On Mon, Sep 28, 2020 at 9:03 PM Fernando Q. Gouvea <fqgou...@colby.edu> wrote:
>
> 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.
this is Maxima weirdness. Note that the following works without assumptions.
integrate(sin(t)/t,t,0,x,algorithm='sympy')
>
> The second weirdness is that the Taylor series is wrong! Taylor(Si(x),x,0,10)
> gives the same answer.
this is broken in 9.1, but seems to have been fixed in our latest betas.
Dima
>
> Fernando
>
>
> --
> ==================================================================
> Fernando Q. Gouvea
> Carter Professor of Mathematics
> Colby College
> Mayflower Hill 5836
> Waterville, ME 04901
> fqgou...@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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