I agree with the general analysis, but I think the statement "Any answer
that supplies only one answer is wrong." goes too far. It may be the case
that sage works inherently in the complex domain, and is unable to
understand that elementary calculus and certain other fields want to remain
in the real domain, but it would not be "wrong" to have a program that
operates differently. It is not "wrong" to work in the real domain and
understand that "\sqrt{2}" means 1.414... (the "principal square root"),
not -1.414... Indeed, I think sage would need to be able to do to be
really useful for most 1st semester calculus students. In this situation,
there is a unique correct answer, so returning two answers is "wrong".
On Wednesday, August 5, 2020 at 12:59:01 PM UTC-6, rjf wrote:
>
> 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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