test all symbolic functions?

2015-02-26 10:02 UTC+01:00, Ralf Stephan <gtr...@gmail.com>:

Ralf Stephan

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Feb 26, 2015, 10:48:50 AM2/26/15
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Assuming fp values cannot be equal, would it make more sense
to test elementship in CC by implementing ComplexField.__contains__()
instead of trusting Python or Maxima == ?

Ralf Stephan

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Feb 27, 2015, 11:36:52 AM2/27/15
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On Thursday, February 26, 2015 at 10:10:03 AM UTC+1, vdelecroix wrote:
We also have

sage: RR(tan(pi/20)) == CC(tan(pi/20))
False
The utility code in #17866 uncovers more:

sage: bool(csc(2)==CC(csc(2)))
False
sage: bool(csch(2)==CC(csch(2)))
False
sage: bool(arcsec(2)==CC(arcsec(2)))
False
sage: bool(arcsech(pi/10)==CC(arcsech(pi/10)))
False
sage: bool(arcsech(2)==CC(arcsech(2)))
AttributeError: 'sage.rings.complex_interval.ComplexIntervalFieldElement' object has no attribute 'arcsech'
sage: bool(coth(2)==CC(coth(2)))
False

and so on (argument pi/10): zetaderiv, spherical_harmonic, dilog, elliptic_pi, exp_integral_e, 
(gen_)laguerre, Ei.

Which of these do not use Maxima? 

Nils Bruin

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Feb 27, 2015, 1:58:24 PM2/27/15
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On Friday, February 27, 2015 at 8:36:52 AM UTC-8, Ralf Stephan wrote:
Which of these do not use Maxima?
 
You can figure that out by making sure that maxima doesn't work anymore:

sage: integrate(x,x) #trigger maxima initialization
1/2*x^2
sage: sage.libs.ecl.shutdown_ecl() #any existing ecl objects are now corrupted
sage: integrate(x,x)
RuntimeError: ECL says: Detected access to an invalid or protected memory address.

or alternatively (this has a lighter touch)

sage: integrate(x,x)
1/2*x^2
sage: sage.calculus.calculus.maxima=None
sage: integrate(x,x)
AttributeError: 'NoneType' object has no attribute 'sr_integral'

A little warning: if we have a very bad try/except somewhere that catches arbitrary RuntimeError or AttributeError, the above trick might not quite work. To be completely sure, you should probably patch ecllib to log something anytime it gets called.

Ralf Stephan

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Feb 28, 2015, 4:34:38 AM2/28/15
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On Friday, February 27, 2015 at 7:58:24 PM UTC+1, Nils Bruin wrote:
On Friday, February 27, 2015 at 8:36:52 AM UTC-8, Ralf Stephan wrote:
Which of these do not use Maxima?
 
You can figure that out by making sure that maxima doesn't work anymore:

Thanks. It appears to have nothing to do with Maxima. There are two different
groups of these errors: one is associated with class HyperbolicFunction and
the comparison fails always with those functions. The other affects all functions
and the comparison fails on varying conditions, like the argument(s) being
expressions involving symbolic constants, e.g.

sage: ex=sin(1+pi)
sage: bool(ex==CC(ex))
False

Maybe it's FP noise, no idea. Since it only affects "ex in CC" in a ticket branch
I tend to turn to more important things.
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