integrating sin(t)/t

[Fernando Q. Gouvea]

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.

[David Lowry-Duda]

On Mon, Sep 28, 2020 at 04:03:48PM -0400, Fernando Q. Gouvea 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

That's odd. I get the same behavior in sage8.9 and my current develop
branch of sage.

Annoyingly, I notice that if you get the Taylor series as you might in a
calculus class, by first getting the Taylor series and then integrating
it term by term, it comes out differently (and correctly).

var('t')
littlef(t) = taylor(sin(t)/t, t, 0, 10)
bigf(x) = integrate(littlef(t), t, 0, x)
x |--> -1/439084800*x^11 + 1/3265920*x^9 - 1/35280*x^7 + 1/600*x^5 - 1/18*x^3 + x

I don't know why what you tried fails. This seems to be a bug.

On the trac, this seems closely related to

1. https://trac.sagemath.org/ticket/11164
2. https://trac.sagemath.org/ticket/30389

- DLD

--
David Lowry-Duda <da...@lowryduda.com> <davidlowryduda.com>

[Emmanuel Charpentier]

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,

​

[Eric Gourgoulhon]

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.

[Dima Pasechnik]

On Mon, Sep 28, 2020 at 9:03 PM Fernando Q. Gouvea <fqgo...@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
> 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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[Fernando Gouvea]

I'm running Sage 9.0 on a Windows 10 machine.

I get the same incorrect series from the built-in sin_integral function, so the problem is not the integration.

sage: taylor(sin_integral(x),x,0,10)

73/466560*x^9 - 127/35280*x^7 + 31/600*x^5 - 7/18*x^3 + x

Fernando

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-- 
=============================================================
Fernando Q. Gouvea         http://www.colby.edu/~fqgouvea
Carter Professor of Mathematics
Dept. of Mathematics and Statistics
Colby College              
5836 Mayflower Hill        
Waterville, ME 04901       

"Verily and forsooth," replied Goodgulf darkly. "In the past year
strange and fearful wonders I have seen. Fields sown with barley reap
crabgrass and fungus, and even small gardens reject their artichoke
hearts. There has been a hot day in December and a blue
moon. Calendars are made with a month of Sundays and a blue-ribbon
Holstein bore alive two insurance salesmen. The earth splits and the
entrails of a goat were found tied in square knots. The face of the
sun blackens and the skies have rained down soggy potato chips."
  -- Harvard Lampoon, "Bored of the Rings"

[Fernando Gouvea]

Good news! When is 9.2 expected to be ready?

Fernando

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[Henri Girard]

Now if you build it :)

To view this discussion on the web visit https://groups.google.com/d/msgid/sage-support/5214e93f-8636-38a6-127b-4d7e5d5e8e1c%40colby.edu.

[Dima Pasechnik]

On Tue, Sep 29, 2020 at 1:36 PM Henri Girard <henri....@gmail.com> wrote:
>
> Now if you build it :)
>

TBF, building Sage on Windows is less than trivial. :-(

> To view this discussion on the web visit https://groups.google.com/d/msgid/sage-support/f77c7b29-b5cd-1df8-547e-81dc04eb9759%40gmail.com.

[Eric Gourgoulhon]

Le mardi 29 septembre 2020 à 14:27:38 UTC+2, fqgo...@colby.edu a écrit :

Good news! When is 9.2 expected to be ready?

Sage 9.2 should be released within a few weeks (the beta cycle is almost over and the release candidate cycle should start soon). Meanwhile, you can take a look at the new features:  https://wiki.sagemath.org/ReleaseTours/sage-9.2

Best wishes,

Eric.

[Karima Shahzad]

Do you recommend Sage-9.2 for the users if they're working with Sage-9.1?

[slelievre]

2020 21:18:46 UTC, Karima Shahzad:

>

> Do you recommend Sage-9.2 for the users if they're working with Sage-9.1?

Preliminary release notes to help you decide:

  https://wiki.sagemath.org/ReleaseTours/sage-9.2

Personally I would recommend upgrading to the latest

development version, which has lots of improvements,

if you don't mind building it from source.

That's the version I use daily.