#12047: numerical_integral(f, a, a) should always be zero
------------------------+---------------------------------------------------
Reporter: jdemeyer | Owner: burcin
Type: defect | Status: new
Priority: major | Milestone: sage-4.8
Component: calculus | Keywords:
Work_issues: | Upstream: N/A
Reviewer: | Author:
Merged: | Dependencies:
------------------------+---------------------------------------------------
Description changed by jdemeyer:
Old description:
> Currently, in sage-4.7.2:
> {{{
> sage: integral_numerical(log(x), 0, 0)
> (nan, nan)
> }}}
>
> Mathematically, the integral should certainly be zero: there is a
> primitive function which is continuous and defined at 0. Symbolically,
> we can compute the integral correctly:
> {{{
> sage: integral(log(x), (x,0,0))
> 0
> }}}
>
> So I would like to add a special-case check for `integral_numerical()`:
> if the interval of integration is a point, then always return 0.
>
> I realize that this means that also the integral of 1/x from 0 to 0
> would be 0, even though 1/x has no continuous primitive at 0. But
> according to the Lebesgue theory of integration, I think this is not
> even a problem.
>
> Also: remove various unused things from the file
> `sage/gsl/integration.pyx`.
New description:
Currently, in sage-4.7.2:
{{{
sage: integral_numerical(log(x), 0, 0)
(nan, nan)
}}}
Mathematically, the integral should certainly be zero: there is a
primitive function which is continuous and defined at 0. Symbolically, we
can compute the integral correctly:
{{{
sage: integral(log(x), (x,0,0))
0
}}}
So I would like to add a special-case check for `integral_numerical()`: if
the interval of integration is a point, then always return 0.
I realize that this means that also the integral of 1/x from 0 to 0
would be 0, even though 1/x has no continuous primitive at 0. But
according to the Lebesgue theory of integration, I think this is not
even a problem.
Also: remove various unused things from the file
`sage/gsl/integration.pyx` and clean up the documentation.
--
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/12047#comment:2>
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 post to this group, send email to [email protected].
To unsubscribe from this group, send email to
[email protected].
For more options, visit this group at
http://groups.google.com/group/sage-trac?hl=en.
