"integrate" fails to integrate a convergent integral (sin(x^2)/x^2).

[lfousse]

sage: N(integrate(sin(x^2)/(x^2), x, 1, infinity))
[...]
ValueError: Integral is divergent.

This worked fine until v4.5.3, fails from v4.6.1 onward. The expected output (with Maxima 5.29.1) is:

0.285736646322858

[kcrisman]

This is in Maxima. In the latest:

(%i1) integrate(sin(x^2)/(x^2),x,1,inf);

defint: integral is divergent.

It used to just return the integral.

(%i1) integrate(sin(x^2)/(x^2),x,1,inf);
                                 inf
                                /         2
                                [    sin(x )
(%o1)                           I    ------- dx
                                ]       2
                                /      x
                                 1

I think this integral should converge, right? By the p-test (well, with absolute values) for p=2? And numerical_integral agrees with your thing. This is probably a bug in Maxima, I'll put it there.

[kcrisman]

This is tracked at  this Maxima bug artifact.

[lfousse]

The absolute value of the function is dominated by 1/x^2, which is integrable on this particular interval.

[kcrisman]

You say potato, I say potahto :)

[zimmerma]

Karl-Dieter, please can you check the bug is fixed upstream? Laurent (Fousse) says it was caused by commit 59775311e53ef8a8fb5a3ad067a6c1cc153075d2 of maxima.

Paul

[kcrisman]

As far as I can tell, it's not fixed upstream - I have 5.25.1. The bug report had a resolution but it was something where they apparently typed in the wrong integral.

I am ignorant of how to use git and I can't do a text search for that commit line, unfortunately, so I'll take Laurent's word for it. I've put that info on the bug tracker as well.

[zimmerma]

Laurent tested with both 5.24.0 and the last git maxima version (commit 01679c735de525a39fa1d893f9e1d9f86bd65f91) and he got:

    % ./maxima-local
    Maxima 5.25post/branch-5_25-base-231-g01679c7
    http://maxima.sourceforge.net
    using Lisp CLISP 2.49 (2010-07-07)
    Distributed under the GNU Public License. See the file COPYING.
    Dedicated to the memory of William Schelter.
    The function bug_report() provides bug reporting information.
    (%i1) integrate(sin(x^2)/(x^2),x,1,inf);
    defint: integral is divergent.
     -- an error. To debug this try: debugmode(true);

Please can you add this to the maxima bug tracker?

Paul

[kcrisman]

Please can you add this to the maxima bug tracker?

I think that you may have missed the fact that I already did so in comment:4 three months ago. The person from Maxima who first looked at it must have tried something else incorrect, and I updated it yesterday with your information about the commit in question.

[kcrisman]

This is now fixed upstream.

(%i1) display2d:false;
(%o1) false
(%i2) float(integrate(sin(x^2)/(x^2),x,1,inf));
(%o2) -.1767766952966368*(.2733129188747918*%i-.5348723621187719)*%i
 +.1767766952966368*(-.2733129188747918*%i-.5348723621187719)*%i
 -.1767766952966368*(.2733129188747918*%i-.5348723621187719)
 -.1767766952966368*(-.2733129188747918*%i-.5348723621187719)
(%i3) integrate(sin(x^2)/(x^2),x,1,inf);
(%o3) %i*gamma_incomplete(-1/2,%i)/2^(5/2)
 -gamma_incomplete(-1/2,%i)/2^(5/2)-%i*gamma_incomplete(-1/2,-%i)/2^(5/2)
 -gamma_incomplete(-1/2,-%i)/2^(5/2)

[zimmerma]

Karl-Dieter, do you know in which release of Maxima this will be fixed? Or is there a simple patch we can integrate in Sage?

Paul

[kcrisman]

It's in the latest stable release, 5.27.0. Probably it will be easiest to just upgrade.

[dimpase]

Both new Maxima and  Wolfram Alpha give the value about 0.2857367, and not 0.28625044 (what you see in the ticket description). Changing the latter to reflect the reality.

[kcrisman]

This is fixed (and doctested) at #13364.