On Sun, Jan 22, 2012 at 12:44 PM, Edwin Woollett <woollett at charter.net>wrote:
> On Jan. 21, 2012, Raymond Toy wrote
> ---------------------------
>
> You didn't take enough samples. I plotted r1(x) - r2(x) for x from %pi
>> to 5. and the plot is not zero. It is zero for x from 1 to %pi.
>>
> ------------------------------**------------------------------**---
> You are right, I did not sample far enough. The two
> expressions agree up to %pi, and r2(x) is undefined
> for x > %pi (while r1(x) = 0 for x > %pi).
> ------------------------------**-----------------------------
> (%i1) r1(x):= realpart(1/sqrt(sin(x)))$
> (%i2) r2(x) := 1/realpart(sqrt(sin(x)))$
>
> (%i3) r1(5);
> (%o3) 0
>
> (%i4) r2(5);
> expt: undefined: 0 to a negative exponent.
> #0: r2(x=5)
> -- an error. To debug this try: debugmode(true);
>
> (%i5) r1(u);
> (%o5) cos(atan2(0,sin(u))/2)/sqrt(**abs(sin(u)))
>
> (%i6) r2(u);
> (%o6) 1/(cos(atan2(0,sin(u))/2)***sqrt(abs(sin(u))))
>
> (%i7) r1(3);
> (%o7) 1/sqrt(sin(3))
>
> (%i8) r2(3);
> (%o8) 1/sqrt(sin(3))
> -------------------------
>
> So I guess realpart is buggy in this case, although ratsimp(r1(x)-r2(x))
>> is zero.
>>
> ------------------------------**----
> realpart looks unreliable here, but how do you get ratsimp to
> give zero?
>
Sorry, I clearly made a mistake. Unfortunately, I don't know what because
that session is gone.
Ray