True, which leads to a _much_ longer discussion about sqrt's (& powers, in general).
At 09:19 AM 12/13/2012, Stavros Macrakis wrote:
>Not sure that (sqrt(a)+conjugate(sqrt(a)))/2 is much better!
>
> -s
>
>On Thu, Dec 13, 2012 at 12:16 PM, Henry Baker <hbaker1 at pipeline.com> wrote:
>This is only just one of the reasons why I've given up on "realpart(z)" and use
>
>(z+conjugate(z))/2
>
>instead.
>
>At 09:09 AM 12/13/2012, Stavros Macrakis wrote:
>>Currently,
>>
>> realpart(sqrt(a)) =>
>> cos(atan2(0,a)/2)*sqrt(abs(a))
>>
>>This is of course correct, but not very useful.
>>
>>For one thing, it gives an error for a=0.
>>For another, it doesn't simplify to sqrt(-a) with assume(a<=0). (Though it does simplify to sqrt(a) for a>=0.)
>>
>>Is there some way to force realpart to use asksign in cases like this? I seem to remember that that was always what it did, but I couldn't find a discussion of a change in my mail archives.
>>
>>As we improve support for conditionals, another useful value would be (if a>0 then sqrt(a) else 0) -- or maybe (if a>=0 then sqrt(a) else 0). But again, currently we have the problem that the simplifier doesn't do a very good job on expressions like this.
>>
>> -s