There are two square roots. In this (classic) integration example/bug, a
choice has
to be made. You know that 4 has two square roots, -2 and 2.
The integrand, which also can be rewritten as sqrt ( 4-4*cos(x/2)^2) ,
has 2 square roots.
Therefore there are two potential different values for the integral. Any
answer
that supplies only one answer is wrong.
On Tuesday, August 4, 2020 at 1:56:16 AM UTC-7, Emmanuel Charpentier wrote:
>
> BTW :
>
> sage: integrate(sqrt(2-2*cos(x)),x, algorithm="fricas")
> -2*(cos(x) + 1)*sqrt(-2*cos(x) + 2)/sin(x)
> sage: integrate(sqrt(2-2*cos(x)),x, algorithm="mathematica_free")
> -2*sqrt(-2*cos(x) + 2)*cot(1/2*x)
>
> Both are visually (on plot) and numerically correct ; both differentiate
> to expressions very hard to show equal to the original function.
>
> HTH,
>
> Le lundi 3 août 2020 10:50:12 UTC+2, Dima Pasechnik a écrit :
>
> This is a well-known bug in Sage. A workaround is to set the domain to
>> "real":
>>
>> sage: maxima_calculus.eval('domain: real');
>> sage: integrate(sqrt(2-2*cos(x)),x,0,2*pi) # correct answer
>> 8
>>
>> sage: maxima_calculus.eval('domain: complex'); # restore the state back
>> sage: integrate(sqrt(2-2*cos(x)),x,0,2*pi) # now here the result is again
>> wrong, of course
>> 0
>>
>>
>> On Sun, Aug 2, 2020 at 5:26 PM Nico Guth <nico.j...@gmail.com> wrote:
>>
>>> Hi,
>>>
>>> I discovered a bug, where a definite integral is calculated wrong!
>>> WolframAlpha result for comparison.
>>>
>>> Code:
>>> integrate(sqrt(2-2*cos(x)),x,0,2*pi)
>>>
>>> Also if I type show() instead of print() SageMathCell just doesn't show
>>> anything.
>>>
>>> Also the form in which the indefinite integral is given is not very
>>> pretty.
>>> WolframAlpha does a much better job simplifying.
>>>
>>> [image: sage_wrong_integral.png][image: sage_wrong_integral_wolfram.png]
>>> [image: sage_wrong_integral_wolfram_2.png]
>>>
>>> --
>>> You received this message because you are subscribed to the Google
>>> Groups "sage-devel" group.
>>> To unsubscribe from this group and stop receiving emails from it, send
>>> an email to sage-...@googlegroups.com.
>>> To view this discussion on the web visit
>>> https://groups.google.com/d/msgid/sage-devel/487d0db8-5711-41a8-a7d4-1548286b5573n%40googlegroups.com
>>>
>>> <https://groups.google.com/d/msgid/sage-devel/487d0db8-5711-41a8-a7d4-1548286b5573n%40googlegroups.com?utm_medium=email&utm_source=footer>
>>> .
>>>
>>
>
--
You received this message because you are subscribed to the Google Groups
"sage-devel" group.
To unsubscribe from this group and stop receiving emails from it, send an email
to sage-devel+unsubscr...@googlegroups.com.
To view this discussion on the web visit
https://groups.google.com/d/msgid/sage-devel/74e290bf-d169-4f9a-b999-6196c078b693o%40googlegroups.com.
