On Jan 25, 6:21 pm, William Stein <wst...@gmail.com> wrote:
> On Wed, Jan 25, 2012 at 7:25 AM, kcrisman <kcris...@gmail.com> wrote:
>
> >> > 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).
>
> > Though that would be a red herring if we wanted Mma-like behavior, as
> > Ginac would handle the initial bit.
>
> > My guess is that Maxima has good reasons for not doing this
> > automatically; you are welcome to email them with an example like
>
> > (%i2) display2d:false;
>
> > (%o2) false
> > (%i3) cos(7/8*%pi);
>
> > (%o3) cos(7*%pi/8)
>
> > and ask why it doesn't return what you expect, and I would hope they
> > have a pretty well-reasoned answer for this.
>
> That's all fine and good in the abstract, but I really can't see any
> possible argument that this is anything but bad:
>
> sage: z = cos((1/7)*pi) + cos((6/7)*pi)
> sage: z.numerical_approx(200)
> 6.2230152778611417071440640537801242405902521687211671331011e-61
> sage: bool(z == 0)
> False
>
> That's bad, because z is zero after all. Yes, "bool(foo==bar)" being
> True means that Sage couldn't prove that foo == bar, but in this case,
> since z does equal z, and it isn't difficult to change Sage that it
> would know this, I don't see why we don't do it.
>
> -- William
sage: maxima('load("spangl")')
sage: maxima('cos((1/7)*%pi) + cos((6/7)*%pi)')
0
sage: maxima('cos((6/7)*%pi)')
-cos(%pi/7)
Andrzej Chrzeszczyk
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