#18599: Maxima integral wrong
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Reporter: kcrisman | Owner:
Type: defect | Status: new
Priority: major | Milestone: sage-6.8
Component: calculus | Resolution:
Keywords: | Merged in:
Authors: | Reviewers:
Report Upstream: Reported upstream. No | Work issues:
feedback yet. | Commit:
Branch: | Stopgaps:
Dependencies: |
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Description changed by rws:
Old description:
> See [https://groups.google.com/forum/#!topic/sage-devel/GX-hYs0grdE this
> sage-devel discussion].
>
> {{{
> sage: from sage.symbolic.integration.external import maxima_integrator
> sage: maxima_integrator(sqrt(cot(x)^2),x)
> -1/2*log(tan(x)^2 + 1) + log(tan(x))
> sage: maxima_integrator(cot(x),x)
> log(sin(x))
> sage: maxima_integrator(sqrt(cot(x)^2),x,pi/4,3*pi/4)
> 0
> sage: maxima_integrator(cot(x),x, pi/4,3*pi/4)
> 0
> sage: f(x) = maxima_integrator(sqrt(cot(x)^2),x)
> sage: f(pi/4)
> -1/2*log(2)
> sage: f(3*pi/4)
> I*pi - 1/2*log(2)
> }}}
>
> But that is wrong, as this function is nonnegative and usually positive.
> The problem is in Maxima.
>
> {{{
> (%i1) domain:complex;
> (%o1) complex
> (%i2) sqrt(cot(x)^2);
> 2
> (%o2) sqrt(cot (x))
> (%i3) integrate(sqrt(cot(x)^2),x,%pi/4,%pi/4*3);
> (%o3) 0
> (%i4) integrate(sqrt(cot(x)^2),x);
> 2
> log(tan (x) + 1)
> (%o4) log(tan(x)) - ----------------
> 2
> }}}
>
> Reported upstream [https://sourceforge.net/p/maxima/bugs/2971/ at bug
> 2971].
New description:
See
* https://groups.google.com/forum/#!topic/sage-devel/GX-hYs0grdE
* https://groups.google.com/forum/#!topic/sage-devel/PSWsQPl1TBA
{{{
sage: from sage.symbolic.integration.external import maxima_integrator
sage: maxima_integrator(sqrt(cot(x)^2),x)
-1/2*log(tan(x)^2 + 1) + log(tan(x))
sage: maxima_integrator(cot(x),x)
log(sin(x))
sage: maxima_integrator(sqrt(cot(x)^2),x,pi/4,3*pi/4)
0
sage: maxima_integrator(cot(x),x, pi/4,3*pi/4)
0
sage: f(x) = maxima_integrator(sqrt(cot(x)^2),x)
sage: f(pi/4)
-1/2*log(2)
sage: f(3*pi/4)
I*pi - 1/2*log(2)
}}}
But that is wrong, as this function is nonnegative and usually positive.
The problem is in Maxima.
{{{
(%i1) domain:complex;
(%o1) complex
(%i2) sqrt(cot(x)^2);
2
(%o2) sqrt(cot (x))
(%i3) integrate(sqrt(cot(x)^2),x,%pi/4,%pi/4*3);
(%o3) 0
(%i4) integrate(sqrt(cot(x)^2),x);
2
log(tan (x) + 1)
(%o4) log(tan(x)) - ----------------
2
}}}
Reported upstream [https://sourceforge.net/p/maxima/bugs/2971/ at bug
2971].
--
--
Ticket URL: <http://trac.sagemath.org/ticket/18599#comment:2>
Sage <http://www.sagemath.org>
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