Thanks a lot for an explanatory reply :-)
Unfortunately I still have some comments...
I typed this instead, and got a nice line at 0:
>
> plot(simplify(sin((2*pi) + x) - sin(x)),-100,100)
>
This is not working for a little bit more complicated arguments, for
instance, the second sin(x/pi) function:
http://aleph.sagemath.org/?c=plot%28simplify%28sin%28%282%2Api%5E2+%2B+x%29%2Fpi%29+-+sin%28x%2Fpi%29%29%2C-100%2C100%29
You could use:
> bool (sin(((2*pi^2 + x)/pi).expand()).full_simplify() == sin(x/pi))
>
What a nice hack :-)
Nonetheless, is there a way to do this trick in a more general way? The
thing is, I need all this for testing periodicity of real-valued
functions given by user.
E. g. Through investigating stationary points my program is able to find
out that 1 candidate for the potential period of `sin(x/pi)` is `2*pi^2`.
Nevertheless, I cannot just test this candidate with:
||
iff(x)==f(x +period):...
now, can I?
||I would need to expand the inner function (which is, in addition
to
that, in general *not* always the inner function) but I can't get
access
to it since the input function is a blackbox for the
program.
Is it somehow possible to /force/ full testing of (at least) goniometric
identities?
I might consider it a bug that not every identity is used by default,
>
> but I would add that I expect it to be an unsolvable problem:
>
> 1) We want it fast.
> 2) We want it to use all simplification methods.
>
In my case I would want that second option - can I make Sage to always go
this
way for me?
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