blatantly wrong symbolic integral (via maxima) - bug report

[William Stein]

Hi,

In Sage, this gives a totally wrong answer:

sage: f(x) = sqrt(2+sqrt(2+sqrt(2+2*cos(5*sqrt(x)+4))))*x^(-1/2)
sage: integral(f, x)

It takes about 10 seconds, and plotting f.derivative(x) - f makes it
clear the answer is wrong.

I tried sympy, but after several minutes it didn't return a result.

Here's a public worksheet that illustrates things:

https://cloud.sagemath.com/projects/4a5f0542-5873-4eed-a85c-a18c706e8bcd/files/support/2015-02-12-121421-integral.sagews

--
William (http://wstein.org)

[R. Andrew Ohana]

It is wrong, but not as wrong as you make it out to be. Your function is f = abs(h), where h = 2*cos(5/8*sqrt(x)+1/2)/sqrt(x). Rather that integrating f, it seems to have integrated h.

[William Stein]

Andrew -- very good point! That's not nearly as bad as I made it out.
Thanks,

-- William

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--
William (http://wstein.org)

[Rodrigo Sambade Saá]

Dear William,

Andrew is wrong.

Best wishes,

Rodrigo 

[Emmanuel Charpentier]

Indeed. But no need for Mathematica :

sage: f(x)= sqrt(2+sqrt(2+sqrt(2+2*cos(5*sqrt(x)+4))))*x^(-1/2)

sage: h(x)= 2*cos(5/8*sqrt(x)+1/2)/sqrt(x)

sage: P1=plot(f(x),(x,0,120),ymin=-0.5, ymax=0.85)

sage: P2=plot(h(x),(x,0,120),ymin=-0.5, ymax=0.85)

sage: P1+P2

BTW: How did you came to exhume a 4-years old thread ? 

Le samedi 24 août 2019 14:17:48 UTC+2, Rodrigo Sambade Saá a écrit :

Dear William,

Andrew is wrong.

Best wishes,

Rodrigo 

El jue., 12 feb. 2015 a las 21:57, William Stein (<wst...@gmail.com>) escribió:

On Thu, Feb 12, 2015 at 12:55 PM, R. Andrew Ohana
<andre...@gmail.com> wrote:
> It is wrong, but not as wrong as you make it out to be. Your function is f =
> abs(h), where h = 2*cos(5/8*sqrt(x)+1/2)/sqrt(x). Rather that integrating f,
> it seems to have integrated h.

Andrew -- very good point!  That's not nearly as bad as I made it out.
  Thanks,

 -- William

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> You received this message because you are subscribed to the Google Groups
> "sage-support" group.
> To unsubscribe from this group and stop receiving emails from it, send an

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[Emmanuel Charpentier]

BTW, both Fricas and Mathematica give expressions whose derivatives numerically coincide with f(x) on the range (0..120), up to numerical noise. But I haven't been able to prove that those expressions (or their derivatives) are equal, nor than these derivattives are equal to f(x).

HTH,

[Rodrigo Sambade Saá]

I swear now it's worth reviving this.

A user on Math StackExchange found the steps to integrate the function. Now it's as simple as implementing it in Sage.

Best wishes,

Rodrigo

Rodrigo Sambade

rodrigos...@gmail.com

+34 608 030 077

Let's take care of the environment. Think at least twice before printing this e-mail: The environment is everyone's responsibility.

El mié, 9 feb 2022 a las 20:52, Rodrigo Sambade Saá (<rodrigos...@gmail.com>) escribió:

On Wed, Feb 9 2022 at 20:49, Rodrigo Sambade Saá (<rodrigos...@gmail.com>) wrote:

I swear now it's worth reviving this.

A user on Math StackExchange found the steps to integrate the function. Now it's as simple as implementing it in Sage.

Best wishes,

Rodrigo

Rodrigo Sambade

rodrigos...@gmail.com

+34 608 030 077

Let's take care of the environment. Think at least twice before printing this e-mail: The environment is everyone's responsibility.

El sáb, 24 ago 2019 a las 12:53, Rodrigo Sambade Saá (<rodrigos...@gmail.com>) escribió:

Dear William,

Sorry 🙏, the link is wrong. This is the correct one: |2*cos(5/8*sqrt(x)+1/2)/sqrt(x)| = sqrt(2+sqrt(2+sqrt(2+2*cos(5*sqrt(x)+4))))*x^(-1/2): https://www.wolframalpha.com/input/?i=%7C2*cos%285%2F8*sqrt%28x%29%2B1%2F2%29%2Fsqrt%28x%29%7C+%3D+sqrt%282%2Bsqrt%282%2Bsqrt%282%2B2*cos%285*sqrt%28x%29%2B4%29%29%29%29*x%5E%28-1%2F2%29

Best wishes, 

Rodrigo