Bill Page wrote:
>
> Do you mean that 'sqrt(x^2)' is generated internally in transformation
> Kurt's (1), resulting in incorrect sign?
We have (equivalent of 'realElementary' is done in first
stage of 'normalize'):
(1) -> realElementary(asin(sin(x)))
x
2tan(-)
2
(1) atan(--------------------------------------)
+----------------------+
| x 4 x 2
|tan(-) - 2tan(-) + 1
x 2 | 2 2
(tan(-) + 1) |----------------------
2 | x 4 x 2
|tan(-) + 2tan(-) + 1
\| 2 2
Type: Expression(Integer)
so really 'sqrt(((1 - tan(x/2)^2)/(1 + tan(x)^2))^2)'. However
the issue with 'sqrt(x^2)' is the same, so I used smaller
example.
> I suppose that you must have meant to write the transformation using
> 'sqrt(x^2)/x', i.e.
>
> 'f(sqrt(x^2))' into (1 + sqrt(x^2)/x)/2*f(x) + (1 - sqrt(x^2)/x)/2*f(-x)
>
Yes.
> It looks interesting but I guess this is for real-valued x only?
It is valid for complex x.
> For complex z
>
> sqrt(z*conjugate(z))/z = exp(argument(z))
>
> is the "complex sign".
'conjugate' is different story -- ATM I do not know of similar
transformation including 'conjugate'.
--
Waldek Hebisch
[email protected]
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