FWIW, I found variations of the same problematic behaviour, so far in 
sahe(-maxima), mpmath and R. See this worksheet 
<https://cloud.sagemath.com/projects/ec50c702-c618-4167-be42-ec4381d49144/files/Minimal%20numerical%20integration%20problem%20demonstration.sagews>
 
for examples...

--
Emmanuel Charpentier
Where did I put those syndesmotomes ?

Le jeudi 16 avril 2015 17:02:14 UTC+2, Emmanuel Charpentier a écrit :
>
> Indeed, using quad (hich is from mpbath, by the way (by bad !)) is easy. 
> But it doesn't solve my problem : it *worsens* it. I must catch special 
> cases of conversions from rationals to reals. See the updated worksheet 
> (still public).
>
> --
> Emmanuel Charpentier
> Contemplating reverting to dental surgery (simpler...)
>
> Le jeudi 16 avril 2015 14:48:08 UTC+2, William a écrit :
>>
>> On Thu, Apr 16, 2015 at 5:45 AM, Emmanuel Charpentier 
>> <emanuel.c...@gmail.com> wrote: 
>> > Thank you very much, William. The interface of Sagemath cloud is a bit 
>> ... 
>> > cloudy... for me. 
>> > 
>> > I'm pursuing my problem. The numerical_integral docstring shows that 
>> this 
>> > function has arguments looking suspiciously like Maxima's quad_qag*, 
>> > interface to quadpack. And indeed, Maxima has the same problem 
>> > (documentation on the above worksheet to come). 
>> > 
>> > Now sympy (part of sage) has a nice "quad" function for (low-dimension) 
>> > quadrature. If I could figure a way to use it from sage... 
>>
>> You should be able to just use sympy from Sage, following any of their 
>> examples/documentation: 
>>
>>  http://docs.sympy.org/dev/modules/mpmath/calculus/integration.html 
>>
>> ?? 
>>
>> > 
>> > Are you aware of other numerical integration/quadrature function in 
>> > Sagemath's components (allowing for infinite bounds) that could be used 
>> for 
>> > this purpose ? 
>>
>>
>>
>> > 
>> > To be continued, 
>> > 
>> > -- 
>> > Emmanuel Charpentier 
>> > 
>> > Le jeudi 16 avril 2015 14:22:06 UTC+2, William a écrit : 
>> >> 
>> >> On Thu, Apr 16, 2015 at 3:27 AM, Emmanuel Charpentier 
>> >> <emanuel.c...@gmail.com> wrote: 
>> >> > Never mind the plots (you can paste plots in the Web editor, but 
>> they do 
>> >> > not 
>> >> > record...). 
>> >> > 
>> >> > Instead, see this minimal example on Sagemath cloud: 
>> >> 
>> >> Hi -- content is private by default on SageMathCloud (unlike github). 
>> >> I've taken the liberty to make just that one worksheet public 
>> >> 
>> >> 
>> >> 
>> https://cloud.sagemath.com/projects/ec50c702-c618-4167-be42-ec4381d49144/files/Minimal%20numerical%20integration%20problem%20demonstration.sagews
>>  
>> >> 
>> >> by clicking "i", then "Share publicly". 
>> >> 
>> >> > 
>> >> > Any idea ? 
>> >> > 
>> >> > -- 
>> >> > Emmanuel Charpentier 
>> >> > 
>> >> > -- 
>> >> > You received this message because you are subscribed to the Google 
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>> >> > To post to this group, send email to sage-s...@googlegroups.com. 
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>> >> 
>> >> 
>> >> 
>> >> -- 
>> >> William (http://wstein.org) 
>> > 
>> > -- 
>> > You received this message because you are subscribed to the Google 
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>>
>>
>> -- 
>> William (http://wstein.org) 
>>
>

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