>
>
> Something is happening in the interface, yes, but
>
>
Apparently sympy can't do it either (?). Here is my experiment.
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)
so I see already a problem there, though not the same problem exactly.
Note that
(%i6) sqrt(cot(x)^2);
(%o6) abs(cot(x))
which is a good sign, but in a fresh start
(%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
So this is indeed a Maxima bug, I guess.
http://trac.sagemath.org/ticket/18599
Greg, always good to hear from you! Such doctests could be useful, but (as
you know) the difference between ones that are possible to integrate
symbolically and those which aren't is pretty tricky to navigate, so I
don't know how to generate them randomly. If you have some specific
integrals to propose, of course, please open a ticket (I think you have a
Trac account?) and we can definitely include more in our tests.
- kcrisman
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