On Tue, Aug 18, 2009 at 3:51 AM, Golam Mortuza
Hossain<[email protected]> wrote:
>
> Hi,
>
> While testing new integral SFunction class for Sage,
> I encountered this weird bug.
>
> ----------
> sage: f(x) = function('f',x)
>
> sage: f(x).integral(x)
> integrate(f(x), x)
>
> sage: f(x).integral(x^2)
> x^2*f(x)
> -----------
Indeed, what does that mean? If forced to, I would interpret this as
int f(x) d(x^2) = int f(x) 2 x dx
= 2x integrate(f(x),x)
So I think the Sage/Maxima answer of x^2*f(x) is bizarre.
Matheamatica just considers this input to be invalid:
sage: mathematica.eval('Integrate[f[x],x^2]')
2
Integrate::ilim: Invalid integration variable or limit(s) in x .
2
Integrate[f[x], x ]
Unless you can give a explanation of what you want integrating wrt x^2
to mean, I think we should also raise an error in Sage.
>
> It appears to be a Maxima bug
> ----------
> (%i10) integrate(f(x), x^2);
> 2
> (%o10) x f(x)
> ----------
>
> However, even "integral" of calculus.py seems to do crazy thing as well.
> In line 566, it does
>
> elif not is_SymbolicVariable(v):
> v = var(repr(v))
>
> Above imply
>
> --------
> sage: v = var(repr(x^2))
> sage: v
> x^2
> sage: v.diff(x)
> 0
> -------
>
> The next commented out line in calculus.py seems to be the right
> thing do here!!
>
> Cheers,
> Golam
>
> >
>
--
William Stein
Associate Professor of Mathematics
University of Washington
http://wstein.org
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