Alas, Maxima is not smart enough to realize that acos(sin(x)) is real for
real x. In fact, Maxima doesn't even know that -1 <= sin(x) <= 1 for real
x. (By the way, Maxima treats undeclared variables as real in most
cases....)
I'd think the right way to handle that would be (symbolic) interval
analysis where sin(x) => [-1,1] for real x and acos([-1,1]) => [0,%pi]
(assuming the principal value interpretation). But Maxima doesn't
currently do that, sorry.
-s
On Wed, Apr 18, 2012 at 22:54, Jean Vittor <jean.vittor at free.fr> wrote:
> Hi,
>
>
> I would have expected last command of the following sequence to return
> true.
>
> (%i1) declare(x,real);
> (%o1) done
> (%i2) featurep(x,real);
> (%o2) true
> (%i3) featurep(sin(x),real);
> (%o3) true
> (%i4) featurep(acos(sin(x)),real);
> (%o4) false
>
> Am I wrong ?
> If so, is there a way to assume that acos(sin(x)) is real when x is real.
>
>
> Thanks,
>
> Jean
>
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