Comment #10 on issue 2949 by trel...@psu.edu: trig functions do not return
exact results for half angles
http://code.google.com/p/sympy/issues/detail?id=2949
All right. I'll see what I can do. Attached is a working version of
trigonometry.py that can handle potentially handle all arguments with exact
closed forms. It passes all of the tests in test_trigonometric.py EXCEPT
assert sin(oo) == S.NaN
this test seems to contradict the earlier assertion that
assert sin(oo).args[0] == oo
If we're thinking sin(oo) == limit(sin(x),x,oo),
then sin(oo) should really return an interval of accumulation points [-1,1].
Another issue is that I don't know how to canonically simply radical
expressions. This becomes a little bit of an issue, as sometimes the
radical expression returned depends on the exact execution path, and two
different radical expressions for the same value can appear.
I consider things like sin(pi/12) simple and sin(pi/15) not simple, so
that's the bar I'd use. But it's not clear to me who will make use of
things like sin(3*pi/85),
and in which form they'd prefer it. Might be good to just wait and see
what people want.
Attachments:
trigonometric.py 41.5 KB
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