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

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