On Jan 27, 12:38 pm, Loïc <xl...@free.fr> wrote:
> Hi list,
>
> I found a problem with simplify_radical()
>
> sage: f(x)=asin(2*x/(x^2+1))
> sage: g=f.derivative();g
> x |--> -2*(2*x^2/(x^2 + 1)^2 - 1/(x^2 + 1))/sqrt(-4*x^2/(x^2 + 1)^2 +
> 1)
> sage: g.simplify_radical()
> x |--> -2/(x^2 + 1)
>
> The last answer should be:
>
> x |--> -2/(x^2 + 1)* (x^2-1)/abs(x^2-1)
>
> or easier
>
> x |--> -2/(x^2 + 1)*sign(x^2-1)
Hmm, I'm not sure that's exactly a bug. Well, at least I don't know
that the Maxima people would say so. But here's a simpler example.
sage: h = (2*x^2/(x^2+1)-1)/sqrt(-4*x^2/(x^2+1)^2+1)
sage: h.simplify_radical()
1
sage: h = ((2*x^2-x^2-1)/(x^2+1))/sqrt((x^2-1)^2/(x^2+1)^2) # same as
the other one, but common denominators gotten
sage: h.simplify_radical()
(x^2 - 1)/abs(x^2 - 1)
So I think that Maxima is treating these two expressions differently
in that it might be factoring something out of the square root first
which removes the abs() piece. Simplification does simplify, after
all.
Also, FYI, If you look at the documentation, you'll see "DETAILS: This
uses the Maxima radcan() command." And it does
from sage.calculus.calculus import maxima
maxima.eval('domain: real$')
res = self.parent()(self._maxima_().radcan())
maxima.eval('domain: complex$')
return res
But maybe it should be treated as a bug after all; I'm starting to
think so. In which case we'd want to check it in a newer version of
Maxima.
- kcrisman
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