#14274: Numerical approximation of a divergent integral
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Reporter: eviatarbach | Owner: burcin
Type: defect | Status: new
Priority: major | Milestone: sage-5.9
Component: calculus | Resolution:
Keywords: | Work issues:
Report Upstream: N/A | Reviewers:
Authors: | Merged in:
Dependencies: | Stopgaps:
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Description changed by eviatarbach:
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
> sage: numerical_integral(x^3/sqrt(x^7+1), 1, oo)
> (-2.0585298599983344, 1.1214140727133781e-11)
> }}}
>
> `numerical_integral` also fails on simpler divergent integrals:
>
> {{{
> sage: numerical_integral(1/x, 1, oo)
> (65.94931131932763, 8.156214940519742)
> }}}
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)
}}}
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Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/14274#comment:1>
Sage <http://www.sagemath.org>
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