I confirm the issue with the Taylor series with Sage 9.1. Fortunately, the
bug seems to have been fixed for Sage 9.2. As Emmanuel, I get the correct
Taylor series with Sage 9.2.beta13.
Le mardi 29 septembre 2020 à 09:36:09 UTC+2, Emmanuel Charpentier a écrit :
> I can’t reproduce your problem :
>
> sage: sage.version.version
> '9.2.beta13'
> sage: var('t')
> t
> sage: assume(x>0)
> sage: f(x)=integrate(sin(t)/t,t,0,x)
> sage: f
> x |--> sin_integral(x)
> sage: taylor(f(x),x,0,10)
> 1/3265920*x^9 - 1/35280*x^7 + 1/600*x^5 - 1/18*x^3 + x
>
> My platform is Debian testing running on core i7 + 16 GB RAM ; sage is
> built to use as much system packages as possible. hat are your platforms ?
>
> HTH,
> Le lundi 28 septembre 2020 à 22:03:56 UTC+2, fqgo...@colby.edu a écrit :
>
>> I am trying to see how to do a standard calculus exercise in Sage. I want
>> a power series for the integral of sin(x)/x. I tried:
>>
>> sage: var('t')
>> t
>> sage: assume(x>0)
>> sage: f(x)=integrate(sin(t)/t,t,0,x)
>> sage: f
>> x |--> sin_integral(x)
>> sage: taylor(f(x),x,0,10)
>> 73/466560*x^9 - 127/35280*x^7 + 31/600*x^5 - 7/18*x^3 + x
>>
>> The first weirdness is that Sage can't compute the integral unless I add
>> the "assume(x>0)"; I'm not sure why.
>>
>> The second weirdness is that the Taylor series is wrong!
>> Taylor(Si(x),x,0,10) gives the same answer.
>>
>> Fernando
>>
>>
>> --
>> ==================================================================
>> Fernando Q. Gouvea
>> Carter Professor of Mathematics
>> Colby College
>> Mayflower Hill 5836
>> Waterville, ME 04901 fqgo...@colby.edu
>> http://www.colby.edu/~fqgouvea
>>
>> The object of opening the mind, as of opening the mouth, is to shut it
>> again on something solid.
>> -- G. K. Chesterton, Autobiography.
>>
>>
>>
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