@rjf Isn't the square root defined to be positive?
Sure: x^2=y <=> x=+/-sqrt(y)
But I think you would never consider f(x):=sqrt(x) to have the codomain of
all negative numbers.
At least I would expect a CAS to interpret a square root to be positive.
rjf schrieb am Mittwoch, 5. August 2020 um 20:59:01 UTC+2:
> 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]
>>>>
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>>>> <https://groups.google.com/d/msgid/sage-devel/487d0db8-5711-41a8-a7d4-1548286b5573n%40googlegroups.com?utm_medium=email&utm_source=footer>
>>>> .
>>>>
>>>
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