Bill Page wrote:
>
> It seems to me that algebraically any transformation that eliminates or
> adds an extra sqrt is likely incorrect. So I would say that (1) in your
> example is very suspicious.
>
> On 25 September 2014 20:04, kfp <[email protected]> wrote:
>
> >
> > Indeed. Since we get
> >
> > (1) -> normalize sqrt(1-sin(z)^2)
> >
> > z 2
> > tan(-) - 1
> > 2
> > (1) -----------
> > z 2
> > tan(-) + 1
> > 2
We have problem when roots exist in base field. That is
lone 'sqrt(x)' does not cause correctness problems.
So, as long as there are no roots in base field we can
add them. OTOH 'sqrt(x^2)' is problematic. In principle
we could transform 'f(sqrt(x^2))' into
(1 + sqrt(x^2))/2*f(x) + (1 - sqrt(x^2))/2*f(-x)
and then handle 'f(x)' and 'f(-x)' separately. However,
there are many places where we would need to implement
such transformation. Also this leads to ugly results.
--
Waldek Hebisch
[email protected]
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