#14274: Numerical approximation of a divergent integral
-------------------------------+------------------------
Reporter: eviatarbach | Owner: burcin
Type: defect | Status: new
Priority: major | Milestone: sage-6.4
Component: calculus | Resolution:
Keywords: | Merged in:
Authors: | Reviewers:
Report Upstream: N/A | Work issues:
Branch: | Commit:
Dependencies: | Stopgaps:
-------------------------------+------------------------
Description changed by tmonteil:
Old description:
> Sage is numerically approximating this integral, even though it's
> divergent:
>
> {{{
> sage: integrate(x^3/sqrt(x^7+1), x, 1, oo).n()
> -2.0585298599983344
> }}}
>
> It seems that if we don't allow Maxima to detect its divergence
> (`numerical_integral` passes it directly to GSL), GSL will also fail on
> simpler divergent integrals:
>
> {{{
> sage: numerical_integral(1/x, 1, oo)
> (65.94931131932763, 8.156214940519742)
> sage: numerical_integral(x,1,oo)
> (-0.4999999993521234, 1.3615531480049015e-09)
> }}}
New description:
Sage is numerically approximating this integral, even though it's
divergent:
{{{
sage: integrate(x^3/sqrt(x^7+1), x, 1, oo).n()
-2.0585298599983344
}}}
It seems that if we don't allow Maxima to detect its divergence
(`numerical_integral` passes it directly to GSL), GSL will also fail on
simpler divergent integrals:
{{{
sage: numerical_integral(1/x, 1, oo)
(65.94931131932763, 8.156214940519742)
sage: numerical_integral(x,1,oo)
(-0.4999999993521234, 1.3615531480049015e-09)
}}}
See also [http://ask.sagemath.org/question/30620/sage-says-that-a
-divergent-integral-converges/ this ask question]:
{{{
sage: numerical_integral(e^(-x)/x,0,oo)
(37.191280375549404, 6.239196965189217)
}}}
--
--
Ticket URL: <http://trac.sagemath.org/ticket/14274#comment:11>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica,
and MATLAB
--
You received this message because you are subscribed to the Google Groups
"sage-trac" group.
To unsubscribe from this group and stop receiving emails from it, send an email
to [email protected].
To post to this group, send email to [email protected].
Visit this group at http://groups.google.com/group/sage-trac.
For more options, visit https://groups.google.com/d/optout.
