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 <[email protected]
> <javascript:>> 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]
>>
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>>
>
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