Hi all!
This is my 1st message here, so I hope not to do something not
appropriate.
Working through a simple problem, I noticed that Sage fails in
simplifying things like
cos((1/7)*pi) + cos((6/7)*pi)
to zero, which Mathematica does correctly. I have tested it up to the
5.0 beta1
Curiously,
x=var('x')
print bool(cos(pi-x*pi)==-cos(x*pi))
print bool(cos(pi-(1/7)*pi)==-cos((1/7)*pi))
gives
True
False
Taking a closer look at the problem, it seems that it could be solved
simply if, as Mathematica does, every angle inside a trigonometric
function were automatically sent to the 1st quadrant: [0,pi/2].
Indeed, in Mathematica one gets
in: Cos[7/8*Pi]
out: -Cos[Pi/8]
Probably that should be implemented inside the trigonometric functions
code itself, instead of in any of the "simplify"'s.
What do you think?
Jesús TC
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