On Tue, Jan 24, 2012 at 4:11 AM, Jesús TC <jesu...@gmail.com> wrote:
> 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?
+1
It's indeed annoying that Sage doesn't do this simplification (because
Maxima doesn't).
-- william
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